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We theoretically study the electric pulse-driven non-linear response of interacting bosons loaded in an optical lattice in the presence of an incommensurate superlattice potential. In the non-interacting limit $(U=0)$, the model admits both localized and delocalized phases depending on the strength of the incommensurate potential $V_0$. We show that the particle current contains only odd harmonics in the delocalized phase in contrast to the localised phase where both even and odd harmonics are identified. The relative magnitudes of these even and odd harmonics and sharpness of the peaks can be tuned by varying frequency and the number of cycles of the applied pulse, respectively. In the presence of repulsive interactions, the amplitudes of the even and odd harmonics further depend on the relative strengths of the interaction $U$ and the potential $V_0$. We illustrate that the disorder and interaction-induced phases can be distinguished and characterized through the particle current. Finally, we discuss the dynamics of field induced excitation responsible for exhibiting higher harmonics in the current spectrum., 11 pages, 11 figures

We theoretically study 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 the real-time evolution of the ground state subjected to a perturbation suitable to excite a density or a spin mode. We have also calculated a few low-lying modes analytically and found a 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.

A paramagnetic-ferromagnetic quantum phase transition is known to occur at zero temperature in a two-dimensional coherently-coupled Bose mixture of dilute ultracold atomic gases provided the interspecies interaction strength is large enough. Here we study the fate of such a transition at finite temperature by performing numerical simulations with the stochastic (projected) Gross-Pitaevskii formalism, which includes both thermal and beyond mean-field effects. By extracting the average magnetization, the magnetic fluctuations and characteristic relaxation frequency (or, critical slowing down), we identify a finite temperature critical line for the transition. We find that the critical point shifts linearly with temperature and, in addition, the three quantities used to probe the transition exhibit a temperature power-law scaling. The scaling of the critical slowing down is found to be consistent with thermal critical exponents and is very well approximated by the square of the spin excitation gap at the zero-temperature., Comment: 10 pages, 5 figures

We theoretically study the stationary-state vortex lattice configurations of rotating spin-orbit (SO)- and coherently-coupled spin-1 Bose–Einstein condensates (BECs) trapped in quasi-two-dimensional harmonic potentials. The combined effects of rotation, SO and coherent couplings are analyzed systematically from the single-particle perspective. Through the single-particle Hamiltonian, which is exactly solvable for one-dimensional coupling, we illustrate that a boson in these rotating SO- and coherently-coupled condensates are 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 formalism 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. On rapid rotation, we further find that the spin-expectation per particle of an antiferromagnetic spin-1 BEC approaches unity indicating a similarity in the response with ferromagnetic SO-coupled condensates.

A rich variety of physical effects in spin dynamics arises at the interface between different magnetic materials. Engineered systems with interlaced magnetic structures have been used to implement spin transistors, memories and other spintronic devices. However, experiments in solid state systems can be difficult to interpret because of disorder and losses. Here, we realize analogues of magnetic junctions using a coherently-coupled mixture of ultracold bosonic gases. The spatial inhomogeneity of the atomic gas makes the system change its behavior from regions with oscillating magnetization -- resembling a magnetic material in the presence of an external transverse field -- to regions with a defined magnetization, as in magnetic materials with a ferromagnetic anisotropy stronger than external fields. Starting from a far-from-equilibrium fully polarized state, magnetic interfaces rapidly form. At the interfaces, we observe the formation of short-wavelength magnetic waves. They are generated by a quantum torque contribution to the spin current and produce strong spatial anticorrelations in the magnetization. Our results establish ultracold gases as a platform for the study of far-from-equilibrium spin dynamics in regimes that are not easily accessible in solid-state systems., 9 pages, 5 figures

We develop a FORTRAN code to compute fluctuations in atomic condensates (FACt) by solving the Bogoliubov-de Gennes (BdG) equations for two component Bose-Einstein condensate (TBEC) in quasi two dimensions. The BdG equations are recast as matrix equations and solved self consistently. The code is suitable for handling quantum fluctuations as well as thermal fluctuations at temperatures below the critical point of Bose-Einstein condensation. The code is versatile, and the ground state density profile and low energy excitation modes obtained from the code can be easily adapted to compute different properties of TBECs -- ground state energy, overlap integral, quasi particle amplitudes of BdG spectrum, dispersion relation and structure factor and other related experimental observables., The manuscript contains 28 pages and 6 figures. The code including sample input file and README file can be found in a tar file 'hfb2d2s.tar' by clicking on the "other formats" in the paper download page

