Starting from the three-dimensional (3D) time-dependent nonlinear Gross-Pitaevskii equation for a Bose-Einstein condensate (BEC) and density functional (DF) equation for a Fermi superfluid at the unitarity and Bardeen-Cooper-Schrieffer (BCS) limits, we derive effective one- (1D) and two-dimensional (2D) mean-field equations, respectively, for the dynamics of a trapped cigar- and disk-shaped BEC and Fermi superfluid by using the adiabatic approximation. The reduced 1D and 2D equations for a cigar- and disk-shaped Fermi superfluid have simple analytic nonlinear terms and at unitarity produce results for stationary properties and non-stationary breathing oscillation and free expansion in excellent agreement with the solution of the full 3D equation.
Within the formalism of the Gross-Pitaevskii equation, we derive effective one- and two-dimensional equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. These are based on an ansatz for the condensate wavefunction whose width in the tightly-confined direction/s is treated variationally. The equations constitute a coupled partial differential for the low-dimensional wavefunction and algebraic equations for the width parameters. This approach accurately predicts the ground state densities of cigar-shaped and pancake-shaped dipolar Bose-Eins…
We compute the Tan's contact of a weakly interacting Bose gas at zero temperature in a cigar-shaped configuration. Using an effective one-dimensional Gross-Pitaeskii equation and Bogoliubov theory, we derive an analytical formula that interpolates between the three-dimensional and the one-dimensional mean-field regimes. In the strictly one-dimensional limit, we compare our results with Lieb-Liniger theory. Our study can be a guide for actual experiments interested in the study of Tan's contact in the dimensional crossover.
We show that the dipole-dipole coupling between Wannier modes in cigar-shaped Bose-Einstein condensates (BECs) is significantly enhanced while the short-range coupling strongly suppressed. As a result, the dipole-dipole interaction can become the dominant interaction between ultracold alkali Bose atoms. In the long length limit of a cigar-shaped BEC, the resulting effective one-dimensional models possess an effective inverse squared interacting potential, the Calogero-Sutherland potential, which plays a fundamental role in many fields of contemporary physics; but its direct experimental realiz…
In a cigar shaped Bose-Einstein condensate, explicit solutions of the coupled mean-field equations, describing defect-grey soliton dynamics are obtained, demonstrating the coexistence of grey soliton and a localized defect. Unlike the case of dark soliton, where the defect trapping center has vanishing superfluid density, the moving grey soliton necessarily possesses a finite superfluid component at the defect location. The wave vector of the impurity is controlled by the velocity of the grey soliton, which has an upper bound. It is found that the presence of the impurity lowers the speed of t…
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 …
We study the statics and dynamics of dark solitons in a cigar-shaped Bose-Einstein condensate confined in a double-well potential. Using a mean-field model with a non-cubic nonlinearity, appropriate to describe the dimensionality crossover regime from one to three dimensional, we obtain branches of solutions in the form of single- and multiple-dark soliton states, and study their bifurcations and stability. It is demonstrated that there exist dark soliton states which do not have a linear counterpart and we highlight the role of anomalous modes in the excitation spectra. Particularly, we show …
In the case of tight transverse confinement (cigar-shaped trap) the three-dimensional (3D) nonlinear Schrödinger equation, describing superfluid Fermi atoms at unitarity (infinite scattering length $|a|\to \infty$), is reduced to an effective one-dimensional form by averaging over the transverse coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger equation, which produces results in good agreement with the original 3D one. In the limit of small and large fermion number $N$ the nonlinearity is of simple power-law type. A similar reduction of the 3D theory to a two-dim…
