Spinor Bose-Einstein Condensate Research Articles

Core structure of static ferrodark solitons in a spin-1 Bose-Einstein condensate

We develop an analytical description of static ferrodark solitons, the $\mathbb{Z}_2$ topological defects in the magnetic order, in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. We find that the type-I ferrodark soliton has a single width while the type-II ferrodark soliton exhibits two characteristic length scales. The proposed ansatzes show excellent agreement with numerical results. Spin-singlet amplitudes, nematic tensor densities and nematic currents of ferrodark solitons are also discussed. The $\mathbb{Z}_2$ topological defects in the mass superfluid order, dark-dark-dark vector solitons, are obtained exactly in the parameter regime where exact ferrodark solitons exist. The dark-dark-dark vector soliton has higher excitation energy than ferrodark solitons.

Dynamics of Rotating Spin-Orbit-Coupled Spin-1 Bose-Einstein Condensates With In-Plane Gradient Magnetic Field in an Anharmonic Trap

We investigate the dynamics of rotating spin-orbit-coupled spin-1 Bose–Einstein condensates (BECs) in an in-plane gradient magnetic field, which is confined in an anharmonic trap. In the case of rotating spin-orbit-coupled spin-1 BECs with given parameters, the system evolves from initial disk-shaped condensates into drastic turbulent oscillations and ghost vortices on the surface of the component densities due to surface wave excitations and then into two final vortex necklaces along the azimuthal direction with an irregular density hole, in which the vortices differ by one quantum number in turn. For the case of rotating spin-orbit-coupled spin-1 BECs with in-plane gradient magnetic field, with the dynamic evolution, the system undergoes a transition from an initial central polar-core vortex to violent turbulent oscillations and then to a final vortex chain along the diagonal of BECs, with the remaining vortices symmetrically distributed on both sides in the individual component. In addition, the corresponding spin texture undergoes a transition from plane-wave phase to double half-antiskyrmion necklaces for the former case and a transition from a structure similar to a quadrupole magnetic field to a half-antiskyrmion chain with the rest of the half-antiskyrmions on both sides. During the dynamic evolution process, the angular momentum increases gradually and then approaches a convergent value.

Spin current in a spinor Bose–Einstein condensate induced by a gradient magnetic field

We develop a research of spin currents in a 23Na spinor Bose–Einstein condensate (BEC) by applying a magnetic field gradient. The spin current is successfully induced by the spin-dependent force arising from the magnetic field gradient. The dynamics of the spin components under the magnetic force is investigated. The study is promising to be extended to produce a longer spin-coherence and to enhance the sensitivity of the spin-mixing interferometry in a spinor BEC.

Collective excitations in cigar-shaped spin-orbit-coupled spin-1 Bose-Einstein condensates

We study theoretically the collective excitations of a spin-orbit-coupled spin-1 Bose-Einstein condensate with antiferromagnetic spin-exchange interactions in a cigar-shaped trapping potential at zero and finite temperatures using the Hartree-Fock-Bogoliubov theory with Popov approximation. The collective modes at zero temperature are corroborated by real-time evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode. We also calculate a few low-lying modes analytically and find very good agreement with the numerical results. We confirm the presence of excitations belonging to two broad categories, namely, density and spin excitations, based on the calculation of dispersion. The degeneracy between a pair of spin modes is broken by the spin-orbit coupling. At finite temperature, spin and density excitations show qualitatively different behavior as a function of temperature.

Elementary excitations in a spin–orbit-coupled spin-1 Bose–Einstein condensate

While a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC) has been experimentally observed, its elementary excitations remain unclear in the stripe phase. Here, we systematically study the elementary excitations in three distinct phases of a spin–orbit-coupled spin-1 BEC. We find that the excitation spectrum as well as the corresponding static response function and structure factor depend strongly on spin–orbit coupling parameters such as the quadratic Zeeman field and the Rabi frequency. In the stripe phase, besides two gapless Goldstone modes, we show the existence of roton excitations. Finally, we demonstrate that quantum phase transitions between these different phases including the zero-momentum, plane wave and stripe phases are characterized by the sound velocities and the quantum depletion.

