Decoherence suppression via non-Markovian coherent feedback control

Shi-Bei Xue, Re-Bing Wu, Wei-Min Zhang, Jing Zhang, Chun-Wen Li, and Tzyh-Jong Tarn

Phys. Rev. A 86, 052304 – Published 5 November 2012

Abstract

In this paper, we present a coherent feedback control scheme for non-Markovian bosonic systems, in which an engineered quantum control field is introduced to couple both the system and the noise bath. The closed-loop dynamics of the system is described by an exact non-Markovian quantum Langevin equation, where the spectral density functions of the noise and the quantum control field, as well as their coupling, are combined into a single memory kernel function. We show that the coupling between the quantum control field with the noise bath can be used as a feedback control to modulate the memory kernel function. As a result, the noise bath can be driven out of resonance with the system and the decoherence can be efficiently suppressed. The effectiveness of the controllability is demonstrated with a photonic circuit in photonic crystals.

Received 2 April 2012

DOI:https://doi.org/10.1103/PhysRevA.86.052304

Authors & Affiliations

Shi-Bei Xue^1,2,*, Re-Bing Wu^1,2,†, Wei-Min Zhang³, Jing Zhang^1,2, Chun-Wen Li^1,2, and Tzyh-Jong Tarn^1,2,4

¹Department of Automation, Tsinghua University, Beijing 100084, People's Republic of China
²Center for Quantum Information Science and Technology, TNList, Beijing 100084, People's Republic of China
³Department of Physics and Center for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan
⁴Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, USA

^*xueshibei@gmail.com
^†rbwu@tsinghua.edu.cn

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Vol. 86, Iss. 5 — November 2012

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Images

Figure 1
The structure diagram of the coherent feedback loop, where the quantum control field and the noise bath jointly form a structured bath. The Hamiltonians of the system, the noise bath, and the quantum control field are denoted as $H_{S}$ , $H_{B}$ , $H_{C}$ , respectively, and their mutual interaction Hamiltonians are denoted as $H_{S B}$ , $H_{S C}$ , $H_{B C}$ , respectively. The interaction Hamiltonian $H_{B C}$ between the quantum control field and the noise bath is tunable. The feedback system consists of closed loops flowing in both clockwise and anticlockwise directions.Reuse & Permissions
Figure 2
The shape of the noise spectrum without and with feedback $r (ω) = r_{0}$ . (a) The noise spectrum without feedback, where the system characteristic frequency $ω_{0}$ is in the noise band and its resonance with the noise leads to decoherence. (b) The noise spectrum under constant feedback coupling function $r (ω) = r_{0}$ , where the noise spectrum is split and a noise-free band appears under sufficient large feedback coupling strength. The resulting off-resonance with the noise can be used to suppress non-Markovian decoherence.Reuse & Permissions
Figure 3
The schematic diagram of actual coherent feedback loop in photonic crystal system where the cavity (system) is a point defect and the waveguides are linear defects. The introduced quantum control field and its interaction with the noise bath are realized by a waveguide and a coupler, respectively.Reuse & Permissions
Figure 4
The feedback modulated spectral function in the memory kernel [(a)–(c)] and the corresponding dynamics of scaled cavity amplitude $| u (t) |$ [(d)–(f)] under the constant coupling strength $r (ω) = r_{0}$ , where $ω_{0}$ is the system's characteristic frequency. The figures in each row correspond to different values of the phase variant $θ_{0}$ , i.e., $θ_{0} = 0$ in (a) and (d), $θ_{0} = \frac{π}{4}$ in (b) and (e), and $θ_{0} = \frac{π}{2}$ in (c) and (f), which modulate the amplitudes of the two branches. In each case, e.g., $θ_{0} = 0$ , when the feedback coupling strength $r_{0}$ is increased, the separation of the noise bands induces noise-free bands and the decay of $| u (t) |$ is seen to be remarkably reduced.Reuse & Permissions
Figure 5
The time evolution curves of the photon number $n (t) = 〈 {\hat{a}}^{†} (t) \hat{a} (t) 〉$ in the cavity under different values of the constant coupling strength $r_{0}$ in (a) the low-temperature $T = 5 mK$ case and (b) the high-temperature $T = 5 K$ case. The initial photon number is $n (0) = 5$ . When the feedback coupling strength $r_{0}$ is increased, the processes of the injecting and absorbing photons are slowed down.Reuse & Permissions

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