We propose the implementation of a quantum heat pump with ultracold atoms. It is based on two periodically driven coherently coupled quantum dots using ultracold atoms. Each dot possesses two relevant quantum states and is coupled to a fermionic reservoir. The working principle is based on energy-selective driving-induced resonant tunneling processes, where a particle that tunnels from one dot to the other either absorbs or emits the energy quantum $\hbar\omega$ associated with the driving frequency, depending on its energy. We characterize the device using Floquet theory and compare simple analytical estimates to numerical simulations based on the Floquet-Born-Markov formalism. In particular, we show that driving-induced heating is directly linked to the micromotion of the Floquet states of the system., Comment: 6 pages, 5 figures

We theoretically study the non-linear response of interacting neutral bosonic gas in a synthetically driven one-dimensional optical lattice. In particular, we examine the bosonic analogue of electronic higher harmonic generation in a strong time-dependent synthetic vector potential manifesting itself as the synthetic electric field. We show that the vector potential can generate reasonably high harmonics in the insulating regime, while the superfluid regime exhibits only a few harmonics. In the insulating regime, the number of harmonics increases with the increase in the strength of the vector potential. This originates primarily due to the field-driven resonant and non-resonant excitations in the neutral Mott state and their recombination with the ground state. If the repulsive interaction between two atoms ($U$) is close to the strength of the gauge potential ($A_0$), the resonant quasiparticle-quasihole pairs on nearest-neighbor sites, namely dipole states are found to a play a dominant role in the generating higher harmonics. However, in the strong-field limit $A_0\gg U$, the nonresonant states where quasiparticle-quasihole pairs are not on nearest-neighbor sites give rise to higher harmonics., 8 pages, 8 figures

Here, we present simple and efficient numerical scheme to study static and dynamic properties of spin-1 Bose–Einstein condensates (BECs) with spin–orbit (SO) coupling by solving three coupled Gross–Pitaevskii equations (CGPEs) in three-, quasi-two and quasi-one dimensional systems. We provide a set of three codes developed in FORTRAN 90/95 programming language with user defined ‘option’ of imaginary and real-time propagation. We present the numerical results for energy, chemical potentials, and component densities for the ground state and compare with the available results from the literature. The results are presented for both the ferromagnetic and antiferromagnetic spin-1 BECs with and without SO coupling. To improve the computational speed, all the codes have the option of OpenMP parallelization. We have also presented the results for speedup and efficiency of OpenMP parallelization for the three codes with both imaginary and real-time propagation. Program summary Program Title: FORTRESS CPC Library link to program files: https://doi.org/10.17632/st7md3ss85.1 Licensing provisions: MIT Programming language: (OpenMP) FORTRAN 90/95 External routines/libraries: FFTW 3.3.8 Nature of problem: To solve the coupled Gross–Pitaevskii equations for spin-1 BEC with anisotropic spin–orbit coupling using the time-splitting spectral method. Solution method: We use the time-splitting Fourier spectral method to solve the coupled Gross–Pitaevskii equations. The resulting equations are evolved in imaginary time to obtain the ground state of the system or in real-time to study the dynamics.

We examine the role of thermal fluctuations in uniform two-dimensional binary Bose mixtures of dilute ultracold atomic gases. We use a mean-field Hartree-Fock theory to derive analytical predictions for the miscible-immiscible transition. A nontrivial result of this theory is that a fully miscible phase at $T=0$ may become unstable at $T\neq0$, as a consequence of a divergent behaviour in the spin susceptibility. We test this prediction by performing numerical simulations with the Stochastic (Projected) Gross-Pitaevskii equation, which includes beyond mean-field effects. We calculate the equilibrium configurations at different temperatures and interaction strengths and we simulate spin oscillations produced by a weak external perturbation. Despite some qualitative agreement, the comparison between the two theories shows that the mean-field approximation is not able to properly describe the behavior of the two-dimensional mixture near the miscible-immiscible transition, as thermal fluctuations smoothen all sharp features both in the phase diagram and in spin dynamics, except for temperature well below the critical temperature for superfluidity., Comment: 13 pages, 8 figures

We explore the effects of finite temperature on the dynamics of Bose-Einstein condensates (BECs) after it is released from the confining potential. In addition, we examine the variation in the expansion dynamics of the BECs as the confining potential is transformed from a multiply to a simply connected geometry. To include the effects of finite temperatures we use the frozen thermal cloud approximation, and observe unique features of the condensate density distribution when released from the confining potential. We find that at T not equal 0, during the initial stages of expansion, the multiply connected condensate has more pronounced interference rings compared to the case of zero temperature. Such difference in the dynamical evolution is also evident for simply connected condensates. (C) 2017 Elsevier B.V. All rights reserved.

