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arXiv:1907.00522 · Physical Review Letters

Squeezed Light Induced Symmetry Breaking Superradiant Phase Transition

Chengjie Zhu, Leilei Ping, Yaping Yang, G. S. Agarwal

Published Feb 19, 2020• 107 citations
arXivHTMLPDF

Abstract

We theoretically investigate the quantum phase transition in the collective systems of qubits in a high quality cavity, where the cavity field is squeezed via the optical parametric amplification process. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase transition can be controlled by the nonlinear gain coefficient, which is sensitive to the pump field. These features also lead to an optical switching from the normal phase to the superradiant phase by just increasing the pump field intensity. The signature of these phase transitions can be observed by detecting the phase space Wigner function distribution with different profiles controlled by the squeezed light intensity. Such superradiant phase transition can be implemented in various quantum systems, including atoms, quantum dots, and ions in optical cavities as well as the circuit quantum electrodynamics system.

DOI
10.1103/physrevlett.124.073602

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We theoretically investigate the quantum phase transition in the collective systems of qubits in a high quality cavity, where the cavity field is squeezed via the optical parametric amplification process. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase transition can be controlled by the nonlinear gain coefficient, which is sensitive to the pump field. These features also lead to an optical switching from the normal phase to the superradiant phase by just increasing the pump field intensity. The signature of these phase transitions can be observed by detecting the phase space Wigner function distribution with different profiles controlled by the squeezed light intensity. Such superradiant phase transition can be implemented in various quantum systems, including atoms, quantum dots, and ions in optical cavities as well as the circuit quantum electrodynamics system.
Quantum phase transition and quench dynamics in the Jaynes-Cummings model with squeezed light are investigated. We find a special unitary transformation that removes the nonintegrable squeezing interaction when the qubit frequency far outweighs the field frequency. The eigenenergies and the eigenstates of the normal and superradiant phases are derived analytically. We demonstrate that the system exhibits a second-order quantum phase transition at a phase-boundary-induced nonlinearly by squeezed light. This phase boundary requires neither an ultrastrong coupling regime nor multiqubits, which lessens the difficulty of the experiment. The entanglement entropy is very close to its maximum value as the squeezing strength increases in the superradiant phase. In quench dynamics, the nonlinear relation between the residual energy and the squeezing strength is obtained analytically.
We demonstrate the emergence of nonreciprocal superradiant phase transitions and novel multicriticality in a cavity quantum electrodynamics system, where a two-level atom interacts with two counterpropagating modes of a whispering-gallery-mode microcavity. The cavity rotates at a certain angular velocity and is directionally squeezed by a unidirectional parametric pumping χ^{(2)} nonlinearity. The combination of cavity rotation and directional squeezing leads to nonreciprocal first- and second-order superradiant phase transitions. These transitions do not require ultrastrong atom-field couplings and can be easily controlled by the external pump field. Through a full quantum description of the system Hamiltonian, we identify two types of multicritical points in the phase diagram, both of which exhibit controllable nonreciprocity. These results open a new door for all-optical manipulation of superradiant transitions and multicritical behaviors in light-matter systems, with potential applications in engineering various integrated nonreciprocal quantum devices.
