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arXiv:2508.01654 · Comptes Rendus Physique

Parametric pair production of collective excitations in a Bose–Einstein condensate

Victor Gondret, Rui Dias, Clothilde Lamirault, Léa Camier, Amaury Micheli, Charlie Leprince, Quentin Marolleau, Scott Robertson, Denis Boiron, Christoph Ira Westbrook

Published Nov 3, 2025• 1 citation
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Abstract

By exciting the transverse breathing mode of an elongated Bose–Einstein condensate, we parametrically produce longitudinal collective excitations in a pairwise manner. This process, also referred to as Faraday wave generation, can be seen as an analog to cosmological particle production. Building upon single particle detection, we investigate the early time dynamics of the exponential growth and compare our observations with a Bogoliubov description. The growth rate we observe experimentally is in very good agreement with theoretical predictions, demonstrating the validity of the Bogoliubov description and thereby confirming the smallness of quasiparticle interactions in such an elongated gas. We also discuss the presence of oscillations in the atom number, which are due to pair correlations and to the rate at which interactions are switched off.

DOI
10.5802/crphys.266

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By exciting the transverse breathing mode of an elongated Bose–Einstein condensate, we parametrically produce longitudinal collective excitations in a pairwise manner. This process, also referred to as Faraday wave generation, can be seen as an analog to cosmological particle production. Building upon single particle detection, we investigate the early time dynamics of the exponential growth and compare our observations with a Bogoliubov description. The growth rate we observe experimentally is in very good agreement with theoretical predictions, demonstrating the validity of the Bogoliubov description and thereby confirming the smallness of quasiparticle interactions in such an elongated gas. We also discuss the presence of oscillations in the atom number, which are due to pair correlations and to the rate at which interactions are switched off.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.
We observe entanglement between collective excitations of a Bose-Einstein condensate in a configuration analogous to particle production during the preheating phase of the early Universe. In our setup, the oscillation of the inflaton field is mimicked by the transverse breathing mode of a cigar-shaped condensate, which parametrically excites longitudinal quasiparticles with opposite momenta. After a short modulation period, we observe entanglement of these pairs that reveals the role played by vacuum fluctuations in seeding the parametric growth, confirming the quantum origin of the excitations. As the system continues to evolve, we observe a decrease in correlations and a disappearance of nonclassical features. These point toward future experimental probes of the late-time nonlinear regime where further analogies can be drawn with reheating, i.e., the thermalization of the postinflationary Universe.
Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.
We study the formation of Faraday waves in an elongated Bose-Einstein condensate in the presence of a one-dimensional optical lattice. The waves are parametrically excited by modulating the radial confinement of the condensate close to a transverse breathing mode of the system. For very shallow optical lattices, phonons with a well-defined wave vector propagate along the condensate, as in the absence of the lattice, and we observe the formation of a Faraday pattern. We find that by increasing the potential depth the local sound velocity decreases, and when it equals the condensate local phase velocity, the condensate develops an incoherent superposition of several modes and the parametric excitation of Faraday waves is suppressed.
We present a numerical study of the dynamical effects following a sudden change of the transverse trapping frequency in an elongated Bose-Einstein condensate, which induces periodic oscillations of the radial density. At early times, we observe an exponential growth of the number of resonant longitudinal phonons, in agreement with the predictions of the Bogoliubov-de Gennes treatment. We then observe an ordered sequence of phenomena induced by the nonlinearities of the Gross-Pitaevskii equation. The first is a loss of the nonseparability of the resonant phonon pairs. This is followed by the saturation of the exponential growth and a strong depletion of condensed atoms. Notably, these effects are well-described by effective 1D dynamics, and are hardly affected by the damping of the radial oscillations. Finally, the atomic spectrum becomes broad, featureless and almost incoherent, in agreement with experimental results obtained in [J.-C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012)]. The link between this sequence of events and the preheating scenario in inflationary cosmology is striking.