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arXiv:1805.04727

Observation of phonon parametric down-conversion in a spherical Bose-Einstein condensate

Tianyou Gao, Jian-Song Pan, Dongfang Zhang, Lingran Kong, Ruizong Li, Xing Quan Shen, Xiao-Long Chen, Shi-Guo Peng, Mingsheng Zhan, W. Vincent Liu, Kaijun Jiang

Published May 12, 2018• 2 citations
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Abstract

We report the observation of parametric down-conversion of phonons in a spherical Bose-Einstein condensate. The spherical symmetry, which is crucial for observing this phenomenon, is experimentally demonstrated by measuring the collective mode and expansion behavior of the condensate. The low-energy monopole mode is excited by coupling with a high-energy mode with a nearly twice eigen-frequency. The population of the low-energy mode becomes maximum only when the high-energy mode is resonantly excited. Furthermore, we directly observe the parametric down-conversion process in the driving process, through simultaneously probing the two coupling modes. The experimental observation is consistent with the perturbation theory including the gravity effect. This work opens the challenge in related study of the condensate beyond mean-field theory and has potential applications in quantum information.

DOI
10.48550/arxiv.1805.04727

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We report the observation of parametric down-conversion of phonons in a spherical Bose-Einstein condensate. The spherical symmetry, which is crucial for observing this phenomenon, is experimentally demonstrated by measuring the collective mode and expansion behavior of the condensate. The low-energy monopole mode is excited by coupling with a high-energy mode with a nearly twice eigen-frequency. The population of the low-energy mode becomes maximum only when the high-energy mode is resonantly excited. Furthermore, we directly observe the parametric down-conversion process in the driving process, through simultaneously probing the two coupling modes. The experimental observation is consistent with the perturbation theory including the gravity effect. This work opens the challenge in related study of the condensate beyond mean-field theory and has potential applications in quantum information.
We report the first experimental observation of Beliaev coupling between collective excitations of a Bose-Einstein condensed gas. Beliaev coupling is not predicted by the Gross-Pitaevskii equation and so this experiment tests condensate theory beyond the mean field approximation. Measurements of the amplitude of a high frequency scissors mode show that the Beliaev process transfers energy to a lower-lying mode and then back and forth between these modes, unlike Landau processes which lead to a monotonic decrease in amplitude. To enhance the Beliaev process we adjusted the geometry of the magnetic trapping potential to give a frequency ratio of 2 to 1 between the two scissors modes.
We experimentally and theoretically observe the expansion behaviors of a spherical Bose–Einstein condensate. A rubidium condensate is produced in an isotropic optical dipole trap with an asphericity of 0.037. We measure the variation of the condensate size in the expansion process after switching off the trap. The free expansion of the condensate is isotropic, which is different from that of the condensate usually produced in the anisotropic trap. We derive an analytic solution of the expansion behavior based on the spherical symmetry, allowing a quantitative comparison with the experimental measurement. The interaction energy of the condensate is gradually converted into the kinetic energy during the expansion and after a long time the kinetic energy saturates at a constant value. We obtain the interaction energy of the condensate in the trap by probing the long-time expansion velocity, which agrees with the theoretical calculation. This work paves a way to explore novel quantum states of ultracold gases with the spherical symmetry.
Summary form only given. The microscopic theory of interacting Bose gases developed more than 50 years ago by Bogoliubov plays an essential role in the description of these systems. However, processes such as Beliaev damping are not predicted by the mean field approximation. Recently, the observation of Beliaev damping for a scissors mode of a BEC of rubidium atoms has been reported allowing the consideration of theory beyond the mean field. The Beliaev damping process is, in a sense, analogous to parametric down conversion of light, where one photon incident on a nonlinear crystal with second order susceptibility is split into two new photons of lower frequencies. Parametric down conversion has long been considered as an important source of squeezed states. In this paper we point out that similar processes can be observed in BEC.
A description of the dynamical response of uniformly trapped Bose–Einstein condensates (BECs) to oscillating external gravitational fields is developed, with the inclusion of damping. Two different effects that can lead to the creation of phonons in the BEC are identified; direct driving and parametric driving. Additionally, the oscillating gravitational field couples phonon modes, which can lead to the transition of excitations between modes. The special case of the gravitational field of a small, oscillating sphere located closely to the BEC is considered. It is shown that measurement of the effects may be possible for oscillating source masses down to the milligram scale, with a signal to noise ratio of the order of 10. To this end, noise terms and variations of experimental parameters are discussed and generic experimental parameters are given for specific atom species. The results of this article suggest the utility of BECs as sensors for the gravitational field of very small oscillating objects which may help pave the way towards gravity experiments with masses in the quantum regime.
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We explore, both experimentally and theoretically, the response of an elongated Bose-Einstein condensate to modulated interactions. We identify two distinct regimes differing in modulation frequency and modulation strength. Longitudinal surface waves are generated either resonantly or parametrically for modulation frequencies near the radial trap frequency or twice the trap frequency, respectively. The dispersion of these waves, the latter being a Faraday wave, is well-reproduced by a mean-field theory that accounts for the 3D nature of the elongated condensate. In contrast, in the regime of lower modulation frequencies we find that no clear resonances occur, but with increased modulation strength, the condensate forms an irregular granulated distribution that is outside the scope of a mean-field approach. We find that the granulated condensate is characterized by large quantum fluctuations and correlations, which are well-described with single-shot simulations obtained from wavefunctions computed by a beyond mean-field theory at zero temperature, the multiconfigurational time-dependent Hartree for bosons method.