The interaction of confined atoms with a single mode radiation field is the main subject in the theory of cavity quantum electrodynamics . The constraints imposed by the cavity on matter and radiation fields give rise to collective phenomena. One possible outcome is the enhanced and coherent spontaneous emission of photons by the atoms: the superradiance. As predicted by Dicke, conservation laws are essential in superradiance and are derived from the matter-interaction Hamiltonian . Here, we consider N two-level ultracold atoms interacting with a single mode bosonic field, in the Dicke Hamiltonian, and trapped inside a non-dissipative optical cavity . Numerical and analytical results derived from finite size regime indicate the matter–radiation coupling strength, λ , is insufficient to draw the complete picture of the system. Instead, they support the relevance of U ( 1 ) symmetry, which prompts the study of (i) particle and angular momentum conservation, (ii) the constraints imposed to correlation functions and (iii) the influence of symmetries in the system dynamics . Further exploring the U ( 1 ) and rotational symmetries permits a simple interpretation of antirotating contributions as spin–orbit operators. As application, we show two species of ultracold clouds develop interactions due to antirotating operators.
The interaction of confined atoms with a single mode radiation field is the main subject in the theory of cavity quantum electrodynamics . The constraints imposed by the cavity on matter and radiation fields give rise to collective phenomena. One possible outcome is the enhanced and coherent spontaneous emission of photons by the atoms: the superradiance. As predicted by Dicke, conservation laws are essential in superradiance and are derived from the matter-interaction Hamiltonian . Here, we consider N two-level ultracold atoms interacting with a single mode bosonic field, in the Dicke Hamiltonian, and trapped inside a non-dissipative optical cavity . Numerical and analytical results derived from finite size regime indicate the matter–radiation coupling strength, λ , is insufficient to draw the complete picture of the system. Instead, they support the relevance of U ( 1 ) symmetry, which prompts the study of (i) particle and angular momentum conservation, (ii) the constraints imposed to correlation functions and (iii) the influence of symmetries in the system dynamics . Further exploring the U ( 1 ) and rotational symmetries permits a simple interpretation of antirotating contributions as spin–orbit operators. As application, we show two species of ultracold clouds develop interactions due to antirotating operators.
Ultracold atomic gases loaded into optical cavities constitute one of the most versatile platforms for the study of out-of-equilibrium dynamics and quantum simulation of many- body systems. In this thesis, we explore these two possibilities, motivated by current state-of-the-art atom-cavity experiments, uncovering novel phenomena and opening up new theoretical and experimental avenues into the intriguing world of quantum many- body physics. First, we study a gas of ultracold atoms coupled to three optical resonators. We show that the inherent Z2 symmetries, associated with each atom-cavity coupling, can be combined into a global SO(3) rotational symmetry which can be spontaneously broken. We determine the phase diagram of the system, which shows the emergence and breaking of the continuous symmetries and displays first- and second-order phase transitions. We argue that by coupling the atoms equally to n different modes, it will in general be possible to generate a global SO(n) symmetry. Second, we investigate the dynamics of a spinor BEC inside an optical cavity. We focus on a two-component Dicke model with complex light-matter couplings, accounting for photon losses. We compute the steady-state phase diagram and find dynamical in- stabilities in the form of limit cycles, heralded by the presence of exceptional points and level attraction. We show that the instabilities are induced by dissipative processes that generate nonreciprocal couplings between the two collective spins. Lastly, we explore the dynamics of a BEC inside an optical cavity in the presence of an optical lattice. We derive an effective master equation by adiabatically eliminating the cavity field. In the bad-cavity regime, we find an infinite-temperature steady state, but with relaxation dynamics that can be highly nontrivial. For small hopping, the interplay between dissipation and strong interactions leads to an algebraic relaxation of the system, whereas for large hopping, the approach to the steady state is exponential. In the good- cavity regime, we show that the system allows for optical pumping between momentum modes, enabling cavity cooling.
