• Open Access

Dynamical Symmetry and Breathers in a Two-Dimensional Bose Gas

R. Saint-Jalm, P. C. M. Castilho, É. Le Cerf, B. Bakkali-Hassani, J.-L. Ville, S. Nascimbene, J. Beugnon, and J. Dalibard
Phys. Rev. X 9, 021035 – Published 21 May 2019
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Abstract

A fluid is said to be scale invariant when its interaction and kinetic energies have the same scaling in a dilation operation. In association with the more general conformal invariance, scale invariance provides a dynamical symmetry which has profound consequences both on the equilibrium properties of the fluid and its time evolution. Here we investigate experimentally the far-from-equilibrium dynamics of a cold two-dimensional rubidium Bose gas. We operate in the regime where the gas is accurately described by a classical field obeying the Gross-Pitaevskii equation, and thus possesses a dynamical symmetry described by the Lorentz group SO(2,1). With the further simplification provided by superfluid hydrodynamics, we show how to relate the evolutions observed for different initial sizes, atom numbers, trap frequencies, and interaction parameters by a scaling transform. Finally, we show that some specific initial shapes—uniformly filled triangles or disks—may lead to a periodic evolution corresponding to a novel type of breather for the two-dimensional Gross-Pitaevskii equation.

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  • Received 19 March 2019

DOI:https://doi.org/10.1103/PhysRevX.9.021035

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalNonlinear DynamicsCondensed Matter, Materials & Applied PhysicsFluid DynamicsGeneral PhysicsParticles & Fields

Authors & Affiliations

R. Saint-Jalm, P. C. M. Castilho, É. Le Cerf, B. Bakkali-Hassani, J.-L. Ville, S. Nascimbene, J. Beugnon, and J. Dalibard*

  • Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France

  • *jean.dalibard@lkb.ens.fr

Popular Summary

Symmetries play a central role in the investigation of a physical system. Most often they underlie conserved quantities, which considerably simplifies studies of system evolution. For example, spatial symmetries associated with translation and rotation lead to the conservation of linear and angular momentum. Here, we investigate a more subtle case: the dynamical symmetry related to scale or conformal invariance (SCI), which shows up for systems with no intrinsic length scale.

We explore experimentally the consequences of SCI on the evolution of 2D Bose gases, which are known to exhibit this symmetry. We prepare a uniform gas confined in a boxlike potential, and we release it in a harmonic potential. We look at the temporal evolution of the gas and show that trajectories corresponding to different initial conditions can be connected with each other, thanks to this dynamical symmetry. We also observe and numerically confirm a spectacular and unexpected phenomenon related to SCI: the existence of “breathers,” which are triangular- or disk-shaped gases (initially imposed by us) that periodically deform and then recover their shape in the potential.

Our findings are twofold. First, they fully support the validity of scale invariance for a weakly interacting 2D gas, which thus constitutes a good test bed for investigating this dynamical symmetry. Second, they show the existence of breathers for a 2D system described by a nonlinear equation, thus generalizing a phenomenon that until now was studied in 1D.

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Vol. 9, Iss. 2 — April - June 2019

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