December 2008

A Solid-State Light-Matter Interface at the single photon level

Nature 456, 773 (2008)

Hugues de Riedmatten, Mikael Afzelius, Matthias U. Staudt, Christoph Simon and Nicolas Gisin

QAP researchers from the University of Geneva have demonstrated a storage device for photons in a solid state environment. This technique enables the coherent and reversible transfer of quantum information between light and a solid state system, which provides a promising tool for the realization of quantum repeaters and quantum networks.

Coherent and reversible mapping of quantum information between light and matter is an important experimental challenge in quantum information science. In particular, it is an essential requirement for the implementation of quantum networks and quantum repeaters. Up to now, experiments in photonic quantum storage have been performed with atomic gases or single atoms in cavities. In a recent Nature paper, QAP researchers from the University of Geneva report the coherent and reversible mapping of a light field with less than one photon per pulse on average onto an ensemble of 107 Neodymium atoms naturally trapped in a solid, cooled at 3 K.

In order to achieve the mapping, the authors take advantage of the inhomogeneous broadening of the optical transition of the Nd atoms. By optically pumping some of the atoms out of the ground state, the absorption spectrum is tailored with a series of periodic narrow peaks, an atomic frequency comb. The weak incident light field is collectively absorbed by all the atoms in the comb, and the state of the light is transferred to collective atomic excitations at the optical transition. After absorption, the atoms at different frequencies will dephase, but thanks to the periodic structure of the absorption profile, a rephasing will occur after a time which depends on the comb spacing (up to 1 µs in the present experiment). When the atoms are all in phase again, the light is re-emitted in the forward direction as a result of a collective interference between all the emitters.

 

Figure 1. Picture of the crystal containing Nd impurities.

In the actual experiment, the storage and retrieval efficiency is low (about 1 %), mainly because of imperfect preparation of the atomic frequency comb. Much higher efficiencies (which in theory can go up to unity) should be however readily achieved with simple improvements of the experiment. Despite the low efficiency, the quantum coherence of the incident weak light field is almost perfectly conserved during the storage, as demonstrated by performing an interference experiment with a stored time-bin qubit. The researchers also demonstrate experimentally that the interface makes it possible to store light in multiple temporal modes (See Fig 2). This last feature is particularly interesting, as it enables temporal multiplexing in future quantum repeaters architectures.

 

Figure 2: Storage and retrieval of weak light pulses in single (left) and multiple (right) temporal modes

 

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How many classical resources are needed to simulate quantum measurements?

Physical Review Letters 101, 190402 (2008)

B. Dakic, M. Šuvakov, T. Paterek, and C. Brukner

Overview

The question from the title is relevant if one wants to make a fair comparison between complexities of quantum and classical algorithms. It was previously known that the results of a finite set of general quantum measurements on an arbitrary dimensional quantum system can be simulated using an exponential (in measurements) number of "hidden-variable" (classical) states. In Physical Review Letter 101, 190402 (2008), Dakic, Suvakov, Paterek and Brukner, have constructed an explicit model in which the number of hidden-variable (HV) states scales polynomially with the number of quantum measurements, thus bringing an exponential improvement. In addition to the relevance for quantum information science the work is motivated by a fundamental question.

John Bell showed that it is impossible to explain all of the predictions of quantum mechanics using a theory which still satisfies the basic concepts of locality and realism, but which (if not both) is violated is still an open question. Dakic et al. ask how plausible realism -- the idea that external reality exists prior to and independent of observations -- is, by considering the amount of resources in terms of the number of HV states realism consumes. In the limit of large number of measurements, the model of Dakic et. al confirms the result of Montina, that no successful realistic theory could use less HV states than the one in which every quantum state is associated with a HV. This shows that, for any given system size, realistic theories cannot describe nature more efficiently than quantum theory itself. The paper extends the work of Hardy, who showed that, even for the simplest quantum system like electron spin or photon polarisation, realism is extremely resource demanding, requiring infinitely many HV states to explain all possible measurements.

Editor’s Reading Suggestion

A. Montina, Phys. Rev. A 77, 022104 (2008).
L. Hardy, Stud. Hist. Philos. Mod. Phys. 35, 267 (2004).

 

Figure 1:   Hidden-variable (HV) models for quantum measurements (a) The vertices of the octahedron inside the Bloch sphere define the three complementary qubit measurements. A HV model for these measurements for arbitrary quantum state requires eight HV states, which are written near their representative vertices of the cube containing the sphere.(b) Here, the measurement directions form a cube inside the sphere. Although more measurements are to be simulated, the universal HV model requires only six HV states, which are written near their representative vertices of the octahedron containing the sphere.

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October 2008

Multipartite Entanglement Among Single Spins in Diamond

Science 320, 1326 (2008)

P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup

Since Entanglement of quantum states is a benefit or even a prerequisite for quantum information protocols, proving this for a candidate system is a necessary benchmark. In the case of a single Nitrogen-Vacancy (NV) center in diamond we have demonstrated entanglement among its electron spin and two adjacent nuclear spins of the ¹³C isotope coupled via their hyperfine interaction. Due to the almost spinless and stiff diamond lattice it was possible to perform these experiments under ambient conditions without suffering the loss of coherence due to e.g. lattice phonons. Some quantum correlations even persist on a millisecond timescale.

The NV center in diamond consists of a nitrogen atom at one lattice site and a vacancy on a neighbouring lattice site (fig. 1a). Since its negatively charged version has a spin triplet ground state a qubit can be encoded among two of these ground state levels e.g. m_S=0 → “0”, m_S=-1 → “1”. The defect center shows very strong fluorescence in the red when excited with green laser light which allows us to investigate single centers with a confocal microscope. Moreover the fluorescence depends on the electronic spin state making it possible to read out the electron spin optically. Finally by laser excitation the NV center can be polarized in one of its spin triplet levels in the ground state (namely m_S=0 (“0”)). This serves as initialization of our system. Coherent transitions between spin levels in the ground state are mediated via microwave radiation.

In the present center two of the closest carbon atoms are ¹³C isotopes with nuclear spin ½ which serve as additional qubits. Their strong hyperfine coupling to the electron spin of the NV center allows us to address and manipulate the nuclear spins individually by applying appropriate radiofrequencies (fig. 1b,c).
 

