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arXiv:2305.09422 · Physical Review A

Rotating quantum droplets confined in a harmonic potential

Sofoklis Nikolaou, G. M. Kavoulakis, Magnus Ögren

Published Nov 13, 2023• 16 citations
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Abstract

We investigate the rotational properties of a two-component, two-dimensional self-bound quantum droplet, which is confined in a harmonic potential and compare them with the well-known problem of a single-component atomic gas with contact interactions. For a fixed value of the trap frequency, choosing some representative values of the atom number, we determine the lowest-energy state, as the angular momentum increases. For a sufficiently small number of atoms, the angular momentum is carried via center-of-mass excitation. For larger values, when the angular momentum is sufficiently small, we observe vortex excitation instead. Depending on the actual atom number, one or more vortices enter the droplet. Beyond some critical value of the angular momentum, however, the droplet does not accommodate more vortices and the additional angular momentum is carried via center-of-mass excitation in a ``mixed'' state. Finally, the excitation spectrum is also briefly discussed.

DOI
10.1103/physreva.108.053309

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We investigate the rotational properties of a two-component, two-dimensional self-bound quantum droplet, which is confined in a harmonic potential and compare them with the well-known problem of a single-component atomic gas with contact interactions. For a fixed value of the trap frequency, choosing some representative values of the atom number, we determine the lowest-energy state, as the angular momentum increases. For a sufficiently small number of atoms, the angular momentum is carried via center-of-mass excitation. For larger values, when the angular momentum is sufficiently small, we observe vortex excitation instead. Depending on the actual atom number, one or more vortices enter the droplet. Beyond some critical value of the angular momentum, however, the droplet does not accommodate more vortices and the additional angular momentum is carried via center-of-mass excitation in a ``mixed'' state. Finally, the excitation spectrum is also briefly discussed.
We consider a “symmetric” quantum droplet in two spatial dimensions, which rotates in a harmonic potential, focusing mostly on the limit of “rapid” rotation. We examine this problem using a purely numerical approach, as well as a semianalytic Wigner-Seitz approximation (first developed by Baym, Pethick, and their co-workers) for the description of the state with a vortex lattice. Within this approximation we assume that each vortex occupies a cylindrical cell, with the vortex-core size treated as a variational parameter. Working with a fixed angular momentum, as the angular momentum increases and depending on the atom number, the droplet accommodates none, few, or many vortices, before it turns to center-of-mass excitation. For the case of a “large” droplet, working with a fixed rotational frequency of the trap Ω , as Ω approaches the trap frequency ω , a vortex lattice forms, the number of vortices increases, the mean spacing between them decreases, while the “size” of each vortex increases as compared to the size of each cell. In contrast to the well-known problem of contact interactions, where we have melting of the vortex lattice and highly correlated many-body states, here no melting of the vortex lattice is present, even when Ω = ω . This difference is due to the fact that the droplet is self-bound. For Ω = ω , the “smoothed” density distribution becomes a flat top, very much like the static unconfined droplet. When Ω exceeds ω , the droplet maintains its shape and escapes to infinity, via center-of-mass motion. Published by the American Physical Society 2024
Abstract We consider a two-dimensional self-bound quantum droplet, which consists of a mixture of two Bose–Einstein condensates. We start with the ground state and then turn to the rotational response of this system, in the presence of an external (harmonic) potential. We identify various phases, depending on the atom number, the strength of the external confinement and the angular momentum. These include center of mass excitation, ghost vortices, as well as vortices of single and multiple quantization. According to our results, this is an excellent system for the study of superfluid states.
We investigate the rotational response of a confined, two-dimensional quantum droplet, which emerges in an attractive binary Bose mixture that is stabilized against collapse by beyond-mean-field effects. We consider both a harmonic and an anharmonic form for the external confining potential. We go beyond the widely employed ``phase-locked" single-order-parameter model, maintaining two separate order parameters for the two components, and calculating the lowest-energy state for various values of the angular momentum. For a population-balanced quantum droplet and sufficiently tight confinement, we find that near certain half-integer values of the angular momentum the droplet is excited in a ``heterosymmetric" manner, with the two components carrying different vorticities. This mode is naturally missed by the single-order-parameter model. We additionally investigate the effects of a small population imbalance in the droplet. Apart from an energy increase associated with the population difference, the imbalance also lifts the double degeneracy of the heterosymmetric states, which characterizes the Z2\mathbb{Z}_2Z2​-symmetric balanced droplet. The heterosymmetric mode is found to be favored by the energy term which captures the beyond-mean-field effects in the mixture.
We investigate the rotational properties of quantum droplets, which form in a mixture of two Bose-Einstein condensates, in the presence of an anharmonic trapping potential. We identify various phases as the atom number and the angular momentum or angular velocity of the trap vary. These phases include center-of-mass–like excitation (without or with vortices), vortices of single and multiple quantization, etc. Finally, we compare our results with those of the single-component problem. Published by the American Physical Society 2024
We investigate the ground and low excited states of a rotating, weakly interacting Bose-Einstein condensed gas in a harmonic trap for a given angular momentum. Analytical results in various limits as well as numerical results are presented, and these are compared with those of previous studies. Within the mean-field approximation and for repulsive interaction between the atoms, we find that for very low values of the total angular momentum per particle, $L/\stackrel{\ensuremath{\rightarrow}}{N}0,$ where $L\ensuremath{\Elzxh}$ is the angular momentum and N is the total number of particles, the angular momentum is carried by quadrupole (∣m∣=2)(|m|=2)(∣m∣=2) surface modes. For L/N=1,L/N=1,L/N=1, a vortexlike state is formed and all the atoms occupy the m=1m=1m=1 state. For small negative values of $L/N\ensuremath{-}1,$ the states with m=0m=0m=0 and m=2m=2m=2 become populated, and for small positive values of $L/N\ensuremath{-}1,$ atoms in the states with m=5m=5m=5 and m=6m=6m=6 carry the additional angular momentum. In the whole region 0< L/N< 1,0<~L/N<~1,0< L/N< 1, we have strong analytic and numerical evidence that the interaction energy drops linearly as a function of L/N.L/N.L/N. We have also found that an array of singly quantized vortices is formed as L/NL/NL/N increases. Finally, we have gone beyond the mean-field approximation and have calculated the energy of the lowest state up to order N for small negative values of $L/N\ensuremath{-}1,$ as well as the energy of the low-lying excited states.
We study the stationary and excitation properties of a one-dimensional quantum droplet in a two-component Bose mixture trapped in a harmonic potential. By constructing the energy functional for the inhomogeneous mixture, we elaborate the extended Gross-Pitaevskii equation applicable to both symmetric and asymmetric mixtures into a universal form, and the equations in two different dimensionless schemes are in a duality relation; that is, the unique parameters that are left are the inverse of each other. The Bogoliubov equations for the trapped droplet are obtained by linearizing the small density fluctuation around the ground state, and the low-lying excitation modes are calculated numerically. It is found that the confinement trap easily changes the flat-top structure for large droplets and intensively alters the mean-square radius and the chemical potential. The breathing mode of the confined droplet connects the self-bound and ideal-gas limits, with the excitation in the weakly interacting Bose condensate for large particle numbers lying in between. We explicitly show how the continuum spectrum of the excitation is split into discrete modes and finally taken over by the harmonic trap. Two critical particle numbers are identified by the minimum size of the trapped droplet and the maximum breathing-mode energy, both of which are found to decrease exponentially with the trapping parameter.