Space-time dual quantum Zeno effect: Interferometric engineering of open quantum system dynamics

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Space-time dual quantum Zeno effect: Interferometric engineering of open quantum system dynamics

Jhen-Dong Lin, Ching-Yu Huang, Neill Lambert, Guang-Yin Chen, Franco Nori, and Yueh-Nan Chen

Phys. Rev. Research 4, 033143 – Published 22 August 2022

Abstract

Superposition of trajectories, which modify quantum evolutions by superposing paths through interferometry, has been utilized to enhance various quantum communication tasks. However, little is known about its impact from the viewpoint of open quantum systems. Thus we examine this subject from the perspective of system-environment interactions. We show that the superposition of multiple trajectories can result in quantum state freezing, suggesting a space-time dual to the quantum Zeno effect. Moreover, nontrivial Dicke-like super(sub)radiance can be triggered without utilizing multiatom correlations.

Received 17 March 2022
Accepted 8 August 2022

DOI:https://doi.org/10.1103/PhysRevResearch.4.033143

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Open quantum systems & decoherence Quantum Zeno dynamics Quantum channels Quantum engineering

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Jhen-Dong Lin^1,2,*, Ching-Yu Huang^1,2, Neill Lambert ³, Guang-Yin Chen ⁴, Franco Nori ^3,5,6, and Yueh-Nan Chen ^1,2,†

¹Department of Physics, National Cheng Kung University, 701 Tainan, Taiwan
²Center for Quantum Frontiers of Research & Technology, NCKU, 70101 Tainan, Taiwan
³Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
⁴Department of Physics, National Chung Hsing University, Taichung 402, Taiwan
⁵RIKEN Center for Quantum Computing (RQC), Wakoshi, Saitama 351-0198, Japan
⁶Department of Physics, The University of Michigan, Ann Arbor, 48109-1040 Michigan, USA

^*jhendonglin@gmail.com
^†yuehnan@mail.ncku.edu.tw

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Vol. 4, Iss. 3 — August - October 2022

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Figure 1
Superposed quantum dynamics achieved by a multiarm interferometer. To produce superposition of paths, the qubit is first sent into the multiport beam splitter (MBS1) such that the path of the qubit is prepared in $| χ_{C} 〉 = \sum_{i = 1}^{N} | i_{C} 〉 / \sqrt{N}$ . Thus the qubit can travel through (a) different independent environments ${E_{i}}$ or (b), different positions ${r_{i}}$ of a single environment in a quantum superposition. One can further manipulate the interference effect between the evolution paths by using the other beam splitter (MBS2) along with phase shifters labeled by ${ϕ_{i}}$ . The modified dynamics can be obtained through a post-selection, as illustrated by the trash cans. For the independent-environments scenario, one can obtain a space-time dual to (c), usual quantum Zeno effect induced by a temporal sequence of measurements. For the indefinite-position scenario, one can obtain a collective decay akin to (d): the Dicke effect that can be observed by an ensemble of qubits embedded in a common environment.
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Figure 2
Effective decay within a given time $t = ω_{q} / 5$ of the dissipative model for superposed trajectories and the usual quantum Zeno effect, which are described by a spectral density and the filter functions. $F^{diss} (N)$ , given by Eq. (15), is the filter function with $N$ superposed trajectories with $n = 0$ . $\tilde{F} (\tilde{N})$ is the filter function for the Zeno effect induced by $\tilde{N}$ periodic measurements of the qubit energy; it can be obtained by replacing $N$ with $\tilde{N}$ and ${sinc}^{2} [(ω - ω_{q}) t / 2]$ with ${sinc}^{2} [(ω - ω_{q}) t / 2 \tilde{N}]$ in $F (N)$ . $J (ω) = exp [- {(ω - ω_{M})}^{2} / Δ]$ represents a given spectral density with $ω_{M} = 3 ω_{q} / 2$ and $Δ = ω_{q} / 5$ . The qualitative difference between the traditional Zeno effect and the space-time dual Zeno effect induced by superposed trajectories is that $\tilde{F} (\tilde{N})$ smears out, whereas $F (N)$ remains localized when increasing $\tilde{N}$ and $N$ , respectively.
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Figure 3
Comparison of the two-atom super(sub)radiance, with qubits' distance $d$ , with the single-atom decay modified by three superposed trajectories, where the position vectors form an equilateral triangle with edge length $d$ . This can be implemented by a Young's type triple-slit experiment. One can place the atom detectors at certain positions and perform quantum state tomography to verify the super(sub)radiant dynamics. Here, we set the collective factor $sinc (q d) = 1 / 6$ and the spontaneous emission rate $Γ_{0} / ω_{q} = 0.01$ .
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Figure 4
Time evolutions of the trace distance for different factors $(N, n)$ . (a) For the dissipative model, we consider the Lorentzian spectral density given by Eq. (B4) with $λ / γ_{0} = 0.1$ . For the pure dephasing model, we consider a family of Ohmic spectral densities given by Eq. (B5) with $η = 1 / 3$ and $ω_{c} = 1$ . (b) We present result for $s = 1$ (Ohmic), where the single-path evolution experiences Markovian monotonic dephasing. (c) Further, we present result for $s = 4$ (super-Ohmic), where nonmonotonic behavior and coherence trapping can be observed for single-path dynamics.
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