Motivated by the recent experiment [Takafumi Tomita \emph{et al.}, Sci. Adv. {\bf 3}, (2017)], we study the dynamics of interacting bosons in a two-dimensional optical lattice with local dissipation. Together with the Gutzwiller mean-field theory for density matrices and Lindblad master equation, we show how the onsite interaction between bosons affects the particle loss for various strengths of dissipation. For moderate dissipation, the trend in particle loss differs significantly near the superfluid-Mott boundary than the deep superfluid regime. While the loss is suppressed for stronger dissipation in the deep superfluid regime, revealing the typical quantum Zeno effect, the loss near the phase boundary shows non-monotonic dependence on the dissipation strength. We furthermore show that close to the phase boundary, the long-time dynamics is well contrasted with the dissipative dynamics deep into the superfluid regime. Thus the loss of particle due to dissipation may act as a probe to differentiate strongly-correlated superfluid regime from its weakly-correlated counterpart., Comment: 7 pages, 5 figures

We present new features of low energy Bogoliubov quasiparticle excitations of a two-component Bose-Einstein condensate (TBEC) in quasi-2D geometry at zero temperature using Hartree-Fock-Bogoliubov formalism. We, in particular, consider the TBECs of Cs-133-Rb-87 and Rb-85-Rb-87, and show specific features in the low energy excitation spectrum as a function of the interaction strength. For Rb-85-Rb-87 TBEC, the appearance of a new zero energy mode is observed. Whereas for Cs-133-Rb-87 TBEC we report a bifurcation of the slosh mode at the point of transition from miscible to immiscible domain. The lower energy mode, after the bifurcation, goes soft and becomes a new Nambu-Goldstone mode of the system.

We demonstrate an enhancement in the vortex generation when artificial gauge potential is introduced to condensates confined in a double well potential. This is due to the lower energy required to create a vortex in the low condensate density region within the barrier. Furthermore, we study the transport of vortices between the two wells, and show that the traverse time for vortices is longer for the lower height of the well. We also show that the critical value of synthetic magnetic field to inject vortices into the bulk of the condensate is lower in the double-well potential compared to the harmonic confining potential., Comment: 7 pages, 7 figures, Published in Phys. Lett. A

We examine the dynamics associated with the miscibility-immiscibility transition of trapped two-component Bose-Einstein condensates (TBECs) of dilute atomic gases in presence of vortices. In particular, we consider TBECs of Rb hyperfine states, and Rb-Cs mixture. There is an enhancement of the phase-separation when the vortex is present in both condensates. In the case of a singly charged vortex in only one of the condensates, there is enhancement when the vortex is present in the species which occupy the edges at phase-separation. But, suppression occurs when the vortex is in the species which occupies the core region. To examine the role of the vortex, we quench the inter-species interactions to propel the TBEC from miscible to immiscible phase, and use the time dependent Gross-Pitaevskii equation to probe the phenomenon of phase-separation. We also examine the effect of higher charged vortex., Comment: 9 pages and 9 figures

We report the effects of anisotropy in the confining potential on two component Bose-Einstein condensates (TBECs) through the properties of the low energy quasiparticle excitations. Starting from generalized Gross Pitaevskii equation, we obtain the Bogoliubov de-Gennes (BdG) equation for TBECs using the Hartree-Fock-Bogoliubov (HFB) theory. Based on this theory, we present the influence of radial anisotropy on TBECs in the immiscible or the phase-separated domain. In particular, the TBECs of $^{85}$Rb~-$^{87}$Rb and $^{133}$Cs~-$^{87}$Rb TBECs are chosen as specific examples of the two possible interface geometries, shell-structured and side by side, in the immiscible domain. We also show that the dispersion relation for the TBEC shell-structured interface has two branches, and anisotropy modifies the energy scale and structure of the two branches., Comment: 9 pages, 13 figures

We examine the role of thermal fluctuations in binary condensate mixtures of dilute atomic gases. In particular, we use Hartree-Fock-Bogoliubov with Popov approximation to probe the impact of non-condensate atoms to the phenomenon of phase-separation in two-component Bose-Einstein condensates. We demonstrate that, in comparison to $T=0$, there is a suppression in the phase-separation of the binary condensates at $T\neq0$. This arises from the interaction of the condensate atoms with the thermal cloud. We also show that, when $T\neq0$ it is possible to distinguish the phase-separated case from miscible from the trends in the correlation function. However, this is not the case at $T=0$., 5 pages, 4 figures

We show that the third Goldstone mode in the two-species condensate mixtures, which emerges at phase-separation, gets hardened when the confining potentials have separated trap centers. The {\em sandwich} type condensate density profiles, in this case, acquire a {\em side-by-side} density profile configuration. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution and density profiles for these phase transitions at $T=0$., Comment: 5 pages, 2 figures. Some part of the theory is common to arXiv:1307.5716 and arXiv:1405:6459, so that the article is self-contained for the benefit of the readers

