Three-Level Superfluorescence

Recent advances in optical studies of condensed matter have led to the emergence of phenomena that have conventionally been studied in the realm of quantum optics. These studies have not only deepened our understanding of light-matter interactions but also introduced aspects of many-body correlations inherent in optical processes in condensed matter systems. This article is concerned with superradiance (SR), a profound quantum optical process predicted by Dicke in 1954. The basic concept of SR applies to a general $N$-body system where constituent oscillating dipoles couple together through interaction with a common light field and accelerate the radiative decay of the system. In the most fascinating manifestation of SR, known as superfluorescence (SF), an incoherently prepared system of $N$ inverted atoms spontaneously develops macroscopic coherence from vacuum fluctuations and produces a delayed pulse of coherent light whose peak intensity $\propto N^2$. Such SF pulses have been observed in atomic and molecular gases, and their intriguing quantum nature has been unambiguously demonstrated. Here, we focus on the rapidly developing field of research on SR in solids, where not only photon-mediated coupling but also strong Coulomb interactions and ultrafast scattering exist. We describe SR and SF in molecular centers in solids, molecular aggregates and crystals, quantum dots, and quantum wells. In particular, we will summarize a series of studies we have recently performed on quantum wells in strong magnetic fields. These studies show that cooperative effects in solid-state systems are not merely small corrections that require exotic conditions to be observed; rather, they can dominate the nonequilibrium dynamics and light emission processes of the entire system of interacting electrons.

We have made measurements of force and velocity fluctuations in a variety of dense, gravity-driven granular flows under flow conditions close to the threshold of jamming. The measurements reveal a microscopic state that evolves rapidly from entirely collisional to largely frictional, as the system is taken close to jamming. On coarse-grained time scales, some descriptors of the dynamics-such as the probability distribution of force fluctuations, or the mean friction angle-do not reflect this profound change in the micromechanics of the flow. Other quantities, such as the frequency spectrum of force fluctuations, change significantly, developing low-frequency structure in the fluctuations as jamming is approached. We also show evidence of spatial structure, with force fluctuations being organized into local collision chains. These local structures propagate rapidly in the flow, with consequences far away from their origin, leading to long-range correlations in velocity fluctuations.

It has been recently shown that randomly charged surfaces can exhibit-long range electrostatic interactions even when they are net neutral. These forces depend on the specific realization of charge disorder and thus exhibit sample-to-sample fluctuations about their mean value. We analyze the fluctuations of these forces in the parallel slab configuration and in the sphere-plane geometry via the proximity force approximation. The fluctuations of the normal forces, which have a finite mean value, are computed exactly. Surprisingly, we also show that fluctuations in lateral forces are present, despite the fact that they have a zero mean, and that they have the same scaling behavior as the normal force fluctuations. The measurement of these lateral force fluctuations could help us to characterize the effects of charge disorder in experimental systems, leading to estimates of their magnitudes that are complementary to those given by normal force measurements.

Quantum phase transitions have long been studied in their relation to quantum fluctuations. These fluctuations can be quantified as the degree of spin squeezing in spin models, where one of the two noncommutative observables breaks the standard quantum limit of measurement by minimizing its uncertainty. However, the understanding of their role in dynamical quantum phase transitions (DQPTs) is still incomplete. In this work, we combine the Loschmidt amplitude, which detects DQPTs, and the spin-squeezing parameter (SSP), the quantification of spin squeezing, to study the spin dynamics in a quenched interacting spin model around DQPT. We show that the extremum, mostly maximum, of SSP occurs near DQPTs when the system is quenched between different phases. These phenomena further unveil the spin correlations during DQPTs, for which the highest contribution aligns with the preferred direction of spin interactions in the postquenched phase. We also demonstrate that the time evolution of SSP differs for various quench scenarios. These findings provide us with physical insights into the dynamics of quantum fluctuations around DQPTs and their relation to the equilibrium phase diagrams.

