We consider a far-red-detuned optical cavity, driven by a pump, which contains an ultracold atomic medium. Using coupled partial differential equations which describe the evolution of the atomic and optical fields, we demonstrate that our model leads to novel self-structuring, led by the optical field through the dipole force, within the ultracold atomic medium. Introducing OAM to the optical pump, we demonstrate that these structures may be made to rotate, forming atomic fields analogous to persistent phase currents.
We consider a far-red-detuned optical cavity, driven by a pump, which contains an ultracold atomic medium. Using coupled partial differential equations which describe the evolution of the atomic and optical fields, we demonstrate that our model leads to novel self-structuring, led by the optical field through the dipole force, within the ultracold atomic medium. Introducing OAM to the optical pump, we demonstrate that these structures may be made to rotate, forming atomic fields analogous to persistent phase currents.
We numerically model the propagation of light through a Kerr medium and through a far-red-detuned Bose Einstein condensate (BEC) inside an optical cavity using Lugiato-Lefever and Gross-Pitaevskii equations. We demonstrate the formation of light-atomic ring lattices with rotation speeds and direction that can be controlled by the orbital angular momentum of the light. In the BEC, we show the possibility of moving from a lattice to a ring-shaped atomic circuit by changing the atomic scattering length, and explore the potential generation of rotating BEC cavity solitons. Our results may be of interest as slow light pulses with fully controllable speed and structure for use in optical quantum memories, for particle manipulation and trapping, and for the novel realization of highly controllable, tightly confined, rotating atomic lattices.
Optomechanical pattern forming instabilities in a cloud of cold atoms lead to self-organized spatial structures of light and atoms. Here, we consider the optomechanical self-structuring of a cold atomic cloud in the presence of a phase structured input field, carrying orbital angular momentum. For a planar ring cavity setup, a model of coupled cavity field and atomic density equations describes a wide range of drifting modulation instabilities in the transverse plane. This leads to the formation of rotating self-organized rings of light-atom lattices. Using linear stability analysis and numerical simulations of the coupled atomic and optical dynamics, we demonstrate the presence of macroscopic atomic transport corresponding to the pattern rotation, induced by the structured pump phase profile.
We numerically model the propagation of far-detuned optical beams through a Bose-Einstein condensate (BEC) using coupled nonlinear Schr¨odinger and Gross-Pitaevskii equations. For red atom-field detuning, we show that light carrying orbital angular momentum (OAM) can lead to coupled light-atom solitons carrying angular momentum. We demonstrate the formation of azimuthally rotating wavepackets, toward an atomic persistent current without trapping requirements. For blue atom-field detuning, we show highly exotic BEC distributions, with the atoms trapped in dark regions of the optical field. Our results provide a novel means of atomic transport and of sculpting a BEC into unique transverse distributions.
This thesis summarizes the research work we did in the past years, which focuses on the theoretical study of quantum effects of ordered atomic structures interacting with the quantum electric field of an optical resonator. Within this work we investigated the quantum properties of the light at the cavity output, emitted by this kind of system, and the quantum state of the atoms confined by the light fields of the cavity mode. Following one possible partition, we have organized the thesis in two parts. The first part of the thesis is devoted to the quantum properties of the light at the output of optical cavities, in which atoms are confined. After a brief introduction on the basics of atom-photon interactions, we show theoretically, that two atomic dipoles in a resonator can behave as a quantum non-linear medium, whose response can be controlled through the interactomic distance of the atoms inside the resonator. We identify the parameter regime, for which the system operates as a parametric amplifier, based on the atoms' collective dipole cascade emission. Moreover we also determine the corresponding field squeezing spectrum at the cavity output. These dynamics could be observed as a result of self-organization processes of laser-cooled atoms in resonators. The second part of the thesis studies the quantum ground state of an ultracold atomic gas trapped inside an optical resonator by the mechanical effects of atom-photon interactions. Due to the strong coupling regime, the ultracold atomic gas feels a quantum potential, where the fluctuations at the single photon level may be relevant in determining the trapping conditions. This potential depends on the atomic distribution, which at the same time determines the intracavity field amplitude. Here, after a brief introduction on ultracold atoms in optical lattices, we study the low temperature physics of an ultracold atomic gas in the quantum potential formed inside a pumped cavity, by mapping the dynamics to an effective Bose-Hubbard model. We predict the existence of non-compressible states of the atomic gas, and determine a phase diagram as a function of the cavity parameters. Novel effects are encountered, such as the existence of overlapping stability regions corresponding to competing insulator-like states when the laser pumps the cavity, to provide one example out of many. At the end of the thesis a concluding chapter presents some general outlooks to this thesis work.
We study a transversely pumped atomic Bose-Einstein condensate coupled to a single-mode optical cavity, where effective atom-atom interactions are mediated by pump and cavity photons. A number of experiments and theoretical works have shown the formation of a superradiant state in this setup, where interference of pump and cavity light leads to an optical lattice in which atoms self-consistently organize. This self-organization has been extensively studied using the approximate Dicke model (truncating to two momentum states), as well as through numerical Gross-Pitaevskii simulations in one and two dimensions. Here, we perform a full mean-field analysis of the system, including all relevant atomic momentum states and the cavity field. We map out the steady-state phase diagram vs pump strength and cavity detuning, and provide an in-depth understanding of the instabilities that are linked to the emergence of spatiotemporal patterns. We find and describe parameter regimes where the mean field predicts bistability, regimes where the dynamics form chaotic trajectories, instabilities caused by resonances between normal mode excitations, and states with atomic dynamics but vanishing cavity field.
When placing an ultracold atomic gas inside a cavity, the light-matter coupling is enhanced and nonlinear atomic dynamics is generated, offering a promising platform for quantum simulation of models with short- and long-range interactions. Recently, superradiant self-organized phases for ultracold atomic gases inside a cavity, pumped by a blue detuned optical lattice, have been observed. Here, we explore the formation of quantum many-body phases of bosonic atoms inside an optical cavity, subject to transverse blue detuned pumping. We investigate the strongly interacting regime, which can be reached by tuning the s-wave scattering length using external fields. We analyze the interplay between superradiant self-organization with superfluid and Mott insulator phases, without the need of including higher lying bands, as the Wannier functions are dynamically linked to the cavity light via backaction. We observe different kinds of structural phase transitions driven by the light inside the cavity and the interplay with atomic collisions. We observe the mode softening at the critical points in the quantum phase transitions which can be measured in future experiments. We obtain our results within a full self-consistent theoretical framework, the light-matter density matrix renormalization group (DMRG), which employs the computation of light dependent Wannier functions for the full quantum optical lattice in combination with DMRG for the atomic dynamics. The methods introduced here can be used to analyze the effects of strong quantum correlations in strongly interacting light-matter systems.