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arXiv:1606.01589 · Proceedings of the National Academy of Sciences

Matter wave speckle observed in an out-of-equilibrium quantum fluid

P. E. S. Tavares, A. R. Fritsch, Gustavo Deczka Telles, Mahir Saleh Hussein, François Impens, Robin Kaiser, Vanderlei Salvador Bagnato

Published Nov 13, 2017• 12 citations
arXivHTMLPDF

Abstract

Significance In recent years, significant progress concerning matter–wave creation and manipulation has been achieved. Fresnel diffraction, atom lasers, and nonlinear matter wave phenomena are just a few examples of recent interesting research topics. There have also been numerous studies related to the propagation of matter waves interacting with disordered potentials, but not as many concerning the disorder existing into the matter wave itself. In the present study, we analyze the disorder imprinted into a Bose–Einstein condensate (BEC) and its characteristic spatial evolution afterward. We performed careful analyses and traced a few analogies that led us to the conclusion that the perturbed BECs evolve very much in a speckle-like manner, in close analogy with a traveling-light (optical) speckle.

DOI
10.1073/pnas.1713693114

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Significance In recent years, significant progress concerning matter–wave creation and manipulation has been achieved. Fresnel diffraction, atom lasers, and nonlinear matter wave phenomena are just a few examples of recent interesting research topics. There have also been numerous studies related to the propagation of matter waves interacting with disordered potentials, but not as many concerning the disorder existing into the matter wave itself. In the present study, we analyze the disorder imprinted into a Bose–Einstein condensate (BEC) and its characteristic spatial evolution afterward. We performed careful analyses and traced a few analogies that led us to the conclusion that the perturbed BECs evolve very much in a speckle-like manner, in close analogy with a traveling-light (optical) speckle.
In this thesis, we present the generation and studies of a 87 Rb Bose-Einstein condensate (BEC) perturbed by an oscillatory excitation. The atoms are trapped in a harmonic magnetic trap where, after an evaporative cooling process, we produce the BEC. In order to study the effect caused by oscillatory excitations, a quadrupole magnetic field time oscillatory is superimposed to the trapping potential. Through this perturbation, collective modes were observed. The dipole mode is excited even for low excitation amplitudes. However, a minimum excitation energy is needed to excite the condensate quadrupole mode. Observing the excited cloud in TOF expansion, we note that for excitation amplitude in which the quadrupole mode is excited, the cloud expands without invert its aspect ratio. By looking these clouds, after long time-of-flight, it was possible to see vortices and, sometimes, a turbulent state in the condensed cloud. We calculated the momentum distribution of the perturbed BECs and a power law behavior, like the law to Kolmogorov turbulence, was observed. Furthermore, we show that using the method that we have developed to calculate the momentum distribution, the distribution curve (including the power law exponent) exhibits a dependence on the quadrupole mode oscillation of the cloud. The randomness distribution of peaks and depletions in density distribution image of an expanded turbulent BEC, remind us to the intensity profile of a speckle light beam. The analogy between matter-wave speckle and light speckle is justified by showing the similarities in the spatial propagation (or time expansion) of the waves. In addition, the second order correlation function is evaluated and the same dependence with distance was observed for the both waves. This creates the possibility to understand the properties of quantum matter in a disordered state. The propagation of a three-dimensional speckle field (as the matter-wave speckle described here) creates an opportunity to investigate the speckle phenomenon existing in dimensions higher than 2D (the case of light speckle).
We present a detailed analysis of the 1D expansion of a coherent interacting matterwave (a Bose–Einstein condensate (BEC)) in the presence of disorder. A 1D random potential is created via laser speckle patterns. It is carefully calibrated and the self-averaging properties of our experimental system are discussed. We observe the suppression of the transport of the BEC in the random potential. We discuss the scenario of disorder-induced trapping taking into account the radial extension in our experimental 3D BEC and we compare our experimental results with the theoretical predictions.
