Ramsey spectroscopy in large, dense ensembles of ultra-cold atoms trapped in optical lattices suffers from dipole-dipole interaction induced shifts and collective superradiance limiting its precision and accuracy. We propose a novel geometry implementing fast signal readout with minimal heating for large atom numbers at lower densities via an optical cavity operated in the weak single atom but strong collective coupling regime. The key idea is controlled collective transverse $π/2$-excitation of the atoms to prepare a macroscopic collective spin protected from cavity superradiance. This requires that the two halves of the atomic ensemble are coupled to the cavity mode with opposite phase, which is naturally realized for a homogeneously filled volume covering odd and even sites of the cavity mode along the cavity axis. The origin of the superior precision can be traced back to destructive interference among sub-ensembles in the complex nonlinear collective atom field dynamics. In the same configuration we find surprising regular self-pulsing of the cavity output for suitable continuous illumination. Our simulations for large atom numbers employing a cumulant expansion are qualitatively confirmed by a full quantum treatment of smaller ensembles.
A superfluid atomic gas is prepared inside an optical resonator with an ultra-narrow band width on the order of the single photon recoil energy. When a monochromatic off-resonant laser beam irradiates the atoms, above a critical intensity the cavity emits superradiant light pulses with a duration on the order of its photon storage time. The atoms are collectively scattered into coherent superpositions of discrete momentum states, which can be precisely controlled by adjusting the cavity resonance frequency. With appropriate pulse sequences the entire atomic sample can be collectively accelerat…
Following the experimental realization of Dicke superradiance in Bose gases coupled to cavity light fields, we investigate the behavior of ultra cold fermions in a transversely pumped cavity. We focus on the equilibrium phase diagram of spinless fermions coupled to a single cavity mode and establish a zero temperature transition to a superradiant state. In contrast to the bosonic case, Pauli blocking leads to lattice commensuration effects that influence self-organization in the cavity light field. This includes a sequence of discontinuous transitions with increasing atomic density and tricrit…
The Dicke model and the superradiance of two-level systems in a radiation field have many applications. Recently, a Dicke quantum phase transition has been realized with a Bose-Einstein condensate in a cavity. We numerically solve the many-body Schrödinger equation and study correlations in the ground state of interacting bosons in a cavity as a function of the strength of a driving laser. Beyond a critical strength, the bosons occupy multiple modes macroscopically while remaining superradiant. This fragmented superradiance can be detected by analyzing the variance of single-shot measurements.
In this letter we consider spinless Fermi gases placed inside a cavity and study the critical strength of pumping field for driving a superradiance transition. We emphasize that Fermi surface nesting effect strongly enhances 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 strongly enhanced, because of which a much smaller (sometime even vanishingly small) critical pumping field strength can lead to superradiance. This leads to interes…
We consider an ensemble of ultracold bosonic atoms within a near-planar cavity, driven by a far detuned laser whose phase is modulated at a frequency comparable to the transverse cavity mode spacing. We show that a strong, dispersive atom-photon coupling can be reached for many transverse cavity modes at once. The resulting Floquet polaritons involve a superposition of a set of cavity modes with a density excitation of the atomic cloud. The mutual interactions between these modes lead to distinct avoided crossings between the polaritons. Increasing the laser drive intensity, a low-lying multim…
Atom-Molecule Superradiance and Entanglement with Cavity-Mediated Three-Body Interactions
State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系、低维量子物理国家重点实验室）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭恒武教育与研究中心）
The quantum dynamics of the electromagnetic light mode of an optical cavity filled with a coherently driven Fermi gas of ultracold atoms strongly depends on geometry of the Fermi surface. Superradiant light generation and self-organization of the atoms can be achieved at low pumping threshold due to resonant atom-photon Umklapp processes, where the fermions are scattered from one side of the Fermi surface to the other by exchanging photon momenta. The cavity spectrum exhibits sidebands, that, despite strong atom-light coupling and cavity decay, retain narrow linewidth, due to absorptionless tr…