We present new solutions to the nonautonomous nonlinear Schroedinger equation that may be realized through convenient manipulation of Bose-Einstein condensates. The procedure is based on the modulation of breathers through an analytical study of the one-dimensional Gross-Pitaevskii equation, which is known to offer a good theoretical model to describe quasi-one-dimensional cigar-shaped condensates. Using a specific Ansatz, we transform the nonautonomous nonlinear equation into an autonomous one, which engenders composed states corresponding to solutions localized in space, with an oscillating …
We consider a Bose-Einstein condensate (BEC), which is characterized by long-range and anisotropic dipole-dipole interactions and vanishing s-wave scattering length, in a double-well potential. The properties of this system are investigated as functions of the height of the barrier that splits the harmonic trap into two halves, the number of particles (or dipole-dipole strength) and the aspect ratio $λ$, which is defined as the ratio between the axial and longitudinal trapping frequencies $ω_z$ and $ω_ρ$. The phase diagram is determined by analyzing the stationary mean-field solutions. Three d…
A comparative study is done of the propagation of sound pulses in elongated Bose liquids and Bose-Einstein condensates in Gross-Pitaevskii and logarithmic models, by means of the Thomas-Fermi approximation. It is shown that in the linear regime the propagation of small density fluctuations is essentially one-dimensional in both models, in the direction perpendicular to the cross section of a liquid's lump. Under these approximations, it is shown that the speed of sound scales as a square root of particle density in the case of the Gross-Pitaevskii liquid/condensate, but it is constant in a cas…
We explore the stability and dynamics of dark-bright solitons in two-component elongated Bose-Einstein condensates by developing effective 1D vector equations as well as solving the corresponding 3D Gross-Pitaevskii equations. A strong dependence of the oscillation frequency and of the stability of the dark-bright (DB) soliton on the atom number of its components is found. Spontaneous symmetry breaking leads to oscillatory dynamics in the transverse degrees of freedom for a large occupation of the component supporting the dark soliton. Moreover, the interactions of two DB solitons are investig…
We consider the dynamical properties of density fluctuations in the cigar-shaped Bose-Einstein condensate described by the logarithmic wave equation with a constant nonlinear coupling by using the Thomas-Fermi and linear approximations. It is shown that the propagation of small density fluctuations along the long axis of a condensed lump in a strongly anisotropic trap is essentially one-dimensional, while the trapping potential can be disregarded in the linear regime. Depending on the sign of nonlinear coupling, the fluctuations either take the form of translationally symmetric pulses and stan…
Faraday and resonant density waves emerge in Bose-Einstein condensates as a result of harmonic driving of the system. They represent nonlinear excitations and are generated due to the interaction-induced coupling of collective oscillation modes and the existence of parametric resonances. Using a mean-field variational and a full numerical approach, we studied density waves in dipolar condensates at zero temperature, where breaking of the symmetry due to anisotropy of the dipole-dipole interaction (DDI) plays an important role. We derived variational equations of motion for the dynamics of a dr…
One-dimensional (1D) Nonlinear Schroedinger Equaation (NLS) provides a good approximation to attractive Bose-Einshtein condensate (BEC) in a quasi 1D cigar-shaped optical trap in certain regimes. 1D NLS is an integrable equation that can be solved through the inverse scattering method. Our observation is that in many cases the parameters of the BEC correspond to the semiclassical (zero dispersion) limit of the focusing NLS. Hence, recent results about the strong asymptotics of the semiclassical limit solutions can be used to describe some interesting phenomena of the attractive 1D BEC. In gene…
We have investigated the quantum dynamics of two ultracold bosons inside an atomic waveguide for two different confinement geometries (cigar-shaped and toroidal waveguides) by quantum Monte Carlo methods. For quasi-1D gases, the confining potential of the waveguide leads to the so-called confinement induced resonance (CIR), results in the phase transition of the gas to the impenetrable bosonic regime (known as TG gas). In this regime the bosons repel each other strongly and behave like fermions. We reproduce CIR for a cigar-shaped waveguide and analyze the behavior of the system for different …
