arXiv subjects

S. K. Adhikari

Publications and source records attributed to S. K. Adhikari.

At least 37 records · Page 2Linked to original sources

arXiv2022

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

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 antiferro-magnetic phases by solving a mean-field model.Interplay of different strengths of SO coupling and interatomic interactions gives rise to a variety of non-trivial density patterns in the emergent solutions. For small SO-coupling strengths $γ$ ($γ\approx 0.5$), the ground state is an axisymmetric multi-ring 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 ($γ\approx 1$), in addition to these solitons, one could have a quasi-degenerate triangular-lattice soliton in all magnetic phases. On further increasing the SO-coupling strength ($γ\gtrapprox 4$), a square-lattice and a superstripe soliton emerge as quasi-degenerate states. The emergence of all these solitons can be inferred from a study of solutions of the single-particle Hamiltonian.

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arXiv2021

Spatial order in a two-dimensional spin-orbit-coupled spin-1/2 condensate: superlattice, multi-ring and stripe formation

We demonstrate the formation of stable spatially-ordered states in a {\it uniform} and also {\it trapped} quasi-two-dimensional (quasi-2D) Rashba or Dresselhaus spin-orbit (SO) coupled pseudo spin-1/2 Bose-Einstein condensate using the mean-field Gross-Pitaevskii equation. For weak SO coupling, one can have a circularly-symmetric $(0,+1)$- or $(0,-1)$-type multi-ring state with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, respectively, where the numbers in the parentheses denote the net angular momentum projection in the two components, in addition to a circularly-asymmetric degenerate state with zero net angular momentum projection. For intermediate SO couplings, in addition to the above two types, one can also have states with stripe pattern in component densities with no periodic modulation in total density. The stripe state continues to exist for large SO coupling. In addition, a new spatially-periodic state appears in the uniform system: a superlattice state, possessing some properties of a supersolid, with a square-lattice pattern in component densities and also in total density. In a trapped system the superlattice state is slightly different with multi-ring pattern in component density and a square-lattice pattern in total density. For an equal mixture of Rashba and Dresselhaus SO couplings, in both uniform and trapped systems, only stripe states are found for all strengths of SO couplings. In a uniform system all these states are quasi-2D solitonic states.

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arXiv2021

Supersolid-like states in a two-dimensional trapped spin-orbit-coupled spin-1 condensate

We study supersolid-like states in a quasi-two-dimensional trapped Rashba and Dresselhaus spin-orbit (SO) coupled spin-1 condensate. For small strengths of SO coupling $γ$ ($γ\lessapprox 0.75$), in the ferromagnetic phase, circularly-symmetric $(0,\pm 1, \pm 2)$- and $(\mp 1, 0,\pm 1)$-type states are formed where the numbers in the parentheses denote the angular momentum of the vortex at the center of the components and where the upper (lower) sign correspond to Rashba (Dresselhaus) coupling; in the antiferromagnetic phase, only $(\mp 1, 0,\pm 1)$-type states are formed. For large strengths of SO coupling, supersolid-like superlattice and superstripe states are formed in the ferromagnetic phase. In the antiferromagnetic phase, for large strengths of SO coupling, supersolid-like superstripe and multi-ring states are formed. For an equal mixture of Rashba and Dresselhaus SO couplings, only a superstripe state is found. All these states are found to be dynamically stable and hence accessible in an experiment and will enhance the fundamental understanding of crystallization onto spatially periodic states in solids.

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arXiv2021

Multi-ring, stripe, and super-lattice solitons in a spin-orbit coupled spin-1 condensate

We demonstrate exotic stable quasi-two-dimensional solitons in a Rashba or a Dresselhaus spin-orbit (SO) coupled hyperfine spin-1 ($F=1$) trap-less antiferromagnetic Bose-Einstein condensate using the mean-field Gross-Pitaevskii equation. For weak SO coupling, the solitons are of the $(-1,0,+1)$ or $(+1,0,-1)$ type with intrinsic vorticity, for Rashba or Dresselhaus SO coupling, where the numbers in the parentheses denote angular momentum in spin components $F_z= +1,0,-1$, respectively. For intermediate SO coupling, the solitons have multi-ring structure maintaining the above-mentioned vortices in respective components. For larger SO coupling, superlattice solitons with a square-lattice structure in total density are found in addition to stripe solitons with stripe pattern in component densities with no periodic modulation in total density.

