Superradiant Phase Research Articles

Emergence of Collective Coherent States from Strong-Light Coupling of Disordered Systems.

An empirical framework for studying the way vacuum fluctuations in a Fabry-Perot cavity produce collective light-matter hybrid states (polariton states) is reported. The reason that the Tavis-Cummings model, where a single mode of the radiation field couples to all the molecules, succeeds is discussed in terms of the strong phase correlation of the vacuum fluctuations in the cavity, which produces a single effective cavity mode (ECM). The model is used to study the onset of the collective state, or "superradiant phase", for ensembles of molecules with significant disorder in their transition energies, as a function of cavity strength factor, from low Q cavities to high Q cavities. A key result is the quantification of the coherence of the ensemble of the lowest energy eigenstate. This is assessed, primarily, using an entropy distance measure. The statistical model provides a physical intuition for the formation of coherence of polariton states when the collective coupling is strong enough that they dominate over the tail of the dark-state density-of-states.

Mean-field theory of superradiant phase transition in complex networks.

In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts for the interaction between a spin-1/2 (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the δ function, random (Poisson), and power-law exponent [p(k)∝k^{-γ}] degree distributions, respectively. To describe paramagnetic (PM)-ferromagrenic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin z component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z and x directions, respectively. For the regular networks and vanishing external field we demonstrate that these phase transitions generally represent prerequisites for the crossover from a disordered spin state to the ordered one inherent to the FM and/or SR phase. Due to the interplay between the spin interaction and the finite-size effects in networks we elucidate novel features of the SR state in the presence of the PM-FM phase transition. In particular, we show that the critical temperature may be high enough and essentially depends on parameters which characterize statistical properties of the network structure. For the scale-free networks we demonstrate that the network architecture, characterized by the particular value of γ, plays a key role in the SR phase transition problem. Within the anomalous regime scale-free networks possess a strong effective spin-spin interaction supporting fully ordered FM state, which is practically nonsensitive to variations of the quantum transverse field or moderate classical magnetic field. In a scale-free regime the networks exhibit vanishing of the collective spin component in z direction with increasing γ accompanied by establishing spontaneous magnetization in the transverse field. The SR phase transition occurs in the presence of some FM state. We establish the conditions for the network parameters, classical and quantum field features to obtain a quantum phase transition in the spin system when the critical temperature approaches zero.

Quantum tricritical behavior and multistable macroscopic quantum states in generalized Dicke model

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.

Collapse of superradiant phase and Dicke phase transition at finite temperature in a hybrid optical-mechanical system

In this paper, we theoretically investigate Dicke phase transition at finite temperature in a hybrid optical-mechanical system. The thermodynamic equilibrium states are presented by means of the functional path-integral approach. We plot the mean photon number of the two cavities and the corresponding phase diagram showing the effects of the coupling strength between the two cavities, the nonlinear photon-phonon interaction strength, the finite temperature, the detuning of the two cavities. The coupling strength between the two cavities can make the phase boundary of the normal phase (NP) to the superradiant phase (SP) shift left with the increase of the atom-field coupling strength. The region of the SP is suppressed completely and the SP disappears completely with the increase of the coupling strength between the two cavities or the nonlinear photon-phonon interaction strength, finally just the NP and the dynamically unstable state (DUS) exist. The nonlinear photon-phonon coupling strength just affects the turning curve, but not the phase boundary. The unstable non-zero photon number state and the SP are coexistent, similar to the optical bistability.

Superradiant phase transition with cavity-assisted dynamical spin-orbit coupling

The superradiant phase transition represents an important quantum phenomenon that shows collective excitations based on the coupling between atoms and cavity modes. Spin-orbit coupling is another quantum effect which is induced by the interaction of the atomic internal degrees of freedom and center-of-mass momentum. In this work we consider the cavity-assisted dynamical spin-orbit coupling which comes from the combination of these two effects. It can generate a series of interesting quantum phenomena such as the flat spectrum and the discontinuity of the excitation energy spectrum around the critical point of the quantum phase transition. We further discuss the influence of atom decay and nonlinear coupling on the phase diagram. The atom decay suppresses the discontinuity of the phase diagram and the nonlinear coupling can break the symmetric properties of the phase transition. Our work provides a theoretical method to research the rich quantum phenomena in this dynamic many-body system.

