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arXiv:2209.00790 · Physical Review Research

Dark quantum droplets and solitary waves in beyond-mean-field Bose-Einstein condensate mixtures

Matthew Edmonds

Published Jun 20, 2023• 30 citations
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Abstract

Quantum liquidlike states of matter have been realized in an ongoing series of experiments with ultracold Bose gases. Using a combination of analytical and numerical methods we identify the specific criteria for the existence of dark solitons in beyond-mean-field binary condensates, revealing how these excitations exist for both repulsive and attractive interactions, the latter leading to dark quantum droplets with properties intermediate between a dark soliton and a quantum droplet. The phenomenology of these excitations is explored within the full parameter space of the model, revealing a spatial profile of the excitation that differs significantly from the Zakharov-Shabat soliton, leading to a negative effective mass that is enhanced in the presence of the quantum fluctuations. Finally the dynamics of pairs of the excitations are explored, showing nonintegrable dynamics and dark soliton bound states in the attractive regime.

DOI
10.1103/physrevresearch.5.023175

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Quantum liquidlike states of matter have been realized in an ongoing series of experiments with ultracold Bose gases. Using a combination of analytical and numerical methods we identify the specific criteria for the existence of dark solitons in beyond-mean-field binary condensates, revealing how these excitations exist for both repulsive and attractive interactions, the latter leading to dark quantum droplets with properties intermediate between a dark soliton and a quantum droplet. The phenomenology of these excitations is explored within the full parameter space of the model, revealing a spatial profile of the excitation that differs significantly from the Zakharov-Shabat soliton, leading to a negative effective mass that is enhanced in the presence of the quantum fluctuations. Finally the dynamics of pairs of the excitations are explored, showing nonintegrable dynamics and dark soliton bound states in the attractive regime.
We look into dark solitons in a quasi-1D dipolar Bose gas and in a quantum droplet. We derive the analytical solitonic solution of a Gross-Pitaevskii-like equation accounting for beyond mean-field effects. The results show there is a certain critical value of the dipolar interactions, for which the width of a motionless soliton diverges. Moreover, there is a peculiar solution of the motionless soliton with a nonzero density minimum. We also present the energy spectrum of these solitons with an additional excitation subbranch appearing. Finally, we perform a series of numerical experiments revealing the coexistence of a dark soliton inside a quantum droplet.
We unravel the existence and stability properties of dark soliton solutions as they extend from the regime of trapped quantum droplets towards the Thomas-Fermi limit in homonuclear symmetric Bose mixtures. Leveraging a phase-plane analysis, we identify the regimes of existence of different types of quantum droplets and subsequently examine the possibility of black and gray solitons and kink-type structures in this system. Moreover, we employ the Landau dynamics approach to extract an analytical estimate of the oscillation frequency of a single dark soliton in the relevant extended Gross--Pitaevskii model. Within this framework, we also find that the single soliton immersed in a droplet is stable, while multisoliton configurations exhibit parametric windows of oscillatory instabilities. Our results pave the way for studying dynamical features of nonlinear multisoliton excitations in a droplet environment in contemporary experimental settings.
Recent theoretical and experimental results show that one-dimensional (1D) weakly interacting atomic Bose-Bose mixtures with repulsive interspecies mean field (MF) interaction are stabilized by attractive quadratic beyond-mean-field (BMF) effects into self-bound quantum droplet (QD) in free space. Here, we construct an exact analytical model to investigate the structure and dynamics of QDs in presence of external harmonic confinement by solving the 1D extended Gross-Pitäevskii equation (eGPE) with temporal variation of MF and BMF interactions. The model provides the analytical form of wavefunction, phase, MF and BMF nonlinearities. The generation of QDs and interesting droplet to soliton transition in presence of regular/expulsive parabolic traps by taking the comparable MF and BMF interactions are illustrated. We derive the phase diagram of the droplet-soliton phase transition between amplitude of MF, BMF interactions and harmonic oscillator frequency. The strength and form of oscillator frequency are identified as key parameter for tuning the compression, fragmentation and transport of droplets. Finally, the stability of the obtained solutions are confirmed from Vakhitov-Kolokolov (VK) criterion and are found stable.
We model the dynamics of formation of multiple, long-lived, bright solitary waves (BSWs) in the collapse of Bose–Einstein condensates with attractive interactions as studied in the experiment of Cornish et al (2006 Phys. Rev. Lett. 96 170401). We use both mean-field and approximate quantum field simulation techniques. While a number of separated wave packets form as observed in the experiment, they do not have a repulsive π phase difference as has been previously inferred. We observe that the inclusion of quantum fluctuations causes soliton dynamics to be predominantly repulsive in one-dimensional (1D) simulations independent of their initial relative phase. However, indicative 3D simulations do not show a similar effect. In contrast, in 3D quantum noise has a negative impact on BSW lifetimes. Finally, we show that condensate oscillations, after the collapse, may serve to deduce three-body recombination rates.
The ultracold and ultradilute bosonic heteronuclear mixture (41K - 87Rb) of Bose-Einstein condensates with tunable interspecies interaction at zero temperature is studied in the self-bound regime, using numerical simulations based on Density Functional Theory within the Local Density Approximation. In particular, the beyond mean-field effects embodied in the Lee-Huang-Yang energy contribution are explicitly included in the total energy functional. The thermodynamic properties of the homogeneous system are investigated to set the stability conditions of the self-bound droplet. The surface properties are discussed with (i) a variational approach, (ii) a numerical method and (iii) by solving the two coupled Gross-Pitaevskii equations associated to the two components of the mixture. The validity of the liquid-drop model is verified by computing the total ground state energy for systems with a different number of particles and, after the confinement in a quasi-1D configuration by means of an optical waveguide, we also discuss the transition between quantum droplets and bright solitons, two localized states of different nature.
The existence of quantum droplets in binary Bose-Einstein condensate mixtures relies on beyond-mean-field effects, competing with mean-field effects. Interestingly, the beyond-mean-field effects change from repulsive in three dimensions (3D) to attractive in 1D leading to drastically different behaviors. We quantitatively model quantum droplets in the beyond-mean-field crossover from 1D to 3D in the relevant case of an elongated harmonic trap and give realistic numbers for experimental realizations. We identify and quantify two main limiting factors: three-body losses and tiny energy scales. The crossover region is appealing as it offers a trade-off between these two main limitations opening the possibility of observing stable flat-top density profiles, a yet unobserved, characteristic feature of quantum droplets. It would permit testing of beyond-mean-field theories to an unprecedented precision.