Cigar-shaped Bose-Einstein Condensate Research Articles

Superfluidity of a laser-stirred Bose-Einstein condensate

We study superfluidity of a cigar-shaped Bose-Einstein condensate (BEC) by stirring it with a Gaussian potential oscillating back and forth along the axial dimension of the condensate, motivated by experiments of C. Raman et al. Phys. Rev. Lett. 83, 2502 (1999). Using classical-field simulations and perturbation theory we examine the induced heating rate, based on the total energy of the system, as a function of the stirring velocity $v$. We identify the onset of dissipation by a sharply increasing heating rate above a velocity $v_c$, which we define as the critical velocity. We show that $v_c$ is influenced by the oscillating motion, the strength of the stirrer, the temperature and the inhomogeneous density of the cloud. This results in a vanishing $v_c$ for the parameters similar to the experiments, which is inconsistent with the measurement of nonzero $v_c$. However, if the heating rate is based on the thermal fraction after a 100 ms equilibration time, our simulation recovers the experimental observations. We demonstrate that this discrepancy is due to the slow relaxation of the stirred cloud and dipole mode excitation of the cloud.

Acoustic oscillations in cigar-shaped logarithmic Bose–Einstein condensate in the Thomas–Fermi approximation

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 standing waves or become oscillations with varying amplitudes. We also study the condensate in an axial harmonic trap, by using elasticity theory’s notions. Linear particle density and energy also behave differently depending on the nonlinear coupling’s value. If it is negative, the density monotonously grows along with lump’s radius, while energy is a monotonous function of density. For the positive coupling, the density is bound from above, whereas energy grows monotonously as a function of density until it reaches its global maximum.

Exact Analytical Model for Bose-Einstein Condensate at Negative Temperature

We present an exact analytical model of a cigar-shaped Bose-Einstein condensate at negative temperature. This work is motivated by the first experimental discovery of negative temperature in Bose-Einstein condensate by Braun et al. We have considered an external confinement which is a combination of expulsive trap, bi-chromatic optical lattice trap, and linear trap. The present method is capable of providing the exact form of the condensate wavefunction, phase, nonlinearity and gain/loss. One of the consistency conditions is shown to map onto the Schrödinger equation, leading to a significant control over the dynamics of the system. We have modified the model by replacing the optical lattice trap by a bi-chromatic optical lattice trap, which imparts better localization at the central frustrated site, delineated through the variation of condensate fraction. Estimation of temperature and a numerical stability analysis are also carried out. Incorporation of an additional linear trap introduces asymmetry and the corresponding temporal dynamics reveal atom distillation at negative temperature.

Creating solitons with controllable and near-zero velocity in Bose-Einstein condensates.

Established techniques for deterministically creating dark solitons in repulsively interacting atomic Bose-Einstein condensates (BECs) can only access a narrow range of soliton velocities. Because velocity affects the stability of individual solitons and the properties of soliton-soliton interactions, this technical limitation has hindered experimental progress. Here we create dark solitons in highly anisotropic cigar-shaped BECs with arbitrary position and velocity by simultaneously engineering the amplitude and phase of the condensate wave function, improving upon previous techniques which explicitly manipulated only the condensate phase. The single dark soliton solution present in true one-dimensional (1D) systems corresponds to the kink soliton in anisotropic three-dimensional systems and is joined by a host of additional dark solitons, including vortex ring and solitonic vortex solutions. We readily create dark solitons with speeds from zero to half the sound speed. The observed soliton oscillation frequency suggests that we imprinted solitonic vortices, which for our cigar-shaped system are the only stable solitons expected for these velocities. Our numerical simulations of 1D BECs show this technique to be equally effective for creating kink solitons when they are stable. We demonstrate the utility of this technique by deterministically colliding dark solitons with domain walls in two-component spinor BECs.

Force sensing in hybrid Bose-Einstein-condensate optomechanics based on parametric amplification

In this paper, the scheme of a force sensor is proposed which has been composed of a hybrid optomechanical cavity containing an interacting cigar-shaped Bose-Einstein condensate (BEC) where the \textit{s}-wave scattering frequency of the BEC atoms as well as the spring coefficient of the cavity moving end-mirror (the mechanical oscillator) are parametrically modulated. It is shown that in the red-detuned regime and under the so-called impedance-matching condition, the mechanical response of the system to the input signal is enhanced substantially, which leads to the amplification of the weak input signal while the added noises of measurement (backaction noises) can be suppressed and lowered much below the standard quantum limit (SQL). In this way, such a hybrid system operates as an ultra-sensitive force sensor which can amplify the input signal and simultaneously suppress the added noises by controlling the amplitudes of modulation and the system cooperativities. The advantage of the presented nonlinear hybrid system accompanied with the mechanical and atomic modulations in comparison to the bare optomechanical cavities is the enhancement of signal amplification as well as the extension of amplification bandwidth.