The development of atom cooling and trapping techniques and the ability to load optical lattices or disordered potentials with Bose-Einstein condensates or degenerate Fermi gases has opened a whole field of research around the strong localization of matter waves. In this theoretical work we study the coherent transport of matter waves evolving in disordered optical potentials (speckle). The influence of correlated disorder is first studied numerically in the framework of the Anderson model. Subsequently, a self-consistent diagrammatic calculation allows us to determine analytically the basic transport parameters in the regime of weak disorder: mean free path, transport mean free path, diffusion constant, localization length. A crucial quantity for these analytical calculations is the spatial correlation function of speckle fluctuations. It determines the degree of anisotropy of a scattering event. We consider in particular the transition from weak localization to strong localization. In this case the diffusion constant of matter waves decreases and approaches zero at the threshold of strong localization. We calculate the renormalization of the diffusion constant due to the interference of matter waves by explicitly considering the correlation of fluctuations of the disordered potential.
Summary form only given. Bose-Einstein condensates (BEC) of weakly interacting gases allow for the new regime of nonlinear atom optics. Of special interest are macroscopically excited states like dark solitons or vortices. Solitons, as particle like excitations of matter wave fields, provide a link from condensate physics to fluid mechanics, nonlinear optics and fundamental particle physics. Dark solitons in matter waves are characterized by a local density minimum and, a steep phase gradient of the wavefunction at the position of the minimum. We report on experimental and theoretical investigation of dark solitons in BECs of /sup 87/Rb which are produced by the method of phase imprinting. A highly anisotropic confining potential allows us to be close to the (quasi) 1D situation where dark solitons are expected to be dynamically stable. By monitoring the evolution of the density profile we observe the evolution of density minima travelling at a smaller velocity than the speed of sound. By comparison to analytical and numerical solutions of the 3D Gross-Pitaevskii equation for our experimental conditions we identify these density minima to be moving dark solitons. We have studied in detail the creation and the dynamics of dark solitons as a function of evolution time and imprinted phase.
In 1958, P.W. Anderson predicted the exponential localization1 of electronic wave functions in disordered crystals and the resulting absence of diffusion. It has been realized later that Anderson localization (AL) is ubiquitous in wave physics2 as it originates from the interference between multiple scattering paths, and this has prompted an intense activity. Experimentally, localization has been reported in light waves 3 microwaves4, sound waves5, and electron gases6 but to our knowledge there is no direct observation of exponential spatial localization of matter-waves (electrons or others). We present here the observation of Anderson localization7 of a Bose-Einstein condensate (BEC) released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle. We also show that, in our one-dimensional speckle potentials whose noise spectrum has a high spatial frequency cut-off, exponential localization occurs only when the de Broglie wavelengths of the atoms in the expanding BEC are larger than an effective mobility edge corresponding to that cut-off. In the opposite case, we find that the density profiles decay algebraically8.
Bose-Einstein condensates (BECs) have proven to be remarkable systems with which to study some of the foundational models of condensed matter physics. The observation of a critical velocity for the breakdown of superfluidity in a BEC and the superfluid to Mott insulator transition observed in a BEC trapped by an optical lattice are but two examples of the, by now, dozens of exciting results in this field, which combines theoretical tools from condensed matter physics with state-of-the-art experimental techniques from ultra-cold atomic physics. However, any real condensed matter system has to contend with the effects of disorder, a phenomena notably absent in the inherently clean BEC systems. We have developed and implemented a way to add well characterized disorder in a controlled way to the otherwise clean BEC system using the light field from a laser speckle pattern. Using this system, we have investigated the effects of disorder or a single Gaussian defect, on the collective dipole motion of a BEC of 7Li in an optical trap. In addition, we perform transport experiments on a weakly interacting BEC expanding in a disordered one-dimensional atom wave-guide. We have observed that in such a system, the wave nature of matter can lead to spectacular and counterintuitive phenomena. Specifically, we verify that this system exhibits Anderson localization, a phenomena fundamentally resulting from the interference of multiply scattered matter waves. In such a state, the localized gas behaves as an insulator in a regime where it is classically expected to be conducting.\nWe also present results of experiments regarding a repulsive BEC scattering from a semi-permeable, single defect potential. We investigate the transport properties of such a system with special emphasis on the velocity and defect strength dependent dissipation of the collective dipole motion of the BEC. Finally, we present the results of our experiments on the scattering properties of bright matter wave solitons. We have observed fragmentation of the soliton in a disordered potential as well as both splitting and recombination of a soliton after interacting with a single repulsive defect potential.