A cold gas of polarizable particles moving in the optical potential of a standing wave high finesse optical resonator acts as a dynamic refractive index. For a sufficiently strong cavity pump the optical forces generated by the intra cavity field perturb the particles phase space distribution, which shifts the optical resonance frequency and induces a nonlinear optical response. By help of the corresponding Vlasov equation we predict that beyond the known phenomenon of optical bi-stability one finds regions in parameter space, where no stable stationary solution exists. The atom field dynamics then exhibits oscillatory solutions converging to stable limit cycles of the system. The linearized analytical predictions agree well with corresponding numerical solutions of the full time dependent equations and first experimental observation in both cases.
A cold gas of polarizable particles moving in the optical potential of a standing wave high finesse optical resonator acts as a dynamic refractive index. For a sufficiently strong cavity pump the optical forces generated by the intra cavity field perturb the particles phase space distribution, which shifts the optical resonance frequency and induces a nonlinear optical response. By help of the corresponding Vlasov equation we predict that beyond the known phenomenon of optical bi-stability one finds regions in parameter space, where no stable stationary solution exists. The atom field dynamics then exhibits oscillatory solutions converging to stable limit cycles of the system. The linearized analytical predictions agree well with corresponding numerical solutions of the full time dependent equations and first experimental observation in both cases.
We investigate a paradigm example of cavity quantum electrodynamics with many body systems: an ultracold atomic gas inside a pumped optical resonator, confined by the mechanical potential emerging from the cavity-field spatial mode structure. When the optical potential is sufficiently deep, the atomic gas is in the Mott-insulator (MI) state as in open space. Inside the cavity, however, the potential depends on the atomic distribution, which determines the refractive index of the medium, thus altering the intracavity-field amplitude. We derive the effective Bose–Hubbard model describing the physics of the system in one-dimension and study the crossover between the superfluid-MI quantum states. We predict the existence of overlapping stability regions corresponding to competing insulator-like states. Bistable behavior, controlled by the pump intensity, is encountered in the vicinity of the shifted cavity resonance.
This is a review of state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the backaction of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is nonconservative and in general enables cooling and confining the motion of polarizable particles. In addition the emitted cavity field allows for real-time monitoring of the particle's position with minimal perturbation up to subwavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides the correlated motion of distant particles, one finds critical behavior and nonequilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum-degenerate gases inside optical resonators can be used to emulate optomechanics as well as novel quantum phases such as supersolids and spin glasses. Nonequilibrium quantum phase transitions as predicted by, e.g., the Dicke Hamiltonian can be controlled and explored in real time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for nondestructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems.
Ultracold atoms in an optical lattice Bloch oscillate when subject to a constant force. In the first work presented in this thesis we have theoretically studied the scenario where the optical lattice potential is provided by the electric field inside an optical cavity. The coherent atom-light interaction in a cavity gives rise to a backaction effect on the light field which can modify the intracavity field amplitude and phase. In our first treatment of this problem we model the cavity light field and atoms by classical fields and solve the coupled atom-light equations of motion. As a result, we find that the amplitude and phase of the transmitted light field is modulated at the Bloch frequency. Remarkably, the Bloch frequency itself is not modified by the backaction. Thus the transmitted light field can be used to observe the oscillations continuously, allowing high-precision measurement with small clouds of atoms. In the second problem presented in this thesis, we explore the band structure of the steady state solutions of the atom-cavity system. A crucial first step towards determining the band structure is the identification of an energy functional that describes the coupled atom-light system. Although, we do not include direct atom-atom interactions in our models, the coupling of the atoms to the single mode light field of the cavity introduces an effective mutual interaction which is correctly taken into account by the energy functional we introduce. Corresponding to each point in the band there exists a steady state light field associated with an average cavity photon number. The dispersive nonlinear atom-light interaction can lead to bistable solutions for this intracavity photon number. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (non-cavity) optical lattices. However, in our case the nonlinearity derives from the cavity backaction rather than from direct interatomic interactions. We find both bi- and tri-stable regimes associated with the lowest band, and show that the multistability we observe can be analysed in terms of swallowtail catastrophes. Dynamic and energetic stability of the meanfield solutions is also studied, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the band structure can lead to a breakdown in adiabaticity during Bloch oscillations as the entire band is sampled during the dynamics. We therefore use the insight gleaned from this work in choosing parameters for the Bloch oscillation measurement proposal presented in the rest of the thesis. In the third work presented in the thesis, we go beyond the mean field description and consider effects of the quantised nature of the light and atomic fields. The cavity light field is always in contact with external electromagnetic fields through the partially transmissive mirrors. This coupling to the external modes enters as quantum noise in the dynamics of the intracavity field and can also be viewed as a manifestation of quantum measurement backaction corresponding to the continuous observation of the transmitted light field. We solve the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical meanfields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio as well as heating effects. One of the hurdles we overcome along the way is the proper treatment of fluctuations about time-dependent meanfields in the context of cold atom cavity-QED.
Abstract Atoms in high-finesse optical resonators interact via the photons they multiply scatter into the cavity modes. The dynamics is characterized by dispersive and dissipative optomechanical long-range forces, which are mediated by the cavity photons, and exhibits a steady state for certain parameter regimes. In standing-wave cavities the atoms can form stable spatial gratings. Moreover, their asymptotic distribution is a Maxwell–Boltzmann whose effective temperature is controlled by the laser parameters. In this work we show that in a two-mode standing-wave cavity the stationary state possesses the same properties and phases of the generalized Hamiltonian mean field model in the canonical ensemble. This model has three equilibrium phases: a paramagnetic, a nematic, and a ferromagnetic one, which here correspond to different spatial orders of the atomic gas and can be detected by means of the light emitted by the cavities. We further discuss perspectives for investigating in this setup the ensemble inequivalence predicted for the generalized Hamiltonian mean field model.
Polarizable particles trapped in a resonator-sustained optical-lattice potential generate strong position-dependent backaction on the intracavity field. In the quantum regime, particles in different energy bands are connected to different intracavity light intensities and optical-lattice depths. This generates a highly nonlinear coupled particle-field dynamics. For a given pump strength and detuning, a factorizing mean-field approach predicts several self-consistent stationary solutions of strongly distinct photon numbers and motional states. Quantum Monte Carlo wave-function simulations of the master equation confirm these predictions and reveal complex multimodal photon-number and particle-momentum distributions. Using larger nanoparticles in such a setup thus constitutes a well-controllable playground to study nonlinear quantum dynamics and the buildup of macroscopic quantum superpositions at the quantum-classical boundary.
The semiclassical dynamics of atoms, when the atoms are confined inside a standing-wave high-finesse resonator, is theoretically studied. The atoms are cooled by scattering processes in which the photons of a transverse laser are coherently scattered into the cavity mode. We derive a Fokker-Planck equation for the atomic center-of-mass variables which allows us to determine the equations of motion in the semiclassical limit for any value of the intensity of the laser field. We extract its prediction for the dynamics when the resonator is essentially in the vacuum state and the atoms are cooled by scattering photons into the cavity mode, which then decays. Its predictions for the stationary atomic distribution are compared with the ones of the Fokker-Planck equation by Domokos et al. [J. Phys. B 34, 187 (2001)], which has been derived under different assumptions. We find full agreement in the considered parameter regime.