We study ultracold atoms in a finite size one-dimensional optical lattice prepared in the Mott insulator phase and commonly coupled to a single cavity mode. Due to resonance dipole-dipole interactions among the atoms, electronic excitations delocalize and form {\it excitons}. These exciton modes are divided into two groups: antisymmetric modes which decouple from the cavity mode forming {\it dark states}, and symmetric modes significantly coupled to the cavity mode called {\it bright states}. In typical setups the lowest and most symmetric exciton is coupled to the cavity photons much stronger than the other bright states and dominates the optical properties response of the atoms ({\it superradiant state}). In the strong coupling regime this superradiant state is coherently mixed with the cavity photon to form a doublet of polariton states with the Rabi splitting.
We report on the observation of collective atomic recoil lasing and superradiant Rayleigh scattering with ultracold and Bose-Einstein condensed atoms in an optical ring cavity. Both phenomena are based on instabilities evoked by the collective interaction of light with cold atomic gases. This publication clarifies the link between the two effects. The observation of superradiant behavior with thermal clouds as hot as several tens of $μ\textrm{K}$ proves that the phenomena are driven by the cooperative dynamics of the atoms, which is strongly enhanced by the presence of the ring cavity.
Collective interaction of light with an atomic gas can give rise to superradiant instabilities. We experimentally study the sudden build-up of a reverse light field in a laser-driven high-finesse ring cavity filled with ultracold thermal or condensed atoms. While superradiant Rayleigh scattering from atomic clouds is normally only observed at very low temperatures (i.e. well below $1 μ$K), the presence of the ring cavity enhances cooperativity and allows for superradiance with thermal clouds as hot as several $10 μ$K. A characterization of the superradiance at various temperatures and cooperat…
We theoretically analyze the collective dynamics of a thermal beam of atomic dipoles that couple to a single mode when traversing an optical cavity. For this setup we derive a semiclassical model and determine the onset of superradiant emission and its stability. We derive analytical expressions for the linewidth of the emitted light and compare them with numerical simulations. In addition, we find and predict two different superradiant phases; a steady-state superradiant phase and a multi-component superradiant phase. In the latter case we observe sidebands in the frequency spectrum that can …
This paper is devoted to energy-spectral analysis for the system of a two-level atom coupled with photons in a cavity. It is shown that the Dicke-type energy level crossings take place when the atom-cavity interaction of the system undergoes changes between the weak coupling regime and the strong one. Using the phenomenon of the crossings we develop the idea of cavity-induced atom cooling proposed by the group of Ritsch, and we lay mathematical foundations of a possible mechanism for another superradiant cooling in addition to that proposed by Domokos and Ritsch. The process of our superradian…
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 …
We in this paper derive the analytical expressions of ground-state energy, average photon-number, and the atomic population by means of the spin-coherent-state variational method for arbitrary number of atoms in an optomechanical cavity. It is found that the existence of mechanical oscil- lator does not affect the phase boundary between the normal and superradiant phases. However, the superradiant phase collapses by the resonant damping of the oscillator when the atom-field coupling increases to a so-called turning point. As a consequence the system undergoes at this point an additional phase …
$\bf A^2$-robust superradiant phase transition in hybrid qubit-cavity optomechanics
Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics and State Key Laboratory of Modern Optical Instrumentation, Zhejiang University（浙江大学量子技术与器件浙江省重点实验室、物理学院与现代光学仪器国家重点实验室）；Department of Physics, Wenzhou University（温州大学物理系）；International Quantum Academy, Shenzhen（深圳国际量子学院）
We investigate a two-way cascaded cavity QED system consisting of microtoroidal resonators coupled through an optical fiber. Each microtoroidal cavity supports two counter-propagating whispering-gallery modes coupled to single atoms through their evanescent fields. We focus on a pair of atom-microtoroid systems and compute the spectrum of spontaneous emission into the fiber with one atom initially excited. Explicit results are presented for strong-coupling and bad-cavity regimes, where the latter allows the effective atom-atom interaction to be controlled through the atom-cavity coupling and d…
