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Communications in Theoretical Physics

Oscillatory stability of quantum droplets in -symmetric optical lattice

Jiehong Lao, Zheng Zhou, Xili Zhang, Fuqiu Ye, Honghua Zhong

Published Mar 22, 2021• 6 citations
Publisher

Abstract

Abstract We study stability and collisions of quantum droplets (QDs) forming in a binary bosonic condensate trapped in parity-time (   )-symmetric optical lattices. It is found that the stability of QDs in the   -symmetric system depends strongly on the values of the imaginary part W 0 of the   -symmetric optical lattices, self-repulsion strength g , and the condensate norm N . As expected, the   -symmetric QDs are entirely unstable in the broken   -symmetric phase. However, the   -symmetric QDs exhibit oscillatory stability with the increase of N and g in the unbroken   -symmetric phase. Finally, collisions between   -symmetric QDs are considered. The collisions of droplets with unequal norms are completely different from that in free space. Besides, a stable   -symmetric QDs collides with an unstable ones tend to merge into breathers after the collision.

DOI
10.1088/1572-9494/abf093

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Abstract We study stability and collisions of quantum droplets (QDs) forming in a binary bosonic condensate trapped in parity-time (   )-symmetric optical lattices. It is found that the stability of QDs in the   -symmetric system depends strongly on the values of the imaginary part W 0 of the   -symmetric optical lattices, self-repulsion strength g , and the condensate norm N . As expected, the   -symmetric QDs are entirely unstable in the broken   -symmetric phase. However, the   -symmetric QDs exhibit oscillatory stability with the increase of N and g in the unbroken   -symmetric phase. Finally, collisions between   -symmetric QDs are considered. The collisions of droplets with unequal norms are completely different from that in free space. Besides, a stable   -symmetric QDs collides with an unstable ones tend to merge into breathers after the collision.
We address the existence and stability of multipole quantum droplets in symmetric binary Bose-Einstein condensates described by the amended Gross-Pitaevskii equation with Lee-Huang-Yang quantum corrections. Quantum droplets trapped in a weakly anharmonic potential can be composed of different numbers of globally linked poles with an azimuthally periodic distribution. Due to the competing Lee-Huang-Yang-augmented nonlinearity, the norm of two branches of droplets with slopes of opposite sign merges together at a lower cutoff of chemical potential. The lower and upper branches of droplets at the same chemical potential, but with a different norm, can evolve stably in certain parameter regions simultaneously. The stability domain of droplets shrinks with the growth of the number of poles. Even unstable necklacelike droplets can survive for a very long time.
Abstract We consider quantum droplets in dipolar Bose–Einstein condensates embedded in optical lattices (OLs) within the framework of Gross–Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole–dipole interaction (DDI) provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the DDI increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of DDI. In presence of OLs, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
We consider quantum droplets in dipolar Bose-Einstein condensates embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
Abstract We study the stability and characteristics of two-dimensional (2D) quasi-isotropic quantum droplets (QDs) of fundamental and vortex types, formed by binary Bose–Einstein condensate with magnetic quadrupole–quadrupole interactions (MQQIs). The magnetic quadrupoles are built as pairs of dipoles and antidipoles polarized along the x-axis. The MQQIs are induced by applying an external magnetic field that varies along the x-axis. The system is modeled by the Gross–Pitaevskii equations including the MQQIs and Lee-Huang-Yang correction to the mean-field approximation. Stable 2D fundamental QDs and quasi-isotropic vortex QDs with topological charges S ⩽ 4 are produced by means of the imaginary-time-integration method for configurations with the quadrupoles polarized parallel to the system’s two-dimensional plane. Effects of the norm and MQQI strength on the QDs are studied in detail. Some results, including an accurate prediction of the effective area, chemical potential, and peak density of QDs, are obtained in an analytical form by means of the Thomas-Fermi approximation. Collisions between moving QDs are studied by means of systematic simulations.
Quantum droplets (QDs) are self-trapped modes stabilized by the Lee-Huang-Yang correction to the mean-field Hamiltonian of binary atomic Bose-Einstein condensates. The existence and stability of quiescent and rotating dipole-shaped and vortex QDs with vorticity S = 1 (DQDs and VQDs, respectively) are numerically studied in the framework of the accordingly modified two-component system. The rotating DQDs trapped in an annular potential are built of two crescentlike components, stretching along the azimuthal direction with the increase of the rotation frequency. Rotating quadrupole QDs (QQDs) bifurcate from the VQDs with S = 2 . Above a certain rotation frequency, they transform back into VQDs with a flat-top shape. Rotating DQDs and QQDs are stable in a broad interval of values of the chemical potential. The results provide the first example of stable modes which are intermediate states between the rotating DQDs and QQDs on the one hand and VQDs on the other. Published by the American Physical Society 2024
Stability of elongated (``slender") quantum droplets (QDs) with embedded unitary and multiple vorticity is a problem that was not solved previously. In this work, we propose a solution which relies upon the use of the spatial modulation of the inter-species scattering length in the binary Bose-Einstein condensates, in the form of a two-dimensional axisymmetric Gaussian, shaped by means of the optical Feshbach resonance. The corresponding effective nonlinear trapping potential supports completely stable elongated QDs with vorticity S=0S=0S=0 and partly stable families of elongated QDs with S=1,2,3,4S=1,2,3,4S=1,2,3,4 (other nonlinear systems do not maintain stability of vortex droplets with ≥2\geq 2≥2). We systematically analyze effects of the amplitude and width of the Gaussian modulation, as well as the total number of atoms, on the shape and stability of the QDs, some effects being explained analytically. Collisions between identical QDs with % S=1 moving in opposite directions along the central axis leads to their merger into still more elongated breathing QDs with the same vorticity, while collisions between QDs with S=±1S=\pm 1S=±1 are quasi-elastic. Moving modulation profiles are able to adiabatically rotate the trapped elongated QDs. Application of a torque to the vector QD sets in the gyroscopic regime of robust precession, which realizes a macroscopic spin-orbit-coupling effect.