Motivated by the recent experiment [R. Lopes et. al., Phys. Rev. Lett. 119, 190404 (2017)] with a homogeneous Bose gas, we investigate a homogeneous dilute Bose gas to calculate the quantum depletion density. By means of the Cornwall-Jackiw-Tomboulis effective action approach within an improved Hartree-Fock approximation, the condensed fraction is recovered in a simpler manner and compared with corresponding findings in experimental data. Additionally, higher-order terms are taken into account for several physical quantities, in particular for the chemical potential and free energy density.
In a manner of Cornwal-Jackiw-Tomboulis effective action approach, the density of condensate of a dilute Bose gas confined between two planar walls is investigated within the framework of improved Hartree-Fock. Thereby, the quantum fluctuations are taken into account with presence of high-order terms in the momentum integrals. Our results show that the quantum fluctuations significantly belittle the density of condensate compared with square of the expectation value of the field operator. The comparison with relating results of Gross-Pitaevskii theory is made.
The Casimir effect in a dilute Bose gas confined between two planar walls is investigated in the canonical ensemble at zero temperature by means of Cornwall-Jackiw-Tomboulis effective action approach within the improved Hartree-Fock approximation. Our results show that: (i) the Casimir energy and the resulting Casimir force in the canonical ensemble remarkably differ from those in the grand canonical ensemble; (ii) when the distance between two planar walls increases, the Casimir energy and Casimir force decay in accordance with a half-integer power law in the canonical ensemble instead of an …
The energy spectrum for the three dimensional Bose gas in Bose-Einstein Condensation phase is calculated with Modified Hartree-Fock-Bogoliubov theory, which is both conserving and gapless. From Improved $Φ-$% derivable theory, the diagrams needed to preserve Ward-Takahashi Identity are resummed in a systematic and nonperturbative way. The results show significant discrepancies with Popov theory at finite temperature. It is valid up to the critical temperature where the dispersion relation of the low energy excitation spectrum changes from linear to quadratic. Because of the repulsive interacti…
The Hohenberg-Martin dilemma of conserving versus gapless theories for systems with Bose-Einstein condensate is considered. This dilemma states that, generally, a theory characterizing a system with broken global gauge symmetry, which is necessary for Bose-Einstein condensation, is either conserving, but has a gap in its spectrum, or is gapless, but does not obey conservation laws. In other words, such a system either displays a gapless spectrum, which is necessary for condensate existence, but is not conserving, which implies that it corresponds to an unstable system, or it respects conservat…
Derivation of the Hartree dynamics for a N-particles fermionic 2D system interacting via long-range electric and magnetic two-body singular potentials in a dilute regime
Critical temperature and thermodynamic properties of a homogeneous dilute weakly interacting Bose gas within the improved Hartree-Fock approximation at finite temperature
In this paper, we studied a dilute quasi two-dimensional dipolar Bose-condensed with two- and three-body contact, and Coulomb interactions using the Hartree-Fock-Bogoliubov-Popov approximation. We analyze numerically the effects of three-body contact, and Coulomb interactions on the energy spectrum, the quantum and thermal noncondensate fraction of the system. We show that increasing the three-body contact and Coulomb interactions leads to the appearance of rotonization and condensate instability at stronger dipole-dipole interaction. Also we find that the temperature dependence of the thermal…
We demonstrate that the precessional frequencies of vortices in Bose Einstein condensates (BECs) are determined by a conservation law, and not by the lowest lying excitation energy mode. We determine the precessional frequency for a single off-axis vortex and vortex lattices in BECs using the continuity equation, and solve this self-consistently with the time-independent Hartree-Fock-Bogoliubov (HFB) equations in the rotating frame. We find agreement with zero temperature calculations (Bogoliubov approximation), and a smooth variation in the precession frequency as the temperature is increased…
