Theory Of Bose-Einstein Condensation Research Articles

Bose–Einstein condensation theory for any integer spin: Approach based in noncommutative quantum mechanics

A Bose–Einstein condensation theory for any integer spin using noncommutative quantum mechanics methods is considered. The effective potential is derived as a multipolar expansion in the non-commutativity parameter [Formula: see text] and, at second order in [Formula: see text], our procedure yields to the standard dipole–dipole interaction with [Formula: see text] playing the role of the strength interaction parameter. The generalized Gross–Pitaevskii equation containing nonlocal dipolar contributions is found. For [Formula: see text] isotopes [Formula: see text] becomes [Formula: see text][Formula: see text][Formula: see text] and, thus for this value of [Formula: see text] one cannot distinguish interactions coming from non-commutativity or those of dynamical origin.

Thermodynamic properties in the extended BCS-Bose crossover theory

Superconductivity in a generalized Bose-Einstein condensation theory is addressed. This theory contains three coupled transcendental equations for all temperatures: two gap-like equations and a particle number density equation that guarantees charge conservation. Here we explore the special case of an extended BCS-Bose crossover picture as two-hole Cooper pairs are explicitly included. Using the dimensionless coupling parameter n/nf where n is the total electron number density and nf that of unpaired electrons at zero absolute temperature, we solved the three associated coupled equations yielding two pure Bose-Einstein-condensation phases of two-electron Cooper pairs and/or of two-hole Cooper pairs plus a mixed phase with varying proportions of both kinds of pairs. We find that the mere inclusion of two-hole Cooper pairs can lead to critical temperatures enhanced by several orders of magnitude compared with BCS theory. We also found a weak-intermediate and strong-coupling regimes. Afterwards, we calculated the entropy within the BCS-Bose crossover theory and from the numerical derivative of the entropy we analysed the rest of the well-known thermodynamic quantities that can be compared with experimental data. Results fit better for elemental superconductors, suggesting that two-hole Cooper pairs might be indispensable to describe this kind of materials.

Do we need a non-perturbative theory of Bose-Einstein condensation?

We recall the experimental data of one-dimensional axial propagation of sound near the center of the Bose-Einstein condensate cloud, which used the optical dipole force method of a focused laser beam and rapid sequencing of nondestructive phase-contrast images. We reanalyze these data within the general quantum fluid framework but without model-specific theoretical assumptions; using the standard best fit techniques. We demonstrate that some of their features cannot be explained by means of the perturbative two-body approximation and Gross-Pitaevskii model, and conjecture possible solutions.

Perturbation theory for Bose–Einstein condensates on bounded space domains

Bose–Einstein condensates (BECs), first predicted theoretically by Bose and Einstein and finally discovered experimentally in the 1990s, continue to motivate theoretical and experimental physics work. Although experiments on BECs are carried out in bounded space domains, theoretical work in the modelling of BECs often involves solving the Gross–Pitaevskii equation on unbounded domains, as the combination of bounded domains and spatial heterogeneity render most existing analytical approaches ineffective. Motivated by a lack of theory for BECs on bounded domains, we first derive a perturbation theory for both ground and excited stationary states on a given bounded space domain, allowing us to explore the role various forms of the self-interaction, external potential and space domain have on BECs. We are able to show that the shape and curvature of a space domain strongly influence BEC structure, and may be used as control mechanisms in experiments. We next derive a non-autonomous perturbation theory to predict BEC response to temporal changes in an external potential. In certain cases, our approach can be extended to unbounded domains, and we conclude by constructing a perturbation theory for bright solitons within external potentials on unbounded domains.

Strong connection between single-particle and density excitations in Bose–Einstein condensates

Strong connection between the single-particle excitation and the collective excitation stands out as one of the features of Bose–Einstein condensates (BECs). We discuss theoretically these single-particle and density excitations of BECs focusing on the exact properties of the one-body and two-body Green’s functions developed by Gavoret and Nozières. We also investigate these excitations by using the many-body approximation theory at nonzero temperatures. First, we revisited the earlier study presented by Gavoret and Nozières, involving the subsequent results given by Nepomnyashchii and Nepomnyashchii, in terms of the matrix formalism representation. This matrix formalism is an extension of the Nambu representation for the single-particle Green’s function of BECs to discuss the density and current response functions efficiently. We describe the exact low-energy properties of the correlation functions and the vertex functions, and discuss the correspondence of the spectra between the single-particle excitation and the density excitation in the low-energy and low-momentum limits at T = 0. After deriving the exact low-energy structures of the one-body and two-body Green’s functions, we develop a many-body approximation theory of BECs with making the use of the matrix formalism for describing the single-particle Green’s function and the density response function at nonzero temperatures. We show how the peaks of the single-particle spectral function and the density response function behave with an increasing temperature. Many-body effect on the single-particle spectral function and the density response function is included within a random phase approximation, where satellite structures emerge because of beyond-mean-field effects. Criticisms are also made on recent theories casting doubt upon the conventional wisdom of the BEC: the equivalence of the dispersion relations between the single-particle excitation and the collective excitation in the low-energy and low-momentum regime.