Ground States of the SU(3) Spin–Orbit Coupled Spin-1 Bose–Einstein Condensate in a Rotating Annular Potential

Ground States of the SU(3) Spin–Orbit Coupled Spin-1 Bose–Einstein Condensate in a Rotating Annular Potential

Optical-plug-assisted spin vortex in a Rb87 dipolar spinor Bose-Einstein condensate

Generating a spin vortex in a $^{87}$Rb dipolar spinor Bose-Einstein condensate in a controllable way is still experimentally challenging. We propose an experimentally easy and tunable way to produce spin vortex by varying the potential barrier height and the width of an additionally applied optical plug. A topological phase transition occurs from the trivial single mode approximation phase to the optical-plug-assisted-vortex one, as the barrier height increases and the width lies in an appropriate range. The optical plug causes radial density variation thus the spin vortex is favored by significantly lowering the intrinsic magnetic dipolar energy. A type of coreless spin vortex, different from the conventional polar core vortex, is predicted by our numerical results. Our proposal removes a major obstacle to investigate the topological phase transition in a $^{87}$Rb dipolar spinor BEC.

Faraday patterns in spin-orbit-coupled Bose-Einstein condensates

We study the Faraday patterns generated by spin-orbit-coupling induced parametric resonance in a spinor Bose-Einstein condensate with repulsive interaction. The collective elementary excitations of the Bose-Einstein condensate, including density waves and spin waves, are coupled as the result of the Raman-induced spin-orbit coupling and a quench of the relative phase of two Raman lasers without the modulation of any of the system's parameters. We observed several higher parametric resonance tongues at integer multiples of the driving frequency and investigated the interplay between Faraday instabilities and modulation instabilities when we quench the spin-orbit-coupled Bose-Einstein condensate from zero-momentum phase to plane-wave phase. If the detuning is equal to zero, the wave number of combination resonance barely changes as the strength of spin-orbit coupling increases. If the detuning is not equal to zero after a quench, a single combination resonance tongue will split into two parts.

FORTRESS: FORTRAN programs to solve coupled Gross-Pitaevskii equations for spin-orbit coupled spin-f Bose-Einstein condensate with spin f = 1 or 2

We provide here the updated versions of OpenMP parallelized FORTRAN 90/95 programs to numerically study the ground states and/or the dynamics of homogeneous or trapped spin-1 or spin-2 Bose-Einstein condensates (BECs) with anisotropic spin-orbit (SO) coupling. The coupled sets of three or five Gross-Pitaevskii (GP) equations, respectively, for a spin-1 or a spin-2 Bose-Einstein condensate (BEC) are solved using a time-splitting Fourier spectral method. New version program summaryProgram Title: FORTRESSCPC Library link to program files:https://doi.org/10.17632/st7md3ss85.2Developer's repository link:https://github.com/arko87/FORTRESSLicensing provisions: MITProgramming language: OpenMP Fortran 90/95Supplementary material: The key details to solve the five coupled Gross-Pitaevskii equations for an SO-coupled spin-2 BEC are presented in the supplementary file. In addition, some sample numerically obtained ground state solutions of SO-coupled spin-2 BECs and OpenMP performance results of the software with spin f=2 are provided.Journal reference of previous version: Comput. Phys. Commun. 259 (2021) 107671Does the new version supersede the previous version?: YesReasons for the new version: The previous version can be used to numerically study an SO-coupled spin-1 BEC only, whereas the new version extends the applicability of the software to the SO-coupled spin-2 BECs.Summary of revisions: The new features and augmentations in the package are as follows:(i) Input parameters relevant to the problem under investigation are now read via an input file. Three sample input files corresponding to quasi-one-dimensional (q1D), quasi-two-dimensional (q2D), and three-dimensional (3D) spinor BECs have been provided. The user can edit these files as per the requirement of the problem. Details of the parameters in the sample input files are described in the README.md file provided with the software.(ii) The software has been augmented to solve the five coupled Gross-Pitaevskii equations for SO-coupled spin-2 BECs. The users can now employ the software to study SO-coupled spin-2 [1] as well as spin-1 [2,3] BECs by merely providing the integer ‘SPIN’ parameter equal to 1 for a spin-1 or 2 for a spin-2 BEC in the input file.(iii) A Makefile has been provided to compile the programs with multiple (intel, GNU, and f95) compiler options. Depending on the availability or the choice of user, any of the above compiler options can be used. The user can furthermore choose the variable DIMENSION = 1D, 2D or 3D in the Makefile to simulate, respectively, q1D, q2D or 3D spinor BECs. Depending on the value of DIMENSION, the relevant input file will be read. All the details about using the Makefile are given in the README.md file.(iv) The double precision reals and arrays have been declared in a processor-independent manner.(v) The various arrays have been declared with ALLOCATABLE attribute to assign the memory dynamically and thus more efficiently manage the memory requirement of the software. For a particular allocatable array, memory is allocated using an ALLOCATE statement and deallocated by using a DEALLOCATE statement.(vi) OpenMP parallelization has been improved further.(vii) A few other minor modifications to the codes, e.g. inclusion of convergence criterion based on energy in addition to the criterion based on the absolute value of the wavefunctions in the previous version, directing error messages to a file, etc.Nature of problem: To solve the coupled Gross-Pitaevskii equations (CGPEs) for an SO-spin-f BEC with f=1 or 2.Solution method: We use a time-splitting Fourier spectral method to solve the CGPEs. The resulting equations are evolved in imaginary time to obtain the ground state of the system or in real time to study the dynamics. Additional details of the solution method applicable to spin-2 BEC are provided in the supplementary material.