A tunable single-photon multi-channel quantum router in a hybrid BEC-optomechanical system

A novel technique for generating a single-photon multi-channel quantum router in a hybrid BEC-optomechanical system is proposed. This system consists of a cigar-shaped Bose–Einstein condensate that is trapped inside a high-finesse Fabry–Pérot cavity with a moving end-mirror. Analytical solutions are given for the spectrum of the reflectance and transmittance of the output field. When the cavity is driven by a coupling laser and probe laser, we can produce a switch for the appropriate of the normalized frequency and the effective coupling strength. Furthermore, the effective coupling strength of the optical field with the condensate mode, the effective coupling strength of the optical field with the mirror, cavity decay and decay rates for the moving mirror are used to control the number of the single-photon quantum router. Finally, we also demonstrate the vacuum, and thermal noise can be insignificant for the single-photon router. We give a certain set of experimental parameters for observing these phenomena in the laboratory. The technique presented may have potential applications in quantum engineering and quantum information networks.

Soliton diffusion in a Bose-Einstein condensate: A signature of the analogue Hawking radiation

The analog Hawking radiation (HR) emanating from a sonic black hole horizon formed in a cigar-shaped Bose-Einstein condensate (BEC) at finite temperature is investigated. In particular, we study the effect of HR on a dark (topological) soliton. We show that, due to thermal fluctuations, the dark soliton in the BEC displays a nonlinear Brownian motion resulting in a specific asymmetric diffusion. Based on numerical simulations we argue that the analog HR formed in the BEC can be detected indirectly through measurement of the dark soliton diffusion.

W-shaped solitons in inhomogeneous cigar-shaped Bose–Einstein condensates with repulsive interatomic interactions

We analyze the formation and dynamics of W-shaped solitons in an inhomogeneous cigar-shaped Bose–Einstein condensate with repulsive interatomic interactions in the presence of spatially and temporally nonuniform nonlinearity and external potential. The condensate is assumed to have a large number of particles; hence it may be approximated by an effective one-dimensional equation, which is derived from the full three-dimensional Gross–Pitaevskii equation. New classes of W-shaped soliton solutions, which may propagate in the condensate system with the same hump value, are found for the first time by means of the similarity transformation technique. The functional form of these localized nonlinear structures is different from the usual ones reported in the setting of optical fibers. The dynamic behaviors of the W-shaped soliton pulses under different nonlinearity and external potential management that are of particular interest for applications in Bose–Einstein condensates are analyzed.

Many-body dissipative flow of a confined scalar Bose-Einstein condensate driven by a Gaussian impurity

The many-body dissipative flow induced by a mobile aussian impurity harmonically oscillating within a cigar-shaped Bose-Einstein condensate is investigated. For very {small and large driving frequencies} the superfluid phase is preserved. Dissipation is identified, for intermediate driving frequencies, by the non-zero value of the drag force whose abrupt increase {signals the spontaneous downstream emission of an array of gray solitons. After each emission event, typically each of the solitary waves formed decays and splits into two daughter gray solitary waves that are found to be robust propagating in the bosonic background for large evolution times.} In particular, a smooth transition towards dissipation is observed, with the {\it critical} velocity for solitary wave formation depending on both the characteristics of the obstacle, namely its driving frequency and width as well as on the interaction strength. The variance of a sample of single-shot simulations indicates the fragmented nature of the system; here it is found to increase during evolution for driving frequencies where the coherent structure formation becomes significant. Finally, we demonstrate that for fairly large particle numbers in-situ single-shot images directly capture the gray soliton's decay and splitting.

Controllable generation of photons and phonons in a coupled Bose–Einstein condensate-optomechanical cavity via the parametric dynamical Casimir effect

We theoretically propose and investigate a feasible experimental scheme for the realization of the dynamical Casimir effect (DCE) in a hybrid optomechanical cavity with a moving end mirror containing an interacting cigar-shaped Bose–Einstein condensate (BEC). We show that in the red-detuned regime of cavity optomechanics together with the weak optomechanical coupling limit by coherent modulation of the s-wave scattering frequency of the BEC and the mechanical spring coefficient of the mechanical oscillator (MO), the mechanical and atomic quantum vacuum fluctuations are parametrically amplified, which consequently lead to the generation of the mechanical/Bogoliubov-type Casimir phonons. Interestingly, in the coherent regime corresponding to the case of largely different optomechanical coupling strengths of the cavity field to the BEC and the MO, or equivalently largely different cooperativities, one can generate a large number of Casimir photons due to the amplification of the intracavity vacuum fluctuations induced by the time modulations of the BEC and the MO. The number of generated Casimir particles are externally controllable by the cooperativities, and the modulation amplitudes of the atomic collisions rate and the mechanical spring coefficient.