We propose a single-atom, cavity quantum electrodynamics system, compatible with recently demonstrated, fiber-integrated micro- and nano-cavity setups, for the on-demand production of optical number-state, $0N$-state, and binomial-code-state pulses. The scheme makes use of Raman transitions within an entire atomic ground-state hyperfine level and operates with laser and cavity fields detuned from the atomic transition by much more than the excited-state hyperfine splitting. This enables reduction of the dynamics to that of a simple, cavity-damped Tavis-Cummings model with the collective spin d…
Nonclassical Many-Body Superradiant States with Interparticle and Spin-Momentum Entanglement
JILA and Department of Physics, University of Colorado（科罗拉多大学物理系与JILA）；Theoretische Physik, Universität des Saarlandes（萨尔兰州立大学理论物理学）；Physikalisches Institut, University of Bonn（波恩大学物理研究所）
A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such …
We study the threshold conditions of spatial self organization combined with collective coherent optical backscattering of a thermal gaseous beam moving in a high Q ring cavity with counter propagating pump. We restrict ourselves to the limit of large detuning between the particles optical resonances and the light field, where spontaneous emission is negligible and the particles can be treated as polarizable point masses. Using a linear stability analysis in the accelerated rest frame of the particles we derive an analytic bounds for the selforganization as a function of particle number,averag…
We develop a stochastic mean-field theory to describe active frequency measurements of pulsed superradiant emission, studied in recent experiments with strontium-87 atoms trapped in an optical lattice inside an optical cavity [M. Norcia, et al., Phys. Rev. X 8, 21036 (2018)]. Our theory reveals the intriguing dynamics of atomic ensembles with multiple transition frequencies, and it reproduces the superradiant beats signal, noisy power spectra, and frequency uncertainty in remarkable agreement with the experiments. Moreover, by reducing the number of atoms, elongating the superradiant pulses an…
An ideal superradiant laser on an optical clock transition of noninteracting cold atoms is predicted to exhibit an extreme frequency stability and accuracy far below mHz-linewidth. In any concrete setup sufficiently many atoms have to be confined and pumped within a finite cavity mode volume. Using a magic wavelength lattice minimizes light shifts and allows for almost uniform coupling to the cavity mode. Never- theless, the atoms are subject to dipole-dipole interaction and collective spontaneous decay which compromises the ultimate frequency stability. In the high density limit the Dicke sup…
We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose-Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions. The cavity frequency is harmonically modulated in time for both the cases. The main quantity of interest is the number of intracavity scattered photons. The system has been investigated under the weak and strong modulation. It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion. Also, initially, th…
Superradiant phase transition in cavity magnonics via Floquet engineering
School of Physics, Hangzhou Normal University（杭州师范大学物理学院）；Interdisciplinary Research Center of Quantum and Photoelectric Information, and Anhui Research Center of Semiconductor Industry Generic Technology, Chizhou University（池州大学量子与光电信息交叉研究中心及安徽省半导体产业通用技术研究中心）；School of Physics and Electronic Information, Yunnan Normal University（云南师范大学物理与电子信息学院）；Zhejiang Key Laboratory of Micro-Nano Quantum Chips and Quantum Control（浙江省微纳量子芯片与量子控制重点实验室）
Lasing in the bad cavity regime has promising applications in precision metrology due to the reduced sensitivity to cavity noise. Here we investigate the spectral properties and phase behavior of pulsed lasing on the $^1$S$_0 - ^3$P$_1$ line of $^{88}$Sr in a mK thermal ensemble, as first described in arxiv:1903.12593. The system operates in a regime where the Doppler-broadened atomic transition linewidth is several times larger than the cavity linewidth. We find that by detuning the cavity resonance, the influence of the cavity noise on the peak lasing frequency can be eliminated to first ord…
We theoretically investigate the effect of long-ranged dipole-dipole interaction (LRDDI) on a superradiant laser (SL). This effect is induced from the atom-photon interaction in the dissipation process. In the bad-cavity limit usually performed to initiate SL, we demonstrate that cavity photon number oscillates as an inter-particle distance of the atoms varies. Similarly the atom-atom coherence alternates with signs, showing critical transitions alternatively in SL operations. This suggests a complexity of the collective effect emerging in a large ensemble of atoms. Therefore this effect in a …
