An ensemble of atoms coupled to a high finesse optical cavity is an ideal test bed for the study of the cooperative behaviour of atom-photon systems. Dicke showed that an ensemble of excited atoms coupled to a light field interacts with the light in a collective and coherent fashion leading to the emission of highly directional spontaneous emission whose intensity scales with the square of the number of atoms, a phenomenon known as superradiance. \nThis thesis describes the build of an experiment to study cooperative atom-photon interactions in a ring cavity. Particular focus is given to the cavities used in the experiment. Firstly a transfer cavity used for transferring stability to off-resonant lasers in the experiment, this was developed with the capability of exploiting Gouy phase degeneracies to produce tightly spaced frequency discriminants to be used as lock points. Secondly the ring cavity for the experiment which is atypical in its design allowing for bidirectional probing of the cavity mode and dynamic manipulation of the intra-cavity optical lattice. An intra-cavity MOT was produced and collective strong coupling was observed in the cavity with an Neff=6400 atoms coupled to the cavity mode.
An ensemble of atoms coupled to a high finesse optical cavity is an ideal test bed for the study of the cooperative behaviour of atom-photon systems. Dicke showed that an ensemble of excited atoms coupled to a light field interacts with the light in a collective and coherent fashion leading to the emission of highly directional spontaneous emission whose intensity scales with the square of the number of atoms, a phenomenon known as superradiance. \nThis thesis describes the build of an experiment to study cooperative atom-photon interactions in a ring cavity. Particular focus is given to the cavities used in the experiment. Firstly a transfer cavity used for transferring stability to off-resonant lasers in the experiment, this was developed with the capability of exploiting Gouy phase degeneracies to produce tightly spaced frequency discriminants to be used as lock points. Secondly the ring cavity for the experiment which is atypical in its design allowing for bidirectional probing of the cavity mode and dynamic manipulation of the intra-cavity optical lattice. An intra-cavity MOT was produced and collective strong coupling was observed in the cavity with an Neff=6400 atoms coupled to the cavity mode.
This thesis describes an experiment which studies a cloud of magneto-optically trapped potassium-39 atoms inside an optical ring cavity. The potassium atoms are firstly cooled in a two-dimensional magneto-optical trap (MOT) and are then transferred into a three dimensional MOT which overlaps with the cavity mode. In this thesis, the optimisation of the MOT systems and the characterisation and construction of the optical ring cavity are discussed. After exploring these two systems independently, the two systems are then coupled together to provide an atom-cavity system, which exhibits collective strong coupling. The system is shown to exhibit normal-mode splitting, with a collective Rabi splitting of G = 2π (6.25±0.50)MHz, corresponding to (4.7±0.6) x 10³ atoms in the cavity. Whilst collective strong coupling has been achieved before in other experiments, we believe this is the first experiment to achieve this with potassium. \n \nThe next goal in the experiment is to control the group refractive index of the atoms inside the cavity. The modification of the group index using electromagnetically-induced transparency (EIT) on hot atoms inside a vapour cell has already been previously demonstrated by this experiment; and using the same laser system we aim to demonstrate EIT on the cold intra-cavity atoms as well. Gain mechanisms could also be used to create a ring laser with a controllable group index. These techniques could lead to a range of applications such as enhanced-sensitivity laser ring gyroscopes and active optical clocks. \n \n
We present experiments on ensemble cavity quantum electrodynamics with cold potassium atoms in a high-finesse ring cavity.Potassium-39 atoms are cooled in a two-dimensional magneto-optical trap and transferred to a three-dimensional trap which intersects the cavity mode.The apparatus is described in detail and the first observations of strong coupling with potassium atoms are presented.Collective strong coupling of atoms and light is demonstrated via the splitting of the cavity transmission spectrum and the avoided crossing of the normal modes.
