Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath | Phys. Rev. A 82, 042306 (2010)

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Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath

Gonzalo A. Álvarez1,*, Ashok Ajoy1,2,3, Xinhua Peng1,4, and Dieter Suter1,†

1Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany

2Birla Institute of Technology and Science, Pilani, Zuarinagar, Goa 403726, India

3NMR Research Centre, Indian Institute of Science, Bangalore 560012, India

4Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China

Received 11 August 2010; published 7 October 2010

Avoiding the loss of coherence of quantum mechanical states is an important prerequisite for quantum information processing. Dynamical decoupling (DD) is one of the most effective experimental methods for maintaining coherence, especially when one can access only the qubit system and not its environment (bath). It involves the application of pulses to the system whose net effect is a reversal of the system-environment interaction. In any real system, however, the environment is not static, and therefore the reversal of the system-environment interaction becomes imperfect if the spacing between refocusing pulses becomes comparable to or longer than the correlation time of the environment. The efficiency of the refocusing improves therefore if the spacing between the pulses is reduced. Here, we quantify the efficiency of different DD sequences in preserving different quantum states. We use 13C nuclear spins as qubits and an environment of 1H nuclear spins as the environment, which couples to the qubit via magnetic dipole-dipole couplings. Strong dipole-dipole couplings between the proton spins result in a rapidly fluctuating environment with a correlation time of the order of 100 μs. Our experimental results show that short delays between the pulses yield better performance if they are compared with the bath correlation time. However, as the pulse spacing becomes shorter than the bath correlation time, an optimum is reached. For even shorter delays, the pulse imperfections dominate over the decoherence losses and cause the quantum state to decay.

© 2010 The American Physical Society

via Phys. Rev. A 82, 042306 (2010): Performance comparison of dynamical decoupling sequences for a qubit in a rapidly fluctuating spin bath.

Relaxation times of different initial conditions under DD conditions as a function of the delay between pulses τ (left panels) and the cycle time τc (right panels). From top to bottom the initial condition is given by S_x, S_y, and S_z respectively. An optimal τ and consequently τc is observed for each sequence. The reduction of the relaxation time to the right side of the optimal value is due to the shifting environment: in this regime the cycle time is longer than the correlation time of the bath, τc > τB . The reduction for short cycle times indicates that in this regime, accumulated pulse errors dominate.
Relaxation times of different initial conditions under DD conditions as a function of the delay between pulses τ (left panels) and the cycle time τc (right panels). From top to bottom the initial condition is given by S_x, S_y, and S_z respectively. An optimal τ and consequently τc is observed for each sequence. The reduction of the relaxation time to the right side of the optimal value is due to the shifting environment: in this regime the cycle time is longer than the correlation time of the bath, τc > τB . The reduction for short cycle times indicates that in this regime, accumulated pulse errors dominate.
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