Ground State Of Bose-Einstein Condensate Research Articles

Density profiles of two-component Bose–Einstein condensates interacting with a Laguerre–Gaussian beam

The density profiles of trapped two-component Bose–Einstein condensates (BEC) and its microscopic interaction with Laguerre–Gaussian (LG) beam are studied. We consider the 87Rb BEC in two hyperfine spin components. The wavelength of the LG beam is assumed to be comparable to the atomic de Broglie wavelength. Competitions between intra- and inter-component interactions produce interesting density structures of the ground state of BEC. We demonstrate vortex–antivortex interference and its dependence on the inter-component interactions and Raman transitions.

A Regularized Newton Method for Computing Ground States of Bose–Einstein Condensates

In this paper, we propose a regularized Newton method for computing ground states of Bose-Einstein condensates (BECs), which can be formulated as an energy minimization problem with a spherical constraint. The energy functional and constraint are discretized by either the finite difference, or sine or Fourier pseudospectral discretization schemes and thus the original infinite dimensional nonconvex minimization problem is approximated by a finite dimensional constrained nonconvex minimization problem. Then an initial solution is first constructed by using a feasible gradient type method, which is an explicit scheme and maintains the spherical constraint automatically. To accelerate the convergence of the gradient type method, we approximate the energy functional by its second-order Taylor expansion with a regularized term at each Newton iteration and adopt a cascadic multigrid technique for selecting initial data. It leads to a standard trust-region subproblem and we solve it again by the feasible gradient type method. The convergence of the regularized Newton method is established by adjusting the regularization parameter as the standard trust-region strategy. Extensive numerical experiments on challenging examples, including a BEC in three dimensions with an optical lattice potential and rotating BECs in two dimensions with rapid rotation and strongly repulsive interaction, show that our method is efficient, accurate and robust.

Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids

By using Bogoliubov transformations to construct the ground states of fermionic Bardeen–Cooper–Schrieffer (BCS) superfluids and weakly-interacting Bose gases supporting Bose Einstein Condensation (BEC), their algebraic structures and implications can be analyzed in detail. Both ground states are generalized squeezed coherent states saturating a generalized Heisenberg uncertainty relation, and they acquire quantized Berry phases when the corresponding systems are transported along a closed path in their parameter spaces. While the Berry phase of the BCS ground state depends on the total particle number, the Berry phase of the BEC ground state depends only on the particles outside the BEC. The Berry phases are associated with magnetic monopoles in the parameter spaces and we found that the Dirac quantization condition is satisfied. Moreover, both ground states are entangled states of the fermion or boson quanta and we found the entanglement entropy quantifying the internal correlations. A fixed particle-number approach of fermionic superfluids does not saturate the generalized uncertainty relation, exhibits internal entanglement, and gives corresponding Berry phase. In addition, the algebraic structures of the ground states can be classified by the q-deformed Hopf algebra, ⨁khqk(1) for bosons and q-deformed Hopf superalgebra ⨁khqk(1|1) for fermions, respectively.

Macroscopic quantum tunneling of Bose-Einstein condensates with long-range interaction

The ground state of Bose-Einstein condensates with attractive particle interactions is metastable. One of the decay mechanisms of the condensate is a collapse by macroscopic quantum tunneling, which can be described by the bounce trajectory as a solution of the time-dependent Gross-Pitaevskii equation in imaginary time. For condensates with an electromagnetically induced gravity-like interaction, the bounce trajectory is computed with an extended variational approach using coupled Gaussian functions and is simulated numerically exact within the mean-field approach on a spacetime lattice. It is shown that the variational computations converge very rapidly to the numerically exact result with increasing number of Gaussians. The tunneling rate of the condensate is obtained from the classical action and additional parameters of the bounce trajectory. The converged variational and numerically exact results drastically improve by several orders of magnitude the decay rates obtained previously with a simple variational approach using a single Gaussian-type orbital for the condensate wave function.

Bose-Einstein supersolid phase for a type of momentum-dependent interaction

A novel class of non-local interactions between bosons is found to favor a crystalline Bose-Einstein condensation ground state. By using both low energy effective field theory and variational wavefunction method, we compare this state not only with the homogeneous superfluid, as has been done previously, but also with the normal (non-superfluid) crystalline phase and obtain the phase diagram. The key characters are: the interaction potential displays a negative minimum at finite momentum which determines the wavevector of this supersolid phase; and the wavelength corresponding to the momentum minimum needs to be greater than the mean inter-boson distance.

What Determines the Wave Function of Electron-Hole Pairs in Polariton Condensates?

The ground state of a microcavity polariton Bose-Einstein condensate is determined by considering experimentally tunable parameters such as excitation density and detuning. During a change in the ground state of Bose-Einstein condensate from excitonic to photonic, which occurs as the excitation density is increased, the origin of the binding force of electron-hole pairs changes from Coulomb to photon-mediated interactions. The change in the origin gives rise to the strongly bound pairs with a small radius, like Frenkel excitons, in the photonic regime. The phase diagram obtained provides valuable information that can be used to build theoretical models for each regime.

PHASE TRANSITIONS IN ULTRA-COLD TWO-DIMENSIONAL BOSE GASES

We briefly review the theory of Bose-Einstein condensation in the two-dimensional trapped Bose gas and, in particular the relationship to the theory of the homogeneous two-dimensional gas and the Berezinskii-Kosterlitz-Thouless phase. We obtain a phase diagram for the trapped two-dimensional gas, finding a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose-Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose-Einstein condensate, a vortex pair plasma with fluctuating condensate phase and a thermal Bose gas. The thermal activation of vortex-antivortex pair formation is confirmed using finite-temperature classical field simulations.