Present-day experiments have started to couple traditional simulations of ultracold atom experiments with quantum light-fields in cavities. This has provided a wealth of op- portunities to enlarge the number of interaction potentials: cavity mediated long-range interactions compete with kinetic energies, longitudinal fields, short-ranged collisional or magnetic spin-spin interactions. The intracavity many-body lattice models often have to be maintained far from equilibrium through the presence of external driving lasers that help to boost and engineer the various interaction potentials. The steady influx of energy is compensated by a steady stream of energy out of the atom-cavity system for example by photon losses or atomic spontaneous emission. Several experiments have demonstrated that such environments can give rise to new competing quantum phases. \nBut this long-standing ambition to push for models with tailorable interaction potentials can bring with it also considerable challenges in their theoretical description, since sponta- neous symmetry breaking transitions in many body lattice systems coupled to dynamical light-fields with single-photon character occur in the presence of drive and dissipation for the photonic force carriers. This clearly calls for model systems where the above men- tioned interplay of interactions, drive, dissipation and cooperative many-body behaviour can be theoretically studied to provide simple, experimentally verifiable predictions. \nThe Dicke model is, through its simplicity (an exactly solved ferromagnet with infinite range atom-atom interactions mediated by a single cavity mode), an exceptionally well- suited candidate. As the generic model for atom-light interactions, it has been experimen- tally realized in a variety of modern quantum optical systems, highlighting its relevance for present-day research. The Dicke model is also highly versatile itself. It has been extended into the dissipative realm, was promoted to account for multiple optical light modes and was used to describe multiple, coupled single-mode cavity structures. It was adapted to treat spin-selective coupling to a cavity to describe superradiance phase tran- sitions in multi-level atomic systems. Moreover, it was realised in electronic circuits where the dipole coupling of real atoms to single mode fields is replaced by a capacitive cou- pling of artificial atoms to a resonator mode. This illustrates that the Dicke model and its extended variants are ’future-proof’ and continue to be of relevance for fundamental light-matter interactions and for driven-dissipative phase transitions. \nIn this thesis, we investigate magnetic phase transitions in driven-dissipative atomic en- sembles interacting with quantum light. We present three research projects on variants of cooperative radiation of an ensemble of laser driven two-level atoms in a single mode optical cavity, as described by the Dicke model. \nThroughout the chapters 2,3 and 4 that contain the main body of research of this thesis, we investigate phase transitions between non-equilibrium stationary states in engineered quantum-optical systems each of which extends the conventional Dicke model physics. As a starting point, we map the quantum equations of motion onto a set of semiclassical nonlinear stochastic equations and analyse their stationary states and instabilities with master equations for atomic spin and photon mean-field amplitudes. These are used to obtain experimentally relevant parameters such as critical atom-light couplings for phase transitions, phase diagrams and properties of stationary non-equilibrium states in addition to cavity output spectra that identify the imprint of magnetic correlations in the light-field. \nIn chapter 2, we help resolve a discrepancy between earlier experimental investigations of the critical atom-light coupling strength for the superradiance transition in the Dicke model: higher external pumping strengths than theoretically predicted were needed to observe a coherent, superradiant state of the light field in an optical cavity. By including incoherent spontaneous emission of atomic excitations, we extend the dissipative Dicke model to a two loss channel variant containing both photon leakage and atomic decay that reproduces the experimentally observed critical atom-light coupling. \nRecent experiments have started to interface quantum many body lattice models with coherent cavity fields, thereby allowing to realize new quantum phases through competing atom-cavity and atom-atom interactions. In chapter 3, we consider a simplified model for such a set-up where a single quantized mode of the light-field interacts with an ensemble of Rydberg-dressed atoms inside a high finesse optical cavity. This model provides a base case for further studies of quantum magnets in optical cavities. At the heart of this model is a competition of short- (dipolar atom-atom) and long-range (atom-light) interactions at the Hamiltonian level in the presence of both spontaneous emission and photon leak- age through the cavity mirrors. We show that different magnetic phases can coexist with coherent atomic radiation and provide clear experimental signatures to identify the mag- netic structure and intra-cavity dynamics. We suggest an experimental level-scheme for a quantum optical implementation of our model. \nIn chapter 4 we consider a generic, collective decay for many-body excitations in the paradigmatic Dicke model. This extension drastically enriches the dynamics as it induces a bicritical point and a bistable regime dominated by true non-equilibrium fluctuations that induce a dissipative first-order phase transition that can only be resolved by including finite fluctuation corrections with the help of stochastic Langevin equations. We investigate the hysteretic response to time-dependent ramps of the atom-light coupling. Discontinuous first-order phase transitions where metastable states coexist in a hysteresis domain have been investigated in recent dissipative quantum-optical experiments. We review noise- activation far from thermal equilibrium in chapter 5.
