Unravelling-based (auto)control of back-action in atomic Bose−Einstein condensate

doi:10.1007/s11467-023-1375-2

Front. Phys.

2024, Vol. 19

Issue (4) : 41201 https://doi.org/10.1007/s11467-023-1375-2

Unravelling-based (auto)control of back-action in atomic Bose−Einstein condensate

V. A. Tomilin(

), L. V. Il’ichov

Institute of Automation and Electrometry SB RAS 630090, Novosibirsk, Russia

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Abstract

We present a novel feedback control method for quantum systems. Feedback does not affect the controlled system itself. Instead, it controls the unravelling of the quantum channel of interaction between the system and its environment. This interaction can be represented as a history of events. If their informational content is changed, their back-action on the system is also modified. Feedback action is trigged by the events, thus granting the system the degree of control over its own state. The efficiency of the proposed scheme is demonstrated on the example of two-mode atomic Bose-Einstein condensate, with one of its modes subject to phase-contrast imaging in a Mach−Zehnder interferometer. The histories of photocounts in the output channels of the interferometer are used for feedback. Its capabilities of state engineering are studied for different settings of the feedback loop and different numbers of events in the recorded histories.

Keywords quantum feedback control quantum measurements two-mode Bose−Einstein condensates

Corresponding Author(s): V. A. Tomilin

Issue Date: 19 January 2024

Cite this article:

V. A. Tomilin,L. V. Il’ichov. Unravelling-based (auto)control of back-action in atomic Bose−Einstein condensate[J]. Front. Phys. , 2024, 19(4): 41201.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1375-2
https://academic.hep.com.cn/fop/EN/Y2024/V19/I4/41201

Fig.1 Double-well BEC in the Mach−Zehnder interferometer. The control is implemented by phase switchings in the condensate-free arm. Note that the feedback loop lies outside of BEC.

Fig.2 KL-divergences between normalized distributions

P n (+), P n (+ +), P n (+ + +)

and: (a−c) uniform distribution

p n =

1 / (N a t + 1)

; (d−f) distributions

R n (+), R n (+ +), R n (+ + +)

, evaluated for

χ = π / 20, ω = 0.07, N a t = 10

. Color scales to the left and to the right correspond to the respective column. A pair of adjacent maxima are marked on the (e) plot with coordinates

(φ +, φ −) = (− 0.4 π, − 1.4 π)

and

(φ +, φ −) = (− 0.9 π, 0.1 π)

Fig.3 Unity-normalized steady-state distributions for values of unravellings

(φ +, φ −)

, corresponding to the KL-divergence’ maxima highlighted in Fig.2(e). Filled circles represent actual feedback-induced distributions, while triangles represent no-feedback distributions for unravelling set at

((φ + + φ −) / 2, (φ + + φ −) / 2)

. Empty squares represent uniform distributions.

Fig.4 KL-divergences between

P n (+), P n (+ +), P n (+ + +)

and the binomial distribution

p n (b i n o m)

. The color scale is common for all three plots.

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[1]	DONG Dao-yi, CHEN Zong-hai, ZHANG Chen-bin, CHEN Chun-lin. Feedback control of quantum system[J]. Front. Phys. , 2006, 1(3): 256-262.

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