Bose–Einstein condensates in a ring optical lattices trap

The evolution of Bose–Einstein condensates (BECs) loaded into a periodic ring optical lattices (OL) trap is studied. By means of the variational method and direct numerical simulations of the Gross–Pitaevskii (GP) equation, the ground state properties and the vortex stabilities of the condensates for both repulsive and attractive cases are investigated. The results show that the bound states exist for determinate OL strength and interatomic interaction. However, the ground states of BECs undergo delocalizing–localizing transition for both attractive and repulsive cases as the strength of the OL or the interatomic interaction is decreased below the critical value. The ring OL can suppress the delocalizing transition efficiently.

Bose–Einstein condensates: Analytical methods for the Gross–Pitaevskii equation

We present simple analytical methods for solving the Gross–Pitaevskii equation (GPE) for the Bose–Einstein condensation (BEC) in the dilute atomic alkali gases. Using a soliton variational Ansatz we consider the effects of repulsive and attractive effective nonlinear interactions on the BEC ground state. We perform a comparative analysis of the solutions obtained by the variational Ansatz, the perturbation theory, the Thomas–Fermi approximation, and the Green function method with the numerical solution of the GPE finding universal ranges where these solutions can be used to predict properties of the condensates. Also, a generalization of the soliton variational approach for two-species of alkali atoms of the GPE is performed as a function of the effective interaction λi(i=1,2) and the inter-species λ12 and λ21 constants.

Gap-Townes solitons and localized excitations in low-dimensional Bose-Einstein condensates in optical lattices

We discuss localized ground states of Bose-Einstein condensates (BEC's) in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schr\"odinger equation which extends the Gross-Pitaevskii equation to the one-dimensional case. We use both a variational method and a self-consistent approach to show the existence of unstable localized excitations which are similar to Townes solitons of the cubic nonlinear Schr\"odinger equation in two dimensions. These solutions are shown to be located in the forbidden zones of the band structure, very close to the band edges, separating decaying states from stable localized ones (gap solitons) fully characterizing their delocalizing transition. In this context the usual gap solitons appear as a mechanism for arresting the collapse in low-dimensional BEC's in optical lattices with an attractive real three-body interaction. The influence of the imaginary part of the three-body interaction, leading to dissipative effects in gap solitons, and the effect of atoms feeding from the thermal cloud are also discussed. These results may be of interest for both BEC's in atomic chips and Tonks-Girardeau gas in optical lattices.

Transition from the Bose–Einstein condensate to the Berezinskii–Kosterlitz–Thouless phase

We obtain a phase diagram for a trapped two-dimensional ultracold Bose gas. We find a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose–Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose–Einstein condensate, a vortex pair plasma with a fluctuating condensate phase, and a thermal Bose gas. The existence of the vortex pair phase could be verified using current experimental set-ups.

Nonadiabatic effects on population transfer of two Bose-Einstein condensates induced by atomic interaction

We investigate the stimulated Raman adiabatic passage for Bose-Einstein condensate (BEC) states which are trapped in different potential wells or two ground states of BEC in the same trap. We consider that lasers are nearly resonant with the atomic transitions. The difference of population transfer processes between BEC atoms and usual atoms is that the atomic interaction of the BEC atoms can cause some nonadiabatic effects, which may degrade the process. But with suitable detunings of laser pulses, the effects can be remedied to some extent according to different atomic interactions.

Quantum mechanics. To condense or not to condense.

Bosonic particles choose between a classical crystalline or a Bose-Einstein condensed ground state depending on the strength of their interactions. In his Perspective, Rice explains how this competition can be observed in quantum magnets composed of spin-dimer arrays when a magnetic field is applied. This generates spin triplet bosons with a tunable density. Magnetization plateaus correspond to spatially ordered arrays of the spin triplets. The detailed structure of such an array has been unraveled in a recent NMR experiment.

Theory of spin-2 Bose-Einstein condensates: Spin correlations, magnetic response, and excitation spectra

The ground states of Bose-Einstein condensates of spin-2 bosons are classified into three distinct (ferromagnetic, ^^ ^^ antiferromagnetic", and cyclic) phases depending on the s-wave scattering lengths of binary collisions for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic response of the condensate in each of these phases are studied in a mesoscopic regime, while low-lying excitation spectra are investigated in the hermodynamic regime. In the mesoscopic regime, where the system is so tightly confined that the spatial degrees of freedom are frozen, the exact, many-body ground state for each phase is found to be expressed in terms of the creation operators of pair or trio bosons having spin correlations. These pairwise and trio-wise units are shown to bring about some unique features of spin-2 BECs such as a huge jump in magnetization from minimum to maximum possible values and the robustness of the minimum-magnetization state against an applied agnetic field. In the thermodynamic regime, where the system is spatially uniform, low-lying excitation spectra in the presence of magnetic field are obtained analytically using the Bogoliubov approximation. In the ferromagnetic phase, the excitation spectrum consists of one Goldstone mode and four single-particle modes. In the antiferromagnetic phase, where spin-singlet ^^ ^^ pairs" undergo Bose-Einstein condensation, the spectrum consists of two Goldstone modes and three massive ones, all of which become massless when magnetic field vanishes. In the cyclic phase, where boson ^^ ^^ trios" condense into a spin-singlet state, the spectrum is characterized by two Goldstone modes, one single-particle mode having a magnetic-field-independent energy gap, and a gapless single-particle mode that becomes massless in the absence of magnetic field.