Non-adiabatic interaction ramps are considered for trapped Bose-Einstein condensates. The deviation from adiabaticity is characterized through the heating or residual energy produced during the ramp. We find that the dependence of the heat on the ramp time is very sensitive to the ramp protocol. We explain features of this dependence through a single-parameter effective description based on the dynamics of the condensate size.
We investigate a bosonic quantum gas consisting of two interacting species in an optical lattice at zero and finite temperature. The equilibrium properties and dynamics of this system are obtained by means of the Gutzwiller mean-field method. In particular we model recent experiments where the ramp-up of the optical lattice occurs on a time scale comparable to the tunneling time of the bosons. We demonstrate the violation of adiabaticity of this process with respect to the many-body quantum states, and reproduce and explain the oscillations of the visibility as a function of ramp-up time, as s…
We study the quantum evolution of a cloud of hard-core bosons loaded on a one-dimensional optical lattice after its sudden release from a harmonic trap. Just after the trap has been removed, a linear ramp potential is applied, mimicking the so called Galileo ramp experiment. The non-equilibrium expansion of the bosonic cloud is elucidated through a hydrodynamical description which is compared to the exact numerical evolution obtained by exact diagonalization on finite lattice sizes. The system is found to exhibit a rich behavior showing in particular Bloch oscillations of a self-trapped conden…
For harmonic-trapped atomic systems, we report system-independent non-adiabatic features in the response to interaction ramps. We provide results for several different systems in one, two, and three dimensions: bosonic and fermionic Hubbard models realized through optical lattices, a Bose-Einstein condensate, a fermionic superfluid and a fermi liquid. The deviation from adiabaticity is characterized through the heating or excitation energy produced during the ramp. We find that the dependence of the heat on the ramp time is sensitive to the ramp protocol but has aspects common to all systems c…
The dynamics of a weakly interacting Bose gas at low temperatures is close to integrable due to the approximate quadratic nature of the many-body Hamiltonian. While the short-time physics after an abrupt ramp of the interaction constant is dominated by the integrable dynamics, integrability is broken at longer times by higher-order interaction terms in the Bogoliubov Hamiltonian, in particular by Beliaev-Landau scatterings involving three quasiparticles. The two-stage relaxation process is highlighted in the evolution of local observables such as the density-density correlation function: a dep…
The quantum evolution of a cloud of bosons initially localized on part of a one dimensional optical lattice and suddenly subjected to a linear ramp is studied, realizing a quantum analog of the "Galileo ramp" experiment. The main remarkable effects of this realistic setup are revealed using analytical and numerical methods. Only part of the particles are ejected for a high enough ramp, while the others remain self-trapped. Then, the trapped density profile displays rich dynamics with Josephson-like oscillations around a plateau. This setup, by coupling bound states to propagative modes, create…
We suggest a simple scheme for creating a NOON state of repulsively interacting Bose atoms in the double-well potential. The protocol consists of two steps. First, by setting atom-atom interactions to zero, the system is driven to the upper excited state. Second, the interactions is slowly increased and, simultaneously, the inter-well tunneling is decreased to zero. We analyze fidelity of the final state to the NOON state depending on the number of atoms, ramp rate, and fluctuations of the system parameters. It is shown that for a given fidelity the ramp rate scales algebraically with the numb…
We analyze the effect of a linear time-variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible onsite particle distribution are studied as a function of the ramp time using time-dependent exact diagonalization and density-matrix renormalization group techniques. We find that the dynamics of a trapped system typically display two regimes: for long ramp times, the dynamics are governed by density redistribution, while at short ramp times, local dynamics dominate as the…
Inspired by a recent experiment by Steinhauer and co-workers, we present a simple model which describes the formation of an acoustic black hole in a Bose-Einstein condensate, allowing an analytical computation of the evolution in time of the corresponding density-density correlator. We show the emergence of analog Hawking radiation out of a "quantum atmosphere" region significantly displaced from the horizon. This is quantitatively studied both at $T=0$ and even in the presence of an initial temperature T, as is always the case experimentally.
