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Density Modulations in an Elongated BEC Released from a Disordered Potential: What Can We Learn ?

David Clément, Philippe Bouyer, Alain Aspect, Laurent Sanchez-Palencia

Published Jan 24, 2008• 0 citations
OpenAlex

Abstract

We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time-of-flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. We conclude that the observed large density modulations originate from the weak initial density modulations induced by the disorder, and not from initial phase fluctuations (thermal or quantum).

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Density modulations in an elongated Bose-Einstein condensate released from a disordered potential

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We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time of flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. We conclude that the observed large density modulations originate from the weak initial density modulations induced by the disorder and not from initial phase fluctuations (thermal or quantum).

arXiv:0710.1984•Physical Review A•Mar 31, 2008•54 citations

Density Modulations in an Elongated BEC Released from a Disordered Potential

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We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time-of-flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. Our analysis shows how the observed large modulations originate from the weak initial density modulations induced by the disorder, and do not require phase fluctuations (thermal or quantum) in the initial condensate.

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Propriétés statiques et dynamiques d'un condensat de Bose-Einstein dans un potentiel aléatoire

David Clément

Static and dynamical properties of atomic Bose-Einstein condensate in a random potential. The presence of disorder in systems with long-range coherence leads to fascinating effects such as the localization of waves and the appearance of novels quantum phases. While it is often difficult to isolate the effects of disorder in experiments, atomic Bose-Einstein condensates can be manipulated in a controlled random environment. In this report, several aspects of atomic Bose-Einstein condensates in a random potential induced by laser speckles are discussed. After presenting the realization and the characterization of the speckle potential we first study some properties of the trapped, disordered condensates, in particular the enhancement of large density modulations during time-of-flight. We show that this effect is not related to initial phase fluctuations but originates from small initial density modulations in the trap. Secondly, we report on collective modes of a disordered Bose-Einstein condensate. The absence of frequency shifts and the damping of the dipole mode in the presence of disorder are discussed. Then we present measurements of the velocity of sound in a disordered condensate and we show the absence of shift compared to the non-disordered case. At last, we report on the suppression of the 1D expansion of an interacting matter-wave in the presence of disorder in two different regimes. In a regime of strong disorder a detailed experimental analysis supports the proposed scenario of trapping where reflexions on a single modulation of the random potential and interactions play a crucial role. A different regime of weak disorder is then investigated theoretically and we show that Anderson localization can happen in this case under the conditions we establish. This scheme has been realized recently in experiments, leading to the observation of the Anderson localization of a matter-wave.

Annales de Physique•Jan 1, 2008•1 citation
We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time-of-flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. We conclude that the observed large density modulations originate from the weak initial density modulations induced by the disorder, and not from initial phase fluctuations (thermal or quantum).
We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time of flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. We conclude that the observed large density modulations originate from the weak initial density modulations induced by the disorder and not from initial phase fluctuations (thermal or quantum).
We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time-of-flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. Our analysis shows how the observed large modulations originate from the weak initial density modulations induced by the disorder, and do not require phase fluctuations (thermal or quantum) in the initial condensate.
We theoretically investigate the localization of an expanding Bose–Einstein condensate (BEC) with repulsive atom–atom interactions in a disordered potential. We focus on the regime where the initial inter-atomic interactions dominate over the kinetic energy and the disorder. At equilibrium in a trapping potential and for the considered small disorder, the condensate shows a Thomas–Fermi shape modified by the disorder. When the condensate is released from the trap, a strong suppression of the expansion is obtained in contrast to the situation in a periodic potential with similar characteristics. This effect crucially depends on both the momentum distribution of the expanding BEC and the strength of the disorder. For strong disorder as in the experiments reported by Clément et al 2005 Phys. Rev. Lett. 95 170409 and Fort et al 2005 Phys. Rev. Lett. 95 170410, the suppression of the expansion results from the fragmentation of the core of the condensate and from classical reflections from large modulations of the disordered potential in the tails of the condensate. We identify the corresponding disorder-induced trapping scenario for which large atom–atom interactions and strong reflections from single modulations of the disordered potential play central roles. For weak disorder, the suppression of the expansion signals the onset of Anderson localization, which is due to multiple scattering from the modulations of the disordered potential. We compute analytically the localized density profile of the condensate and show that the localization crucially depends on the correlation function of the disorder. In particular, for speckle potentials the long-range correlations induce an effective mobility edge in 1D finite systems. Numerical calculations performed in the mean-field approximation support our analysis for both strong and weak disorder.
We have studied the effects of a disordered optical potential on the transport and phase coherence of a Bose-Einstein condensate (BEC) of 7Li^{7}\text{L}\text{i}7Li atoms. At moderate disorder strengths (VD)({V}_{D})(VD​), we observe inhibited transport and damping of dipole excitations, while in time-of-flight images, random but reproducible interference patterns are observed. In situ images reveal that the appearance of interference is correlated with density modulation, without complete fragmentation. At higher VD{V}_{D}VD​, the interference contrast diminishes as the BEC fragments into multiple pieces with little phase coherence.
The Study of transport and phase coherence in a Bose-Einstein condensate (BEC) of 7 Li subjected to a 1D disordered potential, provides an excellent system to explore the effects of impurities on a quantum gas. Observations of the median cloud position as the BEC is moved through the disorder potential provide evidence of inhibited transport due to classical reflections. Careful study of the damping coefficient for dipole oscillations shows a power law relationship with disorder strength ( V D ). A highly elongated BEC and large disorder length scale, (σ d = 14 pm), allow direct probing of disorder induced density modulations in the in-situ BEC. Large density fluctuations are observed to evolve from the in-situ density modulations for moderate V D , and phase coherence is suppressed at large V D . An improved speckle pattern has been designed, for future experiments, with a reduced σ d and an aspect ratio that more closely matches the BEC.
Static and dynamical properties of atomic Bose-Einstein condensate in a random potential. The presence of disorder in systems with long-range coherence leads to fascinating effects such as the localization of waves and the appearance of novels quantum phases. While it is often difficult to isolate the effects of disorder in experiments, atomic Bose-Einstein condensates can be manipulated in a controlled random environment. In this report, several aspects of atomic Bose-Einstein condensates in a random potential induced by laser speckles are discussed. After presenting the realization and the characterization of the speckle potential we first study some properties of the trapped, disordered condensates, in particular the enhancement of large density modulations during time-of-flight. We show that this effect is not related to initial phase fluctuations but originates from small initial density modulations in the trap. Secondly, we report on collective modes of a disordered Bose-Einstein condensate. The absence of frequency shifts and the damping of the dipole mode in the presence of disorder are discussed. Then we present measurements of the velocity of sound in a disordered condensate and we show the absence of shift compared to the non-disordered case. At last, we report on the suppression of the 1D expansion of an interacting matter-wave in the presence of disorder in two different regimes. In a regime of strong disorder a detailed experimental analysis supports the proposed scenario of trapping where reflexions on a single modulation of the random potential and interactions play a crucial role. A different regime of weak disorder is then investigated theoretically and we show that Anderson localization can happen in this case under the conditions we establish. This scheme has been realized recently in experiments, leading to the observation of the Anderson localization of a matter-wave.