Bo-Bo Wei Chen-Ning Yang
The wave function of a dilute hard sphere Bose gas at low temperatures is discussed, emphasizing the formation of pairs. The pair distribution function is calculated for two values of $\sqrt{ρa^3}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
A mistake of the effective interaction between D-dimensional Bose atoms [arXiv:cond-mat/0503523] that was published by Physical Review B in 2006 is corrected.
We investigate the properties of a dilute boson-fermion mixture at zero temperature. The ground-state energy of the system is calculated to second order in the Bose-Fermi coupling constant. The Green's function formalism is applied to obtain results for the effect of Bose-Fermi interactions on the spectrum of phonon excitations, the momentum distribution, the condensate fraction and the superfluid density of the bosonic component. A quantitative discussion of these effects is presented in the case of mixtures with attractive interspecies interaction.
A ground state energy density of an interacting dilute Bose gas system is studied in the canonical transformation scheme. It is shown that the transformation scheme enables us to calculate a higher order correction of order $n a^3$ in the particle depletion and ground state energy density of a dilute Bose gas system, which corresponds to the density fluctuation contribution from the excited states. The coefficient of $n a^3$ term is shown to be $2(π- 8/3)$ for the particle depletion, and $16(π- 8/3)$ for the ground state energy density.
The Bogoliubov approximation and the Gross-Pitaevskii equation characterize the effect of repulsive interactions on a dilute ideal Bose-Einstein gas in a spherical harmonic trap. For large $N$, the interactions expand the condensate relative to an ideal Bose gas; both the speed of sound and critical angular velocity $Ω_{c1}$ for creation of a quantized vortex depend crucially on the interparticle repulsion through the coherence length $ξ$.
A dilute Bose gas system is studied using the functional Schrödinger picture theory. The ground state properties are obtained by solving the infinite dimensional Schrödinger equation variationally. It is shown that a shifted Gaussian trial wavefunctional enables us to calculate a higher order correction, which corresponds to the fluctuation contribution from the condensate. The obtained term is compared with the quantum correction arising from the low energy $3 \to 3$ scattering.
The low-lying hydrodynamic normal modes of a dilute Bose-Einstein gas in an isotropic harmonic trap determine the corresponding Bogoliubov amplitudes. In the Thomas-Fermi limit, these modes have large low-temperature occupation numbers, and they permit an explicit construction of the dynamic structure function $S(q,ω)$. The total noncondensate number $N'(0)$ at zero temperature increases like $R^6$, where $R$ is the condensate radius measured in units of the oscillator length. The lowest dipole modes are constructed explicitly in the Bogoliubov approximation.
We have observed a superfluid gyroscope effect in a dilute gas Bose-Einstein condensate. A condensate with a vortex possesses a single quantum of angular momentum and this causes the plane of oscillation of the scissors mode to precess around the vortex line. We have measured the precession rate of the scissors oscillation. From this we deduced the angular momentum associated with the vortex line and found a value close to $\hbar$ per particle, as predicted for a superfluid.
The recent observation [Oosawa et al. J. Phys. : Condens. Matter {\bf 11}, 265 (1999)] of the field-induced Néel ordering in a spin-gap magnetic compound TlCuCl$_3$ is interpreted as a Bose-Einstein Condensation of magnons. A mean-field calculation based on this picture is shown to describe well the temperature dependence of the magnetization. The present system opens a new area for studying Bose-Einstein condensation of thermodynamically large number of particles in a grand-canonical ensemble.
The modified Bogoliubov model where the primordial interaction is replaced by the t matrix is reinvestigated. It is shown to provide a negative value of the kinetic energy for a strongly interacting dilute Bose gas, contrary to the original Bogoliubov model. To clear up the origin of this failure, the correct values of the kinetic and interaction energies of a dilute Bose gas are calculated. It is demonstrated that both the problem of the negative kinetic energy and the ultraviolet divergence, dating back to the well-known paper of Lee, Yang and Huang, is connected with an inadequate picture o…
This set of four lectures reviews various aspects of the theory of a dilute low-temperature trapped Bose gas, starting with (I) a review of the Bogoliubov description of the elementary excitations in a uniform system. The treatment is then generalized (II) to include the new physical effects of a confining harmonic trap potential on the condensate and its normal modes. An equivalent hydrodynamic description (III) focuses directly on the density and velocity fluctuations. The physics of vortices (IV) in an incompressible fluid is summarized and extended to the case of a trapped Bose condensate.