Figure 1:   (a) structure of the NV center in the diamond lattice. Two of the three nearest neighbor carbon atoms are 13C isotopes with nuclear spin ½ in this case. The other one is spinless 12C isotope.   (b) Energy levels of this NV center showing the mS=0 and -1 branch with hyperfine splitting due to the 13C atoms. Blue arrows show electron spin transitions and the orange ones nuclear spin transitions.   (c) Electron spin resonance spectrum showing all four transitions shown in panel b.

After initializing the system with a laser pulse our coherent control of the electron and nuclear spins allows us to generate and read out all 4 Bell States among the 2 nuclear spins (fig. 2a,b). These are the maximally entangled states among 2 qubits. In short, the outstanding property of these Bell states are that effective one particle measurements allow to determine the state of the other qubit with certainty. The entanglement lasts for a few milliseconds where the measurement is limited by the electron spin’s T1 time. That is until the spin starts to change its state randomly between “0” and “1”. The existence of a Bell state can be proven by Ramsey fringes (fig. 2a) which show the evolution of the Bell state or by performing a tomography. The resulting tomogram (fig. 2b) shows the expected correlations on its off-diagonal elements (|00><11|, |11><00|).

Taking into account also the electron spin 3-partite entangled states have been created. That is the so called GHZ (Greenberger-Horne-Zeilinger) state and the W state. Similar to the Bell states a measurement of one qubit of a GHZ state determines the state of the remaining 2 qubits. While for the W state depending on the measurement result the remaining qubits are either determined or still entangled among each other. A tomogram (fig. 2c) reveals these correlations on all respective off-diagonal elements.

With this 3 qubit system at hand first quantum algorithms can be tested, e.g. “superdense coding” or the “Deutsch algorithm”. Further scaling up of the system requires additional nuclear or electron spins close to the NV or the coupling of several NV centers by magnetic dipole interaction or by probabilistic entanglement via photons.

 

Figure 2:   (a) These Ramsey fringes show the free evolution of the generated Bell states F+, F-, Y+ and Y-. This is a prove for their generation.   (b) To obtain this tomogram of the state F- all 16 density matrix elements have to measured. Especially the negative columns on the off-diagonal prove the Bell state.   (c) Partial tomogram of the W state showing its off-diagonal elements.

 

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Coherent Control of Decoherence

Science 320, 638 (2008)

Matthijs P. A. Branderhorst, Pablo Londero, Piotr Wasylczyk, Constantin Brif, Robert L. Kosut, Herschel Rabitz, Ian A. Walmsley

Overview

QAP researchers have found a way of protecting quantum systems against noise using adaptively ‘shaped’ pulses of laser light. Quantum systems are notoriously fragile as interactions with their surroundings disturb them – rather like an orchestra trying to stay in tune in a very noisy environment. However, maintaining the stability of quantum systems is critical for future quantum technologies. In a recent Science paper, researchers at the University of Oxford report that they have found a way to prolong the life of a model quantum system.

The advance used light pulses, with a colour spectrum shaped in amplitude and phase, to control the dynamics of the model quantum system. Using a genetic algorithm, the researchers were able to find the optimal pulse shape to protect the system from decay. Contrary to what might be expected, the encoded order from the light pulse makes the quantum system more robust against disorder.

Matthijs Branderhorst, who did the experiment, explained: ‘There have been control techniques before to improve stability but they rely on knowing everything about a given system. The ground-breaking nature of our approach is that, knowing nothing about a system, we can automatically search for and apply a light pulse that makes it more robust. We have shown an improvement of the stability with our experimental test system, but in other cases it could make it completely immune from decay.’

The model system used by the researchers to study the idea consisted of two potassium atoms bound together. However, the approach they have developed could be applied to many other kinds of quantum systems such as those influencing chemical reactions, photosynthesis and quantum computation.

 

Figure 1:   The laser oscillator used to generate light pulses for adaptive coherent control of potassium dimers. Such a laser system could be used to protect the stability of future quantum technologies.

 

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Septemeber 2008

QLib

Shai Machnes

QLib is an open-source Matlab package intended to provide everybody within the Quantum Information community with a comprehensive toolset, and to allow us to

• Quickly and efficiently frame and explore ideas
• Form intuition through the use of visualizations
• Rule-out or validate hypothesis through the use of optimization

QLib currently covers most, if not all, of the "textbook" primitives and provides us with a rich toolset with which to advance knowledge in out field and engage in "experimental theory".

On the QLib site you will find everything you need: the software itself, a “getting started” guide, examples, forums to ask questions, report bugs and request features – everything necessary to get you up and running as quickly as possible.

QLib is free to use and modify, and is licensed under the GPL. Our goal is to have QLib continually developed by the community and for the community, to the benefit of us all.

Further details about QLib can be found in the pdf document below, or at the QLib website.

QLib summary document, © Shai Machnes, Tel-Aviv University

 

Example 1: Bloch “Hyper-Sphere” Have you ever wondered why the Bloch sphere cannot be extended to higher dimensions? With QLib, you can simply generate a few million random density matrices and check. In the graph to the right you see 2d projections of the “hypersphere”.  With a few extra lines of code, you can also easily verify, for example, that all pure states are on the surface, but that not all the surface is pure.

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Scaling Laws for the Decay of Multiqubit Entanglement

Physical Review Letters 100, 080501 (2008)

L. Aolita, R. Chaves, D. Cavalcanti, A. Acin, and L. Davidovich

Overview

In most cases the speed-up gained when using quantum-mechanical systems, instead of classical ones, to process information is only considerable in the limit of large-scale information processing. Within such context, it is therefore  fundamental to understand the scaling properties of disentanglement for multi-particle systems. With this aim, Simon and Kempe showed [1] in 2002 that the genuinely multiparticle-entangled Greenberger-Horne-Zeilinger (GHZ) states,

 

subject to the action of individual depolarization, undergo entanglement sudden death (ESD), that the last bipartitions to loose entanglement are the most balanced ones, and that the time at which such entanglement disappears grows with the number of particles in the system. Soon afterwards it was shown by Dür and Briegel [2] that the first N bipartitions to loose entanglement are the least balanced ones (one particle vs. the others), the time at which this happens decreasing with . A natural question arises from these considerations: is the ESD time a truly physically-relevant quantity to assess the robustness of multi-particle entanglement?

