In this paper we investigate the close relationship between Dicke superradiance, originally predicted for an ensemble of two-level atoms in entangled states, and the Hanbury Brown and Twiss effect, initially established in astronomy to determine the dimensions of classical light sources like stars. By studying the state evolution of the fields produced by classical sources -- defined by a positive Glauber-Sudarshan P function -- when recording intensity correlations of higher order in a generalized Hanbury Brown and Twiss setup we find that the angular distribution of the last detected photon, apart from an offset, is identical to the superradiant emission pattern generated by an ensemble of two-level atoms in entangled symmetric Dicke states. We show that the phenomenon derives from projective measurements induced by the measurement of photons in the far field of the sources and the permutative superposition of quantum paths identical to those leading to superradiance in the case of single photon emitters. We thus point out an important similarity between classical sources and quantum emitters upon detection of photons if the particular photon source remains unknown. We finally present a compact result for the characteristic functional which generates intensity correlations of arbitrary order for any kind of light sources.
Absence of Entanglement Growth in Dicke Superradiance
Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）；TU Darmstadt, Institute for Applied Physics（达姆施塔特工业大学应用物理研究所）
We present a proposal for a probing scheme utilizing Dicke superradiance to obtain information about ultracold atoms in optical lattices. A probe photon is absorbed collectively by an ensemble of lattice atoms generating a Dicke state. The lattice dynamics (e.g., tunneling) affects the coherence properties of that Dicke state and thus alters the superradiant emission characteristics -- which in turn provides insight into the lattice (dynamics). Comparing the Bose-Hubbard and the Fermi-Hubbard model, we find similar superradiance in the strongly interacting Mott insulator regime, but crucial di…
In 1954, Dicke predicted that a system of quantum emitters confined to a subwavelength volume would produce a superradiant burst. For such a burst to occur, the emitters must be in the special Dicke state with zero dipole moment. We show that a superradiant burst may also arise for non-Dicke initial states with nonzero dipole moment. Both for Dicke and non-Dicke initial states, superradiance arises due to a decrease in the dispersion of the quantum phase of the emitter state. For non-Dicke states, the quantum phase is related to the phase of long-period envelopes which modulate the oscillation…
We calculate the field eigenmodes of the superradiant emission from an ensemble of $N$ two-level atoms. While numerical techniques are effective due to the symmetry of the problem, we develop also an analytical method to approximates the modes in the limit of a large number of emitters. We find that Dicke superradiant emission is restricted to a small number of modes, with a little over 90\% of the photons emitted in a single dominant mode.
A thorough understanding of the structure of correlations in multipartite systems is essential for the success of most quantum information processing applications. The problem, however, quickly becomes non-trivial as the size of the multipartition increases. With this motivation in mind, in this paper, we put forth a detailed study of genuine multipartite correlations (GMCs) in the Dicke model of superradiance. We compute all genuine $k$-partite correlations for Dicke states with arbitrary excitations and use these results to characterize the evolution of multipartite correlations during the s…
We consider a driven single mode Dicke-Hamiltonian coupled to a dissipative zero-temperature bath. We derive the cumulant generating function for emitted photons of this quantum-critical system by using a $P$-representation of the master equation in the thermodynamic limit. This cumulant generating function is shown to consist of two parts: a macroscopic component, which is Poissonian in nature with characteristic rate proportional to the order parameter of the system; and a part describing fluctuations which is non-trivial in form and divergent around the quantum phase transition.