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates (BECs). Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective rep…
We study the phase-fluctuating condensate regime of ultra-cold atoms trapped in a ring-shaped trap geometry, which has been realized in recent experiments. We first consider a simplified box geometry, in which we identify the conditions to create a state that is dominated by thermal phase-fluctuations, and then explore the experimental ring geometry. In both cases we demonstrate that the requirement for strong phase fluctuations can be expressed in terms of the total number of atoms and the geometric length scales of the trap only. For the ring-shaped trap we discuss the zero temperature limit…
We analyze the nature of quantum phase transition to a superfluid state of flexible chains in a gas of polar bosonic molecules confined in a stack of $N$ identical 1d ("cigar" type) optical lattice layers and polarized perpendicularly to the layers. Monte Carlo simulations within the $J$-current model show that, in the absence of the inter-tube tunneling, the transition to the $N$-layered superfluid is in the Berezinskii-Kosterlitz-Thouless universality class in the one-particle density matrix channel. The inter-layer tunneling changes it to the $q=N$ 2d Potts universality. The low energy fiel…
We present a numerical study of the interaction quench dynamics in a superfluid ultracold Fermi gas confined in a three-dimensional cigar-shaped harmonic trap. In the present paper we investigate the amplitude mode of the superfluid order parameter after interaction quenches which start deep in the BCS phase and end in the BCS-BEC crossover regime. To this end, we exploit the Bogoliubov-de Gennes formalism which takes the confinement potential explicitly into account and provides a microscopic fully coherent description of the system. We find an anharmonic nonlinear oscillation of the modulus …
We derive rigorously one- and two-dimensional mean-field equations for cigar- and pancake-shaped Bose-Einstein condensates (BEC) with higher order interactions (HOI). We show how the higher order interaction modifies the contact interaction of the strongly confined particles. Surprisingly, we find that the usual Gaussian profile assumption for the strongly confining direction is inappropriate for the cigar-shaped BEC case, and a Thomas-Fermi type profile should be adopted instead. Based on the derived mean field equations, the Thomas-Fermi densities are analyzed in presence of the contact inte…
Recent experimental realizations of superfluid mixtures of Bose and Fermi quantum gases provide a unique platform for exploring diverse superfluid phenomena. We study dipole oscillations of a double superfluid in a cigar-shaped optical dipole trap, consisting of $^{41}$K and $^{6}$Li atoms with a large mass imbalance, where the oscillations of the bosonic and fermionic components are coupled via the Bose-Fermi interaction. In our high-precision measurements, the frequencies of both components are observed to be shifted from the single-species ones, and exhibit unusual features. The frequency s…
We study the expansion behaviours of a Fermionic superfluid in a cigar-shaped optical dipole trap for the whole BEC-BCS crossover and various temperatures. At low temperature ($0.06(1) T_F$), the atom cloud undergoes an anisotropic hydrodynamic expansion over 30~ms, which behaves like oscillation in the horizontal plane. By analyzing the expansion dynamics according to the superfluid hydrodynamic equation, the effective polytropic index $\barγ$ of Equation-of-State of Fermionic superfluid is extracted. The $\barγ$ values show a non-monotonic behavior over the BEC-BCS crossover, and have a good…
A Rossby-Haurwitz (RH) wave is an excitation mode of a fluid on a rotating spherical surface, which propagates westward in the rotating frame of reference. Motivated by the recent realization of the shell-shaped Bose-Einstein condensate in microgravity, we investigate the RH wave in a superfluid rotating on a spherical-surface geometry. We employ the point-vortex model and the three-dimensional Gross-Pitaevskii equation, and numerically demonstrate that RH waves can be observed in the system of a superfluid with quantized vortices.
