Trapped Bosons Research Articles

Energy-level statistics of interacting trapped bosons

It is an well established fact that statistical properties of energy level spectra are the most efficient tool to characterize nonintegrable quantum systems. The study of statistical properties and spectral fluctuation in the interacting many boson systems have developed a new interest in this direction. Specially we are interested in the weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from the collective to single particle nature with the increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson like fluctuations due to the existence of external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are in the 3D confined harmonic potential. We study the nearest neighbour spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that increase in number of energy levels for repulsive BEC induces a transition from a Wigner like form displaying level repulsion to Poisson distribution for P(s). It does not follow the GOE prediction. For repulsive interaction, the lower levels are correlated and manifest level repulsion. For intermediate levels P (s) shows mixed statistic which clearly signifies the existence of two energy scales: external trap and interatomic interaction. Whereas for very high levels the trapping potential dominates, genarating Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shrielman like peak near s=0 which signifies the presence of large number of quasi-degenerate states.

Spectral fluctuation and1/fαnoise in the energy level statistics of interacting trapped bosons

It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by 1/f^{α} noise with 1≤α≤2. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the P(s) distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that 1/f^{α} noise is ubiquitous in nature.

Bose–Einstein condensation of a [formula omitted]-deformed boson system in a harmonic potential trap

Within the framework of the theory of q-deformed bosons, we investigate Bose–Einstein condensation of a q-deformed boson system, which has finite particle number and is trapped in a harmonic potential trap, by using the approach of modified density of states. For such a trapped q-deformed boson system, we obtain the expressions of the effective critical temperature Tc, the ground state population N0/N and the specific heat C. Further numerical calculation shows that Bose–Einstein condensation of such a system has some particular and interesting features which are different from those of a trapped standard boson system. We consider that this work may provide much insight into the theory of q-deformed bosons, and may also be useful for the further study on Bose–Einstein condensation of a concrete trapped q-deformed boson system.

Interferometry with synthetic gauge fields

We propose a compact atom interferometry scheme for measuring weak, time-dependent accelerations. Our proposal uses an ensemble of dilute trapped bosons with two internal states that couple to a synthetic gauge field with opposite charges. The trapped gauge field couples spin to momentum to allow time dependent accelerations to be continuously imparted on the internal states. We generalize this system to reduce noise and estimate the sensitivity of such a system to be S~10^-7 m / s^2 / Hz^1/2.

Perturbative correction to the ground-state properties of one-dimensional strongly interacting bosons in a harmonic trap

We calculate the first-order perturbation correction to the ground-state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the infinite repulsion Tonks-Girardeau limit. With $c$ denoting the interaction strength, we find that, for a large number of particles $N$, the $1/c$ correction to the ground-state energy increases as ${N}^{5/2}$, in contrast to the unperturbed Tonks-Girardeau value that is proportional to ${N}^{2}$. We describe a thermodynamic scaling limit for the trapping frequency that yields an extensive ground-state energy and reproduces the zero temperature thermodynamics obtained by a local-density approximation.

Pair-correlation properties and momentum distribution of finite number of interacting trapped bosons in three dimensions

We study the ground state pair-correlation properties of a weakly interacting trapped Bose gas in three dimensions by using a correlated many-body method. The use of the van der Waals interaction potential and an external trapping potential shows realistic features. We also test the validity of shape-independent approximation in the calculation of correlation properties.

Interacting trapped bosons yield fragmented condensate states in low dimensions

We investigate the level population statistics and degree of coherence encoded in the single-particle density matrix of harmonically trapped low-dimensional [quasi-one-dimensional (quasi-1D) or quasi-two-dimensional (quasi-2D)] Bose gases with repulsive contact interactions. Using a variational analysis, we derive fragmentation of the condensate in the weakly confining directions into two (quasi-1D) respectively three (quasi-2D) mutually incoherent macroscopic pieces, upon increasing a dimensionless interaction measure beyond a critical value. Fragmented condensate many-body states in low-dimensional systems therefore occur well before the thermodynamic limit of infinite extension is reached, in which phase fluctuations of the matter wave field create an infinite number of nonmacroscopic fragments.