Quantum Monte Carlo study of superradiant supersolid of light in the extended Jaynes-Cummings-Hubbard model

Searching for and investigating supersolids is a long-term outstanding problem in physics. In addition to the solid element $^{4}\mathrm{He}$ and cold atoms as potential candidates for the supersolid, the quantum system of light realized by circuit quantum electrodynamics is also a promising platform. In this paper, we propose a supersolid phase, i.e., a superradiant supersolid of light, where superradiant, superfluid, and solid orders coexist. We theoretically simulate the extended Jaynes-Cummings-Hubbard model describing the circuit quantum electrodynamics systems, mainly by the large-scale worm quantum Monte Carlo method, and find that a superradiant supersolid phase exists on triangular lattices due to the antiferromagnetic correlation between photons via light-atom coupling. We also confirm that the previous supersolid of light given by Bujnowski et al. [Phys. Rev. A 90, 043801 (2014)] is not stable. The phase transition between our superradiant supersolid phase and the superradiant solid phase can be continuous (first order) and above (below) the ``symmetry point.'' This is not the same as the pure Bose-Hubbard model on triangular lattices. The results herein could help in the search for a new superradiant supersolid phase in circuit quantum electrodynamic experiments and other light-matter coupling systems.

Switchability of multimodal optical phases in a leaky and nonlinear quantum cavity

In the present report, the question of U(1) symmetry breaking in a system of atoms and electromagnetic fields, interacting inside a leaky cavity, filled with a nonlinear medium, is addressed. In particular, the ${Z}_{2}$ discrete symmetry of the system and the emergence of optical phases are fully discussed. For the nonlinearity of a general order, with an electromagnetic field of any number of modes, conditions under which the resulting field-field interactions destroy the U(1) (and ${Z}_{2}$) symmetry are determined. We then apply the theory to the case of a collection of two-level atoms and three electromagnetic modes. Taking one of the fields as a classically adjustable pumping one, it is demonstrated that the quantized field-field coupling profoundly depends upon the pump field strength. The presence of two competing phenomena, namely, the cavity photonic dissipation and nonlinearity, is shown to lead the system towards steady behavior. The steady-state solutions to the atomic population and field quadratures exhibit the normal and superradiant phases, depending on the strengths of pumping field and atom-field couplings. The conditions for the stability of such steady-state solutions are also discussed in detail. A notable result of the present article is that by adjusting the parameters involved in the system one can switch from the normal to electric and/or magnetic superradiant phases.

Quantum scarring in a spin-boson system: fundamental families of periodic orbits

As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable periodic orbits is directly associated with the phenomenon of quantum scarring, which restricts the degree of delocalization of the eigenstates and leads to revivals in the dynamics. Here, we study the Dicke model in the superradiant phase and identify two sets of fundamental periodic orbits. This experimentally realizable atom–photon model is regular at low energies and chaotic at high energies. We study the effects of the periodic orbits in the structure of the eigenstates in both regular and chaotic regimes and obtain their quantized energies. We also introduce a measure to quantify how much scarred an eigenstate gets by each family of periodic orbits and compare the dynamics of initial coherent states close and away from those orbits.

