Superradiance Transition Research Articles

Many-Body Dynamics in Monitored Atomic Gases without Postselection Barrier.

We study the properties of a monitored ensemble of atoms driven by a laser field and in the presence of collective decay. The properties of the quantum trajectories describing the atomic cloud drastically depend on the monitoring protocol and are distinct from those of the average density matrix. By varying the strength of the external drive, a measurement-induced phase transition occurs separating two phases with entanglement entropy scaling subextensively with the system size. Incidentally, the critical point coincides with the superradiance transition of the trajectory-averaged dynamics. Our setup is implementable in current light-matter interaction devices, and most notably, the monitored dynamics is free from the postselection measurement problem, even in the case of imperfect monitoring.

Formula omitted]symmetric tight-binding 1D chains: Coupling to the continuum and superradiance transition

By the use of the transfer matrix (TM) approach and effective non-Hermitian Hamiltonian (EnHH) approach we study transport and scattering properties of PT−symmetric tight-binding one-dimensional (1D) chains. In the TM approach we derive an exact expression for the transmission T through 1D chains that incorporates all the scattering-system parameters: incident-wave energy E, chain length L, gain/loss amplitude γ, and coupling strength to perfect leads χ. We show that the behavior of T vs. L strongly depends on the value of γ with respect to the critical value γcr, defined through γcr2=4−E2. For γ<γcr, the transmission T is a periodic function of L, however, for γ>γcr, T decreases exponentially with L. We also predict the unforeseen dependence T∝L−2 at γ=γcr. By the use of the EnHH approach to the same model which is now connected to continuum through left and write ends, we focus on the onset of the superradiance transition as a function of E, L, γ, and χ. The main interest here is in the competition between the balanced gain/loss terms in the bulk of the chain and the coupling to continuum through the ends of the chain. Our results demonstrate that the presence of the gain/loss in the bulk strongly modifies the width of non-superradiant states, however, did not change the width of the superradiant ones. The analytical predictions are supported by detailed numerical simulations.

Dicke superradiance of a two-component Fermi gas coupled to a quantized light field

We study the superradiance transition of a two-component three-dimensional Fermi gas interacting with a single-mode light field of Dicke-type coupling. We find that for a noninteracting gas, due to the Fermi blocking, a unique superradiant state with a superradiant outer shell surrounding an inner Fermi sea may appear, and the critical atom-light coupling strength ${g}_{c}$ to trigger the superradiance approaches $\sqrt{{\ensuremath{\omega}}_{c}{E}_{F}/3}$ even for a vanishing transition frequency between a two-spin state (${\ensuremath{\omega}}_{a}\ensuremath{\rightarrow}0$), in contrast to ${g}_{c}\ensuremath{\sim}\sqrt{{\ensuremath{\omega}}_{c}{\ensuremath{\omega}}_{a}}\ensuremath{\rightarrow}0$ for a bosonic or spin system. When the atom-atom attraction is included, we find that the atomic superfluid would compete with the superradiance directly and both orders cannot coexist, giving rise to an interesting ground-state phase diagram with a tricritical point. The resultant phases and phase transitions are characterized by the unique fluctuation spectrum beyond the mean-field level. We further analyze the effects caused by the decay of the light field, which is inevitable for a possible realization in a cavity with a cold atom system. Our results would be beneficial for the understanding of the interplay between Fermi superfluid and superradiance.

Continuous-time quantum walk on an extended star graph: Disorder-enhanced trapping process.

Using a tight binding model, we investigate the dynamics of an exciton on a disordered extended star graph whose central site acts as an energy trap. When compared with what happens in an ordered network, our results reveal that the disorder drastically improves the excitonic absorption that becomes complete. Moreover, we show the occurrence of an optimal disorder for which the absorption time is strongly minimized, a surprising effect that originates in a disorder-induced restructuring process of the exciton eigenstates. Finally, we also show the existence of an optimal value of the absorption rate that reduces even more the absorption time. The resulting superoptimized trapping process is interpreted as a positive interplay between both the disorder and the so-called superradiance transition.

