Ground State Of Condensates Research Articles

On ground state of fractional spinor Bose Einstein condensates

In this paper, we prove the existence of the positive ground state solution to fractional spin-1 Bose-Einstein condensation(BEC) in one dimension.

Analytical solutions of the coupled Gross–Pitaevskii equations for the three-species Bose–Einstein condensates

The coupled Gross–Pitaevskii equations for the ground state of the three-species condensates have been solved analytically under the Thomas–Fermi approximation. Six types of spatial configurations in the miscible phase are found. The whole parameter space has been divided into zones, each of which supports a specific configuration (miscible or immiscible). The boundaries of the zones are described by analytical formulae. Due to the division, the variation of the spatial configuration against the parameters can be visualized, and the effects of the parameters can thereby be understood. There are regions in the parameter space where the configuration is highly sensitive to the parameters. These regions are tunable and valuable for the determination of the parameters.

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.

Increase of the chemical potential and phase transitions in four-component exciton condensates subject to magnetic fields

We analyze the spin structure of the ground state of four-component exciton condensates in coupled quantum wells as a function of spin-dependent interactions and applied magnetic field. The four components correspond to the degenerate exciton states characterized by $\pm2$ and $\pm1$ spin projections to the axis of the structure. We show that in a wide range of parameters, the chemical potential of the system increases as a function of magnetic field, which manifests a pseudo-diamagnetism of the system. The transitions to polarized two- and one-component condensates can be of the first-order in this case. The predicted effects are caused by energy conserving mixing of $\pm2$ and $\pm1$ excitons.

Ground-state properties of microcavity polariton condensates at arbitrary excitation density

The ground state of microcavity polariton Bose-Einstein condensates (BEC's) is determined as a function of experimentally tunable parameters (the excitation density and the detuning of cavity photons), and also a material parameter (the ultraviolet cutoff). To obtain the ground state at an arbitrary excitation density, an interpolation method for the BEC-BCS crossover of excitonic insulators is extended to microcavity polariton systems in two or three dimensions. The ground state of the condensate changes from excitonic to photonic with an increase in the excitation density. This change is accompanied by several interesting features: (i) A laserlike input (excitation density) and output (photon density) relation with a sharp onset for largely detuned systems, which changes to that with a smooth onset for slightly detuned systems. (ii) The origin of the binding force of electron-hole pairs changes from Coulomb attraction to photon-mediated interactions, resulting in the formation of strongly bound pairs with a small radius, such as Frenkel excitons, in the photonic regime. The change in the ground state can be a crossover or a first-order transition, depending on the above-mentioned parameters, and is studied by plotting phase diagrams.

Particle-localized ground state of atom-molecule Bose-Einstein condensates in a double-well potential

We study the effect of atom-molecule internal tunneling on the ground state of atom-molecule Bose-Einstein condensates in a double-well potential. In the absence of internal tunneling between atomic and molecular states, the ground state is symmetric, which has equal-particle populations in two wells. From the linear stability analysis, we show that the symmetric stationary state becomes dynamically unstable at a certain value of the atom-molecule internal tunneling strength. Above the critical value of the internal tunneling strength, the ground state bifurcates to the particle-localized ground states. The origin of this transition can be attributed to the effective attractive interatomic interaction induced by the atom-molecule internal tunneling. This effective interaction is similar to that familiar in the context of BCS-BEC crossover in a Fermi gas with Feshbach resonance. Furthermore, we point out the possibility of reentrant transition in the case of the large detuning between the atomic and molecular states.

Numerical methods for computing the ground state of spin-1 Bose-Einstein condensates in a uniform magnetic field

We propose efficient and accurate numerical methods for computing the ground-state solution of spin-1 Bose-Einstein condensates subjected to a uniform magnetic field. The key idea in designing the numerical method is based on the normalized gradient flow with the introduction of a third normalization condition, together with two physical constraints on the conservation of total mass and conservation of total magnetization. Different treatments of the Zeeman energy terms are found to yield different numerical accuracies and stabilities. Numerical comparison between different numerical schemes is made, and the best scheme is identified. The numerical scheme is then applied to compute the condensate ground state in a harmonic plus optical lattice potential, and the effect of the periodic potential, in particular to the relative population of each hyperfine component, is investigated through comparison to the condensate ground state in a pure harmonic trap.

Exact ground state of finite Bose-Einstein condensates on a ring

The exact ground state of the many-body Schr\"odinger equation for $N$ bosons on a one-dimensional ring interacting via pairwise $\delta$-function interaction is presented for up to fifty particles. The solutions are obtained by solving Lieb and Liniger's system of coupled transcendental equations for finite $N$. The ground state energies for repulsive and attractive interaction are shown to be smoothly connected at the point of zero interaction strength, implying that the \emph{Bethe-ansatz} can be used also for attractive interaction for all cases studied. For repulsive interaction the exact energies are compared to (i) Lieb and Liniger's thermodynamic limit solution and (ii) the Tonks-Girardeau gas limit. It is found that the energy of the thermodynamic limit solution can differ substantially from that of the exact solution for finite $N$ when the interaction is weak or when $N$ is small. A simple relation between the Tonks-Girardeau gas limit and the solution for finite interaction strength is revealed. For attractive interaction we find that the true ground state energy is given to a good approximation by the energy of the system of $N$ attractive bosons on an infinite line, provided the interaction is stronger than the critical interaction strength of mean-field theory.

Stable vortex dipoles in nonrotating Bose-Einstein condensates

We find stable families of vortex dipoles in nonrotating Bose-Einstein condensates. The vortex dipoles correspond to topological excited collective states of the condensed atoms. They exist and are dynamically and structurally stable for a broad range of parameters. We show that they can be generated by phase-imprinting techniques on the ground state of condensates.

Characteristic features of symmetry breaking in two-component Bose-Einstein condensates.

We examine the stability properties of the ground state of two-component Bose-Einstein condensates as a function of the interspecies interactions. A stability criterion is identified from the curvature matrix of the Gross-Pitaevskii energy functional subject to the normalization conditions. By analyzing the stability signature, the characteristic features of the spontaneous spatial symmetry breaking are verified in various types of traps. The details of the differences between the continuous symmetry breaking and discrete symmetry breaking are discussed.