We investigate the collective decay dynamics of atoms with a generic multilevel structure (angular momenta $F\leftrightarrow F'$) coupled to two light modes of different polarization inside a cavity. In contrast to two-level atoms, we find that multilevel atoms can harbour eigenstates that are perfectly dark to cavity decay even within the subspace of permutationally symmetric states (collective Dicke manifold). The dark states arise from destructive interference between different internal transitions and are shown to be entangled. Remarkably, the superradiant decay of multilevel atoms can end…
Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien（维也纳量子科学与技术中心，原子研究所，维也纳工业大学）；Institute for Theoretical Physics, TU Wien（理论物理研究所，维也纳工业大学）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）
Superradiant phase transition represents an important quantum phenomenon that shows the collective excitations based on the coupling between atoms and cavity modes. The spin-orbit coupling is another quantum effect which induced from the interaction of the atom internal degrees of freedom and momentum of center-of-mass. In this work, we consider the cavity assisted dynamical spin-orbit coupling which comes from the combination of these two effects. It can induce a series of interesting quantum phenomena, such as the flat spectrum and the singularity of the excitation energy spectrum around the…
In cavity quantum electrodynamics (QED), the interaction between an atomic transition and the cavity field is measured by the vacuum Rabi frequency $Ω_0$. The analogous term "circuit QED" has been introduced for Josephson junctions, because superconducting circuits behave as artificial atoms coupled to the bosonic field of a resonator. In the regime with $Ω_0$ comparable to the two-level transition frequency, "superradiant" quantum phase transitions for the cavity vacuum have been predicted, e.g. within the Dicke model. Here, we prove that if the time-independent light-matter Hamiltonian is co…
The dynamics of the entanglement for coherent excitonic states in the system of two coupled large semiconductor quantum dots ($R/a_{B}\gg 1$) mediated by a single-mode cavity field is investigated. Maximally entangled coherent excitonic states can be generated by cavity field initially prepared in odd coherent state. The entanglement of the excitonic coherent states between two dots reaches maximum when no photon is detected in the cavity. The effects of the zero-temperature environment on the entanglement of excitonic coherent state are also studied using the concurrence for two subsystems of…
We experimentally study the relaxation oscillations and amplitude stability properties of an optical laser operating deep into the bad-cavity regime using a laser-cooled $^{87}$Rb Raman laser. By combining measurements of the laser light field with nondemolition measurements of the atomic populations, we infer the response of the gain medium represented by a collective atomic Bloch vector. The results are qualitatively explained with a simple model. Measurements and theory are extended to include the effect of intermediate repumping states on the closed-loop stability of the oscillator and the…
For the excitons in the quantum well placed within a leaky cavity, the quantum decoherence of a mesoscopically superposed states is investigated based on the factorization theory for quantum dissipation. It is found that the coherence of the exciton superposition states will decrease in an oscillating form when the cavity field interacting with the exciton is of the form of quasimode. The effect of the thermal cavity fields on the quantum decoherence of the superposition states of the exciton is studied and it is observed that the higher the temperature of the environment is, the shorter the d…
Stability of the Quantum Coherent Superradiant States in Relation to Exciton-Phonon Interactions and the Fundamental Soliton in Hybrid Perovskites
Ioffe Physical-Technical Institute, Russian Academy of Sciences（俄罗斯科学院列别杰夫物理技术研究所）；Tel Aviv University（特拉维夫大学）；Instituto de Alta Investigacion, Universidad de Tarapaca（塔拉帕卡大学高级研究院）；Institute for Advanced Study in Mathematics, Harbin Institute of Technology（哈尔滨工业大学数学高等研究院）；Suzhou Research Institute, Harbin Institute of Technology（哈尔滨工业大学苏州研究院）；Faculty of Sciences, Physics Department, Holon Institute of Technology（霍隆理工学院理学院物理系）
We study Einstein-Podolsky-Rosen (EPR) steering properties of quantum phases in the generalized Dicke model (GDM) generated by a cavity Bose-Einstein condensate (BEC) doped with a single impurity. It is shown that the normal and superradiant phases of the GDM exhibit much rich EPR steerability. In the normal phase, there exist one-way EPR steering from the cavity field (condensed atoms) to condensed atoms (the cavity field). In the superradiant phase, there is either one-way or two-way EPR steering for the cavity field and condensed atoms. It is found that the single impurity can act as a sing…