In this highlighted paper, the QAP researchers have shown that, for an important family of genuine  multipartite entangled states - namely the generalized GHZ states

  

, the answer is no.

For several paradigmatic models of decoherence, they have derived analytical expressions for the time of disappearance of entanglement, which is found to increase with N. However, they have shown that the time at which entanglement becomes arbitrarily small decreases with the number of particles, independently of ESD. This implies that for multi-particle systems, the amount of entanglement can become too small for any practical application long before it vanishes.  The situation is exemplified in Fig. 1, where the entanglement (quantified by the negativity) of the most robust bipartitions is plotted versus the probability p of depolarization due to the interaction with the environment, for generalized GHZ states of α =1/3 and β=√8/3, of systems of 4, 40 and 400 two-level particles (qubits). Even though the 40-qubit and 400-qubit negativities cross the 4-qubit one and vanish much later, they become orders of magnitude smaller than their initial value - and therefore negligible for all practical purposes - long before reaching the crossing point. This same behaviour is also found for all other parameters and maps.

 

Fig. 1: Negativity versus probability p of depolarization for N=4, 40 and 400 and for the most balanced partitions, which are the last ones to loose their entanglement. The inset shows a magnification of the region in which the four-qubit system’s negativity vanishes. Even though the other two negativities cross the latter and vanish much later, they  become orders of magnitude smaller than their initial value long before reaching the crossing point.

 

As a by product, the researchers have also shown that in several cases the action of the environment can naturally lead to multi-particle bound (non-distillable) entangled states, in the sense that, for a period of time, it is not possible to extract pure-state entanglement from the system

through local operations and classical communication, even though the state is still entangled. This, in view of the lack of a general recipe for the creation of bound entanglement, is very interesting because it means that, despite its detrimental action on quantum correlations, the environment can effectively act as a generator of this very mysterious form of entanglement (See Fig. 2).

 

Fig. 2: Negativity as a function of p for a four-qubit GHZ (α  = 1/√2 = β) state and independent depolarizing channels again. After the 1:3 negativities vanish (all four of them vanish together) no pure-state entanglement can be extracted from the state through local operations even with the assistance of classical communication. Nevertheless, the state is still entangled, as witnessed by the negativities of the balanced 2:2 partitions.

 

Concluding, the time at which entanglement becomes arbitrarily small characterizes better the robustness of the states’ entanglement than the time at which entanglement death itself occurs; and in several cases the action of the environment can naturally lead to bound entangled states. Finally, this work establishes a new venue for future research: in a forthcoming work, for example, the researchers will show that it is indeed possible to extend these results to other quantifiers of entanglement apart from the negativity. And also open questions are left: how do other genuinely multipartite entangled states, such as graph states, or matrix-product states behave? W states on the other hand are expected to be more robust, since they have always only one excitation, regardless of N, as will also be shown in forthcoming work by the same authors. Nevertheless, the results already obtained suggest that maintaining a significant amount of multi-qubit entanglement in macroscopic systems might be an even harder task than believed so far.

 

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July 2008

Cryptography from Noisy Storage

Physical Review Letters 100, 220502 (2008)

Stephanie Wehner, Christian Schaffner and Barbara M. Terhal

With the arrival of widespread electronic communication new cryptographic tasks have become increasingly important. We are no longer satisfied with the secure and reliable transmissions of messages, but want to solve a large number of tasks where the protocol participants themselves do not trust each other. Important examples of such tasks are secure identification, electronic voting, and contract signing. Unfortunately, it has been shown that it is impossible to implement such tasks securely without making assumptions on how powerful an attacker can be, even if we allow quantum communication. Classically a commonly used assumption is that it is difficult to factor a large number. This assumption, however, no longer holds once a quantum computer is built, and it is presently unknown whether this assumptions even holds classically. It is therefore an important problem to find realistic assumptions that allows us to achieve such tasks. Can quantum communication be of any help us?

Recently, it has been shown by QAP researchers that we can implement two-party protocols securely if we assume that it is difficult to store quantum states without errors. Here, the very problem that makes it so hard to implement a quantum computer can actually be turned to our advantage. Practically, such noise can arise as a result of transferring a photonic qubit onto a different physical carrier, such as for example an atomic ensemble or atomic state. In addition, a quantum state will undergo noise once it has been transferred into 'storage' if such quantum memory is not 100% reliable.

As a proof of principle, the QAP researchers have shown that we can obtain the two-party protocol 1-out-of-2 oblivious transfer in this model. This important primitive, that may indeed appear rather bizarre at first glance, can actually be used as a fundamental building block to implement any two party protocol. In oblivious transfer (see Figure 1), Alice holds two input bits s₀ and s₁. The goal of the protocol is to allow Bob to retrieve one of the two bits s_c according to his choice bit c, in such a way that Alice cannot learn which of the two bits Bob has retrieved. Thus, Bob cannot simply ask for one of the bits. At the same time, the protocol should guarantee that Bob can only learn exactly one of the two bits. Hence, Alice cannot simply send her two inputs to Bob. In their work, the QAP researchers have examined a simple protocol for this task, that can be implemented using hardware that is already used today to implement quantum key distribution (QKD). No quantum storage is thereby required for the honest participants. The key idea behind the protocol is to show that if Bob is dishonest (that is he tries to learn more than one of Alice's inputs) and attempts to store the quantum states sent by Alice until maybe later he received some additional information that would help him, he has already lost too much information due to the noise in the storage process. (see Figure 2)

In a real world setting, the honest players Alice and Bob do of course also experience some noise in their operations. In more recent work (arxiv:0807.1333) however it was shown that the protocol for oblivious transfer still remains secure, even if the honest participants experience 11% of noise and the noise on the channel and in their operations is strictly less than the noise in the quantum storage. This value may seem small, but unlike QKD, it is still interesting to implement such protocols even over very short distances. This is particularly the case for secure identification that is of relevance to banking applications.

This work shows that noise can indeed sometimes be a good thing and help us to implement cryptographic primitives which are otherwise impossible to obtain without making any assumptions. It opens the door for much further research in this direction. Can we find efficient protocols for other tasks? (without using the primitive oblivious transfer) What security to we obtain from more generalized noise models than the ones considered here? Finally, what are the fundamental limits of this model?

