Bose Systems Research Articles

Phase transitions in ideal and weakly interacting Bose gases with a finite number of particles confined in a box

We generalize the scheme to characterize phase transitions of finite systems in a complex temperature plane and approach the classifications of phase transitions in ideal and weakly interacting Bose gases of a finite number of particles, confined in a cubic box of volume L3 with different boundary conditions. For this finite ideal Bose system, by extending the classification parameters to all regions, we predict that the phase transition for periodic boundary conditions is of second order, while the transition in Dirichlet boundary conditions is of first order. For a weakly interacting Bose gas with periodic boundary conditions, we discuss the effects of finite particle numbers and inter-particle interactions on the nature of the phase transitions. We show that this homogenous weakly interacting Bose gas undergoes a second-order phase transition, which is in accordance with universality arguments for infinite systems. We also discuss the dependence of transition temperature on interaction strengths and particle numbers.

Bose–Einstein condensation of a finite-size Bose system

Bose–Einstein condensation (BEC) of a finite number of noninteracting bosons confined in a finite-size container is investigated by using numerical calculation. It is revealed that the characteristics of finite-size BEC are significantly different from those for the system satisfying the condition of thermodynamic limit, and some well-known conclusions about BEC described in textbooks are not valid for a finite-size Bose system. This paper may be helpful for the further understanding of the concept of BEC and thermostatistics in small systems. It is suitable for readers including undergraduate and graduate students, general physicists and so on.

Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems

We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove the compressibility of the system on the superfluid-insulator critical line and in its neighborhood. These conclusions follow from a general theorem of inclusions, which states that for any transition in a disordered system, one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: the critical disorder bound Delta(c) corresponding to the onset of disorder-induced superfluidity, satisfies the relation Delta(c)>Eg/2, with Eg/2 the half-width of the Mott gap in the pure system.

Study of Kosterlitz-Thouless Transition with Random Chemical Potential Using Quantum Monte Carlo Simulations

Disordered Bose systems have been investigated extensively theoretically and experimentally. While most studies are made for three-dimensional systems, we focus our studies on two-dimensional systems. In two-dimensional Bose systems, it is well-known that Kosterlitz-Thouless (KT) transition occurs. Our motivation is to investigate the effects of randomness on KT transition. The hardcore-Bose-Hubbard model with random chemical potential is investigated using quantum Monte Carlo simulations. Random distribution is assumed to obey the Gaussian distribution, and superfluid density and correlation functions are calculated. By changing the dispersion of the Gaussian distribution, we found that the transition temperature decreases as the dispersion increases. We obtained the phase diagram showing the superfluid (KT) phase and the disorder phase.

Interacting bosons beyond the Gross–Pitaevskii mean field

Systems consisting of cold interacting bosons show interesting collective phenomena such as Bose–Einstein condensation or superfluidity and are currently studied in condensed matter and atomic physics. Of particular interest are nonideal bosons which exhibit strong correlation and spatial localisation effects. Here we analyse the ground-state of a two-dimensional Bose system with a Hartree–Fock type approximation that was first introduced by Romanovsky et al. [Phys. Rev. Lett. 93 (2004) 230405]. We apply this method to a one-dimensional system of charged bosons and analyse the behaviour at strong coupling.

The relation between fractional statistics and finite bosonic systems in the one-dimensional case

The equivalence is established between a one-dimensional (1D) Bose system with a finite number of particles and a system obeying fractional (intermediate) Gentile statistics, in which the maximum occupation of single-particle energy levels is limited. A system of 1D harmonic oscillators, providing a model for a harmonically trapped Bose gas, is considered. The results are generalized for a system with a power-law energy spectrum.

NMR quadrupolar system described as Bose–Einstein-condensate-like system

This paper presents a description of nuclear magnetic resonance (NMR) of quadrupolar systems using the Holstein-Primakoff (HP) formalism and its analogy with a Bose-Einstein condensate (BEC) system. Two nuclear spin systems constituted of quadrupolar nuclei I=3/2 ((23)Na) and I=7/2 ((133)Cs) in lyotropic liquid crystals were used for experimental demonstrations. Specifically, we derived the conditions necessary for accomplishing the analogy, executed the proper experiments, and compared with quantum mechanical prediction for a Bose system. The NMR description in the HP representation could be applied in the future as a workbench for BEC-like systems, where the statistical properties may be obtained using the intermediate statistic, first established by Gentile. The description can be applied for any quadrupolar systems, including new developed solid-state NMR GaAS nanodevices.

