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Physica Scripta

Quantum fluctuation in the segregation phase of two-component weakly interacting Bose–Einstein condensates

L Ng Dung, L Th Lam, Luong Van Tien, Phạm Thế Song

Published Jul 2, 2024• 0 citations
Publisher

Abstract

Abstract Our investigation focuses on the condensate density, excited and condensed fractions of bosons in a mixture of two-component segregated weakly interacting Bose–Einstein condensates (BECs) at zero temperature based on the Gross–Pitaevskii (GP) and Cornwall-Jackiw-Tomboulis (CJT) theories. We find that the repulsive interaction among interspecies of bosons is the origin of the local behavior and the decline of quantum fluctuation. These features are disparate to the single BEC or miscible BECs. The numerical evaluation of the condensed fraction is provided to support the experimental observation.

DOI
10.1088/1402-4896/ad5e0c

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Abstract Our investigation focuses on the condensate density, excited and condensed fractions of bosons in a mixture of two-component segregated weakly interacting Bose–Einstein condensates (BECs) at zero temperature based on the Gross–Pitaevskii (GP) and Cornwall-Jackiw-Tomboulis (CJT) theories. We find that the repulsive interaction among interspecies of bosons is the origin of the local behavior and the decline of quantum fluctuation. These features are disparate to the single BEC or miscible BECs. The numerical evaluation of the condensed fraction is provided to support the experimental observation.
We study the dynamics of two-component atomic Bose gases initially in a mixture encountering a sudden quench of the interspecies interactions. The dynamics above the critical temperature Tc{T}_{c}Tc​ is studied using a leading-order large-NNN approximation that predicted a phase transition from mixing to phase separation as a function of the interspecies coupling. Here, we explore the dynamics of this phase transition following a quench and compare our results to those found at zero temperature using the time-dependent Gross-Pitaevskii equations which ignore quantum and thermal fluctuations. In the regime above Tc{T}_{c}Tc​ where no condensate is present, however, the time evolution of the densities following the quench exhibits features similar to those found at zero temperature where only the condensates contribute to the densities. When the interspecies interaction jumps above the critical value, we observe dynamical transitions from a homogeneous mixture to a phase-separated structure for both cases. Our simulations suggest that at temperatures above Tc{T}_{c}Tc​ where no condensate is present this dynamical transition should still be observable in experiments.
Abstract The density of condensates of a binary mixture of Bose gases restricted by two parallel planar walls is investigated within the framework of Cornwal-Jackiw-Tomboulis effective action approach in improved Hartree-Fock approximation. It results that the density of condensates strongly depend not only on the distance between two walls but also on the interspecies interaction strength and they are equal their expectation values of the field operators after adding a term associated with the quantum fluctuations.
We study the properties of a homogeneous dilute Bose-Bose gas in a weak-disorder potential at zero temperature. By using the perturbation theory, we calculate the disorder corrections to the condensate density, the equation of state, the compressibility, and the superfluid density as a function of density, strength of disorder, and miscibility parameter. It is found that the disorder potential may lead to modifying the miscibility-immiscibility condition and a full miscible phase turns out to be impossible in the presence of the disorder. We show that the intriguing interplay of the disorder and intra- and interspecies interactions may strongly influence the localization of each component, the quantum fluctuations, and the compressibility, as well as the superfluidity of the system.
In this Thesis we study steady state solutions and dynamical evolutions of two– component atomic Bose–Einstein Condensates. We initially investigate the equilibrium properties of condensate mixtures in harmonic trapping potentials at zero temperature. Subsequently we simulate the coupled growth of these condensates by inclusion of damping terms. Finally, we investigate the evolution of coupled Bose gases via the so-called classical–field method. A recent experiment [D. J. McCarron et al., Phys. Rev. A, 84, 011603(R) (2011)] achieved Bose–Einstein Condensation of a two–species 87Rb–133Cs phase segregated mixture in harmonic trapping potentials. Depending on relative atom numbers of the two species, three distinct regimes of density distributions were observed. For these experimental parameters, we investigate the corresponding time–independent ground state solutions through numerical simulations of the coupled Gross–Pitaevskii equations. By including experimentally relevant shifts between the traps, we observe a range of structures including ‘ball and shell’ formations and axially/radially separated states. These are found to be very sensitive to the trap shifts. For all three experimental regimes, our numerical simulations reveal good qualitative agreement. The observed experimental profiles cannot be guaranteed to be fully equilibrated. This, coupled with the rapid sympathetic cooling of the experimental system, leads to a situation where growth may play a determining factor in the density structures formed. To investigate this further, we introduce phenomenological damping to describe the associated condensate growth/decay, revealing a range of transient structures. However, such a model always predicts the predominance of one condensate species over longer evolution times. Work undertaken by collaborators with the more elaborate Stochastic Projected Gross–Pitaevskii equations, which can describe condensate formation by coupling to a heat bath, predicts the spontaneous formation of dark–bright solitons. Motivated by this, we show how the presence of solitons can affect the condensate distribution, thus highlighting the overall dynamical role in the emerging patterns. Finally, we use classical field methods to analyse the evolution of non trapped Bose gases from strongly nonequilibrium initial distributions. The contrast between miscible (overlapping) and immiscible (phase segregated) components gives rise to important distinctions for condensate fractions and the formation of domains and vortices. In addition, splitting the particles of a single component thermalised state into two components is investigated. We then study the effects of suddenly quenching the strength of the interspecies interactions. Under suitable conditions, this quench generates isotropic vortex tangles. While this tangle subsequently decays over time, we propose how a repeat sequence of quenches at regular intervals could be employed to drive the tangle, thereby potentially providing a novel route to the generation of quantum turbulence.
This work reports studies of a mixture of two interacting Bose condensates in a quasi-one-dimensional geometry using a finite-temperature path-integral Monte Carlo method. For weakly interacting dilute gases, the interactions between atoms are modeled by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interspecies interaction on the static properties, such as the density profile and the superfluid fraction, is discussed. Our results show that for repulsive intra- and interspecies interactions, the presence of the interspecies interactions dramatically changes the structure of both the density profile and the superfluid fraction, and two species are seen to partially separate in space, and there is a finite-size effect on the phase separation between two partially separating Bose-Einstein condensates. In general, our results agree with the theoretical predictions and experimental observations.