Variational self-consistent theory for trapped Bose gases at finite temperature

We apply the time-dependent variational principle of Balian-V\'en\'eroni to a system of self-interacting trapped bosons at finite temperature. The method leads to a set of coupled non-linear time dependent equations for the condensate density, the thermal cloud and the anomalous density. We solve numerically these equations in the static case for a harmonic trap. We analyze the various densities as functions of the radial distance and the temperature. We find an overall good qualitative agreement with recent experiments as well as with the results of many theoretical groups. We also discuss the behavior of the anomalous density at low temperatures owing to its importance to account for many-body effects.

Finite number of trapped bosons interacting through the harmonic Calogero interaction in one dimension

We consider a finite number of trapped bosons in one dimension (1D) interacting through the harmonic Calogero interaction. Using an exact analytic solution for the energy eigenvalues we calculate the condensate fraction, ground-state energy, and specific heat of the system. For weak interaction the behavior of thermodynamic properties is close to that of noninteracting trapped bosons.

Solvable model for pair excitation in trapped Boson gas at zero temperature

Solvable model for pair excitation in trapped Boson gas at zero temperature

Solvable model for pair excitation in trapped Boson gas at zero temperature

In Bose–Einstein condensation (BEC), particles occupy a single-particle quantum state, Φ, macroscopically. At zero temperature, the wavefunction for Φ is usually described via a nonlinear Schrödinger equation (NSE). Our goal is to study time-dependent nonlocal effects beyond the NSE in trapped atomic gases. We adopt the view that atoms are excited from Φ in pairs: the scattering from Φ to other states at positions x and y is described by the pair-excitation function, K0(x, y, t) (Wu 1961 J. Math. Phys. 2 105). This function satisfies a nonlinear, dispersive integrodifferential equation coupled with the NSE. We solve these equations under a slowly varying external potential by assuming that Φ is stationary. For zero initial excitation (K0 ≡ 0 at t = 0) and sufficiently large t, we evaluate K0 asymptotically for any distance |x − y|. Implications of these results are discussed, particularly the connection of non-equilibrium properties to the coalescence of critical points in the Fourier space.

Bragg spectroscopy of trapped one-dimensional strongly interacting bosons in optical lattices: Probing the cake structure

We study Bragg spectroscopy of strongly interacting one-dimensional bosons loaded in an optical lattice plus an additional parabolic potential. We calculate the dynamic structure factor by using Monte Carlo simulations for the Bose-Hubbard Hamiltonian, exact diagonalizations and the results of a recently introduced extended fermionization model. We find that, due to the system's inhomogeneity, the excitation spectrum exhibits a multibranched structure, whose origin is related to the presence of superfluid regions with different densities in the atomic distribution. We thus suggest that Bragg spectroscopy in the linear regime can be used as an experimental tool to unveil the shell structure of alternating Mott insulator and superfluid phases characteristic of trapped bosons.

Rotating quantum liquids crystallize

Small crystallites form when finite quantal systems are set highly rotating. This crystallization is independent of the statistics of the particles, and occurs for both trapped bosons and fermions. The spin degree of freedom does not change the tendency for localization. In a highly rotating state, the strongly correlated bosonic and fermionic systems approach to that of classical particles.

Exciton-polariton kinematic interactions in organic microcavities

We analyze the exciton-exciton and polariton-polariton kinematic interactions in crystalline organic microcavities. The kinematic interactions are derived using the Agranovich-Toshich transformation, which transforms the Frenkel excitons from paulions into bosons. From the calculated exciton-scattering cross section in an organic crystalline monolayer, we find that the scattering due to the exciton-exciton kinematic interaction can be described as the scattering between hard disks. We show that, as in the case of two-dimensional ultracold trapped boson atom gas, excitons in a confined monolayer may behave as a dilute degenerate boson gas at low temperature. In an organic cavity, with an organic crystalline monolayer as a resonant material, we derive the polariton-polariton kinematic interaction, which stems from the polariton excitonic part. We calculate the polariton-scattering cross section due to the polariton-polariton kinematic interaction, and recognize the scattering effective potential. We show that, due to the smallness of the polariton effective mass, polaritons in organic cavities may behave as a dilute degenerate boson gas up to room temperature. The comparison between the polariton-polariton kinematic interaction in organic cavities and the polariton-polariton nonlinear interaction in inorganic semiconductor cavities shows that both interactions are of the same order.

