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Journal of Physics Conference Series

Faraday waves and droplets in quasi-one-dimensional Bose gases

Lauro Tomio, A. Gammal, F. Kh. Abdullaev, R. Kishor Kumar

Published Mar 1, 2020• 1 citation
Publisher

Abstract

Abstract Faraday waves (FW) are studied in mixtures of Bose gases by taking into account quantum fluctuations beyond the GP mean-field formalism with the Lee-Huang-Yang term, with both inter-and intra-species scattering lengths periodically varying in time. In this case, the effect of periodic modulations on the system is studied, with nonlinear resonances shown to be excited in the oscillation widths of quantum droplets. It was shown that the period of the Faraday patterns is quite sensitive to the estimated value obtained by the beyond mean-field contribution, which can be used to measure quantum fluctuations in the ground state of the quasi-one-dimensional mixture. Variational predictions are confirmed by full numerical simulations. We also add an analysis of quantum droplets and quantum fluctuation contributions when considering three-body interactions.

DOI
10.1088/1742-6596/1508/1/012007

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Abstract Faraday waves (FW) are studied in mixtures of Bose gases by taking into account quantum fluctuations beyond the GP mean-field formalism with the Lee-Huang-Yang term, with both inter-and intra-species scattering lengths periodically varying in time. In this case, the effect of periodic modulations on the system is studied, with nonlinear resonances shown to be excited in the oscillation widths of quantum droplets. It was shown that the period of the Faraday patterns is quite sensitive to the estimated value obtained by the beyond mean-field contribution, which can be used to measure quantum fluctuations in the ground state of the quasi-one-dimensional mixture. Variational predictions are confirmed by full numerical simulations. We also add an analysis of quantum droplets and quantum fluctuation contributions when considering three-body interactions.
Abstract Faraday waves in mixtures of Bose gases are studied by taking into account quantum fluctuations beyond the Gross–Pitaevskii mean-field formalism with the Lee–Huang–Yang term. For that, a Bose–Einstein condensed binary atomic mixture is assumed trapped in cigar-type geometry, having the inter- and intra-species scattering lengths periodically varying in time. The period of the Faraday patterns is shown to be quite sensitive to the estimated value obtained by the beyond mean-field contribution, which can be used to measure quantum fluctuations in the ground state of the quasi-one-dimensional mixture. By studying the influence of the above nonlinear periodic modulations on quantum droplet dynamics, we also show that nonlinear resonances are excited in the oscillation widths of the quantum droplets. Variational predictions confirm numerical simulations for the corresponding formalism.
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.
Abstract We consider Bose–Einstein condensates with two- and three-body interactions periodically varying in time. Two models of time-dependent three-body interactions, with quadratic and quartic dependence on the two-body atomic scattering length a s , are studied. It is shown that parametric instabilities in the condensate lead to the generation of Faraday waves (FWs), with wavelengths depending on the background scattering length, as well as on the frequency and amplitude of the modulations of a s . From an experimental perspective, this opens a new possibility to tune the period of Faraday patterns by varying not only the frequency of modulations and background scattering length, but also the amplitude of the modulations. The latter effect can be used to estimate the parameters of three-body interactions from the FW experimental results. Theoretical predictions are confirmed by numerical simulations of the corresponding extended Gross–Pitaevskii equation.
We study liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under variable confinement introduced along one or two spatial dimensions. Although the atom-atom scattering has a three-dimensional character, discreteness of the available modes in the reduced dimension(s) strongly influences the zero-point energy, which for a weakly interacting three-dimensional system is given by the Lee-Huang-Yang term. Here, we generalize the result of Lee, Huang, and Yang and calculate the higher order corrections to the mean-field energy for a single component Bose-Einstein condensate under condition of a tight confinement in one or two spatial directions. We apply our results to the two-component mixture of bosonic species under conditions favorable for the creation of quantum liquid droplets, which constitute a perfect playground for studies of the beyond mean-field effects. Our findings allow one to analyze the properties of quantum droplets at the dimensional crossover and provide demanding conditions for accessing quasilow dimensions. They also pave a way for experimental exploration of this state of matter in reduced dimensions.
Quantum fluctuations play a pivotal role in determining the ground state properties and phase transitions of ultra-cold bosonic systems. This study presents a comprehensive theoretical investigation of fluctuation effects beyond mean-field theory in dilute Bose gases, examining their impact on the superfluid–Mott insulator transition, quantum droplet formation, and critical phenomena. Beginning with the Gross–Pitaevskii mean-field framework , we systematically incorporate quantum corrections through Bogoliubov theory, yielding the Lee–Huang–Yang (LHY) energy correction scaling as . The quantum depletion quantifies the fraction of atoms driven from the condensate by zero-point fluctuations. For the Bose–Hubbard model , quantum Monte Carlo simulations establish the superfluid–Mott insulator critical point at , shifted 15% from the mean-field prediction. Critical exponents and confirm 3D XY universality. Quantum droplets in binary mixtures are stabilized by the repulsive LHY correction against mean-field collapse, with equilibrium densities matching experimental observations in K mixtures. Finite-size scaling analysis and the Ginzburg criterion delineate regimes where fluctuation effects dominate. All theoretical predictions are validated against precision measurements in ultracold atomic gases.