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Journal of Atomic Molecular Condensate and Nano Physics

Optical Bistability and Normal-Mode Splitting of Two-Species Bose-Einstein Condensates in An Optical Cavity

Neha Aggarwal, Shweta, Aranya B. Bhattacherjee, Man Mohan

Published Dec 4, 2015• 0 citations
Publisher

Abstract

We investigate the optical bistable behavior for a weakly interacting two-species Bose-Einstein condensates inside a pumped optical cavity by considering the two possible regimes- the phase mixed regime and the phase segregated regime. We find that the cavity-pump detuning plays a significant role in controlling the threshold of the optical bistability and the constrast between the bistability values depending upon the state we are working in. We also demonstrate the occurence of normal mode splitting in the optical spectrum for both the regimes which further showing the position and amplitude discrepancies in the spectral peaks.

DOI
10.26713/jamcnp.v2i2.302

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Abstract The optical bistability (OB) in a two-mode optomechanical system with a Bose–Einstein condensate (BEC) is studied. By investigating the behavior of steady state solutions, we show that how OB develops in the system for a certain range of cavity-pump detunings and pump amplitudes. We then investigate the effects of the decay rate of the cavity photons and coupling strength between the cavity and the BEC as well as the pump-atom detuning on the optical behaviour of the system. We find that one can control the OB threshold and width of the bistability curve via adjusting properly the coupling strength and the detuning. By applying Routh–Hurwitz criterion, we then derive stability conditions for different branches of the OB curve. Moreover, by introducing an effective potential for the system, a simple physical interpretation is obtained.
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 the normal mode splitting in a system consisting of a Bose–Einstein condensates (BECs) trapped inside a Fabry–Pérot cavity driven by a single mode laser field. We analyze the variations in frequency and damping rate of the collective density excitation of a BEC imparted by the optical field. We study the occurrence of normal mode splitting which appears as consequences of the hybridization of the fluctuations of the intracavity field and the condensate mode. It is shown that normal mode splitting vanishes for weak coupling between the condensate mode and the intracavity field. Moreover, we investigate the normal mode splitting in the transmission spectrum of the cavity field.
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 consider a Bose-Einstein condensate inside an optical cavity and two crossed coherent pump fields. We determine perturbatively the phase boundary separating the normal superfluid phase and the superradiance phase. In the regime of negative cavity detuning, we map out the phase diagrams for both an attractive and a repulsive optical lattice. It turns out that the situation is quite different in the two cases. Specifically, in the case of an attractive lattice, if a system is in the superradiant phase with one pump laser, adding another pump does not drive the system out of the superradiance phase, while for the repulsive lattice, increasing another pump potential has suppressive effects on the superradiance. We also find that, in the case of an attractive lattice, equally increasing two pump lattice potentials can induce a transition from the normal phase to the superradiance phase. In stark contrast, for the repulsive lattice, the system will remain in the normal phase as the pump depths are tuned within a wide range, independently of the cavity detuning and the decay rate.