Single-photon-triggered spin squeezing with decoherence reduction in optomechanics via phase matching

Zhucheng Zhang, Lei Shao, Wangjun Lu, Yuguo Su, Yi-Ping Wang, Jing Liu, and Xiaoguang Wang

Phys. Rev. A 104, 053517 – Published 17 November 2021

Abstract

Quantum spin squeezing is an important resource for quantum information processing, but its squeezing degree is not easy to preserve in an open system with decoherence. Here, we propose a scheme to implement single-photon-triggered spin squeezing with decoherence reduction in an open system. In our system, a Dicke model (DM) with an added quadratic optomechanical coupling is considered, which can be equivalent to an effective DM manipulated by the photon number. Besides, the phonon mode of the optomechanical coupling is coupled to a squeezed-vacuum reservoir with a phase matching, resulting in that its thermal noise can be suppressed completely. We show that squeezing of the phonon mode triggered by a single photon can be transferred to the spin ensemble totally, and pairwise entanglement of the spin ensemble can be realized if and only if there is spin squeezing. Importantly, when considering the impact of the environment, our system can obtain a squeezing degree better than that of the optimal squeezing that can be achieved in the traditional DM. Meanwhile, the spin squeezing generated in our system is immune to the thermal noise. This work offers an effective way to generate spin squeezing with a single photon and to reduce decoherence in an open system, which will have promising applications in quantum information processing.

Received 13 September 2021
Accepted 2 November 2021

DOI:https://doi.org/10.1103/PhysRevA.104.053517

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Entanglement manipulation Optomechanics Quantum information processing Quantum optics Squeezing of quantum noise

Dicke model Quantum correlations, foundations & formalism Schroedinger equation

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Zhucheng Zhang ¹, Lei Shao¹, Wangjun Lu ^1,6, Yuguo Su², Yi-Ping Wang³, Jing Liu ⁴, and Xiaoguang Wang^1,5,*

¹Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou 310027, China
²State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, APM, Chinese Academy of Sciences, Wuhan 430071, China
³College of Science, Northwest A&F University, Yangling 712100, China
⁴MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
⁵Graduate School of China Academy of Engineering Physics, Beijing 100193, China
⁶Department of Maths and Physics, Hunan Institute of Engineering, Xiangtan 411104, China

^*xgwang1208@zju.edu.cn

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Issue

Vol. 104, Iss. 5 — November 2021

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Images

Figure 1
Schematic diagram of the system. A Dicke model [i.e., $N$ two-level systems $σ_{-}$ (e.g., a spin ensemble [59] or superconducting qubits [60]) coupled with resonator B] is introduced into a superconducting circuit that has the ability to simulate the quadratic optomechanical coupling [56, 61]. In the superconducting circuit, the photon and phonon modes are provided by resonator A and resonator B, respectively, and the antisymmetric current distribution in resonator B ensures the opposite flux variations $\pm δ Φ$ . By optimizing the coupling capacitance $C$ , the bias flux, and the geometrical arrangement of the circuit, the circuit analog of quadratic optomechanics can achieve a stronger coupling compared with the version in the membrane-in-the-middle cavity optomechanical system [62].
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Figure 2
(a) Wigner function $W_{b}$ of the phonon mode when there are zero photons and one photon, where the quadrature variables are defined as $P = - i (b - b^{†})$ and $Q = (b + b^{†})$ . (b) Evolution of the squeezing parameter $ξ_{b}^{2} (t)$ of the phonon mode with time $t$ . The parameters we take for the spin ensemble are spin number $N = 100$ and the transition frequency $Ω = 200 G$ ; for the phonon mode, the resonance frequency $ω_{b} = 2300 G$ ; for the quadratic optomechanical coupling, strength $g = 0.2481 ω_{b}$ ; and for the system with decays, $γ = G$ and $κ = 0.01 G$ .
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Figure 3
Panels (a)–(c): Evolutions of the spin Wigner function $W_{s}$ on the Bloch sphere with spin number $N = 10$ and a single photon when $G t = 0$ (a), 0.2 (b), and 0.28 (c). Panels (d)–(g): Evolutions of squeezing for the spin ensemble and the phonon mode with different spin numbers ( $N = 2$ , 10, and 100) and without considering system decays, where panels (d)–(f) are the numerical results and (g) is the analytic result. Panels (h) and (i): Evolutions of the spin squeezing and the spin-spin entanglement (i.e., concurrence) with different spin numbers ( $N = 2$ and 4), where the dashed green curves represent the quantity $ξ_{s}^{2} + (N - 1) C$ . Other parameters are the same as those in Fig. 2.
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Figure 4
Evolution of the expectation value $〈 J_{z} 〉$ of the collective operator $J_{z}$ with different spin numbers ( $N = 2$ , 10, and 100). Other parameters are the same as those in Fig. 2.
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Figure 5
(a) Evolution of the squeezing parameter $ξ_{s}^{2}$ in the system with decays; (b) and (c) minimum ${(ξ_{s}^{2})}_{min}$ of the spin squeezing in the system where the parameters deviate from the optimal squeezing phase and squeezing amplitude; (d) evolution of the spin squeezing in the open system ( $γ = G$ and $κ = 0.01 G$ ), where the solid curve represents our system. Besides, the dashed, dotted, and dot-dashed curves represent a traditional Dicke model (DM) in a squeezed-vacuum reservoir (SR) that is the same as ours, a traditional DM in a thermal reservoir (TR) with thermal phonon number 1, and a traditional DM in a vacuum reservoir (VR), respectively. The initial squeezing degree of the phonon mode in the traditional DM is assumed to be the same as ours, i.e., $exp (- 2 r_{n})$ . Other parameters are the same as those in Fig. 2.
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