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arXiv:1909.08125 · Physical Review Letters

Localization Driven Superradiant Instability

Hong-Hao Yin, Jie Hu, An-Chun Ji, Gediminas Juzeliūnas, Xiong-Jun Liu, Qing Sun

Published Mar 17, 2020• 18 citations
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Abstract

The prominent Dicke superradiant phase arises from coupling an ensemble of atoms to a cavity optical field when an external optical pumping exceeds a threshold strength. Here we report a prediction of the superradiant instability driven by Anderson localization, realized with a hybrid system of the Dicke and Aubry-André (DAA) model for bosons trapped in a one-dimensional (1D) quasiperiodic optical lattice and coupled to a cavity. Our central finding is that for bosons condensed in a localized phase given by the DAA model, the resonant superradiant scattering is induced, for which the critical optical pumping of the superradiant phase transition approaches zero, giving an instability driven by the Anderson localization. The superradiant phase for the DAA model with or without a mobility edge is investigated, showing that the localization driven superradiant instability is in sharp contrast to the superradiance as widely observed for a Bose-Einstein condensate in extended states, and should be insensitive to the temperature of the system. This study unveils a novel effect of localization on the Dicke superradiance, and is well accessible based on the current experiments.

DOI
10.1103/physrevlett.124.113601

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The prominent Dicke superradiant phase arises from coupling an ensemble of atoms to a cavity optical field when an external optical pumping exceeds a threshold strength. Here we report a prediction of the superradiant instability driven by Anderson localization, realized with a hybrid system of the Dicke and Aubry-André (DAA) model for bosons trapped in a one-dimensional (1D) quasiperiodic optical lattice and coupled to a cavity. Our central finding is that for bosons condensed in a localized phase given by the DAA model, the resonant superradiant scattering is induced, for which the critical optical pumping of the superradiant phase transition approaches zero, giving an instability driven by the Anderson localization. The superradiant phase for the DAA model with or without a mobility edge is investigated, showing that the localization driven superradiant instability is in sharp contrast to the superradiance as widely observed for a Bose-Einstein condensate in extended states, and should be insensitive to the temperature of the system. This study unveils a novel effect of localization on the Dicke superradiance, and is well accessible based on the current experiments.
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The Dicke model and the superradiance of two-level systems in a radiation field have many applications. Recently, a Dicke quantum phase transition has been realized with a Bose-Einstein condensate in a cavity. We numerically solve the many-body Schrödinger equation and study correlations in the ground state of interacting bosons in a cavity as a function of the strength of a driving laser. Beyond a critical strength, the bosons occupy multiple modes macroscopically while remaining superradiant. This fragmented superradiance can be detected by analyzing the variance of single-shot measurements.
Understanding the interplay between collective optical response and disorder presents significant challenges in modern many-body physics. While there has been considerable interest and a wealth of theoretical work in recent years, the experimental investigation of the superradiant phase transition and disorder has been unexplored. Here, we report an observation of the localization-driven superradiance with a degenerate Fermi gas in an optical cavity. We show that the dynamics of Fermi gases exhibits Anderson localization in an intracavity incommensurate lattice. The exponential localization is directly observed in both spatial and momentum spaces. We observe the localization driving a nearly vanishing pump threshold in fermionic superradiance when the system is in the localized state. The underlying mechanism of the self-organization and the quantum statistic of the atoms are revealed by measuring the atom momentum distribution and characteristic growth of the superradiant field. Our work provides a platform for studying superradiant quantum phase transition and localization in photon-mediated long-range interacting Fermi gases.
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.
In a recent experiment, Anderson localization was observed directly for non-interacting Bose-Einstein Condensate in one dimension. The experiment was performed using quasiperiodic optical lattice. Their system can be described by the one-dimensional noninteracting Aubry-Andr�e model. This model which simulates disorder with its quasiperiodic potential shows transition from extended to localised states at a critical disorder strength. The ground state gets localised around a single point for disorder larger than the critical value. We find that while inverse participation ratio increases as we increase disorder and rises to one in insulator phase, super uid fraction decreases as we increase disorder and goes to zero sharply in the insulator phase . When we introduce weak repulsive interaction for Bose gas in the model at the mean field level, we see that the ground-state shows multiple-site localization for certain disorder range, which lies above the critical value. For given interaction strength, we find that the inverse participation ratio increases slowly and super uid fraction decreases slowly as we increase disorder. Moreover, by representing our model as a classical two-dimensional nonlinear Hamiltonian map, we distinguish between localised and extended states by studying the trajectories in phase-space. Using this, we find out the localization length of eigenstates as a function of disorder for non-interacting model. Further, we study the time-evolution of a wave-packet in different regimes of disorder and see the effect of interaction on it.