Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes

Here we show how, in the ultra-strongly-coupled spin-boson model, apparently unphysical "Matsubara modes" are required not only to regulate detailed balance, but also to arrive at a correct and physical description of the non-perturbative dynamics and steady-state. In particular, in the zero-temperature limit, we show that neglecting the Matsubara modes results in an erroneous emission of virtual photons from the collective ground state. To explore this difficult-to-model regime we start by using a non-perturbative hierarchical equations of motion (HEOM) approach, based on a partial fitting of the bath correlation-function which takes into account the infinite sum of Matsubara frequencies using only a biexponential function. We compare the HEOM method to both a pseudo-mode model, and the reaction coordinate (RC) mapping, which help explain the nature of the aberrations observed when Matsubara frequencies are neglected. For the pseudo-mode method we present a general proof of validity, which allows for negative Matsubara-contributions to the decomposition of the bath correlation functions to be described by zero-frequency Matsubara-modes with non-Hermitian coupling to the system. The latter obey a non-Hermitian pseudo-Schr\"odinger equation, ultimately justifying why superficially unphysical modes can give rise to physical system behavior.Comment: 21 page

Amplified opto-mechanical transduction of virtual radiation pressure

Here we describe how, utilizing a time-dependent opto-mechanical interaction, a mechanical probe can provide an amplified measurement of the virtual photons dressing the quantum ground state of an ultra strongly-coupled light-matter system. We calculate the thermal noise tolerated by this measurement scheme, and discuss a range of experimental setups in which it could be realized.Comment: 7 + 12 pages, 1 figur

Ground State Electroluminescence

Electroluminescence, the emission of light in the presence of an electric current, provides information on the allowed electronic transitions of a given system. It is commonly used to investigate the physics of strongly-coupled light-matter systems, whose eigenfrequencies are split by the strong coupling with the photonic field of a cavity. Here we show that, together with the usual electroluminescence, systems in the ultrastrong light-matter coupling regime emit a uniquely quantum radiation when a flow of current is driven through them. While standard electroluminescence relies on the population of excited states followed by spontaneous emission, the process we describe herein extracts bound photons by the dressed ground state and it has peculiar features that unequivocally distinguish it from usual electroluminescence.Comment: 6 pages, 3 figure

Multielectron Ground State Electroluminescence

The ground state of a cavity-electron system in the ultrastrong coupling regime is characterized by the presence of virtual photons. If an electric current flows through this system, the modulation of the light-matter coupling induced by this non-equilibrium effect can induce an extra-cavity photon emission signal, even when electrons entering the cavity do not have enough energy to populate the excited states. We show that this ground-state electroluminescence, previously identified in a single-qubit system [Phys. Rev. Lett. 116, 113601 (2016)] can arise in a many-electron system. The collective enhancement of the light-matter coupling makes this effect, described beyond the rotating wave approximation, robust in the thermodynamic limit, allowing its observation in a broad range of physical systems, from a semiconductor heterostructure with flat-band dispersion to various implementations of the Dicke model.Comment: 32 pages (9+23), 9 figures (3+6

Quantum Emulation of Gravitational Waves

Gravitational waves, as predicted by Einstein's general relativity theory, appear as ripples in the fabric of spacetime traveling at the speed of light. We prove that the propagation of small amplitude gravitational waves in a curved spacetime is equivalent to the propagation of a subspace of electromagnetic states. We use this result to propose the use of entangled photons to emulate the evolution of gravitational waves in curved spacetimes by means of experimental electromagnetic setups featuring metamaterials.Comment: 10 pages, 2 figure

A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model

We show that the effect of a Gaussian Bosonic environment linearly coupled to a quantum system can be simulated by a stochastic Lindblad master equation characterized by a set of ancillary Bosonic modes initially at zero temperature and classical stochastic fields. We test the method for Ohmic environments with exponential and polynomial cut-offs against, respectively, the Hierarchical Equations of Motion and the deterministic pseudomode model with respect to which the number of ancillary quantum degrees of freedom is reduced. For a subset of rational spectral densities, all parameters are explicitly specified without the need of any fitting procedure, thereby simplifying the modeling strategy. Interestingly, the classical fields in this decomposition must sometimes be imaginary-valued, which can have counter-intuitive effects on the system properties which we demonstrate by showing that they can decrease the entropy of the system, in contrast to real-valued fields.Comment: 41 pages, 11 figure

The Closed and Open Unbalanced Dicke Trimer Model: Critical Properties and Nonlinear Semiclassical Dynamics

We study a generalization of a recently introduced Dicke trimer model [Phys. Rev. Lett. 128, 163601, Phys. Rev. Research 5, L042016], which allows for cavity losses and unbalanced light-matter interactions (in which rotating and counter-rotating terms can be tuned independently). We find that in the extreme unbalanced limit, the $U(1)$ symmetry of the Tavis-Cummings model is restored, qualitatively altering the critical phenomena in the superradiant phase due to the presence of a zero-energy mode. To analyze this general regime, we develop a semiclassical theory based on a re-quantization technique. This theory also provides further physical insight on a recently reported anomalous finite critical fluctuations in the time-reversal broken regime. Moving to the open-Dicke case, by introducing local dissipation to the cavities, we observe the emergence of a rich range of nonequilibrium phases characterized by trivial and non-trivial dynamical signatures. In the former case, we identify, when time-reversal symmetry is present, a new stationary phase that features superradiant states in two of the three cavities and a normal state in the other cavity. In the latter case, we observe the emergence of dynamical phases in which the system exhibits superradiant oscillations, characterized by periodic or chaotic phase space patterns. The landscape of transitions associated with these dynamical phases features a wide range of qualitatively different behaviours such as Hopf bifurcations, anomalous Hopf bifurcations, collisions between basins of attraction, and exterior crises. We highlight how the two-critical-scalings feature of the closed model is robust under dissipation while the phenomenon of anomalous finite critical fluctuations becomes a mean-field scaling in the open model.Comment: 22 pages, 13 figure

(3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions

Currently, there is much interest in discovering analytically tractable (3+1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of spinless interacting fermions that reproduces, in the low-energy limit, a (3+1)-dimensional Abelian topological quantum field theory called the BF model. By employing a mechanism equivalent to Haldane's Chern insulator, we can turn the noninteracting model into a three-dimensional chiral topological insulator. We then isolate energetically one of the two Fermi points of the lattice model. In the presence of suitable fermionic interactions, the system, in the continuum limit, is equivalent to a generalized (3+1)-dimensional Thirring model. The low-energy limit of this model is faithfully described by the BF theory. Our approach directly establishes the presence of (2+1)-dimensional BF theory at the boundary of the lattice and it provides a way to detect the topological order of the model through fermionic density measurements