 

Figure 1.  Oblivious transfer between Alice and Bob.   Figure 2. Noisy storage precludes Bob from discovering more than one of Alice's inputs.

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 Experimental Decoy-State Quantum Key Distribution with a Sub-Poissionian Heralded Single-Photon Source

Physical Review Letters 100, 090501 (2008)

Q. Wang, W. Chen, G. Xavier， M. Swillo, S. Sauge, M. Tengner, T. Zhang, Z. F. Han, G. C. Guo, A. Karlsson

Overview

Using an optimized heralded single-photon source (HSPS) based on parametric down-conversion, the KTH research group cooperating with a Chinese USTC group has experimentally demonstrated a decoy-state quantum key distribution scheme (QKD) [1-3]. They used a one-way BB84 protocol with a four states and one-detector phase-coding scheme, which is immune to recently proposed time-shift attacks, photon-number splitting attacks, and can also be proven to be secure against Trojan horse attacks and any other standard individual or coherent attacks.

As shown in Fig. 1 (below), using the BB84 protocol and under the same experimental conditions, we compare our HSPS with decoy state scheme to several other schemes, including HSPS without decoy states,
weak coherent state (WCS) with or without decoy states, and also the ideal single-photon source (SPS) case. (In order to give a fair comparison, all these lines are not taken statistical error into account.) As can be seen, our scheme (red solid line) gets the maximum tolerable losses or the highest key generation rate under fixed losses among all these practical schemes. Moreover, if a better HSPS (blue dashed line with 70% correlated photon pairs) is used, its performance comes close to the ideal single-photon source.
Our experimental setup is shown in Fig. 2, and our final experimental results fit our theoretical predictions [4] quite well as shown in Fig. 3.

However, our final key rate is lower than in other systems reported before, because there are large losses in our QKD system. With present technology, it is realistic to decrease the loss by 15 - 18 dB in this QKD system, which is quite considerable for a long distance transmission (>100 km).

Despite of these deficiencies in our present system, this experiment is still sufficient to prove, in principle, that our HSPS based decoy-state scheme can tolerate the highest losses among all practical schemes, which also means the highest secure key generation rate under fixed losses. Therefore, it is a good candidate for future quantum key distribution systems.

 

Fig.1. The key generation rate vs. the total losses comparing several different schemes. The numerical simulations are done in the case of: a) with WCS and without decoy-state method; b). with HSPS and without decoy-state method; c). with WCS based decoy-state method (with optimal values of signal intensity at each points and an infinite number of decoy states); d). with HSPS based decoy-state method with Pcor=30%; e). with HSPS based decoy-state method with Pcor=70%; f). with the ideal SPS.

Fig.2. The experimental setup of the quantum key transmission system: PPLN: periodically-poled LiNbO3, AOM: acousto-optical-modulator, WDM: wavelength-division multiplexing, OS: optical switch, TC: time chopper, BS: beam-splitter, FM: Faraday Mirror, PM: phase modulator, DL: delay line, QC: quantum channel, SPD: single photon detector, CB: control board.

Fig. 3. The top line represents the theoretical counting rate for signal photons; the bottom line represents the theoretical secure key rate (taking statistical fluctuation into account). For each line, we investigated two points at the total loss of 31dB and 36dB individually. The stars and triangles are corresponding experimental results.

References
[1] W. Y. Hwang, Phys. Rev. Lett. 91, 057901 (2003).
[2] X. B. Wang, Phys. Rev. Lett. 94, 230503 (2005).
[3] H. K. Lo, X. Ma, and K. Chen, Phys. Rev. Lett. 94. 230504 (2005).
[4] Q. Wang et al. ArXiv: quant-ph/0803.3643

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June 2008

QAP researcher wins prize for outstanding research!

Congratulations to Dr. Christine Silberhorn for winning the prestigious Heinz Maier-Leibnitz Prize 2008. Dr. Silberhorn is one of 6 young researchers to be recognised by German Research Foundation for outstanding contributions to science. The Prize has been awarded to young researchers annually since 1977 to promote the further development of outstanding independent profiles. The prize of €16,000 is simultaneously a form of recognition of past achievements and an incentive to continue climbing the scientific career ladder. As such, it is held in high regard by the whole scientific community. Dr. Silberhorn's citation for the award is included below.

Christine Silberhorn's research to date is characterised by an extremely broad range of interests and research topics as well as a wide variety of international experience, and she has attained a very good reputation in the field of experimental quantum optics within the period of just a few years. During her studies she was already interested in highly abstract topics relating to topology, before moving on to the entirely different area of quantum cryptography for her PhD thesis. She has been able to establish herself very well in the rapidly progressing and thus highly competitive research field of quantum information processing. Her main area of interest was how to process and transmit quantum information using light, an issue that is of key importance for any quantum computers that may be built in the future. Instead of the discrete variables normally employed, Silberhorn used so-called "continuous variables", thus developing a widely accepted alternative. Silberhorn is currently continuing this work as the leader of an independent Max Planck junior research group, in which she, herself still a young scientist, is combining her successful research work with the opportunity to train other young researchers and scientists.

Figure 1: Dr. Christine Silberhorn (Front, second left) pictured with other winners of the Heinz Maier-Leibnitz Prize 2008.

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Superconducting Nanowire Photon Number Resolving Detector at Telecom Wavelength

Nature Photonics 2, 302 - 306 (2008)

Francesco Marsili, David Bitauld, Aleksander Divochiy, Alessandro Gaggero, Roberto Leoni, Francesco Mattioli, Alexander Korneev, Vitaliy Seleznev, Nataliya Kaurova, Olga Minaeva, Gregory Gol’tsman, Konstantinos G. Lagoudakis, Moushab Benkhaoul, Francis Lévy, Andrea Fiore

Overview

The characterisation of photon number states is an essential tool in photonic quantum information processing, however existing photon-number resolving (PNR) detectors are either too noisy or too slow for practical applications. QAP researchers recently demonstrated a PNR detector, the Parallel Nanowire Detector (PND) [1], which uses spatial multiplexing on a subwavelength scale to provide a single electrical output proportional to the photon number. The basic structure of the PND is the parallel connection of superconducting nanowires (N-PND). The detecting element is a few nm-thick, ~100 nm-wide NbN wire folded in a meander pattern (fig. 2a), which can be integrated in series with a bias resistors R0 (N-PND-R) (fig. 2b). Each branch acts as a superconducting single photon detector (SSPD) [2]. If a superconducting nanowire is biased close to its critical current, the absorption of a photon causes the formation of a normal barrier across its cross section and the bias current is pushed to the external circuit. In the parallel configuration proposed here, the currents from different wires can sum up on the external load, producing an output voltage pulse proportional to the number of photons. The integration of the resistance R0 improves the performance of the device in terms of speed and stability of operation [3].