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arXiv2020

Spontaneous spatial order in two-dimensional ferromagnetic spin-orbit coupled uniform spin-1 condensate solitons

We demonstrate spontaneous spatial order in stripe and super-lattice solitons in a Rashba spin-orbit (SO) coupled spin-1 uniform quasi-two-dimensional (quasi-2D) ferromagnetic Bose-Einstein condensate. For weak SO coupling, the solitons are of the $(- 1,0,+ 1)$ or $(0,+ 1,+ 2)$ type with intrinsic vorticity, where the numbers in the parentheses denote angular momentum in spin components $F_z=+1,0,-1$, respectively. For intermediate SO coupling, three types of solitons are found: (a) circularly-asymmetric solitons, (b) circularly-symmetric $(- 1,0,+ 1)$- and (c) $(0,+ 1,+ 2)$-type multi-ring solitons maintaining the above-mentioned vortices in respective components. For large SO coupling, quasi-degenerate stripe and super-lattice solitons are found in addition to the circularly-asymmetric solitons. A super-lattice soliton forms a 2D square lattice structure in the total density as in a super-solid; in component densities it may have either (i) a 1D stripe pattern or (ii) a 2D square lattice structure.

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arXiv2020

Vortex-lattice formation in a spin-orbit coupled rotating spin-1 condensate

We study the vortex-lattice formation in a rotating {Rashba} spin-orbit (SO) coupled quasi-two-dimensional (quasi-2D) hyper-fine spin-1 spinor Bose-Einstein condensate (BEC) in the $x-y$ plane using a numerical solution of the underlying mean-field Gross-Pitaevskii equation. % The wave function for this system %has three components corresponding to the three projections of hyper-fine spin $F_z= +1,0,-1$. In this case, the non-rotating {Rashba} SO-coupled spinor BEC can have topological excitation in the form of vortices of different angular momenta in the three components, e.g. the $(0,+1,+2)$- and $(-1,0,+1)$-type states in ferromagnetic and anti-ferromagnetic spinor BEC: the numbers in the parenthesis denote the intrinsic angular momentum of the vortex states of the three components with the negative sign denoting an anti-vortex. The presence of these states with intrinsic vorticity breaks the symmetry between rotation with vorticity along the $z$ and $-z$ axes and thus generates a rich variety of vortex-lattice and anti-vortex-lattice states in a rotating quasi-2D spin-1 spinor ferromagnetic and anti-ferromagnetic BEC, not possible in a scalar BEC. {For weak SO coupling, } we find two types of symmetries of these states $-$ hexagonal and "square". The hexagonal (square) symmetry state has vortices arranged in closed concentric orbits with a maximum of $6, 12, 18...$ ($8,12,16...$) vortices in successive orbits. Of these two symmetries, the square vortex-lattice state is found to have the smaller energy.

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arXiv2019

Phase-separated symmetry-breaking vortex-lattice in a binary Bose-Einstein condensate

We study spontaneous-symmetry-breaking circularly-asymmetric phase separation of vortex lattices in a rapidly rotating harmonically-trapped quasi-two-dimensional (quasi-2D) binary Bose-Einstein condensate (BEC) with repulsive inter- and intra-species interactions. The phase separated vortex lattices of the components appear in different regions of space with no overlap between the vortices of the two components, which will permit an efficient experimental observation of such vortices and accurate study of the effect of atomic interaction on such vortex lattice. Such phase separation takes place when the intra-species interaction energies of the two components are equal or nearly equal with relatively strong inter-species repulsion. When the intra-species energies are equal, the two phase-separated vortex lattices have identical semicircular shapes with one being the parity conjugate of the other. When the intra-species energies are nearly equal, the phase separation is also complete but the vortex lattices have different shapes. We demonstrate our claim with a numerical solution of the mean-field Gross-Pitaevskii equation for a rapidly rotating quasi-2D binary BEC.