Theoretical Study and calculation The cold Reaction Rate of Deuteron Fusion In Nickel Metal Using Bose–Einstein Condensate Theory

In this paper, we focused on the investigated and studied the cold fusion reaction rate for D-D using the theory of Bose-Einstein condensation and depending on the quantum mechanics consideration. The quantum theory was based on the concept of single conventional of deuterons in Nickel-metal due to Bose-Einstein condensation, it has supplied a consistent description and explained of the experimental data. The analysis theory model has capable of explaining the physical behaviour of deuteron induced nuclear reactions in Nickel metals upon the five-star matter, it‘s the most expected for a quantitative predicted of the physical theory. Based on the Bose-Einstein condensation theorem formulation, we calculation the cold fusion reaction rate for D-D transfer to Nickel-metal using the astrophysical S factors (S = 110KeV — barn) for d(d,p)T, d(d, n)3He reactions and (S = 110 × 106 and S = 110 × 1013KeV — barn) for D + D × 4 He + 23.8MeV reaction. The results of the calculation for three reactions give rise a wide compatible with the other experimental works.

General theory of Bose-Einstein condensation applied to an ideal quantum gas of photons in an optical microcavity

This paper provides, firstly, a succinct mathematical derivation of Bose-Einstein condensation (BEC) of photons elaborating on previous results [M\"uller, E.E., Annals of Phys. 184, 219-230 (1988); M\"uller, E.E. Physica 139A, 165-174 (1986)] including new results on the condensate function, and, secondly, applies this framework to consistently explain experimental findings reported in Klaers J., Schmitt, J., Vewinger, F & Weitz, M., Nature 468, 545-548 (2010). The theoretical approach presented here invites to significantly widen the experimental framework for BEC of photons including three-dimensional photon resonators and thermalization mechanisms different from a dye medium in the cavity.

Entropy and heat capacity in the generalized Bose–Einstein condensation theory of superconductors

The new generalized Bose–Einstein condensation (GBEC) quantum-statistical theory starts from a noninteracting ternary boson-fermion (BF) gas of two-hole Cooper pairs (2hCPs) along with the usual two-electron Cooper pairs (2eCPs) plus unpaired electrons. Here we obtain the entropy and heat capacity and confirm once again that GBEC contains as a special case the Bardeen–Cooper–Schrieffer (BCS) theory. The energy gap is first calculated and compared with that of BCS theory for different values of a new dimensionless coupling parameter n/n[Formula: see text] where n is the total electron number density and n[Formula: see text] that of unpaired electrons at zero absolute temperature. Then, from the entropy, the heat capacity is calculated. Results compare well with elemental-superconductor data suggesting that 2hCPs are indispensable to describe superconductors (SCs).

Stationary states near the interface with anharmonic properties between linear and nonlinear defocusing media

We consider the nonlinear excitation near the thin layer with nonlinear properties separated linear and media with Kerr-type defocusing nonlinearity. The excitations are described by nonlinear Schrödinger equation with nonlinear potential. The problem is reduced to the solution of linear and nonlinear Schrödinger equations on half spaces with the nonlinear boundary conditions at the interface plane. We propose the generalization of two physical model to describe localized electron phase transition under the framework of Ginsburg-Landau theory and the excitons in a trap under the framework of Bose-Einstein condensation theory. We obtain and analyze the new type nonlinear excitations described by exact solutions of nonlinear Schrödinger equation satisfying the boundary conditions in wide energy range. We derive the energy of localized excitations in explicit form in the long-wave approximation. We calculate the spectral density of stationary states and find its peculiarities. The conditions of existence of localized states are found. The long wave nonlinear excitations can exist for the focusing and defocusing nonlinearity inside the interface.