The quasiparticle excitation spectra of a Bose gas trapped in a highly anisotropic trap is studied with respect to varying total number of particles by numerically solving the effective one-dimensional (1D) Gross-Pitaevskii (GP) equation proposed recently by Mateo \textit{et al.}. We obtain the static properties and Bogoliubov spectra of the system in the high energy domain. This method is computationally efficient and highly accurate for a condensate system undergoing a 1D to three-dimensional (3D) cigar-shaped transition, as is shown through a comparison our results with both those calculate…
Motivated by recent experiments on toroidal Bose-Einstein condensates in all-optical traps with tunable weak links, we study the one-dimensional Bose-Hubbard model on a ring-shaped lattice with a small region of weak hopping integrals using quantum Monte Carlo simulations. Besides the usual Mott insulating and superfluid phases, we find a phase which is compressible but non superfluid with a local Mott region. This `local Mott' phase extends in a large region of the phase diagram. These results suggest that the insulating and conducting phases can be tuned by a local parameter which may provid…
Motivated by the fact that two-component confined fermionic gases in Bardeen-Cooper-Schrieffer-Bose-Einstein condensate (BCS-BEC) crossover can be described through an hydrodynamical approach, we study these systems - both in the cigar-shaped configuration and in the disk-shaped one - by using a polytropic Lagrangian density. We start from the Popov Lagrangian density and obtain, after a dimensional reduction process, the equations that control the dynamics of such systems. By solving these equations we study the sound velocity as a function of the density by analyzing how the dimensionality a…
By means of mean-field theory, we have studied the structure and excitation spectrum of a purely dipolar Bose gas in pancake-shaped trap where the confinement in the x-y plane is provided by a highly anharmonic potential resulting in an almost uniform confinement in the plane. We show that the stable condensates is characterized by marked radially structured density profiles. The stability diagram is calculated by independently varying the strength of the interaction and the trap geometry. By computing the Bogoliubov excitation spectrum near the instability line we show that soft "angular" rot…
We theoretically investigate the generation of the vortex dipoles in superfluid Fermi gas in the BCS limit. The vortex dipoles are generated in superfluid either by moving an obstacle above a critical speed or due to the decay of the shock waves obtained on the sudden mixing of two superfluid fragments. We observe that in pancake-shaped traps, the shock waves can lead to the formation of density ripples, which decay into vortex dipoles due to the onset of snake instability.
We consider a $^{168}$Er-$^{164}$Dy dipolar mixture, trapped by a cigar shaped harmonic potential. We derive the quasi-1D inter-species effective potential exhibiting the tilting angles and show that it is a quite natural generalization of the situation of a single dipolar gas. By solving the coupled Gross-Pitaevskii equations, we observe a transition from miscible to immiscible mixture as the orientations of the magnetic moments are varied. The atom numbers are also shown to lead to noticeable effects on the mixture.
We study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. Considering a Gaussian-shaped radially inhomogeneous scattering length, we show through extensive numerical simulations and detailed variational treatment that the spatial period of the emerging Faraday waves increases as the inhomogeneity of the scattering length gets weaker, and that it saturates once the width of the radial inhomogeneity reaches the radial width of the condensate. In the regime of strongly inhomogeneous scatt…
We present effective reduced equations for the study of a binary Bose-Einstein condensate (BEC), where the confining potentials of the two BEC components have distinct asymmetry so that the components belong to different space dimensions as in a recent experiment [G. Lamporesi et al., Phys. Rev. Lett. 104, 153202 (2010)]. Starting from a binary three-dimensional (3D) Gross-Pitaevskii equation (GPE) and using a Lagrangian variational approach we derive a binary effective nonlinear Schroedinger equation with components in different reduced dimensions, e. g., the first component in one dimension …
We study an experimentally feasible qubit system employing neutral atomic currents. Our system is based on bosonic cold atoms trapped in ring-shaped optical lattice potentials. The lattice makes the system strictly one dimensional and it provides the infrastructure to realize a tunable ring-ring interaction. Our implementation combines the low decoherence rates of of neutral cold atoms systems, overcoming single site addressing, with the robustness of topologically protected solid state Josephson flux qubits. Characteristic fluctuations in the magnetic fields affecting Josephson junction based…
