Theoretical studies on rotating-spin-orbit-coupledand spin-orbital-angular-momentum-coupled spinor condensates

Abstract

The spin-orbital-angular-momentum (SOAM) coupling has emerged as an important theme in the field of spinor Bose-Einstein condensates (BECs) since its experimental realization a few years ago [Chen et al., Phys. Rev. Lett. 121, 113204 (2018), Chen et al., Phys. Rev. Lett. 121, 250401 (2018)]. The coupling emulates the SOAM coupling in atomic physics as it couples the spin and the orbital angular momentum of the atom; in contrast to the spin-orbit (SO) coupling between spin and the linear momentum of the atom [Lin et al., Nature, 471, 7336 (2011)]. This thesis studies the interplay of SO coupling and rotation in spinor BECs, specifically at high rotation frequencies. We consider rotating SO-coupled spin-1 and spin-2 BECs trapped in quasi-two-dimensional harmonic potentials with two types of SO coupling, namely an equal-strength mixture of Rashba and Dresselhaus couplings and Rasbha SO coupling. The combined effect of interactions, SO coupling with moderate to high rotation frequencies are analyzed systematically by variational methods and exact numerical solutions of the single-particle Hamiltonian. Using single-particle Hamiltonian, which is exactly solvable for an equal-strength mixture of Rashba and Dresselhaus couplings, we illustrate that a boson in these rotating SO- and coherently-coupled condensates is subjected to effective toroidal, symmetric double-well, or asymmetric double-well potentials under specific coupling and rotation strengths. In the presence of mean-field interactions, using the coupled Gross–Pitaevskii equations at moderate to high rotation frequencies, the analytically obtained effective potential minima and the numerically obtained coarse-grained density maxima position are in excellent agreement. In the spin-1 system, we observe that at moderate to high rotation frequencies, the spin expectation per particle of even an antiferromagnetic spin-1 Bose-Einstein condensates (BEC) approaches unity, indicating a similarity in the response of ferromagnetic and antiferromagnetic SO-coupled BECs at moderate to fast rotations. Similarly, in spin-2 systems, the antiferromagnetic, cyclic, and ferromagnetic phases exhibit similar behaviour at higher rotations. In the second part of this thesis, motivated by the recent experiments [Chen et al., Phys. Rev. Lett. 121, 113204 (2018), Chen et al., Phys. Rev. Lett. 121, 250401 (2018)], we investigate the low-lying excitation spectrum of the ground-state phases of spin-orbital-angular-momentum-coupled spin-1 condensates. At vanishing detuning, a ferromagnetic SOAM-coupled spin-1 BEC can have two ground-state phases, namely coreless and polar-core vortex states, whereas an antiferromagnetic BEC supports only polar-core vortex solution. The angular momentum per particle, longitudinal magnetization, and excitation frequencies display discontinuities across the phase boundary between the coreless vortex and polar-core vortex phases. The low-lying excitation spectrum evaluated by solving the Bogoliubov-de-Gennes equations is marked by avoided crossings and, hence, the hybridization of the spin and density channels. The spectrum is further confirmed by the dynamical evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode and a variational analysis for the density-breathing mode. Furthermore, we investigate the collective excitation spectrum of the annular stripe phase, which breaks two continuous symmetries: rotational and U(1) gauge symmetry. Since the annular stripe phase becomes more probable in the SOAM-coupling models corresponding to larger orbital angular momentum transfer imparted by the pair of Laguerre-Gaussian beams, we consider the Hamiltonian corresponding to 4ℏ orbital angular momentum transfer. The different considerations of angular-momentum transfer to the atoms by the pair of Laguerre-Gaussian beams yield different single-particle Hamiltonians and, consequently, different phase diagrams. In the presence of antiferromagnetic interactions, for different values of coupling strength and detuning, we observe the annular stripe phase along with two circular symmetric phases identified by the charge singularities of (+4,0,−4) and (+8,+4,0) in the j = +1,0,−1 spin components, respectively, and calculate their low-lying excitation spectrum.