We explore atom-laser-like transport processes of ultracold Bose-condensed atomic vapors in mesoscopic waveguide structures beyond the Gross-Pitaevskii mean-field theory. Based on a microscopic description of the transport process in the presence of a coherent source which models the outcoupling from a reservoir of perfectly Bose-Einstein condensed atoms, we derive a system of coupled quantum evolution equations that describe the dynamics of a dilute condensed Bose gas in the framework of the Hartree-Fock-Bogoliubov approximation. We apply this method to study the transport of dilute Bose gase…
We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields related to the normal and anomalous condensate densities. We derive the loop expansion of the effective action in the composite-field propagators. The lowest-order auxiliary field (LOAF) theory is a conserving mean-field approximation consistent with the Goldstone theorem without some of the difficulties plaguing approximations such as the Hartree and Popov approximations. LOAF predicts a second-order phase transition. We give a set of Feynman rules for improving results to any order in the loop expansion in terms of …
Bose atoms in optical lattices are considered at low temperatures and weak interactions, when Bose-Einstein condensate is formed. A self-consistent approach, based on the use of a representative statistical ensemble, is employed, ensuring a gapless spectrum of collective excitations and the validity of conservation laws. In order to show that the approach is applicable to both weak and tight binding, the problem is treated in the Bloch as well as in the Wannier representations. Both these ways result in similar expressions that are compared for the self-consistent Hartree-Fock-Bogolubov approx…
We systematically study the properties of dipolar Bose gases with two- and three-body contact interactions at finite temperature using the Hartree-Fock-Bogoliubov-Popov approximation. In uniform case, we obtain an exciting new extension of the seminal Lee-Huang-Yang corrected equation of state that depends explicitly on the thermal fluctuations and on the coupling constant of the three-body interaction. We investigate, on the other hand, the effects of thermal fluctuations on the occurrence and stability of a droplet state in a Bose-Einstein condensate with strong dipole-dipole interactions. W…
Using the time-dependent Hartree-Fock-Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings c…
We define a formalism of a self-consistent description of the ground state of a weakly interacting Bose system, accounting for higher order terms in expansion of energy in the diluteness parameter. The approach is designed to be applied to a Bose-Bose mixture in a regime of weak collapse where quantum fluctuations lead to stabilization of the system and formation of quantum liquid droplets. The approach is based on the Generalized Gross -- Pitaevskii equation accounting for quantum depletion and anomalous density terms. The equation is self-consistently coupled to modified Bogoliubov equations…
We investigate effects of three-body contact interactions on a trapped dipolar Bose gas at finite temperature using the Hartree-Fock-Bogoliubov approximation. We analyze numerically the behavior of the transition temperature and the condensed fraction. Effects of the three-body interactions, anomalous pair correlations and temperature on the collective modes are discussed.
We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a 3D speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorde…
We study the problem of disordered interacting bosons within grand-canonical thermodynamics and Bogoliubov theory. We compute the fractions of condensed and non-condensed particles and corrections to the compressibility and the speed of sound due to interaction and disorder. There are two small parameters, the disorder strength compared to the chemical potential and the dilute-gas parameter.
We formulate a self-consistent Hartree-Fock theory for a spin-1 Bose gas at finite temperature and apply it to characterizing the phase diagram. We find that spin coherence between thermal atoms in different magnetic sub-levels develops via coherent collisions with the condensed atoms, and is a crucial factor in determining the phase diagram. We develop analytical expressions to characterize the interaction and temperature dependent shifts of the phase boundaries.