Cavity quantum electrodynamics (CQED) plays an elegant role of studying strong coupling between light and matter. However, a non-mechanical, direct and dynamical control of the used mirrors is still unavailable. Here we theoretically investigate a novel type of dynamically controllable cavity composed of two atomic mirrors. Based on the electromagnetically induced transparency (EIT), the reflectance of atomic mirror is highly controllable through its dispersive properties by varying the intensity of applied coupling fields or the optical depth of atomic media. To demonstrate the uniqueness of …
We study the dynamics of two ensembles of atoms (or equivalently, atomic clocks) coupled to a bad cavity and pumped incoherently by a Raman laser. Our main result is the nonequilibrium phase diagram for this experimental setup in terms of two parameters - detuning between the clocks and the repump rate. There are three main phases - trivial steady state (Phase I), where all atoms are maximally pumped, nontrivial steady state corresponding to monochromatic superradiance (Phase II), and amplitude-modulated superradiance (Phase III). Phases I and II are fixed points of the mean-field dynamics, wh…
The spontaneously broken of translational symmetry is usually due to the competition between local interactions and long-range interactions. However, in this paper, we show how a crystalline order can be generated by the competition between local interaction and long-range correlation by frustration. Here we propose a positive hopping Bose Hubbard model on triangle lattices with a pair creation term which comes from frustrated linked cavity arrays with degenerate quantum gases in them. We find by increasing the strength of pair creation term against local interaction strength, two kinds of den…
We investigate synthesis of a hyperfine spin lattice in an atomic Bose-Einstein condensate, with two hyperfine spin components, inside a one-dimensional high-finesse optical cavity, using off-resonant superradiant Raman scattering. Spatio-temporal evolution of the relative population of the hyperfine spin modes is examined numerically by solving the coupled cavity-condensate mean field equations in the dispersive regime. We find, analytically and numerically, that beyond a certain threshold of the transverse laser pump, Raman superradiance and self-organization of the hyperfine spin components…
We consider laser-pumped one-dimensional two-component bosons in a parabolic trap embedded in a high-finesse optical cavity. Above a threshold pump power, the photons that populate the cavity modify the effective atom trap and mediate a coupling between the two components of the Bose-Einstein condensate. We calculate the ground state of the laser-pumped system and find different stages of self-organization depending on the power of the laser. The modified potential and the laser-mediated coupling between the atomic components give rise to rich many-body physics: an increase of the pump power t…
Parametrically Driven Superradiance of an Interacting Tavis-Cummings Model
University of Science and Technology of China（中国科学技术大学）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）；CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China（中国科学院量子信息与量子物理卓越创新中心）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；Anhui Center for Fundamental Sciences in Theoretical Physics, University of Science and Technology of China（中国科学技术大学安徽理论物理基础科学中心）
We study fermions that are gauge-coupled to a cavity mode via Raman-assisted hopping in a one dimensional lattice. For an infinite lattice, we find a superradiant phase with infinitesimal pumping threshold which induces a directed particle flow. We explore the fate of this flow in a finite lattice with boundaries, studying the non-equilibrium dynamics including fluctuation effects. The short time dynamics is dominated by superradiance, while the long time behaviour is governed by cavity fluctuations. We show that the steady state in the finite lattice is not unique, and can be understood in te…
We predict the existence of a topological superradiant state in a two-component degenerate Fermi gas in a cavity. The superradiant light generation in the transversely driven cavity mode induces a cavity-assisted spin-orbit coupling in the system and opens a bulk gap at half-filling. This mechanism can simultaneously drive a topological phase transition in the system, yielding a topological superradiant phase. We map out the steady-state phase diagram of the system in the presence of an effective Zeeman field, and identify a critical quadracritical point beyond which the topological and the co…
We study ensembles of Rydberg atoms in a confined electromagnetic environment such as provided by a microwave cavity. The competition between standard free space Ising type and cavity-mediated interactions leads to the emergence of different regimes where the particle-particle couplings range from the typical van der Waals $r^{-6}$ behavior to $r^{-3}$ and to $r$-independence. We apply a Ramsey spectroscopic technique to map the two-body interactions into a characteristic signal such as intensity and contrast decay curves. As opposed to previous treatments requiring high-densities for consider…
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 atomic 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 (SR) transition, here both the Solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by the large scale quantum Monte Carlo simulations.