We consider a spinless ultracold Fermi gas tightly trapped along the axis of an optical resonator and transversely illuminated by a laser closely tuned to a resonator mode. At a certain threshold pump intensity the homogeneous gas density breaks a $\mathbf{Z}_2$ symmetry towards a spatially periodic order, which collectively scatters pump photons into the cavity. We show that this known self-ordering transition also occurs for low field seeking fermionic particles when the laser light is blue-detuned to an atomic transition. The emergent superradiant optical lattice in this case is homopolar a…
We theoretically investigate the quantum phase transition in the collective systems of qubits in a high-quality cavity, which is driven by a squeezed light. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase tr…
A new class of laser, which harnesses coherence in both light and atoms, is possible with the use of ultra-cold alkaline earth atoms trapped in an optical lattice inside an optical cavity. Different lasing regimes, including superradiance, superradiant and conventional lasing, are distinguished by the relative coherence stored in the atoms and in the cavity mode. We analyze the physics in two different experimentally achievable regions of the superradiant lasing regime. Our calculations confirm the narrow linewidth of superradiant lasing for the doubly forbidden clock transition ${}^3 P_0 \to …
We theoretically analyze superradiant emission of light from an ultracold gas of bosonic atoms confined in a bad cavity. A metastable dipolar transition of the atoms couples to the cavity field and is incoherently pumped, the mechanical effects of cavity-atom interactions tend to order the atoms in the periodic cavity potential. By means of a mean-field model we determine the conditions on the cavity parameters and pump rate that lead to the buildup of a stable macroscopic dipole emitting coherent light. We show that this occurs when the superradiant decay rate and the pump rate exceed thresho…
We study the resonant electronic excitation dynamics for ultracold atoms trapped in a deep optical lattice prepared in a Mott insulator state. Excitons in these artificial crystals are similar to Frenkel excitons in Noble atom or molecular crystals. They appear when the atomic excited state line width is smaller than the exciton band width generated by dipole-dipole coupling. When the atoms are placed within a cavity the electronic excitations and the quantized cavity mode get coupled. In the collective strong coupling regime excitations form two branches of cavity polaritons with Rabi splitti…
A steady-state superradiant laser can be used to generate ultranarrow-linewidth light, and thus has important applications in the fields of quantum information and precision metrology. However, the light produced by such a laser is still essentially classical. Here, we show that the introduction of a Rydberg medium into a cavity containing atoms with a narrow optical transition can lead to the steady-state superradiant emission of ultranarrow-linewidth $nonclassical$ light. The cavity nonlinearity induced by the Rydberg medium strongly modifies the superradiance threshold, and leads to a Mollo…
We study the two-dimensional Rydberg atom array in an optical cavity with help of the meanfield theory and the large-scale quantum Monte Carlo simulations. The strong dipole-dipole interactions between Rydberg atoms can make the system exhibit the crystal structure, and the coupling between two-level atom and cavity photon mode can result in the formation of the polariton. The interplay between them provides a rich quantum phase diagram including the Mott, solid-1/2, superradiant and superradiant solid phases. As the two-order co-existed phase, the superradiant solid phase breaks both translat…
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 polarisation. We find that the gauge choice controls the extent to which this polarisation is included as part of the radiative quantum subsystem and thereby determines the degree to which the abnormal phase is classed as…
Energy bands of electrons in a square lattice potential threaded by a uniform magnetic field exhibit a fractal structure known as the Hofstadter butterfly. Here we study a Fermi gas in a 2D optical lattice within a linear cavity with a tilt along the cavity axis. The hopping along the cavity axis is only induced by resonant Raman scattering of transverse pump light into a standing wave cavity mode. Choosing a suitable pump geometry allows to realize the Hofstadter-Harper model with a cavity-induced dynamical synthetic magnetic field, which appears at the onset of the superradiant phase transit…
We achieve the strong coupling regime between an ensemble of phosphorus donor spins in a highly enriched $^{28}$Si crystal and a 3D dielectric resonator. Spins were polarized beyond Boltzmann equilibrium using spin selective optical excitation of the no-phonon bound exciton transition resulting in $N$ = $3.6\cdot10^{13}$ unpaired spins in the ensemble. We observed a normal mode splitting of the spin ensemble-cavity polariton resonances of 2$g\sqrt{N}$ = 580 kHz (where each spin is coupled with strength $g$) in a cavity with a quality factor of 75,000 ($γ\ll κ\approx$ 60 kHz where $γ$ and $κ$ a…