We show that the shift in the transition temperature of the dilute homogeneous Bose gas is non-analytic in the scattering amplitude, $a$. The first correction beyond the positive linear shift in $a$ is negative and of order $a^2\ln a$. This non-universal non-analytic structure indicates how the discrepancies between numerical calculations at finite $a$ can be reconciled with calculations of the limit $a \to0$, since the linearity is apparent only for anomalously small $a$.
We solve the Gross-Pitaevskii equation to model the behaviour of a weakly-interacting Bose condensate. Solutions are presented for the eigenstates in one- and two-dimensional harmonic traps. We include the effect of gravity and coupling to a second condensate to simulate an output coupler for Bose condensed atoms, and find that the output pulse shape is in qualitative agreement with experiment. We also model flow under gravity through a constriction, demonstrating excitation and separation of eigenmodes in the condensate.
The ground state energy for a dilute hard "sphere" Bose gas in various dimensions is studied theoretically.
A recently developed local-density current functional formalism for confined Bose-condensed superfluids requires visco-elastic spectra which are defined through a finite-frequency extension of the dissipative coefficients entering the linearized hydrodynamic equations of the two-fluid model. We evaluate these spectra for a superfluid with contact interactions in the collisionless regime at finite temperature, by working to first order beyond the Bogolubov approximation. We find that within this approximation all the visco-elastic spectra take the same value aside from simple multiplicative fac…
We show that the critical temperature of a uniform dilute Bose gas must increase linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.
We propose an optical method for increasing the number of atoms in a pair of dilute gas Bose-Einstein condensates. The method uses laser-driven Raman transitions which scatter atoms between the condensate and non-condensate atom fractions. For a range of condensate phase differences there is destructive quantum interference of the amplitudes for scattering atoms out of the condensates. Because the total atom scattering rate into the condensates is unaffected the condensates grow. This mechanism is analogous to that responsible for optical lasing without inversion. Growth using macroscopic quan…
The fluctuations of a number of particles in the Bose-Einstein condensate are studied in the grand canonical ensemble with an effective single-mode Hamiltonian, which is derived from an assumption that the mode corresponding to the Bose-Einstein condensate does not asymptotically correlate with other modes. The fluctuations are evaluated in the dilute limit with a proposed simple method, which is beyond the mean-field approximation. The accuracy of the latter is estimated; it is shown that the mean-field scheme does not work for the single-mode Hamiltonian, while for the Hartree Hamiltonian it…
The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values $x\sim 0.001$. The condensate fraction in 2D is also computed and found generally l…
We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared divergences and cannot directly determine the transition temperature in the thermodynamic limit. However, in conjunction with finite size scaling, perturbation theory provides a powerful calculation tool. We implement it here to estimate a shift in the transition temperature in the canonical ensemble consistent with grand canonical calculations.
The condensate fraction of a homogeneous and dilute Bose gas is expanded as a power series of $\sqrt{n a^3}$ as $N_0/N = 1 -c_1 (n a^3)^{1/2} -c_2 (n a^3) - c_3 (n a^3)^{3/2}\hdots.$ The coefficient $c_1$ is well-known as $8/3 \sqrtπ$, but the others are unknown yet. Considering two-body contact interactions and applying a canonical transformation method twice we developed the method to obtain the higher order coefficients analytically. An iteration method is applied to make up a cutoff in a fluctuation term. The coefficients ares $c_2=2(π- 8/3)$ and $c_3=(4/\sqrtπ) (π-8/3)(10/3-π)$.