Spin dynamics in spin-orbit-coupled spin-2 dipolar ultracold atomic gases

In this paper, we study the spin dynamics of spin-orbit-coupled (SOC) spin-2 Bose–Einstein condensates (BECs) with dipole–dipole interaction (DDI). Numerical results are obtained by solving the nonlocal Gross–Pitaevskii equation. Our discussions are divided into two parts. In the absence of DDI, the spin dynamics presents periodic oscillation. Increasing the magnetization makes the amplitude increase, and increasing SOC strength accelerates the spin dynamics and thus changes the period. Nevertheless, in the presence of DDI, the periodicity oscillation of spin dynamics is broken. The thermalization time decreases with the increase of magnetization for fixed SOC strength. In addition, the thermalization time becomes zero with strong SOC strength when magnetization is fixed. We also show the formation of domain in density profile when DDI is considered. Moreover, the components m = 2 and m = −2 exchange their location with a little increase of SOC strength. This is a specific reflection of the competition between the SOC and DDI.

Many-body effects of collective neutrino oscillations

Collective neutrino oscillations are critical to determine the neutrino flavor content, which has striking impacts on core-collapse supernovae or compact binary merger remnants. It is a challenging many-body problem that so far has been mainly studied at the mean-field approximation. We use a setup that captures the relevant physics and allows exact solution for a large number of neutrinos. We, for the first time, find quantitative deviation from the mean-field evolution due to many-body decoherence in flavor space. Similar features have been observed in a spin-1 Bose-Einstein condensate, which opens the possibility of experimental explorations of collective flavor phenomena. Our results call for more careful examinations on the possible many-body corrections to collective neutrino oscillations in astrophysical environments.

A variational approach for the ground-state profile of a trapped spinor-BEC: a detailed study of phase transition in spin-1 condensate at zero magnetic field

In this article, we introduce a multi-modal variational method to analytically estimate the full number- and corresponding energy-density profile of a spin-1 Bose-Einstein condensate (BEC) for a number of particles as low as 500 under harmonic confinement. To apply this method, we consider a system of spin-1 BEC under three-dimensional isotropic and effective one-dimensional harmonic confinement in the absence (negligible presence) of the magnetic field which has ground-state candidates of comparable energy. It should be noted that in such circumstances kinetic energy contribution to the ground state cannot be neglected which puts the applicability of Thomas–Fermi (T-F) approximation to question. For anti-ferromagnetic condensates, the T-F approximated energy difference between the competing stationary states (ground state and the first excited state) is approximately 0.5%. As T-F approximation is only good for condensates with a large number of particles, T-F approximated predictions can completely go wrong especially for small condensates. This is where comes the role of a detailed analysis using our variational method, which incorporates the kinetic energy contribution and accurately estimates the number- and energy-density profile even for condensates having a small number of particles. Results of our analytical method are supported by numerical simulation. This variational method is general and can be extended to other similar/higher-dimensional problems to get results beyond the accuracy of the T-F approximation.