We show theoretically that elongated vortex-antivortex dipoles can be created controllably in trapped Bose-Einstein condensates, using known experimental techniques. Vortex dipoles of sufficient length are unstable and cascade into slow vortex rings which ultimately decay via sound emission. This instability of antiparallel vortex line elements, which self-generates Kelvin waves on vortex loops and in trapped atomic gases, may play a role in bridging the Kelvin-wave and Kolmogorov-Richardson cascades of quantum turbulence.
We have calculated the low-lying elementary excitations of three-dimensional few-vortex arrays in trapped Bose-Einstein condensates. The number of different Kelvin-Tkachenko vortex wave branches matches the number of vortices in the condensate. The lowest odd-parity modes exhibit superfluid gyroscopic vortex motion. Experimentally, these modes could be excited and observed individually or in connection with the formation and decay of quantum turbulence.
We have calculated low-lying quasiparticle excitation spectra of rotating three-dimensional Bose-Einstein condensates. As opposed to the prediction of hydrodynamic continuum theories, we find a minimum in the Tkachenko mode spectrum at intermediate rotation frequencies of the harmonic trap. Such a minimum can harbour a Tkachenko quasiparticle with zero excitation energy. We discuss the experimental signatures of such a zero mode.
The ground state of a Bose-Einstein condensate in a two-dimensional trap potential is analyzed numerically at the infinite-particle limit. It is shown that the anisotropy of the many-particle position variance along the $x$ and $y$ axes can be opposite when computed at the many-body and mean-field levels of theory. This is despite the system being $100\%$ condensed, and the respective energies per particle and densities per particle to coincide.
We consider spherically trapped Bose gases in three dimensions with contact interactions, and investigate whether the Bose-Einstein condensate at zero temperature is stable against macroscopic fragmentation into a small number of mutually incoherent pieces. Our results are expressed in terms of a dimensionless interaction measure proportional to the Thomas-Fermi parameter. It is shown that while three-dimensional condensates are inherently much more stable against macroscopic fragmentation than their quasi-one- and quasi-two-dimensional counterparts, they fragment at a sufficiently large value…
We have analytically explored the quantum phenomenon of particle scattering by harmonically trapped Bose and Fermi gases with the short ranged (Fermi-Huang $δ^3_p$ [1]) interactions among the incident particle and the scatterers. We have predicted differential scattering cross-sections and their temperature dependence in this regard. Coherent scattering even by a single boson or fermion in the finite geometry gives rise to new tool of determining energy eigenstate of the scatterer. Our predictions on the differential scattering cross-sections, can be tested within the present day experimental …
The problem of particle fluctuations in arbitrary nonuniform systems with Bose-Einstein condensate is considered. This includes the case of trapped Bose atoms. It is shown that the correct description of particle fluctuations for any nonuniform system of interacting atoms always results in thermodynamically normal fluctuations.
For a Bose-Hubbard dimer, we study quenches of the site energy imbalance, taking a highly asymmetric Hamiltonian to a fully symmetric one. The ramp is carried out over a finite time that interpolates between the instantaneous and adiabatic limits. We provide results for the excess energy of the final state compared to the ground state energy of the final Hamiltonian, as a function of the quench rate. This excess energy serves as the analog of the defect density that is considered in the Kibble-Zurek picture of ramps across phase transitions. We also examine the fate of quantum `self-trapping' …
We present a new theoretical framework for describing an impurity in a trapped Bose system in one spatial dimension. The theory handles any external confinement, arbitrary mass ratios, and a weak interaction may be included between the Bose particles. To demonstrate our technique, we calculate the ground state energy and properties of a sample system with eight bosons and find an excellent agreement with numerically exact results. Our theory can thus provide definite predictions for experiments in cold atomic gases.
