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 ˝ 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 ˝ 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.

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.