Analog spacetimes from nonrelativistic Goldstone modes in spinor condensates

It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudo-spin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analog systems. While this result is general, present day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as $^{87}$Rb, $^{7}$Li, $^{41}$K (Newton-Cartan), and $^{23}$Na (Einstein-Hilbert).

Josephson-like Oscillations in Toroidal Spinor Bose–Einstein Condensates: A Prospective Symmetry Probe

Josephson junctions are essential ingredients in the superconducting circuits used in many existing quantum technologies. Additionally, ultracold atomic quantum gases have also become essential platforms to study superfluidity. Here, we explore the analogy between superconductivity and superfluidity to present an intriguing effect caused by a thin finite barrier in a quasi-one-dimensional toroidal spinor Bose–Einstein condensate (BEC). In this system, the atomic current density flowing through the edges of the barrier oscillates, such as the electrical current through a Josephson junction in a superconductor, but in our case, there is no current circulation through the barrier. We also show how the nontrivial broken-symmetry states of spinor BECs change the structure of this Josephson-like current, creating the possibility to probe the spinor symmetry, solely using measurements of this superfluid current.

Observing Dynamical Currents in a Non-Hermitian Momentum Lattice.

We report on the experimental realization and detection of dynamical currents in a spin-textured lattice in momentum space. Collective tunneling is implemented via cavity-assisted Raman scattering of photons by a spinor Bose-Einstein condensate into an optical cavity. The photon field inducing the tunneling processes is subject to cavity dissipation, resulting in effective directional dynamics in a non-Hermitian setting. We observe that the individual tunneling events are superradiant in nature and locally resolve them in the lattice by performing real-time, frequency-resolved measurements of the leaking cavity field. The results can be extended to a regime exhibiting a cascade of currents and simultaneous coherences between multiple lattice sites, where numerical simulations provide further understanding of the dynamics. Our observations showcase dynamical tunneling in momentum-space lattices and provide prospects to realize dynamical gauge fields in driven-dissipative settings.

Propagating Ferrodark Solitons in a Superfluid: Exact Solutions and Anomalous Dynamics.

Exact propagating topological solitons are found in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates, manifesting themselves as kinks in the transverse magnetization. Propagation is only possible when the symmetry-breaking longitudinal magnetic field is applied. Such solitons have two types: a low energy branch with positive inertial mass and a higher energy branch with negative inertial mass. Both types become identical at the maximum speed, a new speed bound that is different from speed limits set by the elementary excitations. The physical mass, which accounts for the number density dip, is negative for both types. In a finite one-dimensional system subject to a linear potential, the soliton undergoes oscillations caused by transitions between the two types occurring at the maximum speed.

GPU-accelerated solutions of the nonlinear Schrödinger equation for simulating 2D spinor BECs

As a first approximation beyond linearity, the nonlinear Schrödinger equation (NLSE) reliably describes a broad class of physical systems. Though numerical solutions of this model are well-established, these methods can be computationally complex. In this paper, we showcase a code development approach, demonstrating how computational time can be significantly reduced with readily available graphics processing unit (GPU) hardware and a straightforward code migration using open-source libraries. This process shows how CPU computations with power-law scaling in computation time with grid size can be made linear using GPUs. As a specific case study, we investigate the Gross-Pitaevskii equation, a specific version of the nonlinear Schrödinger model, as it describes in two dimensions a trapped, interacting, two-component Bose-Einstein condensate (BEC) subject to a spatially dependent interspin coupling, resulting in an analog to a spin-Hall system. This computational approach lets us probe high-resolution spatial features – revealing an interaction-dependent phase transition – all in a reasonable amount of time. Our computational approach is particularly relevant for research groups looking to easily accelerate straightforward numerical simulation of physical phenomena. Program summaryProgram Title:spinor-gpeCPC Library link to program files:https://doi.org/10.17632/sn6gjp99td.1Developer's repository link:https://github.com/ultracoldYEG/spinor-gpeLicensing provisions: MITProgramming language: PythonNature of problem: Calculate the ground- and time-evolved states to the quasi-2D, pseudospinor (two-component) nonlinear Schrodinger equation, with additional Zeeman interaction and momentum-dependent, interspin coupling.Solution method:spinor-gpe is a high-level, object-oriented Python package built on Numpy and PyTorch. It propagates the pseudospinor NLSE using a time-splitting spectral method. This package accelerates solutions using NVIDIA hardware and PyTorch's cuFFT libraries and tensor functionality.Additional comments including restrictions and unusual features: The NVIDIA CUDA backend of PyTorch is not supported on Mac computers. To run this code on a Mac system, the dependency installation will need to exclude the CUDA toolkit.

