We study the stability of zero-vorticity and vortex lattice quantum droplets (LQDs), which are described by a two-dimensional (2D) Gross–Pitaevskii (GP) equation with a periodic potential and Lee–Huang–Yang (LHY) term. The LQDs are divided in two types: onsite-centered and offsite-centered LQDs, the centers of which are located at the minimum and the maximum of the potential, respectively. The stability areas of these two types of LQDs with different number of sites for zero-vorticity and vorticity with S = 1 are given. We found that the μ–N relationship of the stable LQDs with a fixed number of sites can violate the Vakhitov–Kolokolov (VK) criterion, which is a necessary stability condition for nonlinear modes with an attractive interaction. Moreover, the μ–N relationship shows that two types of vortex LQDs with the same number of sites are degenerated, while the zero-vorticity LQDs are not degenerated. It is worth mentioning that the offsite-centered LQDs with zero-vorticity and vortex LQDs with S = 1 are heterogeneous.

Quantum droplets in two-dimensional optical lattices

We study the stability of zero-vorticity and vortex lattice quantum droplets (LQDs), which are described by a two-dimensional (2D) Gross-Pitaevskii (GP) equation with a periodic potential and Lee-Huang-Yang (LHY) term. The LQDs are divided in two types: onsite-centered and offsitecentered LQDs, the centers of which are located at the minimum and the maximum of the potential, respectively. The stability areas of these two types of LQDs with different number of sites for zerovorticity and vorticity with S = 1 are given. We found that the u-N relationship of the stable LQDs with a fixed number of sites can violate the Vakhitov-Kolokolov (VK) criterion, which is a necessary stability condition for nonlinear modes with an attractive interaction. Moreover, the u-N relationship shows that two types of vortex LQDs with the same number of sites are degenerated, while the zero-vorticity LQDs are not degenerated. It is worth mentioning that the offsite-centered LQDs with zero-vorticity and vortex LQDs with S = 1 are heterogeneous.

For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by the intersection of two domain walls (DWs) separating immiscible species, with opposite signs of the wave functions in each pair of sectors filled by the same species. The cross pattern remains stable up to the zero value of the immiscibility parameter {delta}, while simpler rectilinear (quasi-1D) DWs exist only for values of {delta} essentially exceeding those in BEC mixtures (two spin states of the same isotope) currently available to the experiment. Both symmetric and asymmetric cross configurations are investigated, with equal or different numbers N{sub 1,2} of atoms in the two species. In rotating traps, 'propellers' (stable revolving crosses) are found too. A full stability region for the crosses and propellers in the system's parameter space is identified, unstable crosses evolving into arrays of vortex-antivortex pairs. Stable rotating rectilinear DWs are found too, at larger values of {delta}. All the patterns produced by the intersection of three or more DWs are unstable, rearranging themselves into ones with two DWs. Optical 'propellers' are also predicted in a twisted nonlinear photonic-crystal fiber carrying two different wavelengths or circular polarizations, which can be used formore » applications to switching and routing.« less

Static and rotating domain-wall cross patterns in Bose-Einstein condensates (8 pages)

In this Letter, we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. The dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region as a function of spin-orbit coupling parameters as well as the oscillation amplitude. The anharmonic properties beyond the effective-mass approximation are revealed, such as the amplitude-dependent frequency and finite oscillation frequency at a place with a divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of the spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility--a static physical quantity--can be measured via the dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates the magnetic nonzero-momentum condensate from the nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a benchmark for recently developed theoretical approaches.

http://absimage.aps.org/image/MAR13/MWS_MAR13-2012-020236.pdf

Collective Dipole Oscillations of a Spin-Orbit Coupled Bose-Einstein Condensate

We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose–Einstein condensates. The system is modeled by the Gross–Pitaevskii (GP) equation with the cubic term multiplied by a logarithmic factor (as produced by the Lee-Huang-Yang correction to the mean-field theory) and a potential which is a periodic function of the radial coordinate. Narrow vortex rings with high values of the topological charge, trapped in particular circular troughs of the radial potential, are produced. These results suggest an experimentally relevant method for the creation of vortical QDs (thus far, only zero-vorticity ones have been reported). The 2D GP equation for the narrow rings is approximately reduced to the one-dimensional form, which makes it possible to study the modulational stability of the rings against azimuthal perturbations. Full stability areas are delineated for these modes. The trapping capacity of the circular troughs is identified for the vortex rings with different winding numbers (WNs). Stable compound states in the form of mutually nested concentric multiple rings are constructed too, including ones with opposite signs of the WNs. Other robust compound states combine a modulationally stable narrow ring in one circular potential trough and an azimuthal soliton performing orbital motion in an adjacent one. The results may be used to design a device employing coexisting ring-shaped modes with different WNs for data storage.

https://iopscience.iop.org/article/10.1088/1367-2630/acab26/pdf

Vortex-ring quantum droplets in a radially-periodic potential

Properties of the ground-state solitons, which exist in the spin–orbit coupling (SOC) Bose–Einstein condensates (BEC) in the presence of optical lattices, are presented. Results show that several system parameters, such as SOC strength, lattice depth, and lattice frequency, have important influences on properties of ground state solitons in SOC BEC. By controlling these parameters, structure and spin polarization of the ground-state solitons can be effectively tuned, so manipulation of atoms may be realized.

http://iopscience.iop.org/article/10.1088/1674-1056/26/8/080304/pdf

Tunable ground-state solitons in spin–orbit coupling Bose–Einstein condensates in the presence of optical lattices

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Tunable ground-state solitons in spin–orbit coupling Bose–Einstein condensates in the presence of optical lattices