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arXiv2019

Weak-coupling to unitarity crossover in Bose-Fermi mixtures: Mixing-demixing and spontaneous symmetry breaking in trapped systems

The usual treatment of a Bose-Fermi mixture relies on weak-coupling Gross-Pitaevskii (GP) and density-functional (DF) Lagrangians, often including the more realistic {perturbative} Lee-Huang-Yang (LHY) corrections. We suggest analytic {non-perturbative} beyond-mean-field Bose and Fermi Lagrangians valid along the crossover from weak- to strong-coupling limits of intra-species interactions consistent with the LHY corrections and the strong-coupling (unitarity) limit for small and large scattering lengths $|a|$, respectively, and use these to study the Bose-Fermi mixture. We study numerically mixing-demixing and spontaneous symmetry breaking in Bose-Fermi mixtures in spherically-symmetric and quasi-one-dimensional traps while the intra-species Bose and Fermi interactions are varied from weak-coupling to strong-coupling limits.The LHY correction is appropriate for medium to weak atomic interactions and diverges for stronger interactions (large scattering length $|a|$), whereas the present beyond-mean-field Lagrangian is finite in the unitarity limit ($|a|\to \infty$). We illustrate our results using the Bose-Fermi $^7$Li-$^6$Li mixture under a spherically-symmetric and a quasi-one-dimensional trap. The results obtained with the present model for density distribution of the Bose-Fermi mixture along the crossover could be qualitatively different from the usual GP-DF Lagrangian with or without LHY corrections. Specifically, we identified spontaneous symmetry breaking and demixing in the present model not found in the usual model with the same values of the parameters.

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arXiv2019

Stable controllable giant vortex in a trapped Bose-Einstein condensate

In a harmonically-trapped rotating Bose-Einstein condensate (BEC), a vortex of large angular momentum decays to multiple vortices of unit angular momentum from an energetic consideration. We demonstrate the formation of a robust and dynamically stable giant vortex of large angular momentum in a harmonically trapped rotating BEC with a potential hill at the center, thus forming a Mexican hat like trapping potential. For a small inter-atomic interaction strength, a highly controllable stable giant vortex appears, whose angular momentum slowly increases as the angular frequency of rotation is increased. As the inter-atomic interaction strength is increased beyond a critical value, only vortices of unit angular momentum are formed, unless the strength of the potential hill at the center is also increased: for a stronger potential hill at the center a giant vortex is again formed. The dynamical stability of the giant vortex is demonstrated by real-time propagation numerically. These giant vortices of large angular momentum can be observed and studied experimentally in a highly controlled fashion.

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arXiv2019

Limitation of the Lee-Huang-Yang interaction in forming a self-bound state in Bose-Einstein condensates

The perturbative Lee-Huang-Yang (LHY) interaction proportional to $n^{3/2}$, where $n$ is the density, creates an infinitely repulsive potential at the center of a Bose-Einstein condensate (BEC) with net attraction, which stops the collapse to form a self-bound state in a dipolar BEC and in a binary BEC. However, recent microscopic calculations of the non-perturbative beyond-mean-field (BMF) interaction indicate that the LHY interaction %with the $n^{3/2}$ term is valid only for very small values of gas parameter $x$. We show that a realistic non-perturbative BMF interaction can stop collapse and form a self-bound state only in a weakly attractive binary BEC with small $x$ values ($x\lessapprox 0.01$), whereas the perturbative LHY interaction stops collapse for all attractions. We demonstrate these aspects using an analytic BMF interaction with appropriate weak-coupling LHY and strong coupling limits.