We propose a nonlinear atom-optics experiment to create diffraction catastrophes threaded by quantized vortex skeletons in Bose-Einstein condensed matter waves. We show how atom-optical aberrations induced in trapped Bose-Einstein condensates evolve into specific caustic structures due to imperfect focusing. Vortex skeletons, whose cross-sections are staggered vortex lattices, are observed to nucleate inside the universal diffraction catastrophes. Our observations shed further light on the structure and dynamics of Bose-novae and suggest applications of matter wave diffraction catastrophes, in…
We formulate a general scheme for calculation of thermodynamic properties of ideal Bose gas with microscopic number of static impurities immersed, when the system is loaded in the harmonic trapping potential with quasi-1D and quasi-2D configurations. The binding energy of a single impurity and a detailed study of the medium-induced Casimir-like forces between two impurities in trapped Bose gas are numerically calculated in wide range of temperatures and interaction strengths.
The c-field simulation technique is used to study a trapped quasi-two dimensional Bose gas. We calculate the central curvature of the system density and fluctuations of the condensate mode in the degenerate regime. These results provide new understanding of the system behavior in the region of the superfluid transition.
We investigate dipole modes in a trapped Bose--Fermi mixture gas in the normal phase, composed of single-species bosons and single-species fermions with $s$-wave scattering. In the extremely low temperature regime, Bose--Einstein statistics and Fermi--Dirac statistics may give rise to an interesting temperature dependence of collective modes. Applying the moment method to the linearized Boltzmann equation, we study the transition of the dipole modes between the hydrodynamic regime and the collisionless regime.
We theoretically address magnetic ordering at zero and finite temperature in both homogeneous and trapped Bose-Bose mixtures in optical lattices. By using Bosonic Dynamical Mean-Field Theory, we obtain the phase diagram of the homogeneous two-component Bose-Hubbard model in a three-dimensional (3D) cubic lattice, which features competing magnetic order of XY-ferromagnetic and anti-ferromagnetic type in addition to the Mott and superfluid states. We show that these magnetic phases persist also in the presence of a harmonic trap.
Based on a unified theoretical treatment of the 1D Bogoliubov-de Genes equations, the superfluidity phenomenon of the Bose-Einstein condensates (BEC) loaded into trapped optical lattice is studied. Within the perturbation regime, an all-analytical framework is presented enabling a straightforward phenomenological mapping of the collective excitation and oscillation character of a trapped BEC where the available experimental configurations also fit.
We study a harmonically trapped Bose-Einstein condensate with dipole-dipole interactions in a regime where a roton spectrum emerges. We show that the roton spectrum is clearly revealed in the static and dynamic structure factors which can be measured using Bragg spectroscopy. We develop and validate a theory based on the local density approximation for the dynamic structure factor.
We calculate the stability diagram for a trapped normal Bose gas with dipole-dipole interactions. Our study characterizes the roles of trap geometry, temperature, and short-ranged interactions on the stability. We predict a robust double instability feature in oblate trapping geometries arising from the interplay of thermal gas saturation and the anisotropy of the interaction. Our results are relevant to current experiments with polar molecules and will be useful in developing strategies to obtain a polar molecule Bose-Einstein condensate.
We investigate the accuracy of two mean-field theories of the trapped two-dimensional Bose gas at predicting transition region properties by comparison to non-perturbative classical field calculations. To make these comparisons we examine the density profiles and the predictions for the Berezinskii-Kosterlitz-Thouless superfluid transition temperature over a parameter range in which the degree of thermal activation in the tightly trapped direction varies considerably. These results present an important test of these mean-field theories, and provide a characterization of their typical accuracy.
We investigate the interaction of a laser-cooled trapped ion (Ba$^+$ or Rb$^+$) with an optically confined $^{87}$Rb Bose-Einstein condensate (BEC). The system features interesting dynamics of the ion and the atom cloud as determined by their collisions and their motion in their respective traps. Elastic as well as inelastic processes are observed and their respective cross sections are determined. We demonstrate that a single ion can be used to probe the density profile of an ultracold atom cloud.
