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arXiv:0908.4333 · Physical Review Letters

Cavity-Mediated Strong Matter Wave Bistability in a Spin-1 Condensate

Lu Zhou, Han Pu, Hong Yuan Ling, Weiping Zhang

Published Oct 15, 2009• 48 citations
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Abstract

We study matter-wave bistability in a spin-1 Bose-Einstein condensate dispersively coupled to a unidirectional ring cavity. A unique feature is that the population exchange among different modes of matter fields is accomplished via spin-exchange collisions. We show that the interplay between the atomic spin mixing and the cavity light field can lead to a strong matter-wave nonlinearity, making matter-wave bistability in a cavity at the single-photon level achievable.

DOI
10.1103/physrevlett.103.160403

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We study matter-wave bistability in a spin-1 Bose-Einstein condensate dispersively coupled to a unidirectional ring cavity. A unique feature is that the population exchange among different modes of matter fields is accomplished via spin-exchange collisions. We show that the interplay between the atomic spin mixing and the cavity light field can lead to a strong matter-wave nonlinearity, making matter-wave bistability in a cavity at the single-photon level achievable.
We consider a ferromagnetic spin-1 Bose-Einstein condensate (BEC) dispersively coupled to a unidirectional ring cavity. We show that the ability of the cavity to modify, in a highly nonlinear fashion, matter-wave phase shifts adds an additional dimension to the study of spinor condensates. In addition to demonstrating strong matter-wave bistability as in our earlier publication [L. Zhou et al., Phys. Rev. Lett. 103, 160403 (2009)], we show that the interplay between atomic and cavity fields can greatly enrich both the physics of critical slowing down in spin-mixing dynamics and the physics of spin-domain formation in spinor condensates.
We investigate a system consisting of a two-component Bose-Einstein condensate interacting dispersively with a Fabry-Perot optical cavity where the two components of the condensate are resonantly coupled to each other by another classical field. The key feature of this system is that the atomic motional degrees of freedom and the internal pseudospin degrees of freedom are coupled to the cavity field simultaneously, hence an effective spin-orbital coupling within the condensate is induced by the cavity. The interplay among the atomic center-of-mass motion, the atomic collective spin, and the cavity field leads to a strong nonlinearity, resulting in multistable behavior in both matter wave and light wave at the few-photon level.
A Bose–Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe optical bistability already below the single photon level and strong back-action dynamics which tunes the coupled system periodically out of resonance.
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.
The coupled dynamics of the atom and photon fields in optical ring cavities with two counterpropagating modes give rise to both spin-orbit interactions as well as long-ranged interactions between atoms of a many-body system. At zero temperature, the interplay between the two-body and cavity-mediated interactions determines the ground state of a Bose-Einstein condensate. In this work, we find that cavity quantum electrodynamics in the weak-coupling regime favors a stripe-phase state over a plane-wave phase as the strength of cavity-mediated interactions increases. Indeed, the stripe phase is energetically stabilized even for condensates with attractive intraspecies and interspecies interactions for sufficiently large cavity interactions. The elementary excitation spectra in both phases correspond to linear dispersion relation at long wavelengths, indicating that both phases exhibit superfluidity, although the plane-wave phase also displays a characteristic roton-type feature. The results suggest that even in the weak-coupling regime, cavities can yield interesting new physics in ultracold quantum gases.
A coupled atom–molecule condensate with an intraspecies Feshbach resonance is employed to explore matter wave bistability both in the presence and in the absence of a unidirectional optical ring cavity. In particular, a set of conditions are derived that allow the threshold for bistability, due both to two-body s-wave scatterings and to cavity-mediated two-body interactions, to be determined analytically. The latter bistability is found to support, not only transitions between a mixed (atom–molecule) state and a pure molecular state as in the former bistability, but also transitions between two distinct mixed states.