Complex energies of open one-dimensional disordered wires

We study statistical properties of complex eigenvalues of a non-Hermitian Hamiltonian describing open one-dimensional (1D) models with various types of diagonal disorder. We consider the case of 1D tight-binding wires, with both on-site uncorrelated and correlated disorder, coupled to the continuum through leads attached to the wire edges. In particular, we focus on the location of the eigenvalues in the complex plane as a function of the coupling strength and the disorder strength. Specific interest is paid to the super-radiance transition emerging at the perfect coupling between wire and leads.

Emergent symmetry at superradiance transition of a Bose condensate in two crossed beam cavities

Recently an experiment on superradiant transition of a Bose condensate in two crossed beam cavities has been reported by Léonard et al. in Nature 543, 87 (2017). The surprise is they find that across the superradiant transition, the cavity light can be emitted in any superposition of these two cavity modes. This indicates an additional U(1) symmetry that does not exist in the full Hamiltonian. In this paper we show that this symmetry is an emergent symmetry in the vicinity of the phase transition. We identify all the necessary conditions that are required for this emergent U(1) symmetry and show that this experiment is a special case that satisfies these conditions. We further show that the superradiant transition in this system can also be driven to a first order one when the system is tuned away from the point having the emergent symmetry.

Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition

A tight-binding model is introduced for describing the dynamics of an exciton on an extended star graph whose central node is occupied by a trap. On this graph, the exciton dynamics is governed by two kinds of eigenstates: many eigenstates are associated with degenerate real eigenvalues insensitive to the trap, whereas three decaying eigenstates characterized by complex energies contribute to the trapping process. It is shown that the excitonic population absorbed by the trap depends on the size of the graph, only. By contrast, both the size parameters and the absorption rate control the dynamics of the trapping. When these parameters are judiciously chosen, the efficiency of the transfer is optimized resulting in the minimization of the absorption time. Analysis of the eigenstates reveals that such a feature arises around the superradiance transition. Moreover, depending on the size of the network, two situations are highlighted where the transport efficiency is either superoptimized or suboptimized.

Dissipative Dicke model with collective atomic decay: Bistability, noise-driven activation, and the nonthermal first-order superradiance transition

The Dicke model describes the coherent interaction of a laser-driven ensemble of two level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature dissipation due to e.g. atomic spontaneous emission and cavity photon loss. Spontaneous emission supports the uncorrelated decay of individual atomic excitations as well as the enhanced, collective decay of an excitation that is shared by $N$ atoms and whose strength is determined by the cavity geometry. We derive a many-body master equation for the dissipative Dicke model including both spontaneous emission channels and analyze its dynamics on the basis of Heisenberg-Langevin and stochastic Bloch equations. We find that the collective loss channel leads to a region of bistability between the empty and the superradiant state. Transitions between these states are driven by non-thermal, markovian noise. The interplay between dissipative and coherent elements leads to a genuine non-equilibrium dynamics in the bistable regime, which is expressed via a non-conservative force and a multiplicative noise kernel appearing in the stochastic Bloch equations. We present a semiclassical approach, based on stochastic nonlinear optical Bloch equations, which for the infinite-range Dicke Model become exact in the large-$N$-limit. The absence of an effective free energy functional, however, necessitates to include fluctuation corrections with $\mathcal{O}(1/N)$ for finite $N<\infty$ to locate the non-thermal first-order phase transition between the superradiant and the empty cavity.

Suppressing and Restoring the Dicke Superradiance Transition by Dephasing and Decay.

We show that dephasing of individual atoms destroys the superradiance transition of the Dicke model, but that adding individual decay toward the spin down state can restore this transition. To demonstrate this, we present a method to give an exact solution for the N atom problem with individual dephasing which scales polynomially with N. By comparing finite size scaling of our exact solution to a cumulant expansion, we confirm the destruction and restoration of the superradiance transition hold in the thermodynamic limit.

