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arXiv:1207.1146 · Laser Physics Letters

Out-of-phase oscillation between superfluid and thermal components for a trapped Bose condensate under oscillatory excitation

P. E. S. Tavares, Gustavo Deczka Telles, R. F. Shiozaki, C. Castelo Branco, Kílvia Mayre Farias, Vanderlei Salvador Bagnato

Published Feb 8, 2013• 11 citations
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Abstract

The vortex nucleation and the emergence of quantum turbulence induced by oscillating magnetic fields, introduced by Henn E A L, et al. 2009 (Phys. Rev. A 79, 043619) and Henn E A L, et al. 2009 (Phys. Rev. Lett. 103, 045301), left a few open questions concerning the basic mechanisms causing those interesting phenomena. Here, we report the experimental observation of the slosh dynamics of a magnetically trapped $^{87}$Rb Bose-Einstein condensate (BEC) under the influence of a time-varying magnetic field. We observed a clear relative displacement in between the condensed and the thermal fraction center-of-mass. We have identified this relative counter move as an out-of-phase oscillation mode, which is able to produce ripples on the condensed/thermal fractions interface. The out-of-phase mode can be included as a possible mechanism involved in the vortex nucleation and further evolution when excited by time dependent magnetic fields.

DOI
10.1088/1612-2011/10/4/045501

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The vortex nucleation and the emergence of quantum turbulence induced by oscillating magnetic fields, introduced by Henn E A L, et al. 2009 (Phys. Rev. A 79, 043619) and Henn E A L, et al. 2009 (Phys. Rev. Lett. 103, 045301), left a few open questions concerning the basic mechanisms causing those interesting phenomena. Here, we report the experimental observation of the slosh dynamics of a magnetically trapped 87^{87}87Rb Bose-Einstein condensate (BEC) under the influence of a time-varying magnetic field. We observed a clear relative displacement in between the condensed and the thermal fraction center-of-mass. We have identified this relative counter move as an out-of-phase oscillation mode, which is able to produce ripples on the condensed/thermal fractions interface. The out-of-phase mode can be included as a possible mechanism involved in the vortex nucleation and further evolution when excited by time dependent magnetic fields.
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).
In this work we study a Bose-Einstein condensate of 87Rb under the effects of an oscillatory excitation. The condensate is produced through forced evaporative cooling by radio-frequency in a harmonic magnetic trap. The excitation is generated by an oscillatory quadrupole field superimposed on the trapping potential. For a fixed value of the frequency of the excitation we observe the production of different regimes in the condensate as a function of two parameters of the excitation: the time and the amplitude. For the lowest values of these parameters we observe a bending of the main axis of the condensate. This demonstrates that the excitation is able to transfer angular momentum into the sample. By increasing the time or the amplitude of the excitation we observe the nucleation of an increasing number of quantized vortices. If the value of the parameters of the excitation is increased even further the vortices evolve into a different regime which we have identified as quantum turbulence. In this regime, the vortices are tangled among each other, generating a highly irregular array. For the highest values of the excitation the condensate breaks into pieces surrounded by a thermal cloud. This constitutes a different regime which we have identified as granulation. We present numerical simulations together with other theoretical considerations which allow us to interpret our observations. In this thesis we also describe the construction of a second experimental setup whose objective is to study magnetic properties of a Bose-Einstein condensate of 87Rb. In this new system the condensate is produced in a hybrid trap which combines a magnetic trap with an optical dipole trap. Bose-Einstein condensation has been already achieved in the new apparatus; experiments will be performed in the near future.
In this thesis we have basically studied two aspects of BoseEinstein condensation (BEC) in trapped dilute gases: (i) superfluidity with the possible onset of quantum turbulence (QT), and (ii) nonuniformity, which suggests the definition of new variables in order to build a global thermodynamic description. Both analyses were performed in a 87Rb BEC magnetically trapped in a QuadrupoleIoffe configuration (QUIC) trap. Concerning the first item, vortices and QT were generated by applying an oscillatory excitation formed by a quadrupole magnetic field superimposed onto the QUIC trapping potential. Scanning both the excitation amplitude and its duration allowed us to observe different regimes, particularly one with regular, welldefined vortices and another, where the onset of QT is believed to have occurred. The transition between this two regimes were explained by considering the finitesize characteristic of trapped gases. Additionally, data analyses on three vortex configurations suggested the presence of both vortices and antivortices (opposite circulation sign), and the vortex nucleation mechanism was proposed to be related to a relative motion between the condensate and thermal components, namely a counterflow. As for the second item, the BEC transition in our experiment was characterized in terms of new global thermodynamic variables. A phase diagram was constructed and compared to the superfluid helium phase transition. Finally, we provide preliminary results on the calculation of a global heat capacity, and briefly discuss the advantages of this new approach over the local density approximation alternative, particularly on BEC clouds in the presence of vortices and QT.
We report on the observation of vortex formation in a Bose-Einstein condensate of 87Rb^{87}\text{R}\text{b}87Rb atoms. Vortices are generated by superimposing an oscillating excitation to the trapping potential introduced by an external magnetic field. For small amplitudes of the external excitation field we observe a bending of the cloud axis. Increasing the amplitude we observe formation of a growing number of vortices in the sample. Shot-to-shot variations in both vortex number and position within the condensed cloud are observed, probably due to the intrinsic vortex nucleation dynamics. We discuss the possible formation of vortices and antivortices in the sample as well as possible mechanisms for vortex nucleation.