Recently the ETH group has reported an experiment on superradiant transition of a Bose condensate in two crossed beam cavities. The surprise is that 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 letter 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 the ETH experime…
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 …
Atoms in transversely pumped optical cavities "self-organize" by forming a density wave and emitting superradiantly into the cavity mode(s). For a single-mode cavity, the properties of this self-organization transition are well characterized both theoretically and experimentally. Here, we explore the self-organization of a Bose-Einstein condensate in the presence of two cavity modes---a system that was recently experimentally realized [Leonard \emph{et al.}, \emph{Nature} {\bf 543}, 87 (2017)]. We argue that this system can exhibit a "vestigially ordered" phase in which neither cavity mode exh…
We investigate the nonlinear light-matter interaction of a Bose-Einstein condensate trapped in an external periodic potential inside an optical cavity which is weakly coupled to vacuum radiation modes and driven by a transverse pump field. Based on a generalized Bose-Hubbard model which incorporates a single cavity mode, we include the collective backaction of the atoms on the cavity light field and determine the nonequilibrium quantum phases within the nonperturbative bosonic dynamical mean-field theory.With the system parameters adapted to recent experiments, we find a quantum phase transiti…
Disorder-Induced Enhancement of Fermionic Superradiance
CNR-INO（意大利国家研究委员会光学研究所）；University of Trento（特伦托大学）；INFN-TIFPA（意大利国家核物理研究所-特伦托基础物理与应用研究所）；Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）
We theoretically investigate the generation of atom-light entanglement via Raman superradiance in an optical cavity, and show how this can be used to enhance the sensitivity of atom interferometry. We model a realistic optical cavity, and show that by careful temporal shaping of the optical local oscillator used to measure the light emitted from the cavity, information in the optical mode can be combined with the signal from the atom interferometer to reduce the quantum noise, and thus increase the sensitivity. It was found in Phys. Rev. Lett. 110, 053002 (2013) that an atomic `seed' was requi…
Ultranarrow-linewidth atoms coupled to a lossy optical cavity mode synchronize, i.e. develop correlations, and exhibit steady-state superradiance when continuously repumped. This type of system displays rich collective physics and promises metrological applications. These features inspire us to investigate if analogous spin synchronization is possible in a different platform that is one of the most robust and controllable experimental testbeds currently available: ion-trap systems. We design a system with a primary and secondary species of ions that share a common set of normal modes of vibrat…
We consider ultracold atoms inside a ring optical cavity that supports a single plane-wave mode. The cavity field, together with an external coherent laser field, drives a two-photon Raman transition between two internal pseudo-spin states of the atom. This gives rise to an effective coupling between atom's pseudo-spin and external center-of-mass (COM) motion. For the case of a single atom inside the cavity, We show how the spin-orbit coupling modifies the static and dynamic properties of the Jaynes-Cummings (JC) model. In the case of many atoms in thermodynamic limit, we show that the spin-or…
Tuning Density and Spin Ordering of Degenerate Fermi Gases in an Optical Cavity
College of Physics and Energy, Fujian Normal University（福建师范大学物理与能源学院）；Fujian Provincial Key Laboratory of Quantum Manipulation and New Energy Materials（福建省量子调控与新能源材料重点实验室）；Fujian Provincial Engineering Technology Research Center of Solar Energy Conversion and Energy Storage（福建省太阳能转换与储能工程技术研究中心）
We study the far-from-equilibrium statistical mechanics of periodically driven fermionic atoms in a lossy optical resonator. We show that the interplay of the Fermi surface with cavity losses leads to sub-natural cavity linewidth narrowing, squeezed light, and out-of-equilibrium quantum statistics of the atoms. Adapting the Keldysh approach, we set-up and solve a quantum kinetic Boltzmann equation in a systematic $1/N$ expansion with $N$ the number of atoms. In the strict thermodynamic limit $N,V\rightarrow \infty$, $N/V=\text{const.}$ we find the atoms (fermions or bosons) remain immune again…
We consider a two-dimensional homogeneous ensemble of cold bosonic atoms loaded inside two optical cavities and pumped by a far-detuned external laser field. We examine the conditions for these atoms to self-organize into triangular and honeycomb lattices as a result of superradiance. By collectively scattering the pump photons, the atoms feed the initially empty cavity modes. As a result, the superposition of the pump and cavity fields creates a space-periodic light-shift external potential and atoms self-organize into the potential wells of this optical lattice. Depending on the phase of the…
Recent experiments on Bose--Einstein condensates in optical cavities have reported a quantum phase transition to a coherent state of the matter-light system -- superradiance. The time dependent nature of these experiments demands consideration of collective dynamics. Here we establish a rich phase diagram, accessible by quench experiments, with distinct regimes of dynamics separated by non-equilibrium phase transitions. We include the key effects of cavity leakage and the back-reaction of the cavity field on the condensate. Proximity to some of these phase boundaries results in critical slowin…