Gauge fixing for strongly correlated electrons coupled to quantum light

We discuss the problem of gauge fixing for strongly correlated electrons coupled to quantum light, described by projected low-energy models such as those obtained within tight-binding methods. Drawing from recent results in the field of quantum optics, we present a general approach to write down quantum light-matter Hamiltonian in either dipole or Coulomb gauge which are explicitly connected by a unitary transformation, thus ensuring gauge equivalence even after projection. The projected dipole gauge Hamiltonian features a linear light-matter coupling and an instantaneous self-interaction for the electrons, similar to the structure in the full continuum theory. On the other hand, in the Coulomb gauge the photon field enters in a highly non-linear way, through phase factors that dress the electronic degrees of freedom. We show that our approach generalises the well-known Peierls approximation, to which it reduces when only local, on-site orbital contributions to light-matter coupling are taken into account. As an application, we study a two-orbital model of interacting electrons coupled to a uniform cavity mode, recently studied in the context of excitonic superradiance and associated no-go theorems. Using both gauges we recover the absence of superradiant phase in the ground state and show that excitations on top of it, described by polariton modes, contain instead non-trivial light-matter entanglement. Our results highlight the importance of treating the non-linear light-matter interaction of the Coulomb gauge non-perturbatively, to obtain a well-defined ultrastrong coupling limit and to not spoil gauge equivalence.

Regular and bistable steady-state superradiant phases of an atomic beam traversing an optical cavity

We investigate the different photon emission regimes created by a preexcited and collimated atomic beam passing through a single mode of an optical cavity. In the regime where the cavity degrees of freedom can be adiabatically eliminated, we find that the atoms undergo superradiant emission when the collective linewidth exceeds the transit-time broadening. We analyze the case where the atomic beam direction is slanted with respect to the cavity axis. For this situation, we find that a phase of continuous light emission similar to steady-state superradiance is established providing the tilt of the atomic beam is sufficiently small. However, if the atoms travel more than half a wavelength along the cavity axis during one transit time we predict a dynamical phase transition to a new bistable superradiant regime. In this phase the atoms undergo collective spontaneous emission with a frequency that can be either blue or red detuned from the free-space atomic resonance. We analyze the different superradiant regimes and the quantum critical crossover boundaries. In particular we find the spectrum of the emitted light and show that the linewidth exhibits features of a critical scaling close to the phase boundaries.

Dynamical phase transition and selective energy exchange in dual-cavity optochanical systems

<sec> In recent years, the cavity quantum photomechanics has been developed rapidly, and played a very important role in quantum information processing, quantum basic principle verification, and high-precision measurement. The kinds of quantum mechanical behaviors have also been explored and discovered in the study of cavity mechanics. By placing the Kerr medium in the system, quantum nonlinearity is introduced into the optomechanical system. Quantum phase transition is a relatively important part in the research of condensed matter physics. Since Dicke quantum phase transition was successfully observed experimentally, the problem of quantum phase transition in the optical cavity has attracted more attention. The spin-coherent-state variation method and the Holstein-Primakoff transformation are used to theoretically calculate the ground state energy functional, and the rich structure of the macroscopic multi-particle quantum state is given by adjusting the parameters. The quantum phase transition evolution equation describes the relationship between each phase and the time of generating a new phase when reaching the critical phase transition point. At the same time, the mode squeezing of multi-mode hybrid optomechanical system has also became one of the basic problems of quantum mechanical behavior in cavity quantum dynamics.</sec><sec> In this article, we explore the quantum dynamics of optomechanical devices including single-cavity and dual-cavities. We find that the system will undergo a dynamic phase transition, which is similar to the Dicke-Hepp-Lieb superradiant type phase transition, and a new dynamic critical point appears in the coupling between the momentum quadratures of the two optical fields. By manipulating the coupling parameters, we can achieve selective energy exchange between any two modes and the critical coupling point corresponds to selective energy exchange. Mode squeezing, which is easy to measure by applying the quantum uncertainty relationship, is also revealed and consistent with selective energy exchange. The study of coordinate and momentum variances gives us the revelation that the compressed orthogonal variables are the most suitable for measurement because of the small quantum noise. In fact, phononic modes can store energy in a longer duration, while photonic modes can transfer energy in a long distance. This phenomenon makes the hybrid optomechanical cavities useful in the next-generation quantum communications and quantum information processing units.</sec>

Chiral Waveguide Optomechanics: First Order Quantum Phase Transitions with Z_{3} Symmetry Breaking.

