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arXiv:0710.3047 · New Journal of Physics

Quantum stability of Mott-insulator states of ultracold atoms in optical resonators

Jonas Larson, Sònia Fernández-Vidal, Giovanna Morigi, Maciej Lewenstein

Published Apr 30, 2008• 63 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/10/4/045002

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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.
We study the low temperature physics of an ultracold atomic gas in the potential formed inside a pumped optical resonator. Here, the height of the cavity potential, and hence the quantum state of the gas, depends not only on the pump parameters, but also on the atomic density through a dynamical ac-Stark shift of the cavity resonance. We derive the Bose-Hubbard model in one dimension and use the strong coupling expansion to determine the parameter regime in which the system is in the Mott-insulator state. We predict the existence of overlapping, competing Mott-insulator states, and bistable behavior in the vicinity of the shifted cavity resonance, controlled by the pump parameters. Outside these parameter regions, the state of the system is in most cases superfluid.
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 the many-body state of ultracold bosons in a bistable optical lattice potential in an optomechanical resonator in the weak-coupling limit. Interesting physics arises as a result of bistability and discontinuous jumps in the cavity field. Of particular interest is the situation where the optical cavity is engineered so that a single input beam can result in two radically different stable ground states for the intracavity gas: superfluid and Mott insulator. Furthermore, the system we describe can be used as an adjustable template for investigating the coupling between cavity fields, nanomechanical systems operating in the quantum regime, and ultracold atomic gases.
We study systems of fully polarized ultracold atomic gases obeying Fermi statistics. The atomic transition interacts dispersively with a mode of a standing-wave cavity, which is coherently pumped by a laser. In this setup, the intensity of the intracavity field is determined by the refractive index of the atomic medium, and thus by the atomic density distribution. Vice versa, the density distribution of the atom is determined by the cavity field potential, whose depth is proportional to the intracavity field amplitude. In this work, we show that this nonlinearity leads to an instability in the intracavity intensity that differs substantially from dispersive optical bistability, as this effect is already present in the regime, where the atomic dipole is proportional to the cavity field. Such instability is driven by the matter-wave fluctuations and exhibits a peculiar dependence on the fluctuations in the atomic density distribution.
Cold atoms, driven by a laser and simultaneously coupled to the quantum field of an optical resonator, may self-organize in periodic structures. These structures are supported by the optical lattice, which emerges from the laser light they scatter into the cavity mode and form when the laser intensity exceeds a threshold value. We study theoretically the quantum ground state of these structures above the pump threshold of self-organization by mapping the atomic dynamics of the self-organized crystal to a Bose-Hubbard model. We find that the quantum ground state of the self-organized structure can be the one of a Mott insulator, depending on the pump strength of the driving laser. For very large pump strengths, where the intracavity-field intensity is maximum and one would expect a Mott-insulator state, we find intervals of parameters where the phase is compressible. These states could be realized in existing experimental setups.