Thermalization in quantum many-body systems typically unfolds over timescales governed by intrinsic relaxation mechanisms. Yet, its spatial aspect is less understood. We investigate this phenomenon in the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject to coherent driving and dissipation at its boundaries, a setup inspired by current designs in circuit quantum electrodynamics. The dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators within the truncated Wigner approximation. At intermediate drive strengths, we uncover a two-stage thermalization along the spatial dimension: phase coherence is rapidly lost near the drive, while amplitude relaxation occurs over much longer distances. This separation of scales gives rise to an extended hydrodynamic regime exhibiting anomalous temperature profiles, which we designate as a “prethermal” domain. At stronger drives, the system enters a nonthermal, non-chaotic finite-momentum condensate characterized by sub-Poissonian photon statistics and a spatially modulated phase profile, whose stability is undermined by quantum fluctuations. We explore the conditions underlying this protracted thermalization in space and argue that similar mechanisms are likely to emerge in a broad class of extended driven-dissipative systems.

Multipole symmetries are of interest both as a window on fracton physics and as a crucial ingredient in realizing new universality classes for quantum dynamics. Here we address the question of whether and when multipole symmetries can be spontaneously broken, both in thermal equilibrium and at zero temperature. We derive generalized Mermin-Wagner arguments for the total or partial breaking of multipolar symmetry groups and generalized Imry-Ma arguments for the robustness of such multipolar symmetry breaking to disorder. We present both general results and explicit examples. Our results should be directly applicable to quantum dynamics with multipolar symmetries and also provide a useful stepping stone to understanding the robustness of fracton phases to thermal fluctuations, quantum fluctuations, and disorder.

The quantum theory of the Friedmann cosmological model with dust and cosmological constant () is not exactly solvable analytically. We apply path integral Monte Carlo (PIMC) techniques to study its quantum dynamics using the physical Hamiltonian corresponding to the dust field as a clock. We study (i) quantum fluctuations around classical paths and (ii) formulate the analogues of the no-boundary and tunnelling proposals and simulate the ground state wave functions. For a unique ground state wave function exists. For the physical Hamiltonian is not bounded below, but the path integral for the propagator is convergent over a range of Euclidean time T. We investigate the properties of the convergent propagator. The path integral can be made convergent for all values of T by restricting the integral over paths with action greater than equal to zero. We explore the consequences of such a choice.

We show that the classical (mean-field) description of far from equilibrium superconductivity is exact in the thermodynamic limit for local observables but breaks down for global quantities, such as the entanglement entropy or Loschmidt echo. We do this by solving for and comparing exact quantum and exact classical long-time dynamics of a BCS superconductor with interaction strength inversely proportional to time and evaluating local observables explicitly. Mean field is exact for both normal and anomalous averages (superconducting order) in the thermodynamic limit. However, for anomalous expectation values, this limit does not commute with adiabatic and strong coupling limits and, as a consequence, their quantum fluctuations can be unusually strong. The long-time steady state of the system is a gapless superconductor whose superfluid properties are only accessible through energy resolved measurements. This state is nonthermal but conforms to an emergent generalized Gibbs ensemble. Our study clarifies the nature of symmetry-broken many-body states in and out of equilibrium and fills a crucial gap in the theory of time-dependent quantum integrability.

We investigate the dynamics of classical and quantum N-component phi^4\noscillators in the presence of an external field. In the large N limit the\neffective dynamics is described by two-degree-of-freedom classical Hamiltonian\nsystems. In the classical model we observe chaotic orbits for any value of the\nexternal field, while in the quantum case chaos is strongly suppressed. A\nsimple explanation of this behaviour is found in the change in the structure of\nthe orbits induced by quantum corrections. Consistently with Heisenberg's\nprinciple, quantum fluctuations are forced away from zero, removing in the\neffective quantum dynamics a hyperbolic fixed point that is a major source of\nchaos in the classical model.\n