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arXiv2019

Vortex lattice in a uniform Bose-Einstein condensate in a box trap

We study numerically the vortex-lattice formation in a rapidly rotating uniform quasi-two-dimensional Bose-Einstein condensate (BEC) in a box trap. We consider two types of boxes: square and circle. In a square-shaped 2D box trap, when the number of generated vortices is the square of an integer, the vortices are found to be arranged in a perfect square lattice, although deviations near the center are found when the number of generated vortices is arbitrary. In case of a circular box trap, the generated vortices in the rapidly rotating BEC lie on concentric closed orbits. Near the center, these orbits have the shape of polygons, whereas near the periphery the orbits are circles. The circular box trap is equivalent to the rotating cylindrical bucket used in early experiment(s) with liquid He II. The number of generated vortices in both cases is in qualitative agreement with Feynman's universal estimate. The numerical simulation for this study is performed by a solution of the underlying mean-field Gross-Pitaevskii (GP) equation in the rotating frame, where the wave function for the generated vortex lattice is a stationary state. Consequently, the imaginary-time propagation method can be used for a solution of the GP equation, known to lead to an accurate numerical solution. We also demonstrated the dynamical stability of the vortex lattices in real-time propagation upon a small change of the angular frequency of rotation, using the converged imaginary-time wave function as the initial state.

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arXiv2018

Self-trapped quantum balls in binary Bose-Einstein condensates

We study the formation of a stable self-trapped spherical quantum ball in a binary Bose-Einstein condensate (BEC) with two-body inter-species attraction and intra-species repulsion employing the beyond-mean-field Lee-Huang-Yang and the three-body interactions. We find that either of these interactions or a combination of these can stabilize the binary BEC quantum ball with very similar stationary results, and for a complete description of the problem both the terms should be considered. These interactions lead to higher-order nonlinearities, e.g. quartic and quintic, respectively, in a nonlinear dynamical equation compared to the cubic nonlinearity of the two-body contact interaction in the mean-field Gross-Pitaevskii equation. The higher-order nonlinearity makes the energy infinitely large at the center of the binary ball and thus avoids its collapse. In addition to the formation of stationary binary balls, we also study a collision between two such balls. At large velocities, the collision is found to be elastic, which turns out to be inelastic as the velocity is lowered. We consider the numerical solution of a beyond-mean-field model for the binary ball as well as a single-mode variational approximation to it in this study.

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arXiv2018

Phase-separated vortex-lattice in a rotating binary Bose-Einstein condensate

We study circularly-symmetric phase separation of vortex lattices in a rapidly rotating harmonically-trapped quasi--two-dimensional binary Bose-Einstein condensate (BEC) by introducing a weak quartic trap in one of the components. The increase of the rotational frequency in such a system is also found to generate a phase separation of the vortex lattices of an overlapping non-rotating BEC. The phase-separated vortex lattices have different structures for a binary BEC with inter-species repulsion and inter-species attraction. In the former case of a fully repulsive binary BEC the phase separation of the vortex-lattices is accompanied by a complete phase separation of component densities. In the latter case of inter-species attraction there is a partial phase separation of component densities, although there could be a complete phase separation of the generated vortex lattices in the two components. In the case of inter-species attraction, we need to have different intra-species repulsion in the two components for an efficient phase separation. We compare and contrast our results with the phase separation obtained in a harmonically-trapped binary BEC without any quartic trap.

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arXiv2018

Vortex lattice in the crossover of a Bose gas from weak coupling to unitarity

The formation of a regular lattice of quantized vortices in a fluid under rotation is a smoking-gun signature of its superfluid nature. Here we study the vortex lattice in a dilute superfluid gas of bosonic atoms at zero temperature along the crossover from the weak-coupling regime, where the inter-atomic scattering length is very small compared to the average distance between atoms, to the unitarity regime, where the inter-atomic scattering length diverges. This study is based on high-performance numerical simulations of the time-dependent nonlinear Schrodinger equation for the superfluid order parameter in three spatial dimensions, using a realistic analytic expression for the bulk equation of state of the system along the crossover from weak-coupling to unitarity. This equation of state has the correct weak-coupling and unitarity limits and faithfully reproduces the results of an accurate multi-orbital microscopic calculation. Our numerical predictions of the number of vortices and root-mean-square sizes are important benchmarks for future experiments.