PNDs were fabricated on ultrathin NbN films (4nm) on MgO [4] and R-plane sapphire [5] using electron beam lithography (EBL) and reactive ion etching. The photoresponse pulse is as short as 660ps (full width at half maximum). Counting performance was observed up to 80 MHz repetition rate. Building the histograms of the photoresponse peak (fig. 3), no multiplication noise is observable and the one photon quantum efficiency can be estimated to be 3% (at 700 nm wavelength and 4.2 K temperature). The PND thus significantly outperforms existing PNR detectors in terms of simplicity, sensitivity, speed, and multiplication noise.
 

Figure 2. Scanning electron microscope (SEM) images of a 14-PND (a) and a 8-PND-R (b) fabricated on a 4 nm thick NbN film on MgO. The nanowire width is w=100 nm, the meander fill factor is f=40%. In fig. (b) the active nanowires (in color) are connected in series with Au-Pd bias resistors (in blue).

 

Figure 3. Photoresponse transients of a 10x10 μm2 6-PND-R (□) probed at 5 K under illumination with 1.3 μm pulses from a laser diode, at a repetition rate of 26MHz. The red solid curves are guides to the eyes. The histogram of the photoresponse voltage peak is shown on the left hand side of the picture in turquoise.

 

References

[1] A. Divochiy et al., Nature Photon. 2, 302 (2008).
[2] G. N. Gol'tsman et al., Appl. Phys. Lett. 79, 705 (2001).
[3] F. Marsili et al., J. Mod. Opt. to be published.
[4] F. Marsili et al., Opt. Express 16, 3191 (2008).
[5] G. N. Gol'tsman et al., IEEE Trans. Appl. Supercond. 13, 192 (2003).
 

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May 2008

Migration of bosonic particles across a Mott insulator to superfluid phase interface

Physical Review Letters 100, 070602 (2008)

Michael J. Hartmann and Martin B. Plenio

Overview

Quantum many body systems are, in the forms in which they occur in nature, difficult to study experimentally. These difficulties lead to the development of quantum simulators with which many body effects can be emulated in the laboratory. Recent approaches to quantum simulators now give rise to possibilities for engineering deliberate inhomogeneities in quantum many body systems. This development could allow for the observation of dynamics at the boundary between two areas of a many body system which are in different condensed matter phases.

Recent work by QAP researches studies this dynamics theoretically and finds rather surprising effects. The scientists consider a boundary between a Mott insulator in which mutual particle repulsion strongly suppresses particle movement and an area in a superfluid phase, where particles do only interact very little an move almost freely and frictionless. The work by the QAP researchers shows that, in such a situation, all particles will leave the Mott insulator part and migrate to the superfluid region, leaving the Mott insulator part completely empty. Understanding and hence being able to control and make use of such effects is an important step towards the objectives of QAP.

 

Figure 1: Migration of particles from a Mott insulator to a superfluid. The plot shows particle densities (nj) for a chain of 40 sites as a function of time (t). Initially the particle densities are 1 in both parts of the chain. They drop to zero in the Mott insulator part (sites 1 - 20) and grow in the superfluid part (sites 21 - 40)

 

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Exact Relaxation in a Class of Nonequilibrium Quantum Lattice Systems

Physical Review Letters 100, 030602 (2008)

M. Cramer, C. M. Dawson, J. Eisert, and T. J. Osborne

Open systems dynamics in closed quantum systems: Exact relaxation in quenched quantum many-body systems

Why do systems dynamically relax to a statistical equilibrium state? This intriguing but old question is enjoying a  renaissance recently. With new experimental techniques becoming available, the non-equilibrium dynamics of atoms in optical lattices can be experimentally observed. Specifically, following a quench - that is, a rapid change of the system's parameters - the many-body system undergoes complicated dynamics. So what happens? There is no environment, so how could it possibly relax?

Recent work by QAP researchers published in the Physical Review Letters answers this question rigorously for a class of models that are idealized instances of the Bose-Hubbard model that takes centre stage in this discussion of atoms in optical lattices. The authors demonstrate that while the information on the initial condition is of course stored in the system at all times, it becomes diluted with time. Locally, for any subsystem, one obtains a maximally entropy state compatible with the constants of motion. Remarkably, this is true without a time average: The system just smoothly and nicely relaxes. So when locally looking at the system, we think that the system has reached its equilibrium. But only apparently so, as one day, arbitrarily far in the future, a recurrence will show that all the time, the initial condition was not forgotten.

This work discusses a scenario in which the dynamics of quantum phase transitions in quantum many-body systems can be studied in experiments, in an instance of a quantum simulation of a complex non-equilibrium process. The ideas put forth on the simulation and quantum control of such a quantum man-body system are very much inline with the objectives of QAP.
 

Figure 2: Intuitive picture of the relaxation process in the quenched Bose-Hubbard model: For any lattice site i (or any block of sites) within a cone (dark grey) defined by the speed of information transfer excitations significantly contribute to the local mixing of the state at the site. Contributions from outside this cone (light grey) are exponentially suppressed. The incommensurate influence of the lattice sites in the cone gives rise to a relaxation to maximal entropy for large times t. When the excitations have travelled through the entire lattice, recurrences will occur.

 

Figure 3: Local density of particles as a function of time, for a periodic initial condition of atoms in an optical lattice, including an harmonic trap. This plot shows signatures of local relaxation.

