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arXiv:2103.15283 · Scientific Reports

On the survival of the quantum depletion of a condensate after release from a magnetic trap

J. A. Ross, Piotr Deuar, D. K. Shin, Kieran F. Thomas, B. M. Henson, Sean S. Hodgman, Andrew G. Truscott

Published Aug 1, 2022• 7 citations
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Abstract

We present observations of the high momentum tail in expanding Bose-Einstein condensates of metastable Helium atoms released from a harmonic trap. The far-field density profile exhibits features that support identification of the tails of the momentum distribution as originating in the in-situ quantum depletion prior to release. Thus, we corroborate recent observations of slowly-decaying tails in the far-field beyond the thermal component. This observation is in conflict with the hydrodynamic theory, which predicts that the in-situ depletion does not survive when atoms are released from a trap. Indeed, the depleted tails even appear stronger in the far-field than expected before release, and we discuss the challenges of interpreting this in terms of the Tan contact in the trapped gas. In complement to these observations, full quantum simulations of the experiment show that, under the right conditions, the depletion can persist into the far field after expansion. Moreover, the simulations provide mechanisms for survival and for the the large-momentum tails to appear stronger after expansion due to an acceleration of the depleted atoms by the mean-field potential. However, while in qualitative agreement, the final depletion observed in the experiment is much larger than in the simulation.

DOI
10.1038/s41598-022-16477-9

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We present observations of the high momentum tail in expanding Bose-Einstein condensates of metastable Helium atoms released from a harmonic trap. The far-field density profile exhibits features that support identification of the tails of the momentum distribution as originating in the in-situ quantum depletion prior to release. Thus, we corroborate recent observations of slowly-decaying tails in the far-field beyond the thermal component. This observation is in conflict with the hydrodynamic theory, which predicts that the in-situ depletion does not survive when atoms are released from a trap. Indeed, the depleted tails even appear stronger in the far-field than expected before release, and we discuss the challenges of interpreting this in terms of the Tan contact in the trapped gas. In complement to these observations, full quantum simulations of the experiment show that, under the right conditions, the depletion can persist into the far field after expansion. Moreover, the simulations provide mechanisms for survival and for the the large-momentum tails to appear stronger after expansion due to an acceleration of the depleted atoms by the mean-field potential. However, while in qualitative agreement, the final depletion observed in the experiment is much larger than in the simulation.
We present observations of quantum depletion in expanding condensates released from a harmonic trap. We confirm experimental observations of slowly-decaying tails in the far-field beyond the thermal component, consistent with the survival of the quantum depletion. Our measurements support the hypothesis that the depletion survives the expansion, and even appears stronger in the far-field than expected before release based on the Bogoliubov theory. This result is in conflict with the hydrodynamic theory which predicts that the in-situ depletion does not survive when atoms are released from a trap. Simulations of our experiment show that the depletion should indeed survive into the far field and become stronger. However, while in qualitative agreement, the final depletion observed in the experiment is much larger than in the simulation. In light of the predicted power-law decay of the momentum density, we discuss general issues inherent in characterizing power laws.
Measurements of Tan's contact in expanding condensate conflict with predictions of the in situ quantum depletion. It is unclear how the depletion survives without a condensate, and even appears stronger in the far-field than before the trap release. We confirm experimental observations of a power-law decay in the far-field, consistent with the survival of the quantum depletion. Simulations of our experiment support this conclusion and provide a partial explanation. A gap between the numerical and empirical results is an open question obstructing studies of quantum depletion in the far field.
We study the expansion of an interacting atomic system at zero temperature, following its release from an isotropic three-dimensional harmonic trap and calculate the time dependence of its density and momentum distribution, with special focus on the behavior of the contact parameter. We consider different quantum systems, including the unitary Fermi gas of infinite scattering length, the weakly interacting Bose gas, and two interacting particles with highly asymmetric mass imbalance. In all cases analytic results can be obtained, which show that the initial value of the contact, fixing the 1/k41/{k}^{4}1/k4 tail of the momentum distribution, disappears for large expansion times. Our results raise the problem of understanding the recent experiment of R. Chang et al. [Phys. Rev. Lett. 117, 235303 (2016)] carried out on a weakly interacting Bose gas of metastable 4He^{4}\mathrm{He}4He atoms, where a 1/r41/{r}^{4}1/r4 tail in the density distribution was observed after a large expansion time, implying the existence of the 1/k41/{k}^{4}1/k4 tail in the asymptotic momentum distribution.
We report on the single-atom-resolved measurement of the distribution of momenta ℏk in a weakly interacting Bose gas after a 330 ms time of flight. We investigate it for various temperatures and clearly separate two contributions to the depletion of the condensate by their k dependence. The first one is the thermal depletion. The second contribution falls off as k^{-4}, and its magnitude increases with the in-trap condensate density as predicted by the Bogoliubov theory at zero temperature. These observations suggest associating it with the quantum depletion. How this contribution can survive the expansion of the released interacting condensate is an intriguing open question.
We measure the momentum density in a Bose-Einstein condensate (BEC) with dilute spin impurities after an expansion in the presence of interactions. We observe tails decaying as 1/k^{4} at large momentum k in the condensate and in the impurity cloud. These algebraic tails originate from the impurity-BEC interaction, but their amplitudes greatly exceed those expected from two-body contact interactions at equilibrium in the trap. Furthermore, in the absence of impurities, such algebraic tails are not found in the BEC density measured after the interaction-driven expansion. These results highlight the key role played by impurities when present, a possibility that had not been considered in our previous work [Chang et al., Phys. Rev. Lett. 117, 235303 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.235303]. Our measurements suggest that these unexpected algebraic tails originate from the nontrivial dynamics of the expansion in the presence of impurity-bath interactions.
We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the thermodynamic Bethe ansatz equations. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the known scaling solutions of the hydrodynamic approach corresponding to self-similar expansion. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence on the trap anharmonicity of the shape variation of the density profile during evolution. We also characterize dynamical fermionization of an expanding cloud in terms of its first- and second-order coherences describing phase and density fluctuations.