Bose systems in spatially random or time-varying potentials

Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condensate. Increasing the strength of disorder even more transforms the granular condensate into the normal glass. The influence of time-dependent external potentials is also discussed. Fast varying temporal potentials, to some extent, imitate the action of spatially random potentials. In particular, strong time-alternating potential can induce the appearance of a nonequilibrium granular condensate.

Dynamics of a Two-Dimensional System of Quantum Dipoles

A detailed microscopic analysis of the dynamic structure function S(k,omega) of a two-dimensional Bose system of dipoles polarized along the direction perpendicular to the plane is presented and discussed. Starting from ground-state quantities obtained using a quantum diffusion Monte Carlo algorithm, the density-density response is evaluated in the context of the correlated basis functions (CBF) theory. CBF predicts a sharp peak and a multiexcitation component at higher energies produced by the decay of excitations. We discuss the structure of the phonon-roton peak and show that the Feynman and Bogoliubov predictions depart from the CBF result already at low densities. We finally discuss the emergence of a roton in the spectrum, but find the roton energy not low enough to make the system unstable under density fluctuations up to the highest density considered that is close to the freezing point.

Nonclassical Properties of Para-Bose Superposition States

It is well known that the nonclassical states of the light field play an important role in quantum optics. In the last decade, the nonclassical states which arise as the coherent superposition of two quantum states has attracted much attention [1–3]. In Ref. [1] Wodkiewicz et al. introduce a new kind of superposition states which exhibit squeezing fluctuations and open new possibilities of generating squeezed states. In recent years, simulated by recent experimental observation of fractional quantum Hall effect [4, 5] in two-dimensional electron gas, much attention has been focused on various nontraditional statistics: fractional statistics [6–8] and parastatistics [9–11]. Parastatistics was first introduced by Green [9] as a generalization of the Bose and Fermi statistics. This generalization introduced trilinear relations in place of the bilinear relations that describe the Bose and Fermi systems. Recently, Greenberg and Mishra [11] have shown that the parastatistics can be quantized by using path integrals. In this letter, we present two kinds of generalized para-Bose superposition states and investigate its nonclassical properties. It is shown that these para-Bose superposition states exhibit stronger squeezing and antibunching. The amplitude-squared squeezing for these states is also examined.

Quantum condensation in electron–hole plasmas

AbstractQuantum condensation phenomena occur in Bose systems (Bose–Einstein condensation, BEC) as well as in strongly degenerate Fermi systems (BCS state). In Fermi systems with Bose‐like bound states both phenomena are possible.A theoretical approach to describe quantum condensation in electron‐hole plasmas in the framework of realtime Green's functions is presented. The resulting phase boundary shows that there is a smooth crossover from BEC to BCS. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multiscale theory of finite-size Bose systems: Implications for collective and single-particle excitations

Boson droplets (i.e., dense assemblies of bosons at low temperature) are shown to mask a significant amount of single-particle behavior and to manifest collective, droplet-wide excitations. To investigate the balance between single-particle and collective behavior, solutions to the wave equation for a finite size Bose system are constructed in the limit where the ratio $\ensuremath{\epsilon}$ of the average nearest-neighbor boson distance to the size of the droplet or the wavelength of density disturbances is small. In this limit, the lowest order wave function varies smoothly across the system, i.e., is devoid of structure on the scale of the average nearest-neighbor distance. The amplitude of short range structure in the wave function is shown to vanish as a power of $\ensuremath{\epsilon}$ when the interatomic forces are relatively weak. However, there is residual short range structure that increases with the strength of interatomic forces. While the multiscale approach is applied to boson droplets, the methodology is applicable to any finite size Bose system and is shown to be more direct than field theoretic methods. Conclusions for $^{4}\mathrm{He}$ nanodroplets are drawn.

Effective action approach for quantum phase transitions in bosonic lattices

Based on standard field-theoretic considerations, we develop an effective action approach for investigating quantum phase transitions in lattice Bose systems at arbitrary temperature. We begin by adding to the Hamiltonian of interest a symmetry breaking source term. Using time-dependent perturbation theory, we then expand the grand-canonical free energy as a double power series in both the tunneling and the source term. From here, an order parameter field is introduced in the standard way and the underlying effective action is derived via a Legendre transformation. Determining the Ginzburg-Landau expansion to first order in the tunneling term, expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and compressibility are derived and analyzed in detail. Additionally, excitation spectra in the ordered phase are found by considering both longitudinal and transverse variations of the order parameter. Finally, these results are applied to the concrete case of the Bose-Hubbard Hamiltonian on a three-dimensional cubic lattice, and compared with the corresponding results from mean-field theory. Although both approaches yield the same Mott insulator–superfluid phase boundary to first order in the tunneling, the predictions of our effective action theory turn out to be superior to the mean-field results deeper into the superfluid phase.