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arXiv2017

Three-dimensional vortex-bright solitons in a spin-orbit coupled spin-$1$ condensate

We demonstrate stable and metastable vortex-bright solitons in a three-dimensional spin-orbit-coupled three-component hyperfine spin-1 Bose-Einstein condensate (BEC) using numerical solution and variational approximation of a mean-field model. The spin-orbit coupling provides attraction to form vortex-bright solitons in both attractive and repulsive spinor BECs. The ground state of these vortex-bright solitons is axially symmetric for weak polar interaction. For a sufficiently strong ferromagnetic interaction, we observe the emergence of a fully asymmetric vortex-bright soliton as the ground state. We also numerically investigate moving solitons. The present mean-field model is not Galilean invariant, and we use a Galilean-transformed mean-field model for generating the moving solitons.

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arXiv2017

Symmetry breaking, Josephson oscillation and self-trapping in a self-bound three-dimensional quantum ball

We study spontaneous symmetry breaking (SSB), Josephson oscillation, and self-trapping in a stable, mobile, three-dimensional matter-wave spherical quantum ball self-bound by attractive two-body and repulsive three-body interactions. The SSB is realized by a parity-symmetric (a) one-dimensional (1D) double-well potential and (b) a 1D Gaussian potential, both along the $z$ axis and no potential along the $x$ and $y$ axes. In the presence of each of these potentials, the symmetric ground state dynamically evolves into a doubly-degenerate SSB ground state. If the SSB ground state in the double well, predominantly located in the first well ($z>0$), is given a small displacement, the quantum ball oscillates with a self-trapping in the first well. For a medium displacement one encounters an asymmetric Josephson oscillation. The asymmetric oscillation is a consequence of SSB. The study is performed by a variational and numerical solution of a non-linear mean-field model with 1D parity-symmetric perturbations.

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arXiv2017

Statics and dynamics of a self-bound dipolar matter-wave droplet

We study the statics and dynamics of a stable, mobile, self-bound three-dimensional dipolar matter-wave droplet created in the presence of a tiny repulsive three-body interaction. In frontal collision with an impact parameter and in angular collision at large velocities {along all directions} two droplets behave like quantum solitons. Such collision is found to be quasi elastic and the droplets emerge undeformed after collision without any change of velocity. However, in a collision at small velocities the axisymmeric dipolar interaction plays a significant role and the collision dynamics is sensitive to the direction of motion. For an encounter along the $z$ direction at small velocities, two droplets, polarized along the $z$ direction, coalesce to form a larger droplet $-$ a droplet molecule. For an encounter along the $x$ direction at small velocities, the same droplets stay apart and never meet each other due to the dipolar repulsion. The present study is based on an analytic variational approximation and a numerical solution of the mean-field Gross-Pitaevskii equation using the parameters of $^{52}$Cr atoms.

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arXiv2017

Statics and dynamics of a self-bound matter-wave quantum ball

We study the statics and dynamics of a stable, mobile, three-dimensional matter-wave spherical quantum ball created in the presence of an attractive two-body and a very small repulsive three-body interaction. The quantum ball can propagate with a constant velocity in any direction in free space and its stability under a small perturbation is established numerically and variationally. In frontal head-on and angular collisions at large velocities two quantum balls behave like quantum solitons. Such collision is found to be quasi elastic and the quantum balls emerge after collision without any change of direction of motion and velocity and with practically no deformation in shape. When reflected by a hard impenetrable plane, the quantum ball bounces off like a wave obeying the law of reflection without any change of shape or speed. However, in a collision at small velocities two quantum balls coalesce to form a larger ball which we call a quantum-ball breather. We point out the similarity and difference between the collision of two quantum and classical balls. The present study is based on an analytic variational approximation and a full numerical solution of the mean-field Gross-Pitaevskii equation using the parameters of $^7$Li atoms.

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