We numerically study spin turbulence in a two-dimensional trapped spin-1 spinor Bose--Einstein condensate, focusing on the energy spectrum. The spin turbulence in the trapped system is generated by instability of the helical structure of the spin density vector in the initial state. Our numerical calculation finds that in the trapped system the spectrum of the spin-dependent interaction energy in the ferromagnetic case exhibits a -7/3 power law, which was confirmed in a uniform system by our previous study. The relation between the -7/3 power law and the motion of the spin density vector is di…
We consider the phase transition dynamics of a trapped Bose-Einstein condensate subject to Raman-type spin-orbit coupling (SOC). By tuning the coupling strength the condensate is taken through a second order phase transition into an immiscible phase. We observe the domain wall defects produced by a finite speed quench is described by the Kibble-Zurek mechanism (KZM), and quantify a power law behavior for the scaling of domain number and formation time with the quench speed.
We study thermal properties of a trapped Bose-Bose mixture in a dilute regime using quantum Monte Carlo methods. Our main aim is to investigate the dependence of the superfluid density and the condensate fraction on temperature, for the mixed and separated phases. To this end, we use the diffusion Monte Carlo method, in the zero-temperature limit, and the path-integral Monte Carlo method for finite temperatures. The results obtained are compared with solutions of the coupled Gross-Pitaevskii equations for the mixture at zero temperature. We notice the existence of an anisotropic superfluid den…
Motivated by a recent experiment [J. Catani et al., arXiv:1106.0828v1 preprint, 2011], we study breathing oscillations in the width of a harmonically trapped impurity interacting with a separately trapped Bose gas. We provide an intuitive physical picture of such dynamics at zero temperature, using a time-dependent variational approach. In the Gross-Pitaevskii regime we obtain breathing oscillations whose amplitudes are suppressed by self trapping, due to interactions with the Bose gas. Introducing phonons in the Bose gas leads to the damping of breathing oscillations and non-Markovian dynamic…
We experimentally study the energy-temperature relationship of a harmonically trapped Bose-Einstein condensate by transferring a known quantity of energy to the condensate and measuring the resulting temperature change. We consider two methods of heat transfer, the first using a free expansion under gravity and the second using an optical standing wave to diffract the atoms in the potential. We investigate the effect of interactions on the thermodynamics and compare our results to various finite temperature theories.
We describe a quantum droplet of a Bose-Bose mixture squeezed by an external harmonic forces in one spatial direction. Our approach is based on the self-consistent method formulated in [1]. The true spatial droplet profile in the direction of confinement is accounted for, however local density approximation is assumed in the free directions. We define a numerical approach to find the beyond-mean-field contribution to the chemical potential (Lee-Huang-Yang chemical potential) -- the quantity that determines the droplet's profile. In addition to the numerical approach, we find the Lee-Huang-Yang…
We describe a protocol to prepare solitons in a quasi-1d box-trapped Bose-Einstein condensate using only a quench of the isotropic s-wave scattering length. A quench to exactly four times the initial 1d coupling strength creates one soliton at each boundary of the box, which then propagate in a uniform background density and collide with one another. No nonsolotonic excitations are created during the quench. The procedure is robust against imperfections in the scattering length ramp rate and a mismatch of the final scattering length.
We perform high-precision measurements of the condensation temperature of a harmonically-trapped atomic Bose gas with widely-tuneable interactions. For weak interactions we observe a negative shift of the critical temperature in excellent agreement with mean-field theory. However for sufficiently strong interactions we clearly observe an additional positive shift, characteristic of beyond-mean-field critical correlations. We also discuss non-equilibrium effects on the apparent critical temperature for both very weak and very strong interactions.
