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Journal of Physics Condensed Matter

Simulating the Dicke lattice model and quantum phase transitions using an array of coupled resonators

Si-Yun Leng, Dong‐Yan Lü, Shuang‐Liang Yang, Ming Ma, Yanzhang Dong, Bo-Fang Zhou, Yuan Zhou

Published Jul 27, 2022• 9 citations
Publisher

Abstract

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.

DOI
10.1088/1361-648x/ac84bd

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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.
We study the coherent cooperative phenomena of the system composed of two interacting atomic ensembles in the thermodynamic limit. Remarkably, the system exhibits the Dicke-like quantum phase transition and entanglement behavior although the governing Hamiltonian is fundamentally different from the spin-boson Dicke Hamiltonian, offering the opportunity for investigating collective matter-light dynamics with pure matter waves. The model can be realized with two Bose-Einstein condensates or atomic ensembles trapped in two optical cavities coupled to each other. The interaction between the two separate samples is induced by virtual photon exchange.
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.
Abstract A theoretical scheme is proposed to simulate the quantum phase transitions (QPTs) of the three-level Dicke model. In this designed hybrid system, an ensemble of solid-state spins can simultaneously couple to a superconducting microwave (MW) resonator and a surface-acoustic-wave (SAW) cavity, and then ensure the simulation of the Λ type Dicke model with the acoustic-MW dual-channel transitions. Using a generalized Holstein-Primakoff (HP) mapping in the thermodynamic limit, we derive an effective Hamiltonian that preserves a Z 2 × Z 2 parity symmetry and therefore potentially supports a rich phase diagram. We obtain analytic expressions for the critical couplings of the three phases: the normal, superradiant I and superradiant II phases. We obtain analytic expressions for the critical couplings of three phases: the normal, superradiant I, and superradiant II phases. Among these, we can deterministically identify both first-order (discontinuous) and second-order (continuous) quantum phase transitions with distinct boundary characteristics. Additionally, rigorous diagonalization of the quadratic fluctuation Hamiltonian yields four excitation energies, whose behaviors further clarify the order and continuity of each phase transition. This attempt opens an interesting avenue for simulating multilevel QPTs by jointly using different coupling transducers, including acoustics, mechanics, magnons, and electromagnetics.
Generalized Dicke models can be implemented in hybrid quantum systems built from ensembles of nitrogen-vacancy (NV) centers in diamond coupled to superconducting microwave cavities. By engineering cavity assisted Raman transitions between two spin states of the NV defect, a fully tunable model for collective light-matter interactions in the ultrastrong coupling limit can be obtained. Our analysis of the resulting nonequilibrium phases for a single cavity and for coupled cavity arrays shows that different superradiant phase transitions can be observed using existing experimental technologies, even in the presence of large inhomogeneous broadening of the spin ensemble. The phase diagram of the Dicke lattice model displays distinct features induced by dissipation, which can serve as a genuine experimental signature for phase transitions in driven open quantum systems.
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.
Abstract Spin-tensor-momentum coupling (STMC) induces dramatic change of the single-particle energy spectrum, resulting in rich and novel quantum ground state phases. Here, considering the atomic interactions, the STMC induced Z 2 symmetry breaking of the energy band, the tricritical point and the magnetic phase transitions in trapped STMC Bose–Einstein condensates are presented analytically and numerically. We demonstrate that the ground state momentum and spin tensor are coupled by STMC and the asymmetry of the energy band is persistent in STMC system, resulting in phase transition between magnetized and unmagnetized plane wave phases or between the two unmagnetized plane wave phases. The critical conditions for the phase transitions are obtained analytically, clarifying the physical mechanisms behind the phase transitions. Particularly, a tricritical point is predicted, where different types of energy band merge and the first-order phase transition and the second-order phase transition meet. Interestingly, it is shown that the ground state strongly depends on the external trapping potential, establishing a potential method for manipulating the phase transitions of the system. We provide a theoretical evidence for deep understanding and experimental manipulation of novel quantum phases in STMC systems.