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Journal of the Physical Society of Japan

Bang-Bang Control of Entanglement in Spin-Bus–Boson Model

Robabeh Rahimi, Akira SaiToh, Mikio Nakahara

Published Nov 12, 2007• 1 citation
Publisher

Abstract

A linear coupling model of a spin system with bosonic modes is a typical model to theoretically evaluate decoherence. In this contribution, we consider a dynamical control of decoherence of entanglement in a spin system consisting of an electron spin and nuclear spins (namely, a spin bus system) coupled with bosons whose modes are in resonance with individual spins. Numerical simulations show that bang-bang pulses with a realistic duty ratio can suppress decoherence considerably in an entangled two-qubit system. Simulation results indicate one phenomenon: a very large, as well as very small, dissipation rate of bosons results in a small decoherence.

DOI
10.1143/jpsj.76.114007

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The description and control of decoherence of quantum bit systems have become a field of increasing interest during the last decade. We discuss different techniques to estimate and model decoherence sources of solid state quantum bit realizations. At first, we derive a microscopic, perturbation theoretical approach for Lindblad master equations of a spin-Boson model at low temperatures. A different sort of decoherence is investigate by means of the bistable fluctuator model. For this particular but nevertheless for solid state qubits relevant noise source, we present a suitably designed dynamical decoupling method (so-called quantum bang-bang). This works as a high-pass filter, suppressing low frequency parts of the noise most effectively and thus being a promising method to compensate the ubiquituous 1/f noise. Furthermore, we investigate the behaviour of a two coupled spin system exposed to collective and localized bath. For this dressed-spin system we receive by means of scaling-analysis in first order a quantum phase diagram. On that we can identify the various quantum dynamical and entanglement phases.
We present an open loop (bang-bang) scheme to control decoherence in a quantum NOT gate and implement it in a realistic simulation. The system is consistently described within the spin-boson model, with interactions accounting for both adiabatic and thermal decoherence. The external control is included from the beginning in the Hamiltonian as an independent interaction term. After tracing out the environment modes, reduced equations are obtained for the two-level system in which the effects of both decoherence and external control appear explicitly. The controls are determined exactly from the condition to eliminate decoherence, i.e. to restore unitarity. Numerical simulations show excellent performance and robustness of the proposed control scheme.
It is known that a quantum system with finite degrees of freedom can simulate a composite of a system and an environment if the state of the hypothetical environment is randomized by external manipulation. We show theoretically that any phase decoherence phenomena of a single qubit can be simulated with a two-qubit system and demonstrate experimentally two examples: one is phase decoherence of a single qubit in a transmission line, and the other is that in a quantum memory. We perform NMR experiments employing a two-spin molecule and clearly measure decoherence for both cases. We also prove experimentally that the bang-bang control efficiently suppresses decoherence.