Localized modes in the Gross-Pitaevskii equation with a parabolic trapping potential and a nonlinear lattice pseudopotential

We study localized modes (LMs) of the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a harmonic-oscillator (parabolic) confining potential, and a periodically modulated coefficient in front of the cubic term (nonlinear lattice pseudopotential). The equation applies to a cigar-shaped Bose-Einstein condensate loaded in the combination of a magnetic trap and an optical lattice which induces the periodic pseudopotential via the Feshbach resonance. Families of stable LMs in the model feature specific properties which result from the interplay between spatial scales introduced by the parabolic trap and the period of the nonlinear pseudopotential. Asymptotic results for the shapes and stability of LMs are obtained for small-amplitude solutions and in the limit of a rapidly oscillating nonlinear pseudopotential. We show that the presence of the lattice pseudopotential may result in: (i) creation of new LM families which have no counterparts in the case of the uniform nonlinearity; (ii) stabilization of some previously unstable LM species; (iii) evolution of unstable LMs into a pulsating mode trapped in one well of the lattice pseudopotential.

Optomechanically induced transparency with Bose–Einstein condensate in double-cavity optomechanical system**Project supported by the National Natural Science Foundation of China (Grant Nos. 11564034, 11105062, and 21663026) and the Scientific Research Funds of College of Electrical Engineering, Northwest University, China (Grant No. xbmuyjrc201115).

We propose a novel technique of generating multiple optomechanically induced transparency (OMIT) of a weak probe field in hybrid optomechanical system. This system consists of a cigar-shaped Bose–Einstein condensate (BEC), trapped inside each high finesse Fabry-Pérot cavity. In the resolved sideband regime, the analytic solutions of the absorption and the dispersion spectrum are given. The tunneling strength of the two resonators and the coupling parameters of the each BEC in combination with the cavity field have the appearance of three distinct OMIT windows in the absorption spectrum. Furthermore, whether there is BEC in each cavity is a key factor in the number of OMIT windows determination. The technique presented may have potential applications in quantum engineering and quantum information networks.

Symmetric bound states of Josephson vortices in BEC

A system of two parallel coupled cigar-shaped Bose–Einstein condensates is considered in an effectively one-dimensional limit. The dynamics of the system is characterized by a pair of coupled nonlinear Gross–Pitaevskii equations. In particular, the existence and stability of symmetric bound states of Josephson vortices are investigated. It is realized that the symmetric bound state Josephson vortices solution persists stably in its whole domain of existence for the coupling strength. Nevertheless, the bound states solution converts into a dark soliton at a critical value of coupling parameter.

Controlling steady-state bipartite entanglement and quadrature squeezing in a membrane-in-the-middle optomechanical system with two Bose-Einstein condensates

We study theoretically a driven hybrid optomechanical system with a membrane-in-the-middle configuration containing two identical elongated cigar-shaped Bose-Einstein condensates (BECs) in each side of the membrane. In the weakly interacting regime, the BECs can be considered as single-mode oscillators in the Bogoliubov approximation which are coupled to the optical field through the radiation pressure interaction so that they behave as two quasi-membranes. We show that the degree of squeezing of each BEC and its entanglement with the moving membrane can be controlled by the \textit{s}-wave scattering frequency of the other one. Since the \textit{s}-wave frequency of each BEC depends on the transverse trapping frequency of the atoms which is an experimentally controllable parameter, one can control the entanglement and squeezing of each BEC through the trapping frequency of the other one.

Intrinsic cross-Kerr nonlinearity in an optical cavity containing an interacting Bose-Einstein condensate

An interacting cigar-shaped Bose-Einstein condensate (BEC) inside a driven optical cavity exhibits an intrinsic cross-Kerr (CK) nonlinearity due to the interaction with the optical mode of the cavity. Although the CK coupling is much weaker than those of the radiation pressure and the atom-atom interactions, it can affect the bistability behavior of the system when the intensity of the laser pump is strong enough. On the other hand, there is a competition between the CK nonlinearity and the atom-atom interaction so that the latter can neutralize the effect of the former. Furthermore, the CK nonlinearity causes the effective frequency of the Bogoliubov mode of the BEC as well as the quantum fluctuations of the system to be increased by increasing the cavity driving rate. However, in the dispersive interaction regime the effect of the CK nonlinearity is negligible. In addition, we show that by increasing the $s$-wave scattering frequency of atomic collisions one can generate a strong stationary quadrature squeezing in the Bogoliubov mode of the BEC.