 

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March 2008

Heralded Generation of Ultrafast Single Photons in Pure Quantum States

Physical Review Letters, 100, 133601 (2008)

Peter J. Mosley, Jeff S. Lundeen, Brian J. Smith, Piotr Wasylczyk, Alfred B. U'Ren, Christine Silberhorn, Ian A. Walmsley

Overview

Single photons (discrete wavepackets of light) are not only interesting in terms of fundamental physics, but also from the point of view of applications in the emerging field of quantum information processing - a field that has the potential to revolutionize computing by harnessing the data processing power inherent in quantum mechanics. In this paper, researchers at the University of Oxford present the results of a new technique, based on photon pair generation, that for the first time allows the preparation of single photons of exceptionally high quality, conditioned on the detection of their twin. Furthermore, these photons have a temporal duration of as little as 65 femtoseconds (65 millionths of a billionth of a second), believed to be the shortest single photons ever generated. The precise timing and consistent attributes of these photons make them ideal for implementing photonic quantum logic gates and conducting experiments requiring large numbers of single photons, as required by quantum computing algorithms.

The source is based on the process of parametric downconversion in nonlinear optical crystals. In a single downconversion event, one "parent" photon is destroyed, and two "daughter" photons of lower energy are created (see Figure 1). Downconversion is a commonly used method for generating photon pairs, with the detection of one daughter photon heralding the arrival of the second daughter photon. This simple detection arrangement makes downconversion an attractive prospect for generating the single photons required by many quantum information processing protocols. However, the detection of the herald photon usually ruins the quality (or purity) of the second daughter photon. Energy and momentum conservation in the generation process generally result in strong quantum correlations within each pair (known as entanglement). Upon detection of one photon, the possibility of obtaining distinguishing information about the other photon ruins the purity of its quantum state. Some experiments have countered this problem by spectrally filtering the photons, effectively throwing away the unwanted photons. Unfortunately this process greatly reduces the efficiency of the source, and the purity of the daughter photons only becomes 100% in the limit that all photons are filtered out!

In the work highlighted here, QAP researchers at Oxford have built a source which requires no filtering of the daughter photons but still delivers photons of excellent purity and with a high efficiency. By carefully controlling the parameters which dictate the momentum conservation in the downconversion process, Mosely et al. were able to engineer a source in which detection of one daughter photon does not automatically destroy the purity of the second daughter photon. The purity of the daughter photons was tested by constructing two identical downconversion sources and then combining the heralded daughter photons on a 50:50 beamsplitter (see Figure 1). If the photons from each source are of high quality and are therefore indistinguishable, they will bunch together at the beamsplitter and exit in the same direction: this is the Hong-Ou-Mandel effect. The plot in Figure 1 shows that when the heralded photons from each source reach the beamsplitter at the same time, the number of coincidences between the four detectors drops off dramatically due to this bunching effect. The dip measured in this work indicates that the photons have a purity of over 95%, generated with a high efficiency. This work will be a substantial benefit for future quantum information processing applications requiring high purity photons as it has eliminated the need for lossy spectral filters.

The Oxford group are now using such sources for quantum enhanced precision metrology, heralded entanglement generation and linear optical quantum computation schemes.

Figure1: Scheme of the high purity photon pair generation by parametric downconversion.

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Nonclassical Interference and Entanglement Generation Using a Photonic Crystal Fiber Pair Photon Source

Physical Review Letters, 99, 120501 (2007)

Jérémie Fulconis, Olivier Alibart, Jeremy L. O'Brien, William J. Wadsworth, and John G. Rarity

The scaling of linear optical networks to many qubits is currently limited by the lack of bright single photon sources. Researchers at the University of Bristol, in collaboration with the University of Bath have developed a versatile solution based on photonic crystal fibres. Their work reports on the suitability of these new fibre sources for optical quantum information processing.

Standard pair photon sources usually relied on spontaneous parametric downconversion where the practical limit to multiphoton experiment is five or six photons due to a high pump power requirement (typically a few Watts). Using photonic crystal fibres, a pair of pump photons produces a correlated pair of photons at widely spaced wavelengths, via a χ⁽³⁾ four-wave mixing process. The confined geometry of the fibre enhances the non-linear interaction and the required average photon number per pulse is reached at milliWatt pump powers.

Two key experiments are reported. The demonstration of high visibility nonclassical interference between heralded photons from separate fibre sources and high fidelity entangled photon pair generation by configuring the fibre in a Sagnac loop interferometer. The photons are created within a single fibre mode which can be efficiently coupled into linear optics circuits and on to detectors. This source promises much higher rates of multiphoton generation than conventional sources. This will open the way to a variety of novel experiments including cascaded linear gates, or building large entangled cluster states, which is inline with the objectives of the QAP project.
 

Figure1: Scheme of the non-classical interference setup (left) and entanglement generation (right).

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October 2007

Entangling independent photons by time measurement

Nature Physics, 3, 692 (2007)

Matthaus Halder, Alexios Beveratos, Nicolas Gisin, Valerio Scarani, Christoph Simon and Hugo Zbinden

Overview

Researchers in the Group of Applied Physics (GAP) at Geneva University have demonstrated an entanglement swapping experiment with autonomous sources. Normally, entanglement between two photons is produced by emitting them simultaneously from the same source. In this experiment the researchers show that entanglement can be transferred (or "swapped") on two photons, originating from autonomous sources and hence formerly completely independent. This is the first time that two autonomous photons have been entangled.

The scheme of Entanglement Swapping allows entangling photons, which have been emitted by independent processes in remote sources (A and B, Fig. 1). Each source emits a pair of entangled photons (A1-A2 and B1-B2, respectively). By taking one photon from each pair (A1 and B1) and performing a joint measurement (Bell state measurement, BSM), they are detected in an entangled state, one of the four Bell states. For a successful outcome of the BSM, A2 and B2 are projected onto an entangled state as well, even though they never interacted or share any common past.

To enable a BSM, the photons A1 and B1 must be indistinguishable, which means in particular, arrive at the same time at the beam splitter BS. Until now, this was achieved by the use of pulsed sources with synchronized emission times and matched fiber lengths. This is the first demonstration that precise timing of photons at telecom wavelength can be achieved by detection and postselection. To make this possible, the photons’ coherence length has to exceed the detectors temporal resolution. Single photon detectors based on superconductors and semiconductors, featuring a timing resolution of 70-100ps. By narrowly filtering (10pm) the photons, their coherence length is increased to the order of 300ps. Thus no synchronization between the sources is required anymore which makes them truly autonomous.
 

This setup is compatible with some of the quantum memories currently under development in project QAP, because the source and memory bandwidths are within the same order of magnitude. The work is thus an important step towards quantum repeaters, one of the main QAP objectives.