Superradiance typically requires preparation of atoms in highly entangled multi-particle states, the so-called Dicke states. In this paper we discuss an alternative route where we prepare such states from initially uncorrelated atoms by a measurement process. By measuring higher order intensity intensity correlations we demonstrate that we can simulate the emission characteristics of Dicke superradiance by starting with atoms in the fully excited state. We describe the essence of the scheme by first investigating two excited atoms. Here we demonstrate how via Hanbury Brown and Twiss type of me…
We consider a micromaser model to study the influence of Dicke superradiance in the context of the one-atom maser. The model involves a microwave cavity into which two-level Rydberg atoms are pumped in pairs. We consider a random pump mechanism which allows the presence of at most one pair of atoms in the cavity at any time. We analyze the differences between the present system, called the Dicke micromaser, and an equivalently pumped conventional one-atom micromaser. These differences are attributed to the Dicke cooperativity in the two-atom system. We also show that the two-atom Dicke microma…
We study non-Markovian enhancement effects in the spontaneous emission of a collective excitation in a linear chain of up to 100 qubits coupled to a 1D waveguide. We find that for a critical separation of qubits, the system exhibits super-superradiant (SSR) behavior leading to collective decay stronger than the usual Dicke superradiance. Here, time-delayed coherent quantum feedback effects are at play on top of the usual Dicke superradiance effects. We find a linear scaling for the SSR decay rate with increasing qubit number $N$ such that $Γ_{\rm SSR} \sim 2.277 N γ_0$, where $γ_0$ is the sing…
Symbolic Quantum-Trajectory Method for Multichannel Dicke Superradiance
University of Innsbruck（因斯布鲁克大学）；Harvard University（哈佛大学）；TU Darmstadt（达姆施塔特工业大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Friedrich-Alexander Universität Erlangen-Nürnberg (FAU)（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
We study the quantum quench dynamics in an extended version of the Dicke model where an additional parameter allows a smooth transition to the integrable Tavis-Cummings regime. We focus on the influence of various quantum phases and excited-state quantum phase transitions (ESQPTs) on the survival probability of the initial state. We show that, depending on the quench protocol, an ESQPT can either stabilize the initial state or, on the contrary, speed up its decay to the equilibrated regime. Quantum chaos smears out the manifestations of ESQPTs in quench dynamics, therefore significant effects …
Dicke superradiance, i.e., the enhanced spontaneous emission of coherent radiation, is often attributed to radiation emitted by synchronized dipoles coherently oscillating in phase. At the same time, Dicke derived superradiance assuming atoms in entangled Dicke states which do not display any dipole moment. To shed light on this apparent paradox, we study the intensity distribution arising from two identical two-level atoms prepared either in an entangled Dicke state or in a separable atomic state with non-vanishing dipole moment. We find that the two configurations produce similar far field i…
Dicke superrandiance is a cooperative phenomenon which arises from the collective coupling of an ensemble of atoms to the electromagnetic radiation. Here we discuss the quantifying of quantum coherence for the Dicke model of superradiance in the mean-field approximation. We found the single-atom $l_1$-norm of coherence is given by the square root of the normalized average intensity of radiation emitted by the superradiant system. This validates quantum coherence as a useful figure of merit towards the understanding of superradiance phenomenon in the mean-field approach. In particular, this res…
Collective emission behavior is usually described by the decay dynamics of the completely symmetric Dicke states. To study a more realistic scenario, we investigate alternative initial states inducing a more complex time evolution. Superposition states of the fully inverted Dicke state and the Dicke ground state with unequal mutual weights are studied as examples as well as superradiance stemming from atoms in clusters separated by more than one wavelength. The Monte Carlo wave function method serves as framework to study the dynamics of quantum states, which is determined by quantum jumps on …
We study the focus-focus type of monodromy in an integrable version of the Dicke model. Classical orbits forming a pinched torus represent analogues of the dynamic superradiance under conditions of a closed system. Quantum signatures of monodromy appear in lattices of expectation values of various quantities in the Hamiltonian eigenstates and are related to an excited-state quantum phase transition. We demonstrate the breakdown of these structures with an increasing strength of non-integrable perturbation.
We have applied the concept of superradiance introduced by Dicke in 1954 to astrophysics by extending the corresponding analysis to the magnetic dipole interaction characterizing the atomic hydrogen 21 cm line. Although it is unlikely that superradiance could take place in thermally relaxed regions and that the lack of observational evidence of masers for this transition reduces the probability of detecting superradiance, in situations where the conditions necessary for superradiance are met (i.e., close atomic spacing, high velocity coherence, population inversion, and long dephasing time-sca…
We present theoretical results for superradiance, i.e. the collective coherent decay of a radiating system, in semiconductor structures. An optically active region can become superradiant if a strong magnetic field is applied. Pumping of electrons and holes at a rate T through coupling to external `reservoirs' leads to a novel kind of oscillations with frequency $\sim \sqrt{T}$.}
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 holds in the thermodynamic limit.