We present a direct mapping between the quantum optomechanical problem of the atoms harmonically trapped in the vicinity of a chiral waveguide and a generalized quantum Rabi model, and we discuss the analogy between the self-organization of atomic chains in photonic structures and Dicke-like quantum phase transitions in the ultrastrong coupling regime. We extend the class of the superradiant phase transitions for the systems possessing Z_{3} rather than parity Z_{2} symmetry and demonstrate the emergence of the multicomponent Schrödinger-cat ground states in these systems.

Superradiant Phase Transition in Electronic Systems and Emergent Topological Phases.

We derive a general criterion for determining the onset of superradiant phase transition in electronic bands coupled to a cavity field, with possibly electron-electron interactions. For longitudinal superradiance in 2D or genuine 1D systems, we prove that it is always prevented, thereby extending existing no-go theorems. Instead, a superradiant phase transition can occur to a nonuniform transverse cavity field and we give specific examples in noninteracting models, either through Fermi surface nesting or parabolic band touching. Investigating the resulting time-reversal symmetry breaking superradiant states, we find in the former case Fermi surface lifting down to four Dirac points on a square lattice model, with topologically protected zero modes, and in the latter case topological bands with nonzero Chern number on an hexagonal lattice.

Superradiance, bosonic Peierls distortion, and lattice gauge theory in a generalized Rabi-Hubbard chain

We investigate a one-dimensional Rabi-Hubbard type of model, arranged such that a qdot is sandwiched between every cavity. The role of the qdot is to transmit photons between neighboring cavities, while simultaneously acting as a photon non-linearity. We consider three-level qdots in the $\Lambda$ configuration, where the left and right leg couples exclusively to the left or right cavity. This non-commuting interaction leads to two highly entangled incompressible phases, separated by a second order quantum phase transition: the qdot degrees-of-freedom act as a dynamical lattice for the photons and a Peierls instability breaks a second $\mathbb{Z}_2$ symmetry which leads to a dimerization in entanglement and photon number. We also find a normal insulating phase and a superfluid phase that acts as a quantum many-body superradiant phase. In the superradiant phase, a $\mathbb{Z}_2$ symmetry is broken and the phase transition falls within the transverse field Ising model universality class. Finally, we show that a limit of the model can be interpreted as a $\mathbb{Z}_2$ lattice gauge theory.

Non-Hermitian plasmonic antennas and waveguides: Superradiant and dark states

One-dimensional structures of non-Hermitian plasmonic metallic nanospheres are studied in this paper. For a single sphere, solving Maxwell's equations results in quasi-stationary eigenmodes with complex quantized frequencies. Coupled mode theory is employed in order to study more complex structures. The similarity between the coupled mode equations and the effective non-Hermitian Hamiltonians governing open quantum systems allows us to translate a series of collective phenomenon emerging in condensed matter and nuclear physics to the system of plasmonic spheres. A nontrivial physics emerges as a result of strong non-radiative near field coupling between adjacent spheres. For a system of two identical spheres, this occurs when the width of the plasmonic resonance of the uncoupled spheres is twice the imaginary component of the coupling constant. The two spheres then become coupled through a single continuum channel and the effect of coherent interaction between the spheres becomes noticeable. The eigenmodes of the system fall into two distinct categories: superradiant states with enhanced radiation and dark states with no radiation. The transmission through one-dimensional chains with an arbitrary number of spheres is also considered within the effective Hamiltonian framework which allows us to calculate observables such as the scattering and transmission amplitudes. This nano-scale waveguide can undergo an additional superradiance phase transition through its coupling to the external world. It is shown that perfect transmission takes place when the superradiance condition is satisfied.

