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arXiv:1804.08391 · Physical Review A

Influence of the interaction between quasiparticles on parametric resonance in Bose-Einstein quasicondensates

Maciej Pylak, Paweł Zin

Published Oct 2, 2018• 5 citations
arXivHTMLPDF

Abstract

We perform a simulation of the experiment [J. C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012)] where the temporal modification of the effective one-dimensional interaction constant was used to create pairs of atoms with opposite velocities. The simulations clearly demonstrate the huge impact of the interaction between quasiparticles due to finite temperature on the pair production process, explaining the relatively small atomic pair production and the absence of number squeezing in the experiment.

DOI
10.1103/physreva.98.043603

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We perform a simulation of the experiment [J. C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012)] where the temporal modification of the effective one-dimensional interaction constant was used to create pairs of atoms with opposite velocities. The simulations clearly demonstrate the huge impact of the interaction between quasiparticles due to finite temperature on the pair production process, explaining the relatively small atomic pair production and the absence of number squeezing in the experiment.
We consider elastic scattering of atoms from elongated clouds taking into account an effective, finite duration of the collision due to the expansion of the condensates. We also include the quasicondensate nature of the degenerate quantum gas, due to a finite temperature of the system. We evaluate the pair-correlation function measured experimentally in Kheruntsyan et al. [Phys. Rev. Lett. 108, 260401 (2012)] and show that the finite duration of the collision is an important factor determining the properties of the correlations. Our analytic calculations are in agreement with the measurements. The analytical model we provide, useful for identifying physical processes that influence the correlations, is relevant for experiments with nonclassical pairs of atoms.
In the leading paradigm of cosmology, most particles are created during a reheating period following inflation. Part of this creation proceeds via parametric resonance [1], a process referred to as preheating. Since inflation essentially dilutes any pre-existing particles, particle production proceeds from fields in their vacuum state, a phenomenon of purely quantum origin similar to a dynamical Casimir effect (DCE). While the predicted quantum origin seems hard to test in the cosmological context, experiments involving genuine quantum fields evolving under the same dynamics have been realised. Ref. [2] reports on such an experiment in an elongated cigar-shaped Bose-Einstein condensate (BEC). The BEC is periodically modulated and acts as a classical field exciting its own quantum perturbations (phonons), created in pairs of opposite momenta ±k, with occupation number n_k and correlation amplitude c_k. Entanglement of the generated pairs is known to be a signature of pair production seeded by vacuum fluctuations [3] but is also fragile. Indeed, in [2] the observed pair correlation c_k was much weaker than expected and far from the regime c_k > n_k indicating entanglement. In a series of publications, the theoretical description behind the experiment was re-analysed in increasing detail to account for the absence of entanglement.First, in [3] weak dissipation of the excitations was phenomenologically introduced and shown to be able to prevent the generation of entanglement. A fully nonlinear numerical study of the modulated gas based on the Truncated Wigner Approximation (TWA) was then conducted in [4]. It confirmed that phonon-phonon interactions can induce an effective dissipation acting against the parametric resonance.In [5], we identified the dominant interaction channel for small occupation numbers in 1D quasi-BEC as Beliaev-Landau scatterings between the resonant mode and the thermal population. We analytically derived its rate and checked it against TWA simulations.Finally, in [6], whose results I will present in the talk, we demonstrate that the phenomenological model of [3], when supplemented by the rate derived in [5], accurately reproduces the particle and correlation generation seen in TWA simulations akin to that of [4].In this talk, I will first emphasise the subtle interplay between growth and dissipation, leading to distinct particle generation regimes. Then, informed by these findings, I will briefly discuss different optimal experimental strategies to achieve observation of entanglement.[1] D. Figueroa and F. Torrentí, JCAP02(2017)001 (2016)[2] J.-C. Jaskula et al., Phys. Rev. Lett. 109, 220401 (2012)[3] X. Busch, R. Parentani and S. Robertson, Phys. Rev. A 89, 063606 (2014)[4] S. Robertson, F. Michel and R. Parentani, Phys. Rev. D 98, 056003 (2018)[5] A. Micheli and S. Robertson, Phys. Rev. B 106, 214528 (2022)[6] A. Micheli and S. Robertson, Comptes Rendus Physique, Online first (2024), pp. 1-34. doi: 10.5802/crphys.250
In this thesis a number of aspects on possible manipulation of Bose-Einstein condensate in trapped atomic gases is investigated. First, a model for atom optical experiments involving Bose condensates is proposed and numerical simulations are presented to illustrate its characteristics. We demonstrate ways of focusing and splitting the condensate by modifying experimentally adjustable parameters. We show that there are at least two ways of implementing atom optical elements: one may modulate the interatomic scattering length in space, or alternatively, use a sinusoidal, externally applied potential. The temporal evolution of quasiparticle excitations is studied via the Gross-Pitaevskii Equation. Nonlinear mode mixing of quasiparticles is introduced, and is observed using a quasiparticle projection method. This is used as a basis of time-dependent finite temperature simulations, which we argue to be valid under regimes of high occupation number. An illustration via a closely related evaporative cooling simulation is provided. A phenomenological damping formalism for superfluidity near the λ point is adopted to describe the damping of excitations in a Bose-Einstein condensate. An estimate for the damping parameter is found. The damping formalism as a numerical tool to calculate the ground eigenstate of the condensate is explored. A novel, experimentally realisable interferometry for Bose-Einstein condensates using near-field diffraction is proposed. The scheme is based on the phenomenon of intermode traces or quantum carpets; we demonstrate the structured spatio-temporal pattern for the dilute, atomic Bose-Einstein condensate. The pattern is found to change with temperature, which allows us to perform interferometric temperature measurements. Finally, an output coupler for Bose-Einstein Condensates based on stimulated Raman transition is investigated. The spectrum and coherence are calculated for an atomic beam slowly coupled out of a trap containing a partially condensed Bose gas at finite temperatures. A number conserving Hartree-Fock-Bogliubov formalism has been used to incorporate finite temperature effects. Various different processes are found to become dominant for a suitable choice of the coupling parameters.
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.
A Bose-Einstein condensate in an optical lattice exhibits parametric resonances when the intensity of the lattice is periodically modulated in time. These resonances correspond to an exponential growth of the population of counter-propagating Bogoliubov excitations. A suitable linearization of the Gross-Pitaevskii (GP) equation is used to calculate the stability diagram and the growth rates of the unstable modes. The results agree with the ones extracted from time-dependent GP simulations, supporting our previous claim [M. Kr\"amer et al., Phys. Rev. A 71, 061602(R) (2005)] concerning the key role of parametric resonances in the response observed by St\"oferle et al. [Phys. Rev. Lett. 92, 130403 (2004)] in the superfluid regime. The role of the seed excitations required to trigger the parametric amplification is discussed. The possible amplification of the quantum fluctuations present in the quasiparticle vacuum, beyond GP theory, is also addressed, finding interesting analogies with similar processes in nonlinear quantum optics and with the dynamic Casimir effect. Our results can be used in exploiting parametric instabilities for the purpose of spectroscopy, selective amplification of a particular excitation mode and for establishing a new type of thermometry.