Bose–Einstein Condensation and Superfluidity

This book on Bose–Einstein condensation (BEC) and superfluidity, is an extended version of the notable work by the pioneering researchers Sandro Stringari and Lev Pitaevskii, which first appeared in 2003. The first edition appeared to be a detailed version of a review paper ‘Theory of BEC in trapped gases’ that appeared in the Review of Modern Physics in 1999 by the same authors and their two other colleagues. Back in 2005, my research career started with this book and gave me a fresh feeling each time I went through it. It is one of the first books that appeared in the broad area of ultra-cold atoms and deals with the physics of both bosonic and fermionic atoms that are laser cooled to temperatures of the order of nano- or microkelvin.

Covariant theory of Bose-Einstein condensates in curved spacetimes with electromagnetic interactions: The hydrodynamic approach

We develop a hydrodynamic representation of the Klein-Gordon-Maxwell-Einstein equations. These equations combine quantum mechanics, electromagnetism, and general relativity. We consider the case of an arbitrary curved spacetime, the case of weak gravitational fields in a static or expanding background, and the nonrelativistic (Newtonian) limit. The Klein-Gordon-Maxwell-Einstein equations govern the evolution of a complex scalar field, possibly describing self-gravitating Bose-Einstein condensates, coupled to an electromagnetic field. They may find applications in the context of dark matter, boson stars, and neutron stars with a superfluid core.

Effective field theory of Bose-Einstein condensation ofαclusters and Nambu-Goldstone-Higgs states inC12

An effective field theory of $\alpha$ cluster condensation is formulated as a spontaneously broken symmetry in quantum field theory to understand the raison d'etre and nature of the Hoyle and $\alpha$ cluster states in $^{12}$C. The Nambu--Goldstone and Higgs mode operators in infinite systems are replaced with a pair of canonical operators whose Hamiltonian gives rise to discrete energy states in addition to the Bogoliubov--de Gennes excited states. The calculations reproduce well the experimental spectrum of the $\alpha$ cluster states. The existence of the Nambu--Goldstone--Higgs states is demonstrated and crucial. The $\gamma$ decay transitions are also obtained.

Bose–Einstein condensation in a vapor of sodium atoms in an electric field

Bose–Einstein condensation (BEC) at normal temperature (T=343K) has been observed because an electric field was first applied. There are two ways to achieve phase transition: lower the temperature of Bose gas or increase its density. This article provides more appropriate method: increase the voltage. In theory, 3s and 3p states of sodium are not degenerate, but Na may be polar atom doesnot conflict with quantum mechanics because it is hydrogen-like atom. Our innovation lies in we applied an electric field used for the orientation polarization. Na vapor was filled in a cylindrical capacitor. In order to determine the polarity of sodium, we measured the capacitance at different temperatures. If Na is non-polar atom, its capacitance should be independent of temperature because the nucleus of atom is located at the center of the electron cloud. But our experiment shows that its capacitance is related to temperature, so Na is polar atom. In order to achieve Na vapor phase transition, we measured the capacitance at different voltages. From the entropy of Na vapor S=0, the critical voltage Vc=68volts. When V<Vc, many atoms are in random orientation S>0; when V>Vc, the atoms become aligned with the field S<0, phase transition occurred. When V=390volts »Vc, the capacitance decreased from C=1.9C0 to C≈C0 (C0 is the vacuum capacitance), this result implies that almost all the Na atoms (more than 98%) are aligned with the field, Na vapor entered quasi-vacuum state. We create a BEC with 2.506×1017 atoms, condensate fraction reached 98.9%. This is BEC in momentum space. Our experiment shows that if a Bose gas enters quasi-vacuum state, this also means that it underwent phase transition and generates BEC. Therefore, quasi-vacuum state of alkali gas is essentially large-scale BEC. This is an unexpected discovery. BEC and vacuum theory are two unrelated research areas, but now they are closely linked together. The maximum induced dipole moment dind≤7.8×10−15ecm can be neglected. Ultra-low temperature is in order to make Bose gas phase transition, we achieve the phase transition by the critical voltage, so the ultra-low temperature is not necessary. According to the standard proposed by Ketterle, although we didn’t use laser cooling atoms, our experiment is real ideal BEC. Na material with purity 99.95% was supplied by Strem Chemicals Co., USA. Our experiments are easily repeated because low temperature is not necessary.