Adiabatic Nonlinear Probes of One-Dimensional Bose Gases

We discuss two complimentary problems: adiabatic loading of one-dimensional bosons into an optical lattice and merging two one-dimensional Bose systems. Both problems can be mapped to the sine-Gordon model. This mapping allows us to find power-law scalings for the number of excitations with the ramping rate in the regime where the conventional linear response approach fails. We show that the exponent of this power law is sensitive to the interaction strength. In particular, the response is larger, or less adiabatic, for strongly (weakly) interacting bosons for the loading (merging) problem. Our results illustrate that in general the nonlinear response to slow relevant perturbations can be a powerful tool for characterizing properties of interacting systems.

On the mathematical theory of superfluidity

We provide a general operator algebraic formulation of the theory of superfluidity in Bose systems, with the aim of investigating the relationships of this phenomenon both to off-diagonal long range order (ODLRO) and to a mathematically precise version of Landau's picture of elementary excitations. Our principal results are that ODLRO leads both to rotational superfluidity and to Goldstone excitations, while the neo-Landau picture accounts for the translational superfluidity of flow along a pipe. The latter picture is realized by the Lieb–Liniger–Girardeau model. Open problems are briefly discussed.

Vortices in small Bose or Fermi systems with repulsive interactions

For rotating Bose-Einstein condensates, the occurrence of vortices has been much discussed in the Gross-Pitaevskii approach. Here, we study vortex formation in finite systems with few particles for weak and repulsive two-body interactions, by numerical diagonalization. Vortex formation is surprisingly similar for both (spinless) bosonic and fermionic particles. Breaking the rotational invariance of the Hamiltonian of the system reveals the vortex patterns. A transformation from a many-fermion to a many-boson state is proposed.

COEXISTENCE OF NON-CONVENTIONAL CONDENSATES IN TWO-LEVEL BOSE ATOM SYSTEM

In the framework of the Bogolyubov approximation and using the Bogolyubov inequalities, we give a simple proof of the coexistence of two non-conventional Bose–Einstein condensates in the case of some superstable Bose system whose atoms have an internal two-level structure, and their energy operators in the second quantized form depend on the number operators only.

DIRTY BOSONS: TWENTY YEARS LATER

A concise and somewhat personal review of the problem of superfluidity and quantum criticality in regular and disordered interacting Bose systems is given, concentrating on general features and important symmetries that are exhibited in different parts of the phase diagram, and that govern the different possible types of critical behavior. A number of exact results for various insulating phase boundaries, which may be used to constrain the results of numerical simulations, can be derived using large rare region type arguments. The nature of the insulator-superfluid transition is explored through general scaling arguments, exact model calculations in one dimension, numerical results in two dimensions, and approximate renormalization group results in higher dimensions. Experiments on 4 He adsorbed in porous Vycor glass, on thin film superconductors, and magnetically trapped atomic vapors in a periodic optical potential are used to illustrate many of the concepts.

GROUND STATE ENERGY OF BOSE-EINSTEIN CONDENSATION IN A DISORDERED SYSTEM

A modeled Bose system consisting of N particles with two-body interaction confined within volume V under inhomogeneity of the system is investigated using the Feynman path integral approach. The two-body interaction energy is assumed to be dependent on the two-parameter interacting strength a and the correlation length l. The inhomogeneity of the system or the porosity can be represented as density [Formula: see text] with interacting strength b and correlation length L. The mean field approximation on the two-body interaction in the Feynman path integrals representation is performed to obtain the one-body interaction. This approximation is equivalent to the Hartree approximation in the many-body electron gas problem. This approximation has shown that the calculation can be reduced to the effective one-body propagator. Performing the variational calculations, we obtain analytical results of the ground state energy which is in agreement with that from Bugoliubov's approach.

Collective excitations of strongly coupled bilayer charged Bose liquids in the third-frequency-moment sum rule

We calculate the collective excitation modes of strongly coupled bilayer charged Bose systems. We employ the dielectric matrix formulation to study the correlation effects within the random-phase approximation (RPA), the self consistent field approximation Singwi, Tosi, Land, and Sj\"olander (STLS), and the quasilocalized charge approximation (QLCA), which satisfies the third-frequency-moment $(⟨{\ensuremath{\omega}}^{3}⟩)$ sum rule. We find that the QLCA predicts a long-wavelength correlation-induced energy gap in the out-of-phase plasmon mode, similar to the situation in electronic bilayer systems. The energy gap and the plasmon density of states are studied as a function of interlayer separation and coupling parameter ${r}_{s}$. The results should be helpful for experimental investigations.