Analytical expressions are given for the static structure factor S(k) and the pair correlation function g(r) for uniform ideal Bose-Einstein and Fermi-Dirac gases for all temperatures. In the vicinity of Bose Einstein condensation (BEC) temperature, g(r) becomes long ranged and remains so in the condensed phase. In the dilute gas limit, g(r) of bosons & fermions do not coincide with Maxwell-Boltzmann gas but exhibit bunching & anti-bunching effect respectively. The width of these functions depends on the temperature and is scaled as \surd (inverse atomic mass). Our numerical results provide th…
We investigate a dilute Fermi gas of polar molecules confined into a bilayer setup with dipole moments polarized perpendicular to the layers. In particular, we consider the extreme case of population imbalance, where we have only one particle in one layer and many particles in the other one. The single molecule is attracted by the dilute Fermi-gas through the inter-layer dipole-dipole force presenting an interesting impurity problem with longrange anistropic interaction. We calulate the chemical potential of the impurity, in second order perturbation theory and in ladder approximation with a B…
We study the Bose-condensed ground states of bosons in a two-dimensional optical lattice in the presence of frustration due to an effective vector potential, for example, due to lattice rotation. We use a mapping to a large-S frustrated magnet to study quantum fluctuations in the condensed state. Quantum effects are introduced by considering a 1/S expansion around the classical ground state. The large-S regime should be relevant to systems with many particles per site. As the system approaches the Mott insulating state, the hole density becomes small. Our large-S results show that, even when t…
We investigate the dimensionally induced phase transition from the normal to the Bose-Einstein-condensed phase for a weakly interacting Bose gas in an optical lattice. To this end we make use of the Hartree-Fock-Bogoliubov-Popov theory, where we include numerically exact hopping energies and effective interaction strengths. At first we determine the critical chemical potential, where we find a much better agreement with recent experimental data than a pure Hartree-Fock treatment. This finding is in agreement with the dominant role of quantum fluctuations in lower dimensions, as they are explic…
Once the critical temperature of a cosmological boson gas is less than the critical temperature, a Bose-Einstein Condensation process can always take place during the cosmic history of the universe. Zero temperature condensed dark matter can be described as a non-relativistic, Newtonian gravitational condensate, whose density and pressure are related by a barotropic equation of state, with barotropic index equal to one. In the present paper we analyze the effects of the finite dark matter temperature on the properties of the Bose-Einstein Condensed dark matter halos. We formulate the basic equ…
An easy-plane ferromagnetic insulator in a uniform external magnetic field and in contact with a phonon bath and a normal metal bath is studied theoretically in the presence of dc spin current injection via the spin Hall effect in the metal. The Keldysh path integral formalism is used to model the magnon gas driven into a nonequilibrium steady state by mismatched bath temperatures and/or electrical injection, and we analyze the magnon system in the normal (uncondensed) state, but close to the instability to Bose-Einstein condensation (BEC), within the self-consistent Hartree-Fock approximation…
Multiple phases occurring in a Bose gas with finite-range interaction are investigated. In the vicinity of the onset of Bose-Einstein condensation (BEC) the chemical potential and the pressure show a van-der-Waals like behavior indicating a first-order phase transition although there is no long-range attraction. Furthermore the equation of state becomes multivalued near the BEC transition. For a Hartree-Fock or Popov (Hartree-Fock-Bogoliubov) approximation such a multivalued region can be avoided by the Maxwell construction. For sufficiently weak interaction the multivalued region can also be …
We discuss fluctuations in a dilute two-dimensional Bose-condensed dipolar gas, which has a roton-maxon character of the excitation spectrum. We calculate the density-density correlation function, fluctuation corrections to the chemical potential, compressibility, and the normal (superfluid) fraction. It is shown that the presence of the roton strongly enhances fluctuations of the density, and we establish the validity criterion of the Bogoliubov approach. At T=0 the condensate depletion becomes significant if the roton minimum is sufficiently close to zero. At finite temperatures exceeding th…
The uniform electron gas or UEG (also known as jellium) is one of the most fundamental models in condensed-matter physics and the cornerstone of the most popular approximation --- the local-density approximation --- within density-functional theory. In this article, we provide a detailed review on the energetics of the UEG at high, intermediate and low densities, and in one, two and three dimensions. We also report the best quantum Monte Carlo and symmetry-broken Hartree-Fock calculations available in the literature for the UEG and discuss the phase diagrams of jellium.
