Abstract We consider a condensate of ultra-cold bosonic atoms in a linear optical cavity illuminated by a two-pump configuration where each pump makes different angles with the direction of the cavity axis. We show that such a configuration allows a smooth transition from a one-dimensional quantum optical lattice configuration to a two-dimensional quantum optical lattice configuration induced by the cavity–atom interaction. Using a Holstein–Primakoff transformation, we find the atomic density profile of such a self-organised ground state in the super-radiant phase as a function of the angular orientations of the pumps in such a dynamical quantum optical lattice, and also provide an analysis of their structures in coordinate and momentum space. In the later part of the paper, we show how the corresponding results can also be qualitatively understood in terms of an extended Bose–Hubbard model in such a quantum optical lattice potential.
Abstract We consider a condensate of ultra-cold bosonic atoms in a linear optical cavity illuminated by a two-pump configuration where each pump makes different angles with the direction of the cavity axis. We show that such a configuration allows a smooth transition from a one-dimensional quantum optical lattice configuration to a two-dimensional quantum optical lattice configuration induced by the cavity–atom interaction. Using a Holstein–Primakoff transformation, we find the atomic density profile of such a self-organised ground state in the super-radiant phase as a function of the angular orientations of the pumps in such a dynamical quantum optical lattice, and also provide an analysis of their structures in coordinate and momentum space. In the later part of the paper, we show how the corresponding results can also be qualitatively understood in terms of an extended Bose–Hubbard model in such a quantum optical lattice potential.
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 cavity fields with respect to the pump laser, these minima can either form a triangular or a hexagonal lattice. By numerically solving the dynamical equations of the coupled atom-cavity system, we have shown that the two stable atomic structures at long times are the triangular lattice and the honeycomb lattice with equally populated sites. We have also studied how to drive atoms from one lattice structure to another by dynamically changing the phase of the cavity fields with respect to the pump laser.
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 transition from a normal phase to a self-organized superfluid phase, which is related to the Hepp-Lieb-Dicke superradiance phase transition. For even stronger pumping, a self-organized Mott insulator phase arises.
Ultracold bosonic atoms in optical lattices self-organize into a variety of structural and quantum phases when placed into a single-mode cavity and pumped by a laser. Cavity optomechanical effects induce an atom density modulation at the cavity-mode wavelength that competes with the optical lattice arrangement. Simultaneously short-range interactions via particle hopping promote superfluid order such that a variety of structural and quantum coherent phases can occur. We analyze the emerging phase diagram in two dimensions by means of an extended Bose-Hubbard model using a local mean-field approach combined with a superfluid cluster analysis. For commensurate ratios of the cavity and external lattice wavelengths, the Mott insulator-superfluid transition is modified by the appearance of charge density wave and supersolid phases, at which the atomic density supports the buildup of a cavity field. For incommensurate ratios, the optomechanical forces induce the formation of Bose-glass and superglass phases, namely, nonsuperfluid and superfluid phases, respectively, displaying quasiperiodic density modulations, which in addition can exhibit structural and superfluid stripe formation. The onset of such structures is constrained by the on-site interaction and is favorable at fractional densities. Experimental observables are identified and discussed.
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.
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.
In this paper, we consider the transmission characteristics of an optical cavity loaded with ultra cold atoms in a one dimensional optical lattice at absolute zero temperature. In particular, we consider the situation when the many body quantum state of the ultra cold atoms is an insulating state with fixed number of atoms at each site, which can be either density wave (DW) or Mott insulator (MI) phase, each showing different type of discrete lattice translational symmetry. We provide a general framework of understanding the transmission spectrum from a single and two cavities/modes loaded with such insulating phases. Further, we also discuss how such a transmission spectrum changes when these insulating phases make a cross over to the superfluid (SF) phase with the changing depth of the optical lattice potential.