Single-domain Bose condensate magnetometer achieves energy resolution per bandwidth below ℏ

We present a magnetic sensor with energy resolution per bandwidth [Formula: see text] We show how a 87Rb single-domain spinor Bose-Einstein condensate, detected by nondestructive Faraday rotation probing, achieves single-shot low-frequency magnetic sensitivity of 72(8) fT measuring a volume [Formula: see text] for 3.5 s, and thus, [Formula: see text] We measure experimentally the condensate volume, spin coherence time, and readout noise and use phase space methods, backed by three-dimensional mean-field simulations, to compute the spin noise. Contributions to the spin noise include one-body and three-body losses and shearing of the projection noise distribution, due to competition of ferromagnetic contact interactions and quadratic Zeeman shifts. Nonetheless, the fully coherent nature of the single-domain, ultracold two-body interactions allows the system to escape the coherence vs. density trade-off that imposes an energy resolution limit on traditional spin precession sensors. We predict that other Bose-condensed alkalis, especially the antiferromagnetic 23Na, can further improve the energy resolution of this method.

Spin-current instability at a magnetic domain wall in a ferromagnetic superfluid: A generation mechanism of eccentric fractional skyrmions

Spinful superfluids of ultracold atoms are ideal for investigating the intrinsic properties of spin current and texture because they are realized in an isolated, nondissipative system free from impurities, dislocations, and thermal fluctuations. This study theoretically reveals the impact of spin current on a magnetic domain wall in spinful superfluids. An exact wall solution is obtained in the ferromagnetic phase of a spin-1 Bose-Einstein condensate with easy-axis anisotropy at zero temperature. The bosonic-quasiparticle mechanics analytically show that the spin current along the wall becomes unstable if the velocity exceeds the critical spin-current velocities, leading to complicated situations because of the competition between transverse magnons and ripplons. Our direct numerical simulation reveals that this system has a mechanism to generate an eccentric fractional skyrmion, which has a fractional topological charge, but its texture is not similar to that of a meron. This mechanism is in contrast to the generation of conventional skyrmions in easy-axis magnets. The theoretical findings can be examined in the same situation as in a recent experiment on ultracold atoms. In terms of the universality of spontaneous symmetry breaking, unexplored similar phenomena are expected in different physical systems with the same broken symmetry.

Spin solitons in spin-1 Bose–Einstein condensates

Vector solitons in Bose–Einstein condensates are usually investigated analytically with identical intra- and interatomic interactions (for an integrable model). We obtain six families of exact spin soliton solutions for nonintegrable cases, which can be used to describe spin-1 Bose–Einstein condensates. The stability analyses and numerical simulations indicate that three families of spin solitons are robust against spin-dependent interactions and white noise. We further investigate the motion of these stable spin solitons driven by external linear potentials. Their moving trajectories demonstrate that the spin solitons admit a negative–positive mass transition. Some splitting and diffusing behaviors can emerge during the motion of a spin soliton that are absent in spin-1/2 systems. The collisions between spin solitons are exhibited with varying relative velocity and phase. The nonintegrable properties of the systems can give rise to weak amplitude and location oscillations after collision. These stable spin soliton excitations can be used to study the negative inertial mass of solitons, the dynamics of soliton-impurity systems, and the spin dynamics in Bose–Einstein condensates.