Mean-field regime and Thomas–Fermi approximations of trapped Bose–Einstein condensates with higher-order interactions in one and two dimensions

We derive rigorously one- and two-dimensional mean-field equations for cigar- and pancake-shaped Bose–Einstein condensates (BECs) with higher-order interactions (HOIs), which originate from shape-dependent confinement corrections to the effective two-body atomic interaction potential. 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 the presence of the contact interaction and HOI, and considering the limit of large contact interaction and HOI. For both box and harmonic traps in one, two and three dimensions, we identify the analytical Thomas–Fermi densities, which depend on the competition between the contact interaction and the HOI.

Controlled Electromagnetically Induced Transparency and Fano Resonances in Hybrid BEC-Optomechanics.

Cavity-optomechanics, a tool to manipulate mechanical effects of light to couple optical field with other physical objects, is the subject of increasing investigations, especially with regards to electromagnetically induced transparency (EIT). EIT, a result of Fano interference among different atomic transition levels, has acquired a significant importance in many areas of physics, such as atomic physics and quantum optics. However, controllability of such multi-dimensional systems has remained a crucial issue. In this report, we investigate the controllability of EIT and Fano resonances in hybrid optomechanical system composed of cigar-shaped Bose-Einstein condensate (BEC), trapped inside high-finesse Fabry-Pérot cavity with one vibrational mirror, driven by a single mode optical field and a transverse pump field. The transverse field is used to control the phenomenon of EIT. It is detected that the strength of transverse field is not only efficiently amplifying or attenuating out-going optical mode but also providing an opportunity to enhance the strength of Fano-interactions which leads to the amplification of EIT-window. To observe these phenomena in laboratory, we suggest a certain set of experimental parameters. The results provide a route for tunable manipulation of optical phenomena, like EIT, which could be a significant step in quantum engineering.

Bose–Einstein Condensation of Atoms and Photons

Bose–Einstein condensation has now been observed in diverse physical systems, starting from liquid Helium, excitons, to alkali atoms at nanokelvin temperature. The trapped cold atoms have provided an ideal venue for exploring fascinating ideas, ranging from Kosterlitz–Thouless (KT) phase transition, metal-insulator quantum phase transition to the realization of Abelian and non-Abelian gauge fields and solitonic excitations, in a controlled environment. Here, after a brief introduction to condensation phenomena in free space and trap, we explicate the working of the magneto optical trap, the work horse of the cold-atom laboratories. Subsequently, we illustrate the properties of experimentally realized dark, bright and grey solitons in the cigar shaped Bose–Einstein condensate (BEC). Focusing on a pan-cake type BEC in two dimensions, the basic aspects of the unique vortex excitations on a plane is elaborated, from which the Kosterlitz–Thouless phase transition follows, when the bound vortex–anti-vortex pairs unbind at \(T_{KT}\). We then describe the recent realization of Bose–Einstein condensation of the ubiquitous photons at room temperature. Parametric condition for occurrence of KT phase transition is then obtained for the photon gas.

Giant Kerr nonlinearity and superluminal and subluminal polaritonic solitons in a Bose-Einstein condensate via superradiant scattering

We propose a setup to generate giant Kerr nonlinearity and polaritonic solitons via matter-wave superradiant scattering. The system we consider is a long cigar-shaped Bose-Einstein condensate (BEC), pumped by a red-detuned laser field with a space-dependent intensity distribution in transverse directions. The pump and the scattered fields propagate along the longitudinal direction. We show that by means of the atom-photon and atom-atom interactions in the system it is possible to produce a giant nonlinear optical effect. We further show that a backward scattering of the laser field from the BEC is favorable for the formation and stable propagation of polaritonic solitons, which are collective nonlinear excitations of the BEC coupled with the scattered laser field. In the case of backward Stokes (anti-Stokes) scattering the system may support robust bright (dark) polaritonic solitons propagating with superluminal (subluminal) velocity.

Integrable pair-transition-coupled nonlinear Schrödinger equations

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation. Possibilities to observe them are discussed in a cigar-shaped Bose-Einstein condensate with two hyperfine states. The results would enrich our knowledge on nonlinear excitations in many coupled nonlinear systems with transition coupling effects, such as multimode nonlinear fibers, coupled waveguides, and a multicomponent Bose-Einstein condensate system.