Coupling between quantum emitters and modes of light is foundational to studies of quantum systems. Coherent interactions between matter and light have greatly advanced the development of quantum technologies. When an ensemble of atoms interacts with light that is confined within a cavity---a resonator for photons---light also mediates atom-atom interactions, leading to collective phenomena that cannot be extrapolated from microscopic behaviors. Understanding how interactions among quantum particles lead to macroscopic phenomena, such as phase transitions and breaking of symmetries, remains a challenge in modern physics. In this dissertation, I present results addressing this challenge in the context of mesoscopic arrays of optical-tweezer-trapped atoms interfaced with a high-finesse optical cavity. In particular, the physics we investigate arises from the collective scattering of light. Utilizing the ability to place atoms with nanometer-scale precision, we engineer superradiant and subradiant states, where control over interference of the emission from multiple atoms leads to collectively enhanced or suppressed amounts of scattered light. Building on this work, we investigate the emergence of optomechanical self-organization, mediated by superradiance in the cavity electromagnetic field. By coupling atoms to the same cavity mode, the atoms exert forces on one another through the exchange of photons, leading them to autonomously order themselves spatially. We characterize mesoscopic fluctuations and their effect on symmetry-breaking dynamics associated with self-organization. Finally, we extend this framework to theoretically investigate how the phase of the atom-cavity coupling can be altered to generate higher symmetries. Our analysis reveals first-order phase transitions and instabilities induced by non-reciprocal forces. Altogether, this work establishes a path towards realizing mesoscopic systems of complex phases of matter in cavity quantum electrodynamics with unprecedented programmability.
The electromagnetic mode density of the vacuum can be dramatically \nmodified by the presence of an optical resonator. In the strong coupling \nregime, spontaneous emission in a cavity becomes a reversible process and \nthe intracavity photon number undergoes Rabi oscillations. We load up \nto 200x10^3 ^133Cs atoms into a nearly confocal lossy cavity and reach the \ncollective strong coupling regime. Normal mode splitting, the hallmark of this regime, is observed and cooperativities up to C_coll = (186±5) are measured. In a second experiment we investigate for the first time \nthe multi-mode character of the coupled cavity-atom system. In a confocal \ncavity the higher-order transverse cavity modes are degenerate in frequency and accessible to the spontaneous emission of the atomic ensemble. \nWe observe an increase of the coupling constant measured via modal decomposed transmission analysis, which could be attributed to \nthe presence of the higher-order modes. Normal mode splitting proportional to the square root of the atom number was visible for all of the \ndifferent mode components. Furthermore, we observe a redistribution of the relative weights in the modal transmission composition, which scales with the atom number in the cavity mode. \nIn a second set of experiments, ^87Rb atoms were loaded into a dissipative \nlin ⊥ lin lattice. By driving the lattice with a biharmonic force, transport can be observed when the systems symmetries are broken: the so called ratchet effect. Research in this area is concerned with the appearance \nof current reversals. We were able to identify dissipation related symmetry breaking as the underlying cause of an observed current reversal, which occurs as a function of the driving frequency. Furthermore, in a \nsecond experiment, we use the ratchet effect as a probe of the optical potential depths. We show that an oscillating force with a frequency far above any other system-inherent timescale, can be used to renormalize \nthe optical potential. The ^87Rb atoms experience an average position dependent force, which becomes controllable over the amplitude of the \napplied driving.
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.
This thesis focuses on the construction and development of an experiment to study cold potassium atoms in an optical ring cavity. Firstly we load a potassium-39 magneto optical trap (MOT) inside the ring cavity. To achieve this a laser system, rectangular magnetic coils system and vacuum system are designed and constructed. To stabilise the laser system, a detailed study of various potassium spectroscopy techniques is undertaken and the reference laser is suitably locked to the magnetically induced spectroscopy. We load an ensemble of 10\\(^5\\) potassium atoms inside the ring cavity mode and study their collective strong coupling with the cavity field. In the collective strong coupling regime, the photons are coherently exchanged between the atomic ensemble and cavity field. This rate of exchange is determined by the singlephoton Rabi frequency `2\\(g\\)' which must be larger than the cavity field decay rate `2\\(k\\)' and atomic spontaneous emission rate `2\\(ᵧ\\)'. As a result of this coupling, the peak in the cavity transmission signal undergoes a splitting known as `vacuum Rabi splitting' (or `normal mode splitting'). The vacuum Rabi splitting has been realised and measured to be ~ 2\\(π\\). 18 MHz in our system.