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Conference on Lasers and Electro-Optics

Interplay of Quantum and Classical Dynamics in a Generalized Dicke Model

Kevin C. Stitely, Stuart J. Masson, Andrus Giraldo, Bernd Krauskopf, A. S. Parkins

Published Jan 1, 2022• 1 citation
Publisher

Abstract

We investigate signatures of classical nonlinear behavior in the vicinity of a superradiant quantum phase transition in a generalized Dicke model. Classical multistable behavior is signalled by spontaneous tunneling between macroscopic quantum states.
DOI
10.1364/cleo_at.2022.jtu3b.15

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We study the dynamical properties of the Dicke model for increasing spin length, as the system approaches the limit of a classical spin. First, we describe the emergence of collective excitations above the ground state that converge to the coupled spin-oscillator oscillations found in the classical limit. The corresponding Green functions reveal quantum dynamical signatures close to the superradiant quantum phase transition. Second, we identify signatures of classical quasiperiodic orbits in the quantum time evolution using numerical time propagation of the wave function. The resulting phase-space plots are compared to the classical trajectories. We complete our study with the analysis of individual eigenstates close to the quasiperiodic orbits.
In the vicinity of ground-state phase transitions quantum correlations can display nonanalytic behavior and critical scaling. This signature of emergent collective effects has been widely investigated within a broad range of equilibrium settings. However, under nonequilibrium conditions, as found in open quantum many-body systems, characterizing quantum correlations near phase transitions is challenging. Moreover, the impact of local and collective dissipative processes on quantum correlations is not broadly understood. Here we consider as a paradigmatic setting the superradiant phase transition of the open quantum Dicke model and characterize quantum and classical correlations across the phase diagram. We develop an approach to quantum fluctuations which allows us to show that local dissipation, which cannot be treated within the commonly employed Holstein-Primakoff approximation, rather unexpectedly leads to an enhancement of collective quantum correlations, and to the emergence of a nonequilibrium superradiant phase in which the bosonic and spin degrees of freedom of the Dicke model are entangled.
In this article, we obtain the multistable macroscopic quantum states and quantum tricritical behavior in generalized Dicke model (DM) analytically by means of spin-coherent-state (SCS) variational method for a finite atom number N. The quantum phase transition (QPT) is characterized by the ground state from the normal phase (NP) to the superradiant phases (SP). The second-order QPT turns to the first-order one at the tricritical point of phase boundary. The tricritical behavior of QPT emerges when the coupling strength of the symmetry breaking mechanism increases to a certain extent, which leads to an additional dimension of phase diagram. Beyond the ground state the symmetry-breaking coupling can manipulate the pseudospin flip of higher-level macroscopic states. The critical property of QPT is also demonstrated from the average photon-number, the atomic population as well as Berry phase.
The occurrence of a second-order quantum phase transition in the Dicke model is a well-established feature. On the contrary, a comprehensive understanding of the corresponding open system, particularly in the proximity of the critical point, remains elusive. When approaching the critical point, the system inevitably enters first the system-bath ultrastrong coupling regime and finally the deepstrong coupling regime, causing the failure of usual approximations adopted to describe open quantum systems. We study the interaction of the Dicke model with bosonic bath fields in the absence of additional approximations, which usually relies on the weakness of the system-bath coupling. We find that the critical point is not affected by the interaction with the environment. Moreover, the interaction with the environment is not able to affect the system ground-state condensates in the superradiant phase, whereas the bath fields are i n f e c t e d by the system and acquire macroscopic occupations. The obtained reflection spectra display lineshapes which become increasingly asymmetric, both in the normal and superradiant phases, when approaching the critical point.
We study the effect of spontaneous emission and incoherent atomic pumping on the nonlinear semiclassical dynamics of the unbalanced Dicke model---a generalization of the Dicke model that features independent coupling strengths for the co- and counter-rotating interaction terms. As well as the ubiquitous superradiant behavior the Dicke model is well-known for, the addition of spontaneous emission combined with the presence of strong counter-rotating terms creates a laserlike behavior termed counter-lasing. These states appear in the semiclassical model as stable periodic orbits. We perform a comprehensive dynamical analysis of the appearance of counter-lasing in the unbalanced Dicke model subject to strong cavity dissipation, such that the cavity field can be adiabatically eliminated to yield an effective Lipkin-Meshkov-Glick (LMG) model. If the coupling strength of the corotating interactions is small, then the counter-lasing phase appears via a Hopf bifurcation of the deexcited state. We find that if the rate of spontaneous emission is small, this can lead to resurgent superradiant pulses. However, if the corotating coupling is larger, then the counter-lasing phase must emerge via the steady-state superradiant phase. Such a transition is the result of the competition of the coherent and incoherent processes that drive superradiance and counter-lasing, respectively. We observe a surprisingly complex transition between the two, associated with the formation of a chaotic attractor over a thin transitional parameter region.