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arXiv:1207.4961 · New Journal of Physics

Raman superradiance and spin lattice of ultracold atoms in optical cavities

Shabnam Safaei, Özgür Esat Müstecaplıoğlu, B. Tanatar

Published Aug 20, 2013• 11 citations
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Abstract

We investigate the synthesis of a hyperfine spin lattice in an atomic Bose–Einstein condensate, with two hyperfine spin components, inside a one-dimensional high-finesse optical cavity, using off-resonant superradiant Raman scattering. Spatio-temporal evolution of the relative population of the hyperfine spin modes is examined numerically by solving the coupled cavity–condensate mean-field equations in the dispersive regime. We find, analytically and numerically, that beyond a certain threshold of the transverse laser pump, Raman superradiance and self-organization of the hyperfine spin components occur simultaneously and as a result a magnetic lattice is formed. The effects of an extra laser pump parallel to the cavity axis and the time dependence of the pump strength on the synthesis of a sharper lattice are also addressed.

DOI
10.1088/1367-2630/15/8/083037

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We investigate the synthesis of a hyperfine spin lattice in an atomic Bose–Einstein condensate, with two hyperfine spin components, inside a one-dimensional high-finesse optical cavity, using off-resonant superradiant Raman scattering. Spatio-temporal evolution of the relative population of the hyperfine spin modes is examined numerically by solving the coupled cavity–condensate mean-field equations in the dispersive regime. We find, analytically and numerically, that beyond a certain threshold of the transverse laser pump, Raman superradiance and self-organization of the hyperfine spin components occur simultaneously and as a result a magnetic lattice is formed. The effects of an extra laser pump parallel to the cavity axis and the time dependence of the pump strength on the synthesis of a sharper lattice are also addressed.
We explore the many-body phases of a two-dimensional Bose-Einstein condensate with cavity-mediated dynamic spin-orbit coupling. With the help of two transverse noninterfering, counterpropagating pump lasers and a single standing-wave cavity mode, two degenerate Zeeman sub-levels of the quantum gas are Raman coupled in a double-$\mathrm{\ensuremath{\Lambda}}$-configuration. Beyond a critical pump strength the cavity mode is populated via coherent superradiant Raman scattering from the two pump lasers, leading to the appearance of a dynamical spin-orbit coupling for the atoms. We identify three quantum phases with distinct atomic and photonic properties: the normal ``homogeneous'' phase, the superradiant ``spin-helix'' phase, and the superradiant ``supersolid spin-density-wave'' phase. The last exhibits an emergent periodic atomic density distribution with an orthorhombic centered rectangular-lattice structure due to the interplay between the coherent photon scattering into the resonator and the collision-induced momentum coupling. The transverse lattice spacing of the emergent crystal is set by the dynamic spin-orbit coupling.
We consider a two-component Bose–Einstein condensate in a one-dimensional optical cavity. Specifically, the condensate atoms are taken to be in two degenerate modes due to their internal hyperfine spin degrees of freedom and they are coupled to the cavity field and an external transverse laser field in a Raman scheme. A parallel laser also excites the cavity mode. When the pump laser is far detuned from its resonance atomic transition frequency, an effective nonlinear optical model of the cavity–condensate system is developed under the discrete mode approximation (DMA), while matter–field coupling has been considered beyond the rotating wave approximation. By analytical and numerical solutions of the nonlinear dynamical equations, we examine the mean cavity field and population difference (magnetization) of the condensate modes. The stationary solutions of both the mean cavity field and normalized magnetization demonstrate bistable behavior under certain conditions for the laser pump intensity and matter–field coupling strength.
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.
We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z_{2} symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative phase of the two condensate wave functions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially averaged relative condensate phase is locked at either π/2 or -π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.
We observe the joint spin-spatial (spinor) self-organization of a two-component Bose-Einstein condensate (BEC) strongly coupled to an optical cavity. This unusual nonequilibrium Hepp-Lieb-Dicke phase transition is driven by an off-resonant Raman transition formed from a classical pump field and the emergent quantum dynamical cavity field. This mediates a spinor-spinor interaction that, above a critical strength, simultaneously organizes opposite spinor states of the BEC on opposite checkerboard configurations of an emergent 2D lattice. The resulting spinor density-wave polariton condensate is observed by directly detecting the atomic spin and momentum state and by holographically reconstructing the phase of the emitted cavity field. The latter provides a direct measure of the spin state, and a spin-spatial domain wall is observed. The photon-mediated spin interactions demonstrated here may be engineered to create dynamical gauge fields and quantum spin glasses.