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Journal of Optics B Quantum and Semiclassical Optics

Control of state localization in a two-level quantum system

Xiao-Shu Liu, Wen-Zhang Liu, Re-Bing Wu, Gui Lu Long

Published Jan 12, 2005• 14 citations
Publisher

Abstract

The control of the state of a system to a given state has important applications in quantum engineering and control. In this paper, we study a control scheme that controls the localization of state in a two-level system via homodyne feedback, and analyse the condition for the steady state and stability of the localization. We also give the parameters of the feedback and the driving field for control of the system state to localization at any desired state on the Bloch sphere.

DOI
10.1088/1464-4266/7/2/006

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Summary form only given. Decoherence in quantum systems can be loosely defined as loss of purity. Therefore the ultimate success in using feedback to fight decoherence would be to create an arbitrary stable pure state in the presence of dissipation. This goal was realized by Hoffman, Mahler and Hess (1998) for a very simple system: a resonantly driven two-level atom. They showed that by making part of the coherent driving proportional to the homodyne photocurrent can stabilize the state to any point on the bottom half of the sphere. Here we reanalyze their proposal by using the technique of stochastic master equations, allowing their results to be generalized in three ways.
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Quantum feedback control is a technology that can be used to drive a quantum system into a predetermined eigenstate. In this article, sufficient conditions for the experiment parameters of a quantum feedback control process of a homodyne measurement are given to guarantee feedback control of a spin-1∕21∕21∕2 quantum system in case of imperfect detection efficiency. For the case of pure states and perfect detection efficiency, time scales of feedback control processes are calculated.
We develop a method for controlling the ensemble states of a two-level quantum system on the Bloch sphere. A spectrum of resonance frequencies parametrizes the ensemble. The evolution of the ensemble states under externally applied controls is uniquely determined by their respective resonance frequencies. Therefore, the control fields must be designed to simultaneously evolve the ensemble states across the domain of resonance frequencies. The objective is to evolve the discretized quantum ensemble states from an arbitrary initial dispersion to a targeted final configuration on the Bloch sphere. The proposed method holds potential for broad applicability in areas such as nuclear magnetic resonance (NMR), electron spin resonance (ESR), quantum computing and information processing, sampling-based learning control (SLC), quantum sensing and metrology, and quantum error correction.