Hybrid Boltzmann–Gross-Pitaevskii theory of Bose-Einstein condensation and superfluidity in open driven-dissipative systems

We derive a theoretical model which describes Bose-Einstein condensation in an open driven-dissipative system. It includes external pumping of a thermal reservoir, finite lifetime of the condensed particles, and energy relaxation. The coupling between the reservoir and the condensate is described with semiclassical Boltzmann rates. This results in a dissipative term in the Gross-Pitaevskii equation for the condensate, which is proportional to the energy of the elementary excitations of the system. We analyze the main properties of a condensate described by this hybrid Boltzmann--Gross-Pitaevskii model, namely, dispersion of the elementary excitations, bogolon distribution function, first-order coherence, dynamic and energetic stability, and drag force created by a disorder potential. We find that the dispersion of the elementary excitations of a condensed state fulfills the Landau criterion of superfluidity. The condensate is dynamically and energetically stable as longs as it moves at a velocity smaller than the speed of excitations. First-order spatial coherence of the condensate is found to decay exponentially in one dimension and with a power law in two dimensions, similarly with the case of conservative systems. The coherence lengths are found to be longer due to the finite lifetime of the condensate excitations. We compare these properties with those of a condensate described by the popular ``diffusive'' models in which the dissipative term is proportional to the local condensate density. In the latter, the dispersion of excitations is diffusive which as soon as the condensate is put into motion implies finite mechanical friction and can lead to an energetic instability.

Bose-Einstein condensation of light: General theory

A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation describing the interaction between photons and dye molecules in the microcavity is derived and the equivalence between the hierarchical maximum entropy principle and the master equation approach is shown. The cases of a fixed mean total photon number and a fixed total excitation number are considered, and a much sharper, nonparabolic onset of a macroscopic Bose-Einstein condensation of light in the latter case is demonstrated. The theory does not use the grand canonical approximation, takes into account the photon polarization degeneracy, and exactly describes the microscopic, mesoscopic, and macroscopic Bose-Einstein condensation of light. Under certain conditions, it predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation takes place between the degrees of second-order coherence for these condensates. In the macroscopic case, there appear a sharp jump in the degrees of second-order coherence, a sharp jump and kink in the reduced standard deviations of the fluctuating numbers of photons in the polarized and whole condensates, and a sharp peak, a cusp, of the Mandel parameter for the whole condensate in the critical region. The possibility of nonclassical light generation in the microcavity with the photon Bose-Einstein condensate is predicted.

Theory of Bose-Einstein condensation of light in a microcavity

A theory of Bose-Einstein condensation (BEC) of light in a dye microcavity is developed. The photon polarization degeneracy and the interaction between dye molecules and photons in all of the cavity modes are taken into account. The theory goes beyond the grand canonical approximation and allows one to determine the statistical properties of the photon gas for all numbers of dye molecules and photons at all temperatures, thus describing the microscopic, mesoscopic, and macroscopic light BEC from a general perspective. A universal relation between the degrees of second-order coherence for the photon condensate and the polarized photon condensate is obtained. The photon Bose-Einstein condensate can be used as a new source of nonclassical light.

Bose-Einstein condensates in a ring-shaped trap with a nonlinear double-well potential

We develop the mean-field theory for Bose-Einstein condensates in a one-dimensional ring with two types of nonlinear double-well potentials, based on a pair of $\ensuremath{\delta}$ functions or Gaussian of a finite width, placed at diametrically opposite points. By analyzing the ground states (GSs) in these cases, we find a qualitative difference between them. With the Gaussian profile, the GS always undergoes the phase transition from the symmetric shape to an asymmetric one at a critical value of the norm. In contrast, the symmetry-breaking transition does not happen with the $\ensuremath{\delta}$-functional profile of the nonlinearity, and the GS always remains symmetric. In addition, the numerical analysis for the Gaussian profile demonstrates that the type of symmetry-breaking transition depends on the width of the nonlinear-potential well.