I introduce and analyze chiral light-matter interaction in the ultrastrong coupling limit where the rotating-wave approximation cannot be made. Within this limit, a two-level system with a circularly polarized transition dipole interacts with a copolarized mode through rotating-wave terms. However, the counterrotating terms allow the two-level system to couple to a counterpolarized mode with the same coupling strength, i.e., one that is completely decoupled within the rotating-wave approximation. Although such a Hamiltonian is not particle number conserving, the conservation of angular momentum generates a U(1) symmetry which allows constructing an ansatz. The eigenstates and dynamics of this novel model are computed for single-cavity interactions and for a many-mode system. The form of the ansatz provides significant analytic insight into the physics of the ground state and the dynamics; e.g., it indicates that the ground states are two-mode squeezed. This work has significant implications for engineering light-matter interaction and novel quantum many-body dynamics beyond the rotating-wave approximation.
In this dissertation we focused on two topics: 1. atomic cooperative effect, including superradiance, subradiance and collective Lamb shift in an atomic ensemble; 2. novel topological effect in quantum optics system, such as Haldane model, synthetic magnetic field in superradiance lattice and synthetic spin-orbit interaction in Fock-state lattices. \n\nIn the first part, we start from the Dicke state, an N-particle atomic ensemble excited by a single photon. Due to the interaction of the atoms with a continuum of vacuum modes, the Dicke state has a larger decay rate compared with an isolated atom, termed the single photon superradiance. In the “opposite” case, the single-photon subradiance state does not decay because of the destructive interference of the atomic transitions. We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance in an extended ensemble. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.\n\nIn the second part, we start from introducing the concepts, methods, and models from quantum optics or condensed matter physics. They include the timed-Dicke states, electromagnetically induced transparency, coupled wave equations, tight-binding model, band theory, Floquet theory, superradiance lattice, integer quantum Hall effect, Haldane model, etc.. Based upon these tools, we study three topological quantum optics systems: (i) a Haldane model with in situ tunable topological properties in a two-dimensional momentumspace superradiance lattice composed of timed Dicke states in electromagnetically induced transparency; (ii) a spin-orbit coupled Fock-state lattice, which introduce a novel quantum operation to generate mesoscopic superposition states, e.g., the NOON states and cat states; (iii) a synthetic magnetic field created in a quasi one dimensional superradiance lattice, which is predicted to be observed in thermal vapours of alkali atoms instead of only in cold atoms (as in previous experiments). This study aims to provide a novel, highly tunable platform simulating exotic phenomena in condensed matter physics and offers a basis of topological quantum optics and novel photonic devices.
Abstract Simulating cavity quantum electrodynamics in synthetic platforms offers a route to studying light--matter physics without real photons. We reassess the frequently invoked analogy between harmonically trapped, spin--orbit-coupled atoms and the quantum Rabi and Dicke models, with particular emphasis on squeezing and entanglement. A single non-interacting atom realizes the quantum Rabi Hamiltonian exactly, up to elementary spin and phase-space rotations. For N non-interacting atoms, however, the center-of-mass mode is only one member of a complete orthonormal set containing N−1 relative modes. We prove that, after all modes are included, the spin--spin terms generated by the collective mode cancel exactly against those generated by the relative modes. Equivalently, the original Hamiltonian is a sum of independent one-particle Hamiltonians and therefore cannot create interparticle entanglement from a separable state. Contact interactions invalidate this cancellation but do not remove the relative modes or turn the exact many-body Hamiltonian into a Dicke model. A one-mode Dicke description can arise only as a controlled low-energy approximation after all relevant relative excitations have been shown to be spectrally suppressed. We discuss this distinction together with experimental scales, finite temperature, and possible mode-selection strategies. We also distinguish the single-particle interference underlying density fringes from the interaction-stabilized stripe supersolid observed in many-body condensates.
Strong and ultra-strong light-matter coupling are remarkable phenomena of quantum electrodynamics arising when a matter excitation interacts so strongly with the electromagnetic field that the two systems cannot be distinguished as in usual perturbation theory. This is generally achieved by coupling an excitation with large oscillator strength to the confined electromagnetic mode of an optical microcavity. In this work we report on a phenomenon of non-perturbative spontaneous emission taking place in the absence of optical confinement, when a collective electronic excitation superradiantly decays into free space radiation. By using a quantum model based on the input-output formalism, we calculate the linear optical properties of a dense electron gas displaying superradiant excitations. We show that the commonly used rotating-wave and Markov approximations yield unphysical results when the radiative broadening is comparable to the matter excitation energy, i.e. in the ultra-strong coupling regime. Our formalism also allows computing the electron gas thermal emission, showing that Kirchhoff's law applies in all the regimes of light-matter interaction.