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arXiv:1605.01226 · Physical Review A

Localization transition in the presence of cavity backaction

Katharina Rojan, Rebecca Kraus, Thomás Fogarty, Hessam Habibian, Anna Minguzzi, Giovanna Morigi

Published Jul 20, 2016• 17 citations
arXivHTMLPDF

Abstract

We study the localization transition of an atom confined by an external optical lattice in a high-finesse cavity. The atom-cavity coupling yields an effective secondary lattice potential, whose wavelength is incommensurate with the periodicity of the optical lattice. The cavity lattice can induce localization of the atomic wave function analogously to the Aubry-Andr\'e localization transition. Starting from the master equation for the cavity and the atom we perform a mapping of the system dynamics to a Hubbard Hamiltonian, which can be reduced to the Harper's Hamiltonian in appropriate limits. We evaluate the phase diagram for the atom's ground state and show that the transition between extended and localized wave function is controlled by the strength of the cavity nonlinearity, which determines the size of the localized region and the behavior of the Lyapunov exponent. The Lyapunov exponent, in particular, exhibits resonancelike behavior in correspondence with the optomechanical resonances. Finally we discuss the experimental feasibility of these predictions.

DOI
10.1103/physreva.94.013839

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We study the localization transition of an atom confined by an external optical lattice in a high-finesse cavity. The atom-cavity coupling yields an effective secondary lattice potential, whose wavelength is incommensurate with the periodicity of the optical lattice. The cavity lattice can induce localization of the atomic wave function analogously to the Aubry-Andr'e localization transition. Starting from the master equation for the cavity and the atom we perform a mapping of the system dynamics to a Hubbard Hamiltonian, which can be reduced to the Harper's Hamiltonian in appropriate limits. We evaluate the phase diagram for the atom's ground state and show that the transition between extended and localized wave function is controlled by the strength of the cavity nonlinearity, which determines the size of the localized region and the behavior of the Lyapunov exponent. The Lyapunov exponent, in particular, exhibits resonancelike behavior in correspondence with the optomechanical resonances. Finally we discuss the experimental feasibility of these predictions.
Single-particle localization of an ultracold atom is studied in one dimension when the atom is confined by an optical lattice and by the incommensurate potential of a high-finesse optical cavity. In the strong-coupling regime the atom is a dynamical refractive medium, the cavity resonance depends on the atomic position within the standing-wave mode, and nonlinearly determines the depth and form of the incommensurate potential. We show that the particular form of the quasirandom cavity potential leads to the appearance of mobility edges, even in presence of nearest-neighbor hopping. We provide a detailed characterization of the system as a function of its parameters and, in particular, of the strength of the atom-cavity coupling, which controls the functional form of the cavity potential. For strong atom-photon coupling the properties of the mobility edges significantly depend on the ratio between the periodicities of the confining optical lattice and of the cavity field.
We determine the quantum ground-state properties of ultracold bosonic atoms interacting with the mode of a high-finesse resonator. The atoms are confined by an external optical lattice, whose period is incommensurate with the cavity mode wavelength, and are driven by a transverse laser, which is resonant with the cavity mode. While for pointlike atoms photon scattering into the cavity is suppressed, for sufficiently strong lasers quantum fluctuations can support the buildup of an intracavity field, which in turn amplifies quantum fluctuations. The dynamics is described by a Bose-Hubbard model where the coefficients due to the cavity field depend on the atomic density at all lattice sites. Quantum Monte Carlo simulations and mean-field calculations show that, for large parameter regions, cavity backaction forces the atoms into clusters with a checkerboard density distribution. Here, the ground state lacks superfluidity and possesses finite compressibility, typical of a Bose glass. This system constitutes a novel setting where quantum fluctuations give rise to effects usually associated with disorder.
Ultracold bosonic atoms are confined by an optical lattice inside an optical resonator and interact with a cavity mode whose wavelength is incommensurate with the spatial periodicity of the confining potential. We predict that the intracavity photon number can be significantly different from zero when the atoms are driven by a transverse laser whose intensity exceeds a threshold value and whose frequency is suitably detuned from the cavity and the atomic transition frequency. In this parameter regime the atoms form clusters in which they emit in phase into the cavity. The clusters are phase locked, thereby maximizing the intracavity photon number. These predictions are based on a Bose-Hubbard model, whose derivation is reported here in detail. The Bose-Hubbard Hamiltonian has coefficients which are due to the cavity field and depend on the atomic density at all lattice sites. The corresponding phase diagram is evaluated using quantum Monte Carlo simulations in one dimension and mean-field calculations in two dimensions. Where the intracavity photon number is large, the ground state of the atomic gas lacks superfluidity and possesses finite compressibility, typical of a Bose glass.
Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-Andr\'e model which can cause localization of single-particle wave functions. We show that atomic wave packets in this dynamical lattice generically spread via anomalous diffusion, which can be tuned between superdiffusive and subdiffusive regimes. This anomalous diffusion arises from an interplay between Anderson localization and quantum fluctuations of the cavity field.
We study an ultracold atom-cavity coupling system, which had been implemented in an experiment to display weak light nonlinearity [S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, Phys. Rev. Lett. 99, 213601 (2007)]. The model is described by a noninteracting Bose-Einstein condensate contained in a Fabry-P\'erot optical resonator, in which two incommensurate standing-wave modes are excited and thus form a quasiperiodic optical lattice potential for the atoms. Special emphasis is paid to the variation of the atomic wave function induced by the cavity light field. We show that bistability between the atomic localized and extended states can be generated under appropriate conditions.
We study the collective motion of atoms confined in an optical lattice operating inside a high-finesse ring cavity. A simplified theoretical model for the dynamics of the system is developed upon the assumption of adiabaticity of the atomic motion. We show that in a regime where the light shift per photon times the number of atoms exceeds the linewidth of the cavity resonance, the otherwise tiny retroaction of the atoms upon the light field becomes a significant feature of the system. As a result dispersive optical bistability can arise and the lattice positions is determined by the strength of the atom-cavity coupling rather than by the phases of the incoupled light beams. Solving the complete set of classical equations of motion confirms these findings, however, additional nonadiabatic phenomena are predicted, such as, for example, self-induced radial breathing oscillations. We compare these results with experiments involving laser-cooled 85Rb^{85}\mathrm{Rb}85Rb atoms trapped in an optical lattice inside a ring cavity with a finesse of $1.8\ifmmode\times\else\texttimes\fi{}{10}^{5}$. Our observations are in excellent agreement with our theoretical predictions.