We study Dicke superradiance as collective and coherent absorption and (time-delayed) emission of photons from an ensemble of ultracold atoms in an optical lattice. Since this process depends on the coherence properties of the atoms (e.g., superfluidity), it can be used as a probe for their quantum state. In analogy to pump-probe spectroscopy in solid-state physics, this detection method facilitates the investigation of nonequilibrium phenomena and is less invasive than time-of-flight experiments or direct (projective) measurements of the atom number (or parity) per lattice site, which both de…
Dicke superradiance is an example of emergence of macroscopic quantum coherence via correlated dissipation. Starting from an initially incoherent state, a collection of excited atoms synchronizes as they decay, generating a macroscopic dipole moment and emitting a short and intense pulse of light. While well understood in cavities, superradiance remains an open problem in extended systems due to the exponential growth of complexity with atom number. Here we show that Dicke superradiance is a universal phenomenon in ordered arrays. We present a theoretical framework -- which circumvents the exp…
We present theoretical results for superradiance, i.e. the collective coherent decay of a radiating system, in a semiconductor heterostructure under a strong quantizing magnetic field. We predict a strong peak (`Dicke-peak') in the emission intensity as a function of time, which should be observable after a short initial excitation of electrons into the conduction band. This peak has a characteristic dependence on the magnetic field and should be observable on sub-picosecond time scales. Furthermore, pumping of electrons and holes into the systems at a rate T leads to a novel kind of oscillati…
We report a time-resolved study of collective emission in dense ensembles of two-level atoms. We compare, on the same sample, the build-up of superradiance and subradiance from the ensemble when driven by a strong laser. This allows us to measure the dynamics of the population of superradiant and subradiant states as a function of time. In particular we demonstrate the build up in time of subradiant states through the superradiant dynamics. This illustrates the dynamics of the many-body density matrix of superradiant ensembles of two-level atoms when departing from the ideal conditions of Dick…
We derive analytical results for various quantities related to the excited-state quantum phase transitions in a class of Dicke superradiance models in the semiclassical limit. Based on a calculation of a partition sum restricted to Dicke states, we discuss the singular behavior of the derivative of the density of states and find observables like the mean (atomic) inversion and the boson (photon) number and its fluctuations at arbitrary energies. Criticality depends on energy and a parameter that quantifies the relative weight of rotating versus counter-rotating terms, and we find a close analo…
We apply the concept of superradiance introduced by Dicke in 1954 to the OH molecule 1612 MHz spectral line often used for the detection of masers in circumstellar envelopes of evolved stars. As the detection of 1612 MHz OH masers in the outer shells of envelopes of these stars implies the existence of a population inversion and a high level of velocity coherence, and that these are two necessary requirements for superradiance, we investigate whether superradiance can also happen in these regions. Superradiance is characterized by high intensity, spatially compact, burst-like features taking p…
In the dissipative quantum dynamics of a mesoscopic aggregate of excited two level systems (atoms) coupled to a single resonance mode of a cavity, two physical phenomena associated with superradiance appear. A pronounced emission peak on short time scales is related to the known superradiant burst of excited atoms cooperatively radiating into free space. It is followed by relaxation to a stationary state of the composite system such that for sufficiently large atom-field coupling a strongly correlated state emerges. The crossover to this state can be interpreted as the precursor of the transit…
We consider the Dicke model, describing an ensemble of $N$ quantum spins interacting with a cavity field, and study how the coupling to a non-Markovian environment with power-law spectrum changes the physics of superradiant phase transition. Quite remarkably we find that dissipation can induce, rather than suppress, the ordered phase, a result which is in striking contrast with both thermal and Markovian quantum baths. We interpret this dissipation-induced superradiance as a genuine dissipative quantum phase transition that exists even at finite $N$ due to the coupling with the bath modes and …
Using a non-Hermitian Hamiltonian approach to open systems, we study the interplay of disorder and superradiance in a one- and three-dimensional Anderson model. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, a transition to a superradiant regime is shown to occur. As an effect of openness the structure of eigenstates undergoes a strong change in the superradiant regime: we show that the sensitivity to disorder of the superradiant and the subradiant subspaces is very different; superradiant states remain delocalized as disorder increases, while subradiant states are sensiti…
An individual excited two level system decays to its ground state by emitting a single photon in a process known as spontaneous emission. In accordance with quantum theory the probability of detecting the emitted photon decreases exponentially with the time passed since the excitation of the two level system. In 1954 Dicke first considered the more subtle situation in which two emitters decay in close proximity to each other. He argued that the emission dynamics of a single two level system is altered by the presence of a second one, even if it is in its ground state. Here, we present a close …
Recently it was shown in Ref. [Phys. Rev. Lett. 112, 140402 (2014)] that in the idealized Dicke model of superradiance there is no entanglement among any partitions of the system during the total evolution time of the system. This result immediately conducts us to question if other measures from quantum information theory can explain the characteristic release of energy in a short time interval. In this work we identify the uncertainty of purely quantum origin as the property responsible for Dicke superradiance. The quantum uncertainty on the population of each emitter of the sample captured b…