The time evolution of entanglement for excitons in two quantum dots embedded in a single mode cavity is studied in a ``spin-boson'' regime. It is found that although with the dissipation from the boson mode, the excitons in the two quantum dots can be entangled by only modulating their energy bias $ε$ under the influence of external driving magnetic field. Initially, the two excitons are prepared in a pure separate state. When the time-dependent magnetic field is switched on, a highly entangled state is produced and maintained even in a very long time interval. The mechanism may be used to con…
A scheme of three-particle entanglement purification is presented in this work. The physical system undertaken for investigation is dot-like single quantum well excitons independently coupled through a single microcavity mode. The theoretical framework for the proposed scheme is based on the quantum jump approach for analyzing the progress of the trible-exciton entanglement as a series of conditional measurement has been taken on the cavity field state. We first investigate how cavity photon affects the purity of the double-exciton state and the purification efficiency in two-particle protocol…
We describe how quantum dot semiconductor cavity systems can be engineered to realize anisotropy-induced dipole-dipole coupling between orthogonal dipole states in a single quantum dot. Quantum dots in single-mode cavity structures as well as photonic crystal waveguides coupled to spin states or linearly polarized excitons are considered. We demonstrate pronounced dipole-dipole coupling to control the radiative decay rate of excitons and form pure entangled states in the long time limit. We investigate both field-free entanglement evolution and coherently pumped exciton regimes, and show how a…
Microtubules are biological protein polymers with critical and diverse functions. Their structures share some similarities with photosynthetic antenna complexes, particularly in the ordered arrangement of photoactive molecules with large transition dipole moments. As the role of photoexcitations in microtubules remains an open question, here we analyze tryptophan molecules, the amino acid building block of microtubules with the largest transition dipole strength. By taking their positions and dipole orientations from realistic models capable of reproducing tubulin experimental spectra, and usi…
We investigate the equilibrium behaviour of a superconducting circuit QED system containing a large number of artificial atoms. It is shown that the currently accepted standard description of circuit QED via an effective model fails in an important aspect: it predicts the possibility of a superradiant quantum phase transition, even though a full microscopic treatment reveals that a no-go theorem for such phase transitions known from cavity QED applies to circuit QED systems as well. We generalize the no-go theorem to the case of (artificial) atoms with many energy levels and thus make it more …
We experimentally and theoretically study the response of a superradiant or bad-cavity laser to an applied coherent drive. We observe two forms of synchronization (injection locking) between the superradiant ensemble and the applied drive: one attractive and one repulsive in nature. We explain the region of repulsion as arising from the higher three-dimensional description of the atomic spin state that stores the laser coherence in a superradiant laser, as opposed to a two-parameter description of the electric field in a traditional good-cavity laser. We derive a phase diagram of predicted beh…
Laser cooled and quantum degenerate atoms are widely being pursued as quantum simulators that may explain the behavior of strongly correlated material systems, and as the basis of today's most precise sensors. A key challenge towards these goals is to understand and control coherent interactions between the atoms. Here, we observe long-range exchange interactions mediated by an optical cavity, which manifest as tunable spin-spin interactions on the pseudo spin-1/2 system composed of the millihertz linewidth clock transition in strontium. We observe the so-called one axis twisting dynamics, the…
We propose a solid-state based superradiance laser which is almost insensitive to the cavity mirror vibration. Therefore, it can compete with the best frequency-stable local oscillators. The long coherence time and the large optical density of rare-earth-ions (REIs) doped solids are employed to find a regime to demonstrate a steady-state laser emission with linewidth smaller than the atomic decay rate. The experimental parameters are discussed and intracavity photon number and laser linewidth are calculated based on the mean-field theory. A procedure for measuring absolute laser linewidth is p…
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…