For a more detailed summary, see the News and Views section of Nature Physics, October 2007 on the UNIGE website.

 

Figure1: Scheme of the Entanglement Swapping setup

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Enhancement of the recombination rate of InAs quantum dots coupled to micro-cavities emitting at the telecom wavelengths

Applied Physics Letters 91, 123115 (2007)
L. Balet, M. Francardi, A. Gerardino, N. Chauvin, B. Alloing, C. Zinoni, C. Monat, L. H. Li, N. Le Thomas, R. Houdré and A. Fiore.

Optics Letters 32, 2747 (2007)
N. Chauvin, L. Balet, B. Alloing, C. Zinoni, L. Li, A. Fiore, L. Grenouillet, P. Gilet, N. Olivier, A. Tchelnokov, M. Terrier and J.-M. Gérard.
 

Quantum computing and quantum communication need sources of single indistinguishable photons emitting at telecom wavelengths. Such requirements are reachable using single quantum dots (QDs) embedded in micro-cavities. The coupling of a QD with the cavity mode increases the recombination rate of the QD exciton due to the Purcell effect. Thus the impact of the decoherence processes is reduced and an increase of the repetition rate of the single photon source is possible. Moreover the coupling of the QD emission with the mode enables good collection efficiency.

Micro-photoluminescence (MPL) and time-resolved experiments have been performed on InAs QDs embedded in photonic crystal (PhC) and micro-pillar (MP) cavities. The QD growth and cavity fabrication have been optimized for emission at 1300 nm. The cavity modes present a high quality factor: up to 15000 for the PhC cavities and up to 2500 for the MP cavities.

Studies performed on PhC cavities have revealed an increase in the intensity of single QD lines when tuned with the cavity mode. Time resolved experiments performed on these single QD lines have revealed an enhancement of the recombination rate up to eightfold.
An increase of the recombination rate by a factor 2 is also observed for an ensemble of QDs coupled to one mode of a MP cavity.

These results are very promising for the realization of efficient single photon sources based on single QDs in a micro-cavity.

Figure1: Time resolved dynamics of QDs spatially outside the PhC region (blue squares) and of a single exiton line in resonance of the cavity mode (black triangle)

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August 2007

Entanglement percolation in quantum networks

Nature Physics, 3, 256 (2007)

Antonio Acín, J. Ignacio Cirac and Maciej Lewenstein

Overview

The standard scenario in any quantum communication application consists of several distant nodes that can exchange information encoded on quantum particles through quantum channels, e.g. photons sent through optical fibers. The nodes aim at establishing long-distance perfect quantum correlations, or maximally entangled states, by performing local operations on each node and exchanging classical communication. Therefore, in order to optimize the operation of a quantum network, it is required to design efficient protocols for the establishment of maximally entangled states between different distant nodes.

Until now, the standard solution for the distribution of entanglement between distant nodes was by means of quantum repeaters. In this scenario, two distant nodes are connected by a chain of quantum repeaters in a one-dimensional configuration, see also Figure 1(a), below. General quantum networks, however, have a richer and more connected structure, see also Figure 1(b) and 1(c). Our recent work shows that intriguing quantum phenomena appear when studying the distribution of entanglement through these more connected networks, depending on the way the nodes are connected and the entanglement parameters characterizing these connections. Actually, the distribution of entanglement through these networks defines a new type of phase transition. This entanglement phase transition is related to classical percolation, a concept that is well known in Statistical Mechanics, so we named this phenomenon Entanglement Percolation.

Figure1: Diagram illustrating the distinction between a one-dimensional quantum network (a) and the richer structure of a more general quantum network (b,c).

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July 2007

Twisted photons

Nature Physics, 3, 305 (2007)

G. Molina-Terriza, J. P. Torres and L. Torner

Overview

Quantum optical information applications make use of only a portion of the rich structure of atoms and photons. Most of these applications make use of the polarization or spin angular momentum of photons. This corresponds to using two-dimensional systems, that is systems whose state can be described by a combination of two orthogonal states, as any polarization state can be described by weighted superpositions of two linear or circular polarization states.

But the total angular momentum can also contain an orbital contribution, which comes from a more complex combination of the phase and amplitude profiles of an optical field. Contrary to the case of polarization, the orbital angular momentum lives in an infinite dimensional Hilbert space. Indeed, the dimensions of the working space can be readily tailored. This offers the possibility to explore quantum algorithms that either inherently live in a higher dimensional Hilbert space (qudits), or exhibit enhanced efficiency in increasingly higher dimensions.

In the May 2007 issue of Nature Physics (see Nature Physics 3, 305, 2007 and cover page) researchers Molina-Terriza, Torres and Torner, from ICFO-Institute of Photonic Sciences in Barcelona, review progress in the generation, understanding and use of the orbital angular momentum of photons. The orbital angular momentum of photons can be used to demonstrate the violation of bipartite, three dimensional Bell inequalities, to implement new protocols such as the so called quantum coin tossing, to generate quantum states in ultra-high dimensional spaces, to implement new quantum cryptography protocols, and as an powerful enabling tool to generate and to control multidimensional quantum states of matter, and therefore adds to the existing techniques for the full control of atoms.

The exploration of the orbital angular momentum of photons is an important tool of the Qubit Applications Project (QAP). It is related to the development of theory and design of experiments to exploit the rich structure of photons, which includes the development of techniques for the independent control of polarization and transverse wave-vector, and the investigation of new quantum communication protocols using the space degree of freedom of single photons.