Exactly solvable models for trapped boson systems

The pairing model (PM) hamiltonian was solved exactly for both boson and fermion systems by Richardson in the 1960s. We review here recent work to generalize the boson PM, by using the complete set of integrals of motion of the pairing algebra, so that it can be used to describe finite trapped atomic boson systems. We then show how these integrable models can be further extended for application to atom–molecule mixtures.

Tonks-Girardeau gas of ultracold atoms in an optical lattice.

Strongly correlated quantum systems are among the most intriguing and fundamental systems in physics. One such example is the Tonks-Girardeau gas, proposed about 40 years ago, but until now lacking experimental realization; in such a gas, the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system. In order to minimize their mutual repulsion, the bosons are prevented from occupying the same position in space. This mimics the Pauli exclusion principle for fermions, causing the bosonic particles to exhibit fermionic properties. However, such bosons do not exhibit completely ideal fermionic (or bosonic) quantum behaviour; for example, this is reflected in their characteristic momentum distribution. Here we report the preparation of a Tonks-Girardeau gas of ultracold rubidium atoms held in a two-dimensional optical lattice formed by two orthogonal standing waves. The addition of a third, shallower lattice potential along the long axis of the quantum gases allows us to enter the Tonks-Girardeau regime by increasing the atoms' effective mass and thereby enhancing the role of interactions. We make a theoretical prediction of the momentum distribution based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.

Bose-Einstein condensates in85Rbgases at higher densities

The Bose-Einstein condensation in trapped gases of {sup 85}Rb at densities beyond the dilute regime can now be realized taking advantage of Feshbach resonances. The gas density may be characterized by the parameter na{sup 3}, where n=N/V is the number density and a is the scattering length which is tuned using Feshbach resonance. We explore the properties of interacting trapped bosons in the density range 5x10{sup -3}{<=}na{sup 3}{<=}5x10{sup -2} using Monte Carlo methods to compare with experiments. We find that there is a significant depletion of the condensate at T=0 K, for example, 25% at na{sup 3}=10{sup -2}. The condensate is not concentrated at the center of the trap but is spread out over four or five trap lengths. The condensate density distributions and the total density distributions within the trap are very similar and the condensate fraction is 100% at the edges of the trap.

Operator-algebraic approach to the yrast spectrum of weakly interacting trapped bosons

We present an operator-algebraic approach to derive the low-lying quasidegenerate spectrum of weakly interacting trapped N bosons with total angular momentum $\ensuremath{\Elzxh}L$ for the case of $L/N\ensuremath{\ll}1.$ We demonstrate that the lowest-lying excitation spectrum is given by ${27gn}_{3}{(n}_{3}\ensuremath{-}1)/34,$ where g is the strength of the repulsive contact interaction and ${n}_{3}$ is the number of excited octupole quanta. Our method provides constraints for these quasidegenerate many-body states and gives higher excitation energies that depend linearly on N.

Low-lying excitations from the yrast line of weakly interacting trapped bosons

Through an extensive numerical study, we find that the low-lying, quasi-degenerate eigenenergies of weakly-interacting trapped N bosons with total angular momentum L are given in case of small L/N and sufficiently small L by E = L hbar omega + g[N(N-L/2-1)+1.59 n(n-1)/2], where omega is the frequency of the trapping potential and g is the strength of the repulsive contact interaction; the last term arises from the pairwise repulsive interaction among n octupole excitations and describes the lowest-lying excitation spectra from the Yrast line. In this case, the quadrupole modes do not interact with themselves and, together with the octupole modes, exhaust the low-lying spectra which are separated from others by N-linear energy gaps.

Quantum theory of an atomic parametric oscillator

We present a quantum theory of an atomic parametric oscillator which describes a gas of weakly interacting trapped bosons. The particles are assumed to be confined in a damped atomic cavity pumped by a coherent matter beam. We consider the three trapped levels which are the pumped and two damped modes. The system is described by a Fokker-Planck equation (FPE) for the quasi-distribution function in the complex P-representation for the density operator. Using a known steady-state solution of the FPE we derive the boson number distribution function. On the basis of an exact treatment we investigate the quantum behavior of the device, especially in the critical region. As a result, a quantum noise-induced effect is revealed. We suggest to use the device as a correlated matter waves generator.