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arXiv:2207.12156 · Communications Physics

Sudden change of the photon output field marks phase transitions in the quantum Rabi model

Ye‐Hong Chen, Yuan Qiu, Adam Miranowicz, Neill Lambert, Wei Qin, Roberto Stassi, Yan Xia, Shi‐Biao Zheng, Franco Nori

Published Jan 5, 2024• 20 citations
arXivHTMLPDF

Abstract

Abstract The experimental observation of quantum phase transitions predicted by the quantum Rabi model in quantum critical systems is usually challenging due to the lack of signature experimental observables associated with them. Here, we describe a method to identify the dynamical critical phenomenon in the quantum Rabi model consisting of a three-level atom and a cavity at the quantum phase transition. Such a critical phenomenon manifests itself as a sudden change of steady-state output photons in the system driven by two classical fields, when both the atom and the cavity are initially unexcited. The process occurs as the high-frequency pump field is converted into the low-frequency Stokes field and multiple cavity photons in the normal phase, while this conversion cannot occur in the superradiant phase. The sudden change of steady-state output photons is an experimentally accessible measure to probe quantum phase transitions, as it does not require preparing the equilibrium state.

DOI
10.1038/s42005-023-01457-w

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Abstract The experimental observation of quantum phase transitions predicted by the quantum Rabi model in quantum critical systems is usually challenging due to the lack of signature experimental observables associated with them. Here, we describe a method to identify the dynamical critical phenomenon in the quantum Rabi model consisting of a three-level atom and a cavity at the quantum phase transition. Such a critical phenomenon manifests itself as a sudden change of steady-state output photons in the system driven by two classical fields, when both the atom and the cavity are initially unexcited. The process occurs as the high-frequency pump field is converted into the low-frequency Stokes field and multiple cavity photons in the normal phase, while this conversion cannot occur in the superradiant phase. The sudden change of steady-state output photons is an experimentally accessible measure to probe quantum phase transitions, as it does not require preparing the equilibrium state.
We study an atom-cavity system composed of an ensemble of three-level atoms interacting with a high-finesse single-mode optical resonator. Two examples of physical models, the laser-driven $\ensuremath{\Lambda}$-type atomic system and the three-level ladder-type atomic system, are investigated in detail. By altering the collective atom-cavity dynamics via an intracavity optical parametric amplification process, a spin-boson model is realized when the composite system operates in the far-detuning regime. When the number of atoms exceeds a critical value, the quantum system undergoes a superradiant phase transition whose dependence on different experimentally adjustable parameters is explored in detail. The effects of the spontaneous emission of atoms and the cavity loss on the phase transition are considered, and measuring the cavity output field itself gives an experimental probe of the superradiant phase transition.
Abstract We explore an extended quantum Rabi model describing the interaction between a two-mode bosonic field and a three-level atom. Quantum phase transitions of this few degree of freedom model is found when the ratio η of the atom energy scale to the bosonic field frequency approaches infinity. An analytical solution is provided when the two lowest-energy levels are degenerate. According to it, we recognize that the phase diagram of the model consists of three regions: one normal phase and two superradiant phases. The quantum phase transitions between the normal phase and the two superradiant phases are of second order relating to the spontaneous breaking of the discrete Z 2 symmetry. On the other hand, the quantum phase transition between the two different superradiant phases is discontinuous with a phase boundary line relating to the continuous U (1) symmetry. For a large enough but finite η , the scaling function and critical exponents are derived analytically and verified numerically, from which the universality class of the model is identified.
Abstract Quantum phase transitions (QPTs) are usually associated with many-body systems in the thermodynamic limit when their ground states show abrupt changes at zero temperature with variation of a parameter in the Hamiltonian. Recently it has been realized that a QPT can also occur in a system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report an experimental demonstration of a QPT in the QRM using a 171Yb+ ion in a Paul trap. We measure the spin-up state population and the average phonon number of the ion as two order parameters and observe clear evidence of the phase transition via adiabatic tuning of the coupling between the ion and its spatial motion. An experimental probe of the phase transition in a fundamental quantum optics model without imposing the thermodynamic limit opens up a window for controlled study of QPTs and quantum critical phenomena.
Quantum criticality usually occurs in many-body systems. Recently it was shown that the quantum Rabi model, which describes a two-level atom coupled to a single model cavity field, presents quantum phase transitions from a normal phase to a superradiate phase when the ratio between the frequency of the two-level atom and the frequency of the cavity field extends to infinity. In this work, we study quantum phase transitions in the quantum Rabi model from the fidelity susceptibility perspective. We found that the fidelity susceptibility and the generalized adiabatic susceptibility present universal finite-size scaling behaviors near the quantum critical point of the Rabi model if the ratio between frequency of the two-level atom and frequency of the cavity field is finite. From the finite-size scaling analysis of the fidelity susceptibility, we found that the adiabatic dimension of the fidelity susceptibility and the generalized adiabatic susceptibility of fourth order in the Rabi model are 4/34/34/3 and 2, respectively. Meanwhile, the correlation length critical exponent and the dynamical critical exponent in the quantum critical point of the Rabi model are found to be 3/23/23/2 and 1/31/31/3, respectively. Since the fidelity susceptibility and the generalized adiabatic susceptibility are the moments of the quantum noise spectrum which are directly measurable by experiments in linear response regime, the scaling behavior of the fidelity susceptibility in the Rabi model could be tested experimentally. The simple structure of the quantum Rabi model paves the way for experimentally observing the universal scaling behavior of the fidelity susceptibility at a quantum phase transition.
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.
Abstract Quantum phase transitions (QPTs) are usually associated with many-body systems in the thermodynamic limit when their ground states show abrupt changes at zero temperature with variation of a parameter in the Hamiltonian. Recently it has been realized that a QPT can also occur in a system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report an experimental demonstration of a QPT in the QRM using a 171 Yb + ion in a Paul trap. We measure the spin-up state population and the average phonon number of the ion as two order parameters and observe clear evidence of the phase transition via adiabatic tuning of the coupling between the ion and its spatial motion. An experimental probe of the phase transition in a fundamental quantum optics model without imposing the thermodynamic limit opens up a window for controlled study of QPTs and quantum critical phenomena.