Hidden modes in open disordered media: analytical, numerical, and experimental results

We explore numerically, analytically, and experimentally the relationship between quasi-normal modes (QNMs) and transmission resonance (TR) peaks in the transmission spectrum of one-dimensional (1D) and quasi-1D open disordered systems. It is shown that for weak disorder there exist two types of the eigenstates: ordinary QNMs which are associated with a TR, and hidden QNMs which do not exhibit peaks in transmission or within the sample. The distinctive feature of the hidden modes is that unlike ordinary ones, their lifetimes remain constant in a wide range of the strength of disorder. In this range, the averaged ratio of the number of transmission peaks to the number of QNMs is insensitive to the type and degree of disorder and is close to the value which we derive analytically in the weak-scattering approximation. The physical nature of the hidden modes is illustrated in simple examples with a few scatterers. The analogy between ordinary and hidden QNMs and the segregation of superradiant states and trapped modes is discussed. When the coupling to the environment is tuned by an external edge reflectors, the superradiance transition is reproduced. Hidden modes have been also found in microwave measurements in quasi-1D open disordered samples. The microwave measurements and modal analysis of transmission in the crossover to localization in quasi-1D systems give a ratio of close to In diffusive quasi-1D samples, however, falls as the effective number of transmission eigenchannels M increases. Once is divided by M, however, the ratio is close to the ratio found in 1D.

Superradiance Transition and Nonphotochemical Quenching in Photosynthetic Complexes

We demonstrate numerically that superradiance could play a significant role in nonphotochemical quenching (NPQ) in light-harvesting complexes. Our model consists of a network of five interconnected sites (discrete excitonic states) that are responsible for the NPQ mechanism. Damaging and charge transfer states are linked to their sinks (independent continuum electron spectra), in which the chemical reactions occur. The superradiance transition in the charge transfer (or in the damaging) channel, occurs at particular electron transfer rates from the discrete to the continuum electron spectra, and can be characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. All five excitonic sites interact with their protein environment that is modeled by a random stochastic process. We find the region of parameters in which the superradiance transition into the charge transfer channel takes place. We demonstrate that this superradiance transition has the capability of producing optimal NPQ performance.

Superradiance transition in graphene

We study theoretically the conditions required for the appearance of a superradiance transition in graphene. The electron properties of graphene are described in the single pz-orbital tight-binding approximation, corresponding to the two interacting sub-lattices. The corresponding model is reduced to the effective two-level pseudo-spin 1/2 system. For each sub-lattice we introduce the electron transfer rate of escape into a continuum. We demonstrate that, under some conditions, the superradiance occurs, and it corresponds to the maximal quantum coherent escape to the continuum.

Superradiance of degenerate Fermi gases in a cavity.

In this Letter we consider spinless Fermi gases placed inside a cavity and study the critical strength of a pumping field for driving a superradiance transition. We emphasize that the Fermi surface nesting effect can strongly enhance the superradiance tendency. Around certain fillings, when the Fermi surface is nearly nested with a relevant nesting momentum, the susceptibility of the system toward a checkboard density-wave ordered state is greatly enhanced in comparison with a Bose gas with the same density, because of which a much smaller (sometime even vanishingly small) critical pumping field strength can give rise to superradiance. This effect leads to interesting reentrance behavior and a topologically distinct structure in the phase diagram. Away from these fillings, the Pauli exclusion principle brings about the dominant effect for which the critical pumping strength is lowered in the low-density regime and increased in the high-density regime. These results open the prospect of studying the rich phenomena of degenerate Fermi gases in a cavity.

Rydberg Polaritons in a Cavity: A Superradiant Solid

We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atom-atom interaction and atom-light coupling induces a rich phase diagram. A novel superradiant solid (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance transition, here both the solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by large scale quantum MonteCarlo simulations.

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

We investigate nonequilibrium phase transitions for driven atomic ensembles interacting with a cavity mode and coupled to a Markovian dissipative bath. In the thermodynamic limit and at low frequencies, we show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path-integral approach that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number $N$ of atoms. For finite $N$, the photon mode behaves as a damped classical nonlinear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any $N$ and correctly captures the atoms' depolarization due to dissipative dephasing.