Superradiant switching, quantum hysteresis, and oscillations in a generalized Dicke model

We demonstrate quantum signatures of deterministic nonlinear dynamics in the transition to superradiance of a generalized open Dicke model with different coupling strengths for the co- and counter-rotating light-matter interaction terms. A first-order phase transition to coexisting normal and superradiant phases is observed, corresponding with the emergence of switching dynamics between these two phases, driven by quantum fluctuations. We show that this phase coexistence gives rise to a hysteresis loop also for the quantum mechanical system. Additionally, a transition to a superradiant oscillatory phase can be observed clearly in quantum simulations.

Cooperative Breakdown of the Oscillator Blockade in the Dicke Model.

The Dicke model, which describes the coupling of an ensemble of spins to a harmonic oscillator, is known for its superradiant phase transition, which can both be observed in the ground state in a purely Hamiltonian setting, as well as in the steady state of an open-system Dicke model with dissipation. Wedemonstrate that, in addition, the dissipative Dicke model can undergo a second phase transition to a nonstationary phase, characterized by unlimited heating of the harmonic oscillator. Identifying the mechanism of the phase transition and deriving the scaling of the critical coupling with the system size we conclude that the novel phase transition can be understood as a cooperative breakdown of the oscillator blockade which otherwise prevents higher excitation of the system. We discuss an implementation with trapped ions and investigate the role of cooling, by which the breakdown can be suppressed.

Superradiant phase transition in quantum Rabi dimer with staggered couplings

We study the quantum phase transitions and the critical behavior of the quantum Rabi dimer model, where the two cavities are not equivalent. In our model the coupling strength in each cavity is individually tuned as what usually happens in experimental systems. In the frequency-ratio limit with an infinite ratio of the atomic transition frequency to the cavity frequency, the model is analytically solved so that we find a superradiant phase transition and the order parameter of the system is found to be the normal mode of the linear combination of the two cavity modes. Thus we can determine precisely the critical points and depict the associated phase diagram. We also extract the critical exponents through calculating the universal scaling function and thus conclude that the phase transition of the model belongs to the mean-field universality class. The von Neumann entropy and l1 norm coherence are adopted to analyze the quantum phase transition and the associate critical phenomena. The critical points and critical exponents extracted from these information measures agree with ones distilled by the order parameter. We expect this work could stimulate the further study on the multi-cavity models with disorder, where a series of nonequivalent cavities are cascaded.

Quantum quenches in the Dicke model: Thermalization and failure of the generalized Gibbs ensemble* *Project supported by the National Natural Science Foundation of China (Grant No. 11147110) and the Natural Science Youth Foundation of Shanxi, China (Grant No. 2011021003).

Quantum quenches in the Dicke model were studied both in the thermodynamic limit and the finite systems. For the integrable situation in the thermodynamic limit, the generalized Gibbs ensemble can effectively describe the energy-level occupations for the quench within the normal phase, but it fails for the quench to the superradiant phase. For the finite systems which are considered non-integrable, the post quench systems were studied by comparing with the thermal ensembles. The canonical ensembles are directly available for the quench within the normal phase. With the increasing of the target coupling strength over the equilibrium phase transition critical point, sudden changes take place for the effective temperature and the distance to the thermal ensembles. The thermalization was also studied by comparing with the results of the microcanonical ensembles.

Uniqueness of the Phase Transition in Many-Dipole Cavity Quantum Electrodynamical Systems.

The possibility of a superradiant phase transition in light-matter systems is the subject of much debate, due to numerous apparently conflicting no-go and counter no-go theorems. Using an arbitrary-gauge approach we show that a unique phase transition does occur in archetypal many-dipole cavity QED systems, and that it manifests unambiguously via a macroscopic gauge-invariant polarization. We find that the gauge choice controls the extent to which this polarization is included as part of the radiative quantum subsystem and thereby determines the degree to which the abnormal phase is classed as superradiant. This resolves the long-standing paradox of no-go and counter no-go theorems for superradiance, which are shown to refer to different definitions of radiation.