Formation of Matter-Wave Droplet Lattices in Multi-Color Periodic Confinements

Abstract

In the paper, we introduce a new model that addresses the generation of quantum droplets (QDs) in the binary Bose–Einstein condensate (BEC) mixture with mutually symmetric spinor components loaded in multi-color optical lattices (MOLs) of commensurate wavelengths and tunable intensities. The considered MOL confinement is the combination of the four-color optical lattice with an exponential periodic trap, which includes the complete set of the Fourier harmonics. Employing the one-dimensional (1D) extended Gross–Pitäevskii equation (eGPE), we calculate the exact analytical form of the wavefunction, MF/BMF nonlinearities, and MOL trap parameters. Utilizing the exact solutions, the formation of supersolid-like spatially periodic matter-wave droplet lattices and superlattices is illustrated under the space-periodic nonlinearity management. The precise positioning of the density maxima/minima of the droplet patterns at the center of the trap and tunable Anderson-like localization are observed by tuning the symmetry and amplitude of the considered MOL trap. The stability of the obtained solution is confirmed using the Vakhitov–Kolokolov (VK) criterion.

Droplet to soliton crossover at negative temperature in presence of bi-periodic optical lattices

“…Here, and with and are the transverse oscillator length and the inter- and intra- components atomic scattering lengths, respectively. In the above equations, represents the self interaction coefficients whereas is the cross interaction coefficients along with 41 , 42 . The sign and strength of both: and are dependent on the inter- and intra-components atomic scattering lengths.…”

“… and are the inter-atomic interaction strengths of two-component BEC mixture representing BMF and EMF interactions, respectively. Equation ( 3 ) is the extended form of Gross-Piteäevskii equation added with external confinement which is utilized to investigate droplet dynamics for various physical scenarios 40 – 42 . Here, V ( z , t ) is the external confinement, which is taken as the combination of an expulsive harmonic oscillator, BOL and exponential periodic confinements for obtaining negative temperature scenario 25 , 32 , 33 : Here, , with .…”

“…For , it becomes: From Eqs. ( 4 ) and ( 5 ), depending on the magnitude of , the trap profile is: (a) expulsive harmonic oscillator and BOL for ; and (b) for or , the trap profile is the combination of expulsive harmonic oscillator and multi-color optical lattice which contains complete series of Fourier harmonics 42 . Now, to construct the analytical solution of for Eq.…”

“…Although, in the last few years, droplets are extensively investigated in free space region i.e. without any external confinement 1 , 2 , 38 – 40 and an exact theoretical model for QDs in harmonic and multi-color optical lattice confinements is also recently reported 41 , 42 . However, the generation and dynamics of QDs are not investigated in the negative temperature regime.…”

Symmetry in Many-Body Physics

“…An important role in finding the approximate solutions is played by the knowledge of basic symmetries that determine the accuracy of the used approximations. The purpose of this issue is to demonstrate the principal role of exact and approximate symmetries in solving various problems in many-particle physics, as well as finding approximate solutions for the systems typical of condensed matter, trapped Fermi and Bose gases, nuclear matter, and field theory [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”