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arXiv:2201.07500 · Physical Review A

Supersolid-like solitons in a spin-orbit-coupled spin-2 condensate

Pardeep Kaur, Sandeep Gautam, Sadhan K. Adhikari

Published Feb 2, 2022• 12 citations
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Abstract

We study supersolid-like crystalline structures emerging in the stationary states of a quasi-two-dimensional spin-orbit (SO)-coupled spin-2 condensate in the ferromagnetic, cyclic, and antiferromagnetic phases by solving a mean-field model. Interplay of different strengths of SO coupling and interatomic interactions gives rise to a variety of nontrivial density patterns in the emergent solutions. For small SO-coupling strengths $\ensuremath{\gamma}$ $(\ensuremath{\gamma}\ensuremath{\approx}0.5)$, the ground state is an axisymmetric multiring soliton for polar, cyclic, and weakly ferromagnetic interactions, whereas for stronger ferromagnetic interactions a circularly asymmetric soliton emerges as the ground state. Depending on the values of interaction parameters, with an increase in SO-coupling strength, a stripe phase may also emerge as the ground state for polar and cyclic interactions. For intermediate values of SO-coupling strength $(\ensuremath{\gamma}\ensuremath{\approx}1)$, in addition to these solitons, one could have a quasidegenerate triangular-lattice soliton in all magnetic phases. On further increasing the SO-coupling strength $(\ensuremath{\gamma}⪆4)$, a square-lattice and a superstripe soliton emerge as quasidegenerate states. The emergence of all these solitons can be inferred from a study of solutions of the single-particle Hamiltonian.

