The family of quantum droplets keeps expanding
- PDF / 335,852 Bytes
- 4 Pages / 595.28 x 785.2 pts Page_size
- 49 Downloads / 179 Views
Front. Phys. 16(2), 22504 (2021)
View & perspective
The family of quantum droplets keeps expanding Addition of lattice potentials helps to produce new species of stable fundamental and vortical quantum droplets in two dimensions. Boris A. Malomed1,2 1
Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light–Matter Interaction, Tel Aviv University, P. O. B. 39040, Tel Aviv, Israel 2 Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile E-mail: [email protected] n the course of the past 25 years, several new quantum states of matter have been created in ultracold gases, starting from the celebrated Bose–Einstein condensates (BECs), which were first made in 1995, following the theoretical prediction published in 1924 [1]. This achievement was followed by the creation and detailed exploration of degenerate Fermi gases [2], Tonks–Girardeau gas of hard-core bosons [3, 4], and spin–orbit-coupled BEC [5]. A recent addition to this set of fundamental states of quantum matter is the prediction [6, 7] and experimental demonstration [8–13] of quantum droplets (QDs), built of coherent atomic waves in binary (two-component) BEC. This is an extension of BEC beyond the limits of the usual mean-field (MF, alias semi-classical) approximation [1], with the averaged action of quantum fluctuations around the MF states (known as the Lee–Huang–Yang effect) leading to drastic changes in static and dynamical properties of the quantum gas. The result may be summarized as an effective quartic nonlinear term, |ψ|3 ψ in Eq. (1), competing with the usual cubic MF nonlinearity in the fundamental Gross–Pitaevskii equation for the macroscopic complex wave function [6], ψ, which is written here in the scaled form: ∂ψ 1 i = − ∇2 ψ − g|ψ|2 ψ + |ψ|3 ψ, (1) ∂t 2 where g > 0 is the coefficient of the MF interaction. A remarkable advantage of QDs is that the beyond-MF quartic self-repulsion makes it possible to stabilize self-trapped three-dimensional (3D) and quasi-2D droplets, which are kept together by the usual cubic MF attraction between two BEC components [6–11], or by the dipole–dipole attraction of atoms carrying magnetic moments [12, 13], against the collapse (catastrophic self-compression of the condensate [14]). In the absence of the beyond-MF repul-
I
∗ Received
October 25, 2020. This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467-0 20-1024-y.
sion, 3D and quasi-2D matter-wave solitons are inevitably destroyed by the collapse in the framework of the MF approximation. In the limit when the BEC is strongly confined by an external potential in one direction, Eq. (1) is replaced by the effective 2D equation [7] (see also Refs. [15, 16]) i
( ) ∂ψ 1 = − ∇2 ψ + ln |ψ|2 |ψ|2 ψ, ∂t 2
(2)
which also supports QDs. It is important to identify conserved quantities (dynamical invariants) s supported by Eq. (2). These are the total norm, N = |ψ(x, y)|2 dxdy, Hamiltonian (energy), [ ] 1x |ψ|2 H= |∇ψ(x, y)|2 + |ψ|4 ln √ dxdy, (3
Data Loading...