Scaling theory of decoherence in Dicke superradiance
TU Darmstadt（达姆施塔特工业大学）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；CNRS and Université de Strasbourg（法国国家科学研究中心与斯特拉斯堡大学）
Solving Dicke superradiance analytically: A compendium of methods
Harvard University（哈佛大学）；University of Innsbruck（因斯布鲁克大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔兰根-纽伦堡大学）；Pontificia Universidad Catolica del Peru（秘鲁天主教 Pontificia 大学）；TU Darmstadt, Institute for Applied Physics（达姆施塔特工业大学应用物理研究所）
Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms $N$ and a temporal width reduced by $N$ compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path descript…
Dicke Superradiance in Extended 2D Quantum Arrays Coupled to Metasurface Bound States in the Continuum
University of Manchester（曼彻斯特大学）；Newcastle University（纽卡斯尔大学）；A*STAR (Agency for Science, Technology and Research)（新加坡科技研究局）；Consejo Superior de Investigaciones Científicas（西班牙高等科学研究委员会）
We study generic features of open quantum systems embedded into a continuum of scattering wavefunctions and compare them with results discussed in optics. A dynamical phase transition may appear at high level density in a many-level system and also in a two-level system if the coupling $W$ to the environment is complex and sufficiently large. Here nonlinearities occur. When $W_{ij}$ is imaginary, two singular (exceptional) points may exist. In the parameter range between these two points, width bifurcation occurs as function of a certain external parameter. A unitary representation of the S-ma…
Sonoluminescence is a process in which a strong sound field is used to produce light in liquids. We explain sonoluminescence as a phase transition from ordinary fluorescence to a superradiant phase. We consider a spin-boson model composed of a single bosonic mode and an ensemble of $N$ identical two-level atoms. We assume that the whole system is in thermal equilibrium with a reservoir at temperature $β^{-1}$. We show that, in a ultrastrong-coupling regime, between the two-level atoms and the electromagnetic field it is possible to have a cooperative interaction of the molecules of the gas in …
Dicke superradiance in degenerate quantum matter: interplay of exchange statistics and spatial confinement
Friedrich-Alexander Universität Erlangen-Nürnberg (FAU)（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；TU Darmstadt（达姆施塔特工业大学）
We report the experimental observation of superradiant emission emanating from an elongated dense ensemble of laser cooled two-level atoms, with a radial extent smaller than the transition wavelength. In the presence of a strong driving laser, we observe that the system is superradiant along its symmmetry axis. This occurs even though the driving laser is orthogonal to the superradiance direction. This superradiance modifies the spontaneous emission, and, resultantly, the Rabi oscillations. We also investigate Dicke superradiance in the emission of an almost fully-inverted system as a function…
We use quantum-electrodynamical approach to study the initial stage of Dicke superradiance from a system of two-level atoms. Applying the zeroth-order Magnus approximation, we obtain the expression for the mean number of quanta emitted in the presence of thermal fluctuations of the electromagnetic field.
We consider spin-boson models composed by a single bosonic mode and an ensemble of $N$ identical two-level atoms. The situation where the coupling between the bosonic mode and the atoms generates real and virtual processes is studied, where the whole system is in thermal equilibrium with a reservoir at temperature $β^{-1}$. Phase transitions from ordinary fluorescence to superradiant phase in three different models is investigated. First a model where the coupling between the bosonic mode and the $j-th$ atom is via the pseudo-spin operator $σ^{,z}_{(j)}$ is studied. Second, we investigate the …
Dicke superradiance has been observed in many systems and is based on constructive interferences between many scattered waves. The counterpart of this enhanced dynamics, subradiance, is a destructive interference effect leading to the partial trapping of light in the system. In contrast to the robust superradiance, subradiant states are fragile and spurious decoherence phenomena hitherto obstructed the observation of such metastable states. We show that a dilute cloud of cold atoms is an ideal system to look for subradiance in free space and study various mechanisms to control this subradiance…
Generalized with respect to the Stark interaction of atoms with a vacuum field of zero photon density, Dicke's model is used to describe the Raman superradiance of a localized ensemble of identical atoms in a coherent non-resonant light wave. It is shown that at a certain critical number of atoms in the ensemble the stabilization effect of the excited state of the ensemble relative to collective atomic decay is possible, with superradiance of the atomic ensemble being suppressed. When the number of atoms is close to the critical value, superradiance exhibits features that are opposite to the e…
For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of cumulant generating function and system operators at lowest order, allows us to recover master equation results of the Full Counting Statistics for certain parameter regimes at very low cost of computation. The thermodynamic limit, that is not accessible with the master equation approach, can be derived analytically for different approximations.
Multiensemble Superradiance for Distributed Quantum Sensing
College of Physical Science and Technology, Central China Normal University（华中师范大学物理科学与技术学院）；School of Science, Hubei University of Technology（湖北工业大学理学院）
The superradiant behaviour of the Dicke model is examined using the Yudson representation. This is achieved by computing the time evolution of the mean photon current density and photon number. Extensions of this model including energy splitting and spatial separation are then investigated using this technique.
We demonstrate the emergence of a non-equilibrium superradiant phase in the dissipative Rabi-Dicke model. This phase is characterized by a photonic steady state that oscillates with a frequency close to the cavity frequency, in contrast to the constant photonic steady state of the equilibrium superradiant phase in the Dicke model. We relate this superradiant phase to the population inversion of Floquet states by introducing a Schwinger representation of the driven two-level systems in the cavity. This inversion is depleted near Floquet energies that are resonant with the cavity frequency to su…