Exciton Condensation Under High Magnetic Field

The new results in the theory of Bose-Einstein condensation (BEC) of the two-dimensional (2D) magnetoexcitons formed by the high-density electron-hole (e-h) pairs created on the semiconductor mono-layer in a strong perpendicular magnetic field are reviewed. One of them is the metastable dielectric liquid phase (MDLP) formed by the 2D magnetoexcitons BEG-ed on the single-particle state with sufficiently large values of the wave vector k, so that its product kl with the magnetic length l equals about kl approximate to 3-4. This state was revealed in the conditions when the electrons and holes are situated on the lowest Landau levels (LLLs) and the polarizability of the Bose gas was calculated on the base of the Anderson-type coherent excited states. They give rise to correlation energy and to chemical potential displaying a nonmonotonous dependence on the filling factor v(2) with a relative minimum and with positive compressibility in its vicinity. The influence of the excited Landau levels (ELLs) on the quantum states of the e-h system is due to the virtual quantum transitions of particles from the LLLs to ELLs during the Coulomb scattering processes and to their subsequent return back. These quantum transitions were taken into account in the frame of the second order perturbation theory giving rise to an effective Hamiltonian describing the supplementary indirect interactions between the particles lying on the LLLs. This interaction is characterized by a small parameter equal to the ratio r of the magnetoexciton ionization potential l(ex)(0) to the Landau quantization energy (h) over bar omega(c). The parameter r = l(ex)(0)/(h) over bar omega(c), decreases as H-1/2 with the increasing the magnetic field strength H. The supplementary interaction is attractive, making the magnetoexcitons in the Hartree approximation more robust. Nevertheless its exchange, Fock terms as well as the Bogoliubov u-v transformation terms give rise to positive, repulsion-type contributions to the chemical potential. The Bose gas of magnetoexcitons with k = 0 becomes weakly nonideal when the ELLs are taken into account. The collective elementary excitations of two ground states corresponding to BEG-ed magnetoexcitons forming either a nonideal Bose gas with k = 0 or the MDLP with kl approximate to 3-4 were studied in the frame of the perturbation theory with the infinitesimal parameter v(2)(1 - v(2)), chosen as a product of the filling factor v(2) and of the phase space filling factor (1 - v(2)). The collective elementary excitations in both cases consist from the exciton and plasmon branches. Due to the presence of the condensate there are energy and quasi-energy branches. The self-energy parts containing the unknown frequency in denominators increase the degree of the dispersion equations and give rise to mixed exciton-plasmon and exciton-exciton elementary excitation branches.

Bose–Einstein condensation of magnons in polycrystalline gadolinium with nano-sizegrains

We report the observation of Bose–Einstein condensation (BEC) of magnons in nanocrystallineGd. Employing a self-consistent approach, the variations with magnetic field (H) of the BEC transitiontemperature, Tc(H),and the volume, V (H), over which the condensate wavefunction retains its phase coherence,the temperature and magnetic field variations of the chemical potential,μ(T, H), and the average occupation number for the ground state,⟨n0(T, H)⟩, are accurately determined from the magnetization,M(T, H), and specific heat,C(T, H), data. Thevariation of Tc with magnetic field has the functional formTc(H) = Tc(H = 0) + aH2/3 that is characteristic of BEC. In conformity with the predictions of BEC theory (i) forT ≤ Tc, the condensatefraction ⟨n0(T, H)⟩/⟨n0(T = 1.8 K, H)⟩ at constantH scales with the reducedtemperature as [T/Tc(H)]3/2, (ii) in the limit , for T ≤ Tc and abruptly falls to large negative values as the temperature exceedsTc, and (iii) the magnetic-field-induced change in magnon entropy, deduced from bothM(T, H) andC(T, H), followsthe T3/2 power law at low temperatures and goes through a peak at .

Auxiliary field formalism for dilute fermionic atom gases with tunable interactions

We develop the auxiliary field formalism corresponding to a dilute system of spin-1/2 fermions. This theory represents the Fermi counterpart of the BEC theory developed recently by F. Cooper et al. [Phys. Rev. Lett. 105, 240402 (2010)] to describe a dilute gas of Bose particles. Assuming tunable interactions, this formalism is appropriate for the study of the crossover from the regime of Bardeen-Cooper-Schriffer (BCS) pairing to the regime of Bose-Einstein condensation (BEC) in ultracold fermionic atom gases. We show that when applied to the Fermi case at zero temperature, the leading-order auxiliary field (LOAF) approximation gives the same equations as those obtained in the standard BCS variational picture. At finite temperature, LOAF leads to the theory discussed by by Sa de Melo, Randeria, and Engelbrecht [Phys. Rev. Lett. 71, 3202(1993); Phys. Rev. B 55, 15153(1997)]. As such, LOAF provides a unified framework to study the interacting Fermi gas. The mean-field results discussed here can be systematically improved upon by calculating the one-particle irreducible (1-PI) action corrections, order by order.