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Results in Physics

Collective decay induce quantum phase transition in a well-controlled hybrid quantum system

Dong‐Yan Lü, Guanghui Wang, Yuan Zhou, Li Ping Xu, Yong-Jin Hu, Wei-You Zeng, Qinglan Wang

Published Jan 14, 2021• 6 citations
Publisher

Abstract

Manipulation of the quantum phase transition (QPT) of the general Lipkin-Meshkov-Glick (LMG) model is studied in a well-controlled hybrid quantum system, with respect to the Bose–Einstein condensate (BEC) magnetically coupled to a quantum cantilever. The collective decay treated as a traditional adverse factor, however, plays the key role in changing the systemic symmetry, and then evokes the additional QPTs in this opened system. Basing on the QPT from the ferromagnetic (FM) order to the antiferromagnetic (AFM) order, a further application of steering the collective spins adiabatically into a steady-state spin squeezed state (SSS) is also demonstrated. This investigation may provide a reliable platform for simulating the general long-range spin-spin interactions with the more well-controlled and feasible means.

DOI
10.1016/j.rinp.2021.103832

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Manipulation of the quantum phase transition (QPT) of the general Lipkin-Meshkov-Glick (LMG) model is studied in a well-controlled hybrid quantum system, with respect to the Bose–Einstein condensate (BEC) magnetically coupled to a quantum cantilever. The collective decay treated as a traditional adverse factor, however, plays the key role in changing the systemic symmetry, and then evokes the additional QPTs in this opened system. Basing on the QPT from the ferromagnetic (FM) order to the antiferromagnetic (AFM) order, a further application of steering the collective spins adiabatically into a steady-state spin squeezed state (SSS) is also demonstrated. This investigation may provide a reliable platform for simulating the general long-range spin-spin interactions with the more well-controlled and feasible means.
This study proposes a hybrid quantum system of an ensemble of collective spins coupled to a surface acoustic wave (SAW) cavity through a sideband design. Assisted by a dichromatic optical drive with a phase-dependent control, this spin ensemble can effectively mimic different types of long-range Lipkin–Meshkov–Glick (LMG) interactions and then undergo quantum phase transitions (QPTs) due to phase-induced spontaneous symmetry breaking (SSB). In addition, this phase-controlled scheme also ensures the dynamical preparation of the spin-squeezed state (SSS), which may be a useful application in quantum measurement. This study is a fresh attempt at quantum manipulation based on acoustic control and also provides a promising route toward useful applications in quantum information processing, especially the adiabatic preparation of multiparticle-entangled ground states via QPTs; i.e., the Greenberger–Horne–Zeilinger (GHZ) or W-type states.
Quantum criticality has received extensive attention due to its ability to significantly enhance quantum sensing. But its realization and control in many-body quantum systems remain challenging. We present an effective scheme to simulate the Lipkin-Meshkov-Glick (LMG) model using a coherent Ising machine (CIM) composed of a network of degenerate optical parametric oscillators (DOPO). In our work, the spin variables of the LMG model are mapped onto the phases of DOPO pulses, and the spin-spin interactions are realized by all-to-all couplings among them. Through our investigation of the critical behavior in the antiferromagnetically coupled LMG model in the thermodynamic limit, i.e., N→∞N\rightarrow\inftyN→∞, and its application in quantum sensing near the critical point, we verify that the CIM does not only effectively capture the second-order quantum phase transition (QPT) at the critical point but also reconstructs its complete phase diagram under ferromagnetic coupling. Furthermore, we demonstrate how the critical dynamics of this simulation platform can be utilized for quantum-enhanced metrology, achieving a measurement precision that diverges near the critical point of the LMG model. These results highlight the capability of the CIM as a flexible experimental platform for investigating the QPT in the fundamental quantum magnetic models, providing valuable insights into quantum simulation and critical phenomena.
We study the XYXYXY model with infinite-range interactions (Lipkin-Meshkov-Glick model) in the presence of dissipation from spontaneous decay. We show that independent and collective decay lead to qualitatively different phase transitions of the steady state, even though the phase boundary is the same. Independent decay leads to a second-order phase transition to a ferromagnet, while collective decay leads to a first-order transition to a time-dependent oscillatory phase. Then we show that the addition of a drive leads to infinite spin squeezing for collective decay in the thermodynamic limit. Our results can be experimentally seen in trapped-ion and cavity-QED experiments.
Abstract A proposal for simulating the Dicke-Lattice model in a mechanics-controlled hybrid quantum system is studied here. An array of coupled mechanical resonators (MRs) can homogeneously interact with a group of trapped Bose–Einstein condensates (BECs) via the gradient magnetic field induced by the oscillating resonators. Assisted by the classical dichromatic radio-wave fields, each subsystem with the BEC-MR interaction can mimic the Dicke type spin-phonon interaction, and the whole system is therefore extended to a lattice of Dicke models with the additional adjacent phonon-phonon hopping couplings. In view of this lattice model with the Z 2 symmetry, its quantum phase transitions behavior can be controlled by this periodic phonon-phonon interactions in the momentum space. This investigation may be considered as a fresh attempt on manipulating the critical behaviors of the collective spins through the external mechanical method.
The critical behavior of the light-matter interactions in controllable systems provides an attractive direction for quantum manipulation. Inspired by “the broken symmetry will give rise to the quantum phase transitions (QPTs)”, the open-system QPTs of the Tavis–Cummings (TC) interactions with an extra second-order nonlinearity (SONL) are explored, where the systemic symmetry is reduced from U(1) to Z2. The critical behavior of a generic spins-microwave hybrid system is investigated using the standard mean-field approach in conjunction with different factors such as the SONL phase, the spins’ collective decay and dephasing, cavity dissipation, and detunings. The results show that all of the three decoherence factors and the detunings will affect its critical points, and the phase of SONL can especially exhibit a protective effect on QPTs. This study provides an encouraging example for mimicking the interesting light-matter interactions, and may further evoke some potential applications in quantum manipulations.
We propose an efficient scheme for simulating the Lipkin-Meshkov-Glick (LMG) model with nitrogen-vacancy (NV) center ensembles in diamond magnetically coupled to superconducting coplanar waveguide cavities. With the assistance of external microwave driving fields, we show that the interaction of the NV spins can be easily controlled, and several types of the LMG model can be realized by tuning the different parameters. Under the thermal dynamical limit, the distinct nonequilibrium second-order quantum phase transition of the spin ensemble can be achieved at the critical point. Furthermore, we show that the spin squeezed state can be generated by tailoring the LMG Hamiltonian to possess the two-axis countertwisting form in this hybrid quantum system.