We observe solitonic vortices in an atomic Bose-Einstein condensate after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across…
We discuss an idea to realize a spontaneous current in a superfluid Fermi gas. When a polarized Fermi superfluid ($N_\up > N_\dwn$, where $N_σ$ is the number of atoms in the hyperfine state described by pseudospin $σ=\uparrow, \downarrow$.) is loaded onto a ring-shaped trap with a weak potential barrier, some of excess atoms ($ΔN=N_\uparrow-N_\downarrow$) are localized around the barrier. As shown in our previous paper [T. Kashimura, S. Tsuchiya, and Y. Ohashi, Phys. Rev. A \textbf{82}, 033617 (2010)], this polarized potential barrier works as a $π$-junction in the sense that the superfluid or…
We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equat…
We study Faraday and resonant waves in two-component quasi-one-dimensional (cigar-shaped) collisionally inhomogeneous Bose-Einstein condensates subject to periodic modulation of the radial confinement. We show by means of extensive numerical simulations that, as the system exhibits stronger spatially-localised binary collisions (whose scattering length is taken for convenience to be of Gaussian form), the system becomes effectively a linear one. In other words, as the scattering length approaches a delta-function, we observe that the two nonlinear configurations typical for binary cigar-shaped…
We study the localization of a cigar-shaped super-fluid Bose-Fermi mixture in a quasi-periodic bichromatic optical lattice (OL) for inter-species attraction and intra-species repulsion. The mixture is described by the Gross-Pitaevskii equation for the bosons, coupled to a hydrodynamic mean-field equation for fermions at unitarity. We confirm the existence of the symbiotic localized states in the Bose-Fermi mixture and Anderson localization of the Bose component in the interacting Bose-Fermi mixture on a bichromatic OL. The phase diagram in boson and fermion numbers showing the regions of the s…
We investigate thermal relaxation of superfluid turbulence in a highly oblate Bose-Einstein condensate. We generate turbulent flow in the condensate by sweeping the center region of the condensate with a repulsive optical potential. The turbulent condensate shows a spatially disordered distribution of quantized vortices and the vortex number of the condensate exhibits nonexponential decay behavior which we attribute to the vortex pair annihilation. The vortex-antivortex collisions in the condensate are identified with crescent-shaped, coalesced vortex cores. We observe that the nonexponential …
We investigate the dynamics of a Bose-Einstein condensate in a progressively bended three dimensional cigar shaped potential. The interplay between geometry and nonlinearity is considered. At high curvature, topological localization occurs and becomes frustrated by the generation of curved dispersive shock-waves when the strength of nonlinearity is increased. The analysis is supported by four-dimensional parallel simulations.
We derive a generalized Gross-Pitaevskii density-functional equation appropriate to study the Bose-Einstein condensate (BEC) of dimers formed of singlet spin-half Fermi pairs in the BEC-unitarity crossover while the dimer-dimer scattering length $a$ changes from 0 to $\infty$. Using an effective one-dimensional form of this equation, we study the phenomenon of dynamical self-trapping of a cigar-shaped Fermi super-fluid in the entire BEC-unitarity crossover in a double-well potential. A simple two-mode model is constructed to provide analytical insights. We also discuss the consequence of our s…
We observe a long-lived solitary wave in a superfluid Fermi gas of $^6$Li atoms after phase-imprinting. Tomographic imaging reveals the excitation to be a solitonic vortex, oriented transverse to the long axis of the cigar-shaped atom cloud. The precessional motion of the vortex is directly observed, and its period is measured as a function of the chemical potential in the BEC-BCS crossover. The long period and the correspondingly large ratio of the inertial to the bare mass of the vortex are in good agreement with estimates based on superfluid hydrodynamics that we derive here using the known…
In this work, we study parametric resonances in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical and analytical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric resonances (collapse and revival of the oscillations of the BEC width). Parametric resonances disappear when one of the competing factors i.e strength of harmonic trap or the stren…
We study suppression of the collapse and stabilization of matter-wave solitons by means of time-periodic modulation of the effective nonlinearity, using the nonpolynomial Schroedinger equation (NPSE) for BEC trapped in a tight cigar-shaped potential. By means of systematic simulations, a stability region is identified in the plane of the modulation amplitude and frequency. In the low-frequency regime, solitons feature chaotic evolution, although they remain robust objects.