Figure: What is the shape of a photon which carries orbital angular momentum? (a) and (d) display the typical transverse shape of a photon with orbital angular momentum (OAM). (a) is a theoretical plot, while (d) corresponds to the experimentally obtained image. The light beam exhibits a dark spot in the center, and a ring-like intensity profile. The phase of the beam twists around the central dark spot, producing a staircase-like phase wave-front, as depicted in (b). Such spiraling phase makes that the local momentum of the beam mimics the velocity pattern of a tornado or vortex fluid, as shown in (c), a similarity that causes these singular spots to be named optical vortices. To visualize such a spiral phase, one can observe the interference of the photon beam with OAM with a vorticityless plane wave propagating at a slightly different angle. (e) shows the typical interference pattern obtained, as revealed by the characteristic fork-like structure (Molina-Terriza, Torres and Torner, Nature Physics 3, 305, 2007)

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Trapped Ion Chain as a Neural Network: Error-Resistant Quantum Computation

Physical Review Letters, 98, 023003 (2007)

M. Pons, V. Ahufinger, C. Wunderlich, A. Sanpera, S. Braungardt, A. Sen(De), U. Sen, and M. Lewenstein

Overview

Exposing an ion - that is part of a linear array of ions confined in a Paul trap - to a qubit-state-dependent force gives rise to a long-range interaction between individual ionic qubits. In the January issue of Physical Review Letters QAP researchers show that taking advantage of this long range interaction an array of ions may be employed to realize a neural network composed of individual atoms. This network permits storage of information distributed over the whole atomic array. Moreover, error-resistant quantum computation may be implemented using such a neural network.

As part of Subproject 4 of QAP the research group at the University of Siegen works on the implementation of ion spin molecules and will explore their suitability, for instance, for realizing such a neural network.

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June 2007

Remote preparation of an Atomic Quantum Memory

Physical Review Letters, 98, 050504 (2007)

Wenjamin Rosenfield, Stefan Berner, Jürgen Volz, Markus Weber, and Harald Weinfurter

Overview

Remote state preparation of a distant atomic quantum memory has been demonstrated by researchers at Ludwig Maximillians University (LMU), Germany. This is a significant step towards the development of quantum repeaters, and quantum networks – two of the principal research interests in the EU Project QAP.

Many of the fundamental concepts in quantum communication and quantum information processing are predicated on the ability to faithfully map quantum information between photons and matter-based quantum processors. Entanglement between matter and light is crucial for this task. In this work, researchers at LMU experimentally demonstrate the suitability of atom-photon entanglement as an interface between a quantum memory device and a quantum communication channel.

In the demonstration at LMU, a single rubidium atom acting as the quantum memory is prepared in a desired quantum state by a remote sender (Alice) using a remote state preparation (RSP) protocol. The RSP protocol consists of three main steps. Initially, entanglement is generated between the spin of a single Rubidium atom confined in a dipole trap, and the polarization of a single spontaneously emitted photon; the photon is then transferred to Alice via an optical fiber. Secondly, Alice imprints the desired qubit on the photon using the spatial modes of a polarization-independent Mach-Zehnder interferometer. Finally, the spatially encoded qubit is transferred to the spin state of the atom by performing a Bell-state measurement in the joint polarization - spatial-mode Hilbert space of the photon. This is possible because of the atom-photon entanglement generated in the first step.

The success of the RSP protocol described above has been verified at LMU by conducting full quantum state tomography of the atomic qubit, after the preparation process. The mean fidelity of quantum state transfer was found to be 82.2%. This work marks a significant step towards implementation of an atomic quantum repeater.
 

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Globally Controlled Quantum Wires for Perfect Qubit Transport, Mirroring, and Computing

Physical Review Letters, 97, 090502 (2006)

Joe Fitzsimmons and Jason Twamley

Overview

Recent work by researchers at Oxford and Macquarie Universities has shown that the necessary requirements for practical quantum computing may be lower than previously thought. In their paper, Joe Fitzsimons and Jason Twamley outline a scheme for performing universal quantum computation within a uniform Ising spin chain without the need to control individual spins separately.

The need to individually address qubits within a quantum computer has proved a roadblock to achieving scalable quantum computing within many systems. While a number of architectures exist which overcome this problem using periodic arrangements of different types, or species, of qubits, this new scheme substantially lowers the experimental requirements, requiring only a single physical species of qubit together with a common physical interaction.

The paper includes a prescription for quantum state transfer, the task of moving quantum information from one location to another, as well as a procedure for efficiently mirroring the order of qubits stored within the spin chain. These are both important tasks within quantum communication, and it is likely that similar quantum wires will provide important communications buses within any large scale solid-state quantum processor.

Additionally, the paper describes how universal computing can be achieved within the spin chain without resorting to local control. The density with which logical qubits can be packed (½) within the chain is the highest yet achieved within such a scheme, and has since been increased to the maximum possible density of one qubit per spin (quant-ph/0606188), offering computational power competitive with locally controlled schemes.

Shortly after publication of this paper, a successful experimental implementation of the scheme was reported using NMR techniques (quant-ph/0606188). This work substantially lowers the barriers to scalable solid-state quantum computing.

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May 2007

Observation of Entanglement of a Single Photon with a Trapped Atom

Physical Review Letters, 96, 030404 (2006)

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Saucke, C. Kurtsiefer, and H. Weinfurter

Overview

Entanglement between the polarization of a single photon and the internal state of a single neutral atom has been observed by researchers at Ludwig Maximillians University (LMU), Germany. This is a crucial step towards implementation of long range quantum networks: one of the principal areas of research in the EU Integrated Project QAP .

Entanglement is a key element for quantum communication and information applications. Future applications such as quantum networks and the quantum repeater are predicated on the distrubution of entanglement between separate quantum processors. For this purpose, entanglement between different quantum objects such as atoms and photons forms the interface between atomic quantum processors and photonic quantum communication channels, finally allowing the distibution of quantum information over arbitrary distances.

In this implementation a single Rubidium atom, confined within a dipole trap of radius 3.5µm, acts as a quantum processor. The atom is trapped using a far off-resonance laser field. The instantaneous dipole moment induced on the atom by the field results in an intensity dependent force upon the atom. For a large negative frequency detuning this dipole force pushes atoms towards regions of higher laser intensity, thus allowing confinement of atoms within a region of suitably intersecting laser beams.

Selective pumping prepares the trapped atom in an excited hyperfine state which can decay to three possible ground states with magnetic quantum numbers MF=-1,0 or +1 by spontaneously emitting a σ+, π or σ- polarized photon, respectively. Photons with σ-polarization are detected in the same spatial mode and analysed to determine their polarization while those with π-polarization are ignored. Provided the emission processes are indistinguishable in all degrees of freedom other than polarization, the atom-photon system is in a maximally entangled state. This entanglement has been verified at LMU using a full tomographic analysis of the atomic state via a state selective stimulated Raman adiabatic passage (STIRAP) technique.

The techniques employed at LMU represent an important step towards an interface between a quantum computer and a photonic quantum communication channel.