This study investigates phase-driven symmetry breaking leading to superradiance phase transitions in cascaded non-Hermitian quantum Rabi cavities. Non-Hermiticity is introduced via the phase coupling $\ensuremath{\varphi}$ between the atom and the optical field. In the thermodynamic limit of the quantum harmonic oscillator, we analytically derive the superradiance phase boundary, validated by observables. An unconventional quantum phase transition without a Hermitian analog arises when $|\ensuremath{\varphi}|=\frac{\ensuremath{\pi}}{4}$ or $\frac{3\ensuremath{\pi}}{4}$, where the phase boundary is uniquely determined by the cavity coupling, at J=12\mathcal{J}=\frac{1}{2}J=21​ (J\mathcal{J}J is the ratio of the cavity coupling strength JJJ to the optical field frequency ${\ensuremath{\omega}}_{p}$, and $\mathcal{J}=\frac{J}{{\ensuremath{\omega}}_{p}}$), independent of the atom-photon coupling strength ggg. For other $\ensuremath{\varphi}$, the phase boundary relies on both J\mathcal{J}J and ggg, similar to the scenario observed in Hermitian systems. Furthermore, we identify phase-driven first- and second-order superradiance phase transitions, focusing on the quantum criticality of the second-order transition by determining the critical exponents and the universality class. The feasibility of experimental realization is also discussed, aiming to inspire further studies on non-Hermitian superradiance quantum phase transitions.
A2\bf A^2A2-robust superradiant phase transition in hybrid qubit-cavity optomechanics
The A2\mathbf{A}^2A2 term presents a fundamental challenge to realizing the superradiant phase transition (SPT) in cavity quantum electrodynamics. Here, we propose a hybrid quantum system enabling SPT regardless of the presence of the A2\mathbf{A}^2A2 term. The system consist of a qubit, a mechanical mode, and an optical cavity, where the qubit and mechanical mode constitute a quantum Rabi model, while the mechanical mode and cavity form an optomechanical system. Crucially, the auxiliary cavity introduces a switchable A2\mathbf{A}^2A2 term that effectively counteracts or even fully eliminates the original A2\mathbf{A}^2A2 effect. This allows controllable observation of SPT, diagnosed via the second-order equal-time correlation function g(2)(0)g^{(2)}(0)g(2)(0) of phonons. Furthermore, the auxiliary cavity exponentially reduces the critical coupling strength, significantly relaxing experimental requirements. In addition, we show that phonons in the normal phase display bunching, but coherent in the superradiant phase. Interestingly, higher-order squeezing is found in both phases, with near-perfect higher-order squeezing achieved at the SPT point, establishing it as a probe for SPT behavior. Our work demonstrates that hybridizing optomechanics and cavity quantum electrodynamics provides a promising route to accessing SPT physics in the presence of the A2\mathbf{A}^2A2 term.
The A2{\mathbf{A}}^{2}A2 term presents a fundamental challenge to realizing the superradiant phase transition (SPT) in cavity quantum electrodynamics. Here, we propose a hybrid quantum system enabling SPT regardless of the presence of the A2{\mathbf{A}}^{2}A2 term. The system consists of a qubit, a mechanical mode, and an optical cavity, where the qubit and mechanical mode constitute a quantum Rabi model, while the mechanical mode and cavity form an optomechanical system. Crucially, the auxiliary cavity introduces a switchable A2{\mathbf{A}}^{2}A2 term that effectively counteracts or even fully eliminates the original A2{\mathbf{A}}^{2}A2 effect. This allows controllable observation of SPT, diagnosed via the second-order equal-time correlation function g(2)(0){g}^{(2)}(0)g(2)(0) of phonons. Furthermore, the auxiliary cavity exponentially reduces the critical coupling strength, significantly relaxing experimental requirements. In addition, we show that phonons in the normal phase display bunching but are coherent in the superradiant phase. Interestingly, higher-order squeezing is found in both phases, with near-perfect higher-order squeezing achieved at the SPT point, establishing it as a probe for SPT behavior. Our work demonstrates that hybridizing optomechanics and cavity quantum electrodynamics provides a promising route to accessing SPT physics in the presence of the A2{\mathbf{A}}^{2}A2 term.
Abstract We consider the superradiant transition of a generalized Tavis–Cummings model, where a number of two-level qubits are coupled to a dissipative cavity. The cavity is coherently driven through a parametric medium, and all-to-all interactions between the qubits are introduced. While the nonlinear gain from the parametric drive breaks the U (1) symmetry of the standard Tavis–Cummings model, thus giving rise to superradiance with squeezed cavity fields, we show that the interactions impact the collective excitations and significantly modify the superradiant transition. Insights into the superradiant phase transitions, as well as the interaction effects, are obtained through effective models involving only a handful of low-lying collective states, under which the steady-state phase diagram of the hybrid system is faithfully reproduced. Our study is relevant to Rydberg-atom arrays coupled to a parametrically driven cavity, where the long-range interactions derive from the dipole–dipole interatomic interactions.