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International Conference on Strongly Correlated Electron Systems (SCES)

Quantum Instability in the Ultrastrong Coupling Regime of the Dicke Model

Hiroki Majima

Published Mar 18, 2020• 0 citations
Publisher

Abstract

We study composite quantum systems, like the Dicke model (or the generalized quantum Rabi model), in the absence of external driving by resorting to methods from quantum field theory.It is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the vacuum instability and generates an irreversible time evolution.To discuss the stability of the quantum dissipative system due to the influence of an Jaynes-Cummings Hamiltonian and the dissipative force (counter-rotating term) under situation, we derive a behavior for large time for a vacuum survival probability of the dissipative system.In the ultra-strong coupling regime, we show that the timedependent coherent state generated by an interaction Hamiltonian behaves non-unitary irreversible time evolution.

DOI
10.7566/jpscp.30.011025

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We study composite quantum systems, like the Dicke model (or the generalized quantum Rabi model), in the absence of external driving by resorting to methods from quantum field theory.It is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the vacuum instability and generates an irreversible time evolution.To discuss the stability of the quantum dissipative system due to the influence of an Jaynes-Cummings Hamiltonian and the dissipative force (counter-rotating term) under situation, we derive a behavior for large time for a vacuum survival probability of the dissipative system.In the ultra-strong coupling regime, we show that the timedependent coherent state generated by an interaction Hamiltonian behaves non-unitary irreversible time evolution.
We study composite quantum systems, like atom-cavity systems and coupled optical resonators, in the absence of external driving by resorting to methods from quantum field theory. It is shown that the usually neglected counter-rotating part of the Hamiltonian relates to the vacuum instability and generates an irreversible time evolution. To discuss the stability of the quantum dissipative system due to the influence of an Jaynes-Cummings Hamiltonian and the dissipative force (counter-rotating term) under situation, we derive a behavior for large time for transition amplitudes of the dissipative system with the help of the perturbation analysis.
The dissipative quantum phase transitions experienced by a driven optical system are studied in order to understand the underlying light-matter coupling. The primary system under study is composed of a cavity mode coupled to a two-level system with dissipation being introduced through the interaction with a surrounding environment; an external coherent field is included to drive the system out of the ground state. The coupling is given by a generalized Rabi Hamiltonian, where rotating, gr, and counter-rotating, ngr, couplings are both present and can be adjusted independently. A comprehensive study of the different phases the system can exhibit as gr and n are varied is presented. From this, we construct a bridge between two limiting scenarios: (i) the Jaynes-Cummings limit (n = 0), where the system undergoes a phase transition by means of the breakdown of the photon blockade, and (ii) the driven Dicke limit ( = 1 ), where the normal to super-radiant phase transition is found. Novel behaviour encountered in an intermediate regime (1 > n > 0) is discussed. Attention is drawn towards the strong coupling regime, where changes at the one-photon level induce nonlinear effects and behaviour reminiscent of phase transitions is encountered with just a few photons present. A comparison between weak and strong coupling regimes, and, thus, an exploration of the effect of fluctuations over quantum phase transitions of light, is given through a survey of the phases an auxiliary optical system exhibits. This system is composed of two coupled nonlinear cavities that are driven coherently and damped through the interaction with the environment; it is seen to exhibit three phases. Two phases present high-correlation between the cavities and are differentiated by the photon statistics, transitioning from classical to quantum. The third phase is characterized by a highly localized field in one of the cavities. The departure from mean-field results is highlighted and a new way to characterize the possible phases of the system is proposed. Finally, the crucial role of quantum fluctuations is quantified and used to define the phases at hand.
Environmental influences on the dynamics of a coupled qubit-oscillator system are studied analytically in a regime where deviations from the exactly solvable Jaynes–Cummings model are important. We investigate the case of a quasi-degenerate qubit within the ultra-strong coupling regime for which the qubit frequency is much smaller than the frequency of the oscillator, and the coupling between the qubit and the oscillator is large, both of which invalidate the usually employed rotating wave approximation. In contrast to the standard quantum optics master equation, we explicitly take the qubit-oscillator coupling into account while microscopically deriving a dressed state master equation. Using the derived master equation, we discuss a spectroscopic technique which can be used to probe the dressed energy-level structure of the qubit-oscillator system.
We use a recently derived gauge-invariant formulation of the problem of a two-level system coupled to an optical cavity to explore the transition between the weak and the ultrastrong coupling regimes of light-matter interaction. We explore this transition using the intensity correlations ${g}^{(2)}(\ensuremath{\tau})$ of the emitted light, and we find strong, unbounded bunching of the emission from systems governed by the Rabi Hamiltonian. Surprisingly, this effect is observed not only in the ultrastrong coupling regime, but also for weakly coupled systems, where the Jaynes-Cummings Hamiltonian would predict the opposite, antibunched emission. This suggests that the higher-order correlations are a particularly sensitive probe of the divergence between the Jaynes-Cummings and Rabi Hamiltonians, and they can serve as an indicator of the breakdown of the rotating wave approximation. Our findings indicate also that the boundary between the weakly, strongly, and ultra-strongly-coupled dynamics is much richer than currently accepted.
We study the emission spectra of the dissipative Rabi and Jaynes-Cummings models in the non-Markovian and ultrastrong coupling regimes. We have derived a polaron-transformed Nakajima-Zwanzig master equation (PTNZE) to calculate the emission spectra, which eliminates the well-known limitations of the Markovian approximation and the standard second-order perturbation. Using the time-dependent variational approach with the multiple Davydov ansatz as a benchmark, the PTNZE is found to yield accurate emission spectra in certain ultrastrong coupling regimes where the standard second-order Nakajima-Zwanzig master equation breaks down. It is shown that the emission spectra of the dissipative Rabi and Jaynes-Cummings models are, in general, asymmetric under various initial conditions. Direct comparisons of spectra for the two models illustrate the essential role of the qubit-cavity counter-rotating term and the spectral features under different qubit-cavity coupling strengths and system initial conditions.
The interaction among the components of a hybrid quantum system is often neglected when considering the coupling of these components to an environment. However, if the interaction strength is large, this approximation leads to unphysical predictions, as has been shown for cavity-QED and optomechanical systems in the ultrastrong-coupling regime. To deal with these cases, master equations with dissipators retaining the interaction between these components have been derived for the quantum Rabi model and for the standard optomechanical Hamiltonian. In this article, we go beyond these previous derivations and present a general master equation approach for arbitrary hybrid quantum systems interacting with thermal reservoirs. Specifically, our approach can be applied to describe the dynamics of open hybrid systems with harmonic, quasiharmonic, and anharmonic transitions. We apply our approach to study the influence of temperature on multiphoton vacuum Rabi oscillations in circuit QED. We also analyze the influence of temperature on the conversion of mechanical energy into photon pairs in an optomechanical system, which has been recently described at zero temperature. We compare our results with previous approaches, finding that these sometimes overestimate decoherence rates and underestimate excited-state populations.