Most material properties of great physical interest are directly related to nuclear dynamics, e.g. the ionic thermal conductivity, Raman/IR vibrational spectra, inelastic X-ray, and Neutron scattering. A theory able to compute from first principles these properties, accounting for the anharmonicity and quantum fluctuations in the nuclear energy landscape that can be implemented in systems with hundreds of atoms is missing. Here, we derive an approximate theory for the quantum time evolution of lattice vibrations at finite temperature. This theory introduces the time dynamics in the Self-Consistent Harmonic Approximation (SCHA) and shares with the static case the same computational cost. It is nonempirical, as pure states evolve according to the Dirac least action principle and the dynamics of the thermal ensemble conserves both energy and entropy. The static SCHA is recovered as a stationary solution of the dynamical equations. We apply perturbation theory around the static SCHA solution and derive an algorithm to compute efficiently quantum dynamical response functions. Thanks to this new algorithm, we have access to the response function of any general external time-dependent perturbation, enabling the simulation of phonon spectra without following any perturbative expansion of the nuclear potential or empirical methods. We benchmark the algorithm on the IR and Raman spectroscopy of high-pressure hydrogen phase III, with a simulation cell of 96 atoms. Our work also explores the nonlinear regime of the dynamical nuclear motion, providing a paradigm to simulate the interaction with intense or multiple probes, as in pump-probe spectroscopy, or chemical reactions involving light atoms, as the proton transfer in biomolecules

In nature, there exists superposition of Gaussian light and chaotic light, so we introduce the density operator for describing the Gaussian-enhanced chaotic light (GECL). By virtue of the method of integration within ordered product (IWOP) of operators, we derive its normalization constant. Then, by virtue of the partial trace method, we derive its thermo vacuum state and this may greatly simplify the calculation of photon number average and quantum fluctuation in GECL. It is demonstrated that the second-order degree of coherence of GECL is larger than 2.

The study of optomechanical systems has attracted much attention, most of which are concentrated in the physics in the small-amplitude regime. While in this article, we focus on optomechanics in the extremely-large-amplitude regime and consider both classical and quantum dynamics. Firstly, we study classical dynamics in a membrane-in-the-middle optomechanical system in which a partially reflecting and flexible membrane is suspended inside an optical cavity. We show that the membrane can present self-sustained oscillations with limit cycles in the shape of sawtooth-edged ellipses and exhibit dynamical multistability. Then, we study the dynamics of the quantum fluctuations around the classical orbits. By using the logarithmic negativity, we calculate the evolution of the quantum entanglement between the optical cavity mode and the membrane during the mechanical oscillation. We show that there is some synchronism between the classical dynamical process and the evolution of the quantum entanglement.

What is the meaning of the thermodynamical temperature in quantum mechanics? What is its role in the classical limit? What can we say about the interplay between quantum and thermal fluctuations? Can we impose a constant-temperature constraint within dynamical simulations of quantum systems as we do in simulations of classical systems? These questions will be reviewed here. In particular, it will be shown how a quantum version of the celebrated Nose constant-temperature dynamics can be defined within the phase space formulation of quantum mechanics.

We study phase diffusion in a Bose-Einstein condensate of light in a dye-filled optical microcavity, i.e., the spreading of the probability distribution for the condensate phase. To observe this phenomenon, we propose an interference experiment between the condensed photons and an external laser. We determine the average interference patterns, considering quantum and thermal fluctuations as well as dissipative effects due to the dye. Moreover, we show that a representative outcome of individual measurements can be obtained from a stochastic equation for the global phase of the condensate.

The time-dependent, linearly driven Fokker-Planck equation for the degenerate parametric amplifier is derived when the pump depletion is present both above and below threshold. A model that the driving force εα1 is a product of the classical quantity ε and quantum operator α1 is proposed. It is found that below or near threshold, our results conform to the linear theory or perturbation series expansion, and above threshold, the short-time behavior of our solution is close to the linearization approximation; with the increase of interaction time τ, the long-time behavior of our solution shows that the squeezing is always quite different from the linear theory. It is shown that the maximal squeezing can be obtained at large pump parameter μ=ε/k and interaction time Δτ.