Superradiance transition in a system with a single qubit and a single oscillator

We consider the phase-transition-like behavior in the Rabi model containing a single two-level system, or qubit, and a single harmonic oscillator. The system experiences a sudden transition from an uncorrelated state to an increasingly correlated one as the qubit-oscillator coupling strength is varied and increased past a critical point. This singular behavior occurs in the limit where the oscillator's frequency is much lower than the qubit's frequency; away from this limit one obtains a finite-width transition region. By analyzing the energy-level structure, the value of the oscillator field and its squeezing and the qubit-oscillator correlation, we gain insight into the nature of the transition and the associated critical behavior.

Superradiance Transition in Photosynthetic Light-Harvesting Complexes

We investigate the role of long-lasting quantum coherence in the efficiency of energy transport at room temperature in Fenna-Matthews-Olson photosynthetic complexes. The excitation energy transfer due to coupling of the light-harvesting complex to the reaction center (“sink”) is analyzed using an effective non-Hermitian Hamiltonian. We show that, as the coupling to the reaction center is varied, maximal efficiency in energy transport is achieved in the vicinity of the superradiance transition, characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. Our results demonstrate that the presence of the sink (which provides a quasi-continuum in the energy spectrum) is the dominant effect in the energy transfer which takes place even in the absence of a thermal bath. This approach allows one to study the effects of finite temperature and the effects of any coupling scheme to the reaction center. Moreover, taking into account a realistic electric dipole interaction, we show that the optimal distance from the reaction center to the Fenna-Matthews-Olson system occurs at the superradiance transition, and we show that this is consistent with available experimental data.

Exciton condensation in cavity quantum electrodynamics

We investigate a strong coupling and half-filling Fermi–Hubbard model coupled to a cavity light field. Using a variational approach with coherent state ansatz, we identify the atom–hole pair condensation with the appearance of superradiance transition of the cavity light field. The mechanism that causes atom–hole pairs is analysed. By spin wave approximation, the phase transition at finite temperature is analysed.

Bose-Hubbard models coupled to cavity light fields

Recent experiments on strongly coupled cavity quantum electrodynamics present new directions in "matter-light" systems. Following on from our previous work [Phys. Rev. Lett. 102, 135301 (2009)] we investigate Bose-Hubbard models coupled to a cavity light field. We discuss the emergence of photoexcitations or "polaritons" within the Mott phase, and obtain the complete variational phase diagram. Exploiting connections to the super-radiance transition in the Dicke model we discuss the nature of polariton condensation within this novel state. Incorporating the effects of carrier superfluidity, we identify a first-order transition between the superradiant Mott phase and the single component atomic superfluid. The overall predictions of mean field theory are in excellent agreement with exact diagonalization and we provide details of superfluid fractions, density fluctuations, and finite size effects. We highlight connections to recent work on coupled cavity arrays.

10.1007/s11449-008-2016-7

Based on the analysis of the experimental data on the observation of the fluorescence and superradiance of praseodymium ions in a matrix of lanthanum trifluoride, a model of superradiance of three-level radiators with two close upper levels is developed in the mean-field approximation and studied. The uppermost level is coherently pumped by an ultrashort pulse of electromagnetic field, after which the excitation is transferred to the close energy level, from which the superradiance transition occurs to the lower level. In limiting cases, the considered model is reduced to the known models of superradiance and describes the ordinary regimes of monopulse and multipulse (oscillatory) superradiance. However, in a certain region of parameters, the model under discussion describes such a multipulse superradiance signal in which electromagnetic field spikes composing it follow in time with random intervals and amplitudes, so that the regime of regular chaotic dynamics is demonstrated in a single superradiance signal. In a certain time interval, the proposed model can be described by the Lorenz equations with the parameters corresponding to the chaotic dynamics of spikes composing the superradiance signal. The presented results of the numerical simulation of the model equations qualitatively correspond to the picture of stochastic pulsations observed experimentally.