In the present work we discuss inter-species entanglement in Bose-Bose mixtures trapped in optical lattices. This work is motivated by the observation that, in the presence of a second component, the Mott-insulator lobe shifts {\em{differently}} on the hole- and particle-side with respect to the Mott lobe of the single species system (Phys. Rev. A 82, 021601, Laser Phys. 21, 1443). We use perturbation theory, formulated in a Hilbert space decomposed by means of lattice symmetries, in order to show that the nonuniform shift of the Mott lobe is a consequence of an inter-species entanglement whic…
Combining experiments and numerical simulations, we investigate the redistribution of quasi-momentum in a gas of atoms trapped in an optical lattice when the lattice depth is rapidly reduced. We find that interactions lead to significant momentum redistribution on millisecond timescales, thereby invalidating previous assumptions regarding adiabaticity. We show that this phenomenon is driven by the presence of low-momentum particle-hole excitations in an interacting system. Our results invalidate bandmapping as an equilibrium probe in interacting gases.
We analyze the macroscopic dynamics of a Bose gas axially confined in an optical lattice with a superimposed harmonic trap, taking into account weak tunneling effect. Our results show that upon transition to the quasi-two-dimensional (2D) regime of the trapped gas, the 3D equation of state and equilibrium density profile acquire corrections from 2D many-body effects. The corresponding frequency shift in the transverse breathing mode is accessible within current facilities, suggesting a direct observation of dimensional effects. Comparisons with other relevant effects are also presented.
We study a harmonically confined Bose-Bose mixture using quantum Monte Carlo methods. Our results for the density profiles are systematically compared with mean-field predictions derived through the Gross-Pitaevskii equation in the same conditions. The phase space as a function of the interaction strengths and the relation between masses is quite rich. The miscibility criterion for the homogeneous system applies rather well to the system, with some discrepancies close to the critical line for separation. We observe significant differences between the mean-field results and the Monte Carlo ones…
In the study of trapped two-component Bose gases, a widely used dynamical protocol is to start from the ground state of a one-component condensate and then switch half the atoms into another hyperfine state. The slightly different intra-component and inter-component interactions can then lead to highly nontrivial dynamics. We study and classify the possible subsequent dynamics, over a wide variety of parameters spanned by the trap strength and by the inter- to intra-component interaction ratio. A stability analysis suited to the trapped situation provides us with a framework to explain the var…
We present a method to detect the presence and depth of dark solitons within repulsive one-dimensional harmonically trapped Bose-Einstein condensates. For a system with one soliton, we prove that the shift of the density in Fourier space directly maps onto the depth of the soliton. For multi-soliton systems, combining our spectral method with established imaging techniques, the character of the solitons present in the condensate can be determined. We verify that the detection of solitons by the spectral shift works in the presence of waves induced by density engineering methods. Finally we dis…
We study the anomalous density in an ultra-cold trapped bose gas in a variational framework, for both zero and finite temperature. We show that it is finite in 1D, while it is logarithmically and linearly divergent in 2D and 3D. The renormalization that we adopt is more reliable and compatible with the variational scheme. The main outcome is that the anomalous and non condensate densities are of the
In this paper, the condensate fraction and the critical atom number and its corresponding critical temperature of condensate ultracold boson atoms trapped in optical box traps, are investigated. The semiclassical approximation is employed in this study. The boxes traps are modeled by a general power-law potential. The deviation of the boxes traps from an ideal boxes traps are discussed. The out come results furnish useful quantitative theoretical results for the future BEC experiments in such traps
The generation of isotropic vortex configurations in trapped atomic Bose-Einstein condensates offers a platform to elucidate quantum turbulence on mesoscopic scales. We demonstrate that a laser-induced obstacle moving in a figure-eight path within the condensate provides a simple and effective means to generate an isotropic three-dimensional vortex tangle due to its minimal net transfer of angular momentum to the condensate. Our characterisation of vortex structures and their isotropy is based on projected vortex lengths and velocity statistics obtained numerically via the Gross-Pitaevskii equ…
We show that there exists the inverse Kibble-Zurek scenario, when we start with an equilibrium system with broken symmetry and, by imposing perturbations, transform it to a strongly nonequilibrium symmetric state through the sequence of states with spontaneously arising topological defects. We demonstrate the inverse Kibble-Zurek scenario both experimentally, by perturbing the Bose-Einstein condensate of trapped $^{87}$Rb atoms, and also by accomplishing numerical simulations for the same setup as in the experiment, the experimental and numerical results being in good agreement with each other…
The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ are studied carefully. Detailed calculation of Kim $et$ $al.$ (S. H. Kim, C. K. Kim and K. Nahm, J Phys. Condens. Matter 11 10269 (1999).) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume $C_V$ are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition…
The knot of spin texture is studied within the two-component Bose-Einstein condensates which are described by the nonlinear Gross-Pitaevskii equations. We start from the non-interacting equations including an axisymmetric harmonic trap to obtain an exact solution, which exhibits a non-trivial topological structure. The spin-texture is a knot with an integral Hopf invariant. The stability of the knot is verified by numerically evolving the nonlinear Gross-Pitaevskii equations along imaginary time.