One-dimensional nonlinear Schrödinger equations are derived to describe the axial effective dynamics of cigar-shaped atomic repulsive Bose-Einstein condensates trapped with anharmonic transverse potentials. The accuracy of these equations in the perturbative, Thomas-Fermi, and crossover regimes were verified numerically by comparing the ground-state profiles, transverse chemical potentials and oscillation patterns with those results obtained for the full three-dimensional Gross-Pitaevskii equation. This procedure allows us to derive different patterns of 1D nonlinear models by the control of t…
In this paper we study dark solitons in quasi-one-dimensional Bose-Einstein condensates (BECs) in presence of an anharmonic external potential. The theoretical model is based on the Muñoz-Mateo and Delgado (MMD) equation that describes cigar-shaped BECs with repulsive interatomic interactions. Since MMD equation presents a nonpolynomial form, the soliton-sound recombination cannot display the same pattern presented in the cubic model. We perform numerical simulations to compare both cases.
We revisit here the Kibble-Zurek mechanism for superfluid bosons slowly driven across the transition towards the Mott-insulating phase. By means of a combination of the Time-Dependent Variational Principle and a Tree-Tensor Network, we characterize the current flowing during annealing in a ring-shaped one-dimensional Bose-Hubbard model with artificial classical gauge field on up to 32 lattice sites. We find that the superfluid current shows, after an initial decrease, persistent oscillations which survive even when the system is well inside the Mott insulating phase. We demonstrate that the am…
Ultracold atoms placed in a tight cigar-shaped trap are usually described in terms of the Lieb-Liniger model. We study the extensions of this model which arise when van der Waals interaction between atoms is taken into account. We find that the corrections induced by the finite range of interactions can become especially important in the vicinity of narrow Feshbach resonances and suggest realistic schemes of their experimental detection. The interplay of confinement and interactions can lead to effective transparency where the one-dimensional interactions are weak in a wide range of parameters…
By numerical and variational analysis of the three-dimensional Gross-Pitaevskii equation we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose-Einstein condensate for large repulsive atomic interactions. Phase diagram showing the region of stability of the solitons is obtained. We also study the dynamics of breathing oscillation of the solitons as well as the collision dynamics of two solitons at large velocities. Two solitons placed side-by-side at rest coalesce to form a stable bound soliton molecule due to dipolar attraction.
We suggest and study the stable disk- and cigar-shaped gap solitons of a dipolar Bose-Einstein condensate of $^{52}$Cr atoms localized in the lowest band gap by three optical-lattice (OL) potentials along orthogonal directions. The one-dimensional version of these solitons of experimental interest confined by an OL along the dipole moment direction and harmonic traps in transverse directions is also considered. Important dynamics of (i) breathing oscillation of a gap soliton upon perturbation and (ii) dragging of a gap soliton by a moving lattice along axial $z$ direction demonstrates the stab…
We observe the breakup dynamics of an elongated cloud of condensed $^{85}$Rb atoms placed in an optical waveguide. The number of localized spatial components observed in the breakup is compared with the number of solitons predicted by a plane-wave stability analysis of the nonpolynomial nonlinear Schrödinger equation, an effective one-dimensional approximation of the Gross-Pitaevskii equation for cigar-shaped condensates. It is shown that the numbers predicted from the fastest growing sidebands are consistent with the experimental data, suggesting that modulational instability is the key under…
We determine and analyze collective normal modes of a finite disk-shaped two-dimensional vortex crystal formed in a compressible bosonic superfluid in an artificial magnetic field. Using the microscopic Gross-Pitaevskii theory in the lowest Landau level approximation, we generate vortex crystal ground states and solve the Bogoliubov-de Gennes equations for small amplitude collective oscillations. We find chiral surface waves that propagate at frequencies larger than those of the bulk Tkachenko modes. Furthermore, we study low frequency bulk excitations and identify a torsional Ruderman mode, w…
We investigate the controllability of electromagnetically induced transparency (EIT) and Fano resonances in hybrid optomechanical system which is composed of cigar-shaped Bose-Einstein condensate (BEC) trapped inside high-finesse Fabry-Pérot cavity driven by a single mode optical field along the cavity axis and a transverse pump field. Here, transverse optical field is used to control the phenomenon of EIT in the output probe laser field. The output probe laser field can efficiently be amplified or attenuated depending on the strength of transverse optical field. Furthermore, we demonstrate th…