We explore the topological transformation of quasi-2D Bose-Einstein condensates of dilute atomic gases, and changes in the low-energy quasiparticles associated with the geometry of the confining potential. In particular, we show the density profile of the condensate and quantum fluctuation follow the transition from a multiply to a simply connected geometry of the confining potential. The thermal fluctuations, in contrast, remain multiply connected. The genesis of the key difference lies in the structure of the low-energy quasiparticles. For which we use the Hartree-Fock-Bogoliubov, and study the evolution of quasiparticles, the dipole or the Kohn mode in particular. We, then employ the Hartree-Fock-Bogoliubov theory with the Popov approximation to investigate the density and the momentum distribution of the thermal atoms., 7 pages, 8 figures

We show that the presence of soliton in a single-species condensate, at zero temperature, enhances the quantum depletion sufficient enough to induce dynamical instability of the system. We also predict that for two-species condensates, two Goldstone modes emerge in the excitation spectrum at phase separation. Of these, one is due to the presence of the soliton. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution, and demonstrate that when the anomalous mode collides with a higher energy mode it renders the solitonic state oscillatory unstable. We also report soliton induced change in the topology of the density profiles of the two-species condensates at phase-separation., Comment: arXiv admin note: text overlap with arXiv:1307.5716

We show the emergence of a third Goldstone mode in binary condensates at the phase-separation in quasi-1D optical lattices. We develop the coupled discrete nonlinear Schr\"odinger equations (DNLSEs) using Hartree-Fock-Bogoliubov theory with Popov approximation in the Bose-Hubbard model to investigate the mode evolution at zero temperature. In particular, as the system is driven from miscible to immiscible phase. We demonstrate that the position swapping of the species in $^{87}$Rb-$^{85}$Rb system is accompanied by a discontinuity in the excitation spectrum. Our results show that in quasi-1D optical lattices, the presence of the fluctuations dramatically change the geometry of the ground state density profile of TBEC., Comment: 10 pages, 8 figures

We examine the dynamics of a vortex dipole in the Bose-Einstein condensates (BECs) of trapped dilute atomic gases at zero temperature in the presence of a Gaussian barrier potential. The density-anisotropy induced by the barrier enhances the acoustic radiation from the vortex dipole. This is due to the deviation of the condensate density from the equipotential curves and variation in the curvature of the vortex dipole trajectory. Due to the acoustic radiation, the vortex dipole dissipates energy and spirals towards the edge of the condensate. As a result, we observe an increase in the vortex-antivortex annihilation events. To examine the effect of the Gaussian barrier, we estimate the correction to the Thomas-Fermi condensate density using perturbation expansion method and the results are in very good agreement with the numerical results., 10 pages, 7 figures, extensive modification in the text and figures

We show that the third Goldstone mode, which emerges in binary condensates at phase separation, persists to higher interspecies interaction for density profiles where one component is surrounded on both sides by the other component. This is not the case with symmetry-broken density profiles where one species is entirely to the left and the other is entirely to the right. We, then, use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution at $T\ensuremath{\ne}0$ and demonstrate the existence of mode bifurcation near the critical temperature. The Kohn mode, however, exhibits deviation from the natural frequency at finite temperatures after the phase separation. This is due to the exclusion of the noncondensate atoms in the dynamics.

We study the dynamics of a single and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. We use the stochastic Gross-Pitaevskii equation, which is the Langevin equation for the Bose-Einstein condensate, to this end. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices., Comment: 8 pages, 10 figures

We report the structural transformation of the low-lying spectral modes, especially the Kohn mode, from radial to circular topology as harmonic confining potential is modified to a toroidal one, and this corresponds to a transition from simply to multiply connected geometry. For this we employ the Hartree-Fock-Bogoliubov theory to examine the evolution of low energy quasiparticles. We, then, use the Hartree-Fock-Bogoliubov theory with the Popov approximation to demonstrate the two striking features of quantum and thermal fluctuations. At $T=0$, the non-condensate density due to interaction induced quantum fluctuations increases with the transformation from pancake to toroidal geometry. The other feature is, there is a marked change in the density profile of the non-condensate density at finite temperatures with the modification of trapping potential. In particular, the condensate and non-condensate density distributions have overlapping maxima in the toroidal condensate, which is in stark contrast to the case of pancake geometry. The genesis of this difference lies in the nature of the thermal fluctuations., Comment: 13 pages, 5 figures