DOI
10.1103/physreva.105.023303

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We study supersolid-like crystalline structures emerging in the stationary states of a quasi-two-dimensional spin-orbit (SO)-coupled spin-2 condensate in the ferromagnetic, cyclic, and antiferromagnetic phases by solving a mean-field model. Interplay of different strengths of SO coupling and interatomic interactions gives rise to a variety of nontrivial density patterns in the emergent solutions. For small SO-coupling strengths \ensuremathγ\ensuremath{\gamma}\ensuremathγ (\ensuremathγ\ensuremath≈0.5)(\ensuremath{\gamma}\ensuremath{\approx}0.5)(\ensuremathγ\ensuremath≈0.5), the ground state is an axisymmetric multiring soliton for polar, cyclic, and weakly ferromagnetic interactions, whereas for stronger ferromagnetic interactions a circularly asymmetric soliton emerges as the ground state. Depending on the values of interaction parameters, with an increase in SO-coupling strength, a stripe phase may also emerge as the ground state for polar and cyclic interactions. For intermediate values of SO-coupling strength (\ensuremathγ\ensuremath≈1)(\ensuremath{\gamma}\ensuremath{\approx}1)(\ensuremathγ\ensuremath≈1), in addition to these solitons, one could have a quasidegenerate triangular-lattice soliton in all magnetic phases. On further increasing the SO-coupling strength (\ensuremathγ⪆4)(\ensuremath{\gamma}⪆4)(\ensuremathγ⪆4), a square-lattice and a superstripe soliton emerge as quasidegenerate states. The emergence of all these solitons can be inferred from a study of solutions of the single-particle Hamiltonian.
We study the formation of solitons in a uniform quasi-two-dimensional (quasi-2D) spin-orbit (SO) coupled self-repulsive binary dipolar and nondipolar Bose-Einstein condensate (BEC) using the mean-field Gross-Pitaevskii equation. For a weak SO coupling, in a nondipolar BEC, one can have three types of degenerate solitons: a multiring soliton with intrinsic vorticity of angular momentum projection +1 or -1 in one component and 0 in the other, a circularly asymmetric soliton, and a stripe soliton with stripes in the density. For an intermediate SO coupling, the multiring soliton ceases to exist and a square-lattice soliton appears with a spatially periodic pattern in density on a square lattice, in addition to the degenerate circularly asymmetric and stripe solitons. In the presence of a dipolar interaction, with the polarization direction aligned in the quasi-2D plane, only the degenerate circularly asymmetric and stripe solitons appear.
We demonstrate exotic stable quasi-two-dimensional solitons in a Rashba or a Dresselhaus spin-orbit (SO)-coupled hyperfine spin-1 (F=1F=1F=1) trapless antiferromagnetic Bose-Einstein condensate using the mean-field Gross-Pitaevskii equation. For weak SO coupling, the solitons are of the $(\ensuremath{-}1,0,+1)$ or $(+1,0,\ensuremath{-}1)$ type with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, where the numbers in the parentheses denote the angular momentum in the spin components ${F}_{z}=+1,0,\ensuremath{-}1$, respectively. For intermediate SO coupling, the solitons have a multiring structure maintaining the above-mentioned vortices in the respective components. For larger SO coupling, superlattice solitons with a square-lattice structure in total density are found in addition to stripe solitons with a stripe pattern in the component densities with no periodic modulation in the total density.
Abstract We investigate the ground-state properties of spin–orbit (SO)-coupled Bose–Einstein condensates confined in a spin-dependent asymmetric potential composed of harmonic and quartic contributions. The combined effect of the two potentials gives rise to an effective spatially inhomogeneous Zeeman field along the z -direction, and the complex competition among SO coupling, interatomic interactions, and this effective field leads to the emergence of nontrivial topological phases and complex spin textures in the system. For weak interatomic interactions, as the SO coupling strength increases, the system undergoes a series of transitions between ground-state phases: from a spin-polarized state, to an Anderson–Toulouse (AT) vortex state, a high-order radial dark soliton state, and finally to a domain structure. For strong interatomic interactions, the condensate evolves from a spin-polarized state to an AT vortex state, and then to a spatially coexisting state of AT and Mermin–Ho vortices, which corresponds to a novel topological excitation in pseudospin space: a skyrmion-dominated texture embedded with circular-hyperbolic antimeron pairs, realizing the coexistence and nesting of multiple topological defects. For sufficiently strong SO coupling, both components eventually evolve into similar multiring-shaped higher-order radial dark soliton states, with the number of soliton rings increasing as the SO coupling strength increases. Our results enrich the ground-state phases and topological excitations of cold atomic systems and provide new insights for exploring and manipulating nontrivial topological excitations in such systems.
The ground-state phases of a spin-orbit (SO)-coupled atomic spin-2 Bose-Einstein condensate are studied. Interesting density patterns forme spontaneously are widespread due to the competition between SO coupling and spin-dependent interactions as in an SO-coupled spin-1 condensate. Unlike the case of spin-1 condensates, which are characterized by either a ferromagnetic or a polar phase in the absence of SO, spin-2 condensates can take a cyclic phase, where we find that the patterns formed due to SO are square or triangular in their spin-component densities for axial symmetric SO interaction. Both patterns are found to evolve continuously into striped forms with increased asymmetry of the SO coupling.
We study the formation of spin-1 symbiotic spinor solitons in a quasi-one- (quasi-1D) and quasi-two-dimensional (quasi-2D) hyperfine spin F=1 ferromagnetic Bose-Einstein condensate (BEC). The symbiotic solitons necessarily have a repulsive intraspecies interaction and are bound due to an attractive interspecies interaction. Due to a collapse instability in higher dimensions, an additional spin-orbit coupling is necessary to stabilize a quasi-2D symbiotic spinor soliton. Although a quasi-1D symbiotic soliton has a simple Gaussian-type density distribution, novel spatial periodic structure in density is found in quasi-2D symbiotic SO-coupled spinor solitons. For a weak SO coupling, the quasi-2D solitons are of the (-1,0,+1) or (+1,0,-1) type with intrinsic vorticity and multiring structure, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses are angular momenta projections in spin components F_{z}=+1,0,-1, respectively. For a strong SO coupling, stripe and superlattice solitons, respectively, with a stripe and square-lattice modulation in density, are found in addition to the multiring solitons. The stationary states were obtained by imaginary-time propagation of a mean-field model; dynamical stability of the solitons was established by real-time propagation over a long period of time. The possibility of the creation of such a soliton by removing the trap of a confined spin-1 BEC in a laboratory is also demonstrated.
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