We consider the non-condensate density and density fluctuations of a trapped dipolar Bose-Einstein condensate, focusing on the regime where a roton-like excitation spectrum develops. Our results show that a characteristic peak in the non-condensate density occurs at trap center due to the rotons. In this regime we also find that the anomalous density becomes positive and peaked, giving rise to enhanced density fluctuations. We calculate the non-condensate density in momentum space and show that a small momentum halo is associated with the roton excitations.
We theoretically investigate collective modes of a one-dimensional (1D) interacting Bose gas in harmonic traps at finite temperatures, by using a variational approach and local density approximation. We find that the temperature dependence of collective mode frequencies is notably different in the weakly and strongly interacting regimes. Therefore, the experimental measurement of collective modes could provide a sensitive probe for different quantum phases of a 1D trapped Bose gas, realized by tuning the interatomic interaction strength and temperature. Our prediction on the temperature depend…
Supersolid is an exotic state of matter, showing crystalline order with a superfluid background, observed recently in dipolar Bose-Einstein condensate (BEC) in a trap. Here, we present exact solutions of the desired Bloch form in the self-trapped free-floating quantum fluid. Our general solutions of the amended nonlinear Schr{ö}dinger equation, governing the mean-field and beyond mean-field dynamics, are obtained through a M{ö}bius transform, connecting a wide class of supersolid solutions to the ubiquitous cnoidal waves. The solutions yield the constant condensate, supersolid behavior and the…
We present analysis of the excitation spectrum for a 2 component quasi2D Bose Einstein Condensate. We study how the character of the excitations change across the miscible to immiscible phase transition. We find that the bulk excitations are typical of a single-component BEC with the addition of interface bending excitations. We study how these excitations change as a function of the interaction strength.
Generation of different nonequilibrium states in trapped Bose-Einstein condensates is studied by numerically solving nonlinear Schrodinger equation. Inducing nonequilibrium states by shaking the trap, the following states are created: weak nonequilibrium, the state of vortex germs, the state of vortex rings, the state of straight vortex lines, the state of deformed vortices, vortex turbulence, grain turbulence, and wave turbulence. A characterization of nonequilibrium states is advanced by introducing effective temperature, Fresnel number, and Mach number.
The notion of fluctuation indices, characterizing thermodynamic stability of statistical systems, is advanced. These indices are especially useful for investigating the stability of nonuniform and trapped atomic assemblies. The fluctuation indices are calculated for several systems with Bose-Einstein condensate. It is shown that: the ideal uniform Bose-condensed gas is thermodynamically unstable; trapped ideal gases are stable for the confining dimension larger than two; trapped gases, under the confining dimension two, are weakly unstable; harmonically trapped gas is stable only for the spati…
We find a new physical regime in the trapped Bose-Hubbard Hamiltonian using time-evolving block decimation. Between Mott-insulating and superfluid phases, the latter induced by trap compression, a spatially self-organized state appears in which non-local entropy signals entanglement between spatially distant superfluid shells. We suggest a linear rather than harmonic potential as an ideal way to observe such a self-organized system. We also explore both quantum information and thermal entropies in the superfluid regime, finding that while the former follows the density closely the latter can b…