The phase transition temperature of the homogeneous and dilute Bose gas in D-dimensions ($2 \le D \le 3$) is calculated by a mean field-based statistical method. The shift of the phase transition temperature is written up to the leading order as $ΔT_c/T_c^0 = c \gam^{\al}$, where $\gam=n^{1/3}a$. We derived Huang's result of the phase transition temperature in the generalized dimensions. We show that $ c(D)$ is positive and $\al(D)=2(D/2-1)^2$ in the short-wavelength range. The origin of the difference between $\al=1/2$ and $\al=1$ at D=3 is discussed. The $T_c$ at D=2 is calculated in the sam…
The well-known results concerning a dilute Bose gas with the short-range repulsive interaction should be reconsidered due to a thermodynamic inconsistency of the method being basic to much of the present understanding of this subject. The aim of our paper is to propose a new way of treating the dilute Bose gas with an arbitrary strong interaction. Using the reduced density matrix of the second order and a variational procedure, this way allows us to escape the inconsistency mentioned and operate with singular potentials of the Lennard-Jones type. The derived expansion of the condensate depleti…
In the framework of mean-field approximation the dynamics of Bose-Einstein condensates can be described by the hydrodynamic-like equations. These equations are analyzed here with account of mutual interaction between condensate and non-condensate atoms. The Lagrange invariants and freezing-in invariants of such a system have been found. This allows to get some necessary conditions for creation of an atom laser with controlled parameters of the beam. Particularly, the atom laser beam can carry quite well defined angular momentum. This can be practically realized in the most simple case, when th…
We derive, through analysis of the structure of diagrammatic perturbation theory, the scaling behavior of the condensate and superfluid mass density of a dilute Bose gas just below the condensation transition. Sufficiently below the critical temperature, $T_c$, the system is governed by the mean field (Bogoliubov) description of the particle excitations. Close to $T_c$, however, mean field breaks down and the system undergoes a second order phase transition, rather than the first order transition predicted in Bogoliubov theory. Both condensation and superfluidity occur at the same critical tem…
We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features of the vortex states, and its predictions agree well with available experimental results. We discuss various properties of a single vortex, including its structure, energy, dynamics, normal modes and stability, as well as vortex arrays. When the nonuniform condensate contains a vortex, the excitation spectrum includes unstable (``anomalous'') mode(s) with ne…
We consider a mixture of a single-component Bose gas and a two-component Fermi gas at temperatures where the Bose gas is almost fully condensed. In such a mixture, two fermionic atoms can interact with each other by exchanging a phonon that propagates through the Bose condensate. We calculate the interaction potential due to this mechanism and determine the effective s-wave scattering length for two fermions that interact, both directly by the interatomic potentials, as well as by the above mentioned exchange mechanism. We find that the effective scattering length is quite sensitive to changes…
The Bogoliubov theory of weakly interacting bosons is generalized to Bose-Einstein condensates with internal degrees of freedom so that a single effective Hamiltonian produces various many-body ground states or metastable spin domains and the corresponding collective modes on an equal footing.
The Nambu-Goldstone mode, associated with vortex nucleation in a harmonically confined, two-dimensional dilute Bose-Einstein condensate, is identified with the lowest-lying envelope of octupole-mode branches, which are separated from each other by the admixture of quadrupolar excitations. As the vortex approaches the center of the condensate and the system's axisymmetry is restored, the Nambu-Goldstone mode becomes massive due to its coupling to higher rotational bands.
This article surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and Bose-Einstein condensation is not expected to be realized. Nevertheless, first experimental indications supporting the formation of the condensate in low dimensional systems have been recently obtained. This unexpected behaviour appears to be due to the non-uniformity, introduced into a system by the e…
A survey is given of the present state of the art in studying Bose-Einstein condensation of dilute atomic gases. The bulk of attention is focused on the principal theoretical problems, though the related experiments are also mentioned. Both uniform and nonuniform trapped gases are considered. Existing theoretical contradictions are critically analysed. A correct understanding of the principal theoretical problems is necessary for gaining a more penetrating insight into experiments with trapped atoms and for their proper interpretation.
Considering a moving vortex line in a dilute atomic Bose-Einstein condensate within time-dependent Hartree-Fock-Bogoliubov-Popov theory, we derive a criterion for the quasiparticle excitations to follow the vortex core rigidly. The assumption of adiabaticity, which is crucial for the validity of the stationary self-consistent theories in describing such time-dependent phenomena, is shown to imply a stringent criterion for the velocity of the vortex line. Furthermore, this condition is shown to be violated in the recent vortex precession experiments.
The surface mode spectrum is computed self-consistently for dilute Bose-Einstein condensates, providing the temperature dependence of the surface mode induced vortex nucleation frequency. Both the thermodynamic critical frequency for vortex stability and the nucleation frequency implied by the surface excitations increase as the critical condensation temperature is approached from below. The multipolarity of the destabilizing surface excitation decreases with increasing temperature. The computed finite-temperature critical frequencies support the experimental observations and the zero-temperat…
We compute the structure of a quantized vortex line in a harmonically trapped dilute atomic Bose-Einstein condensate using the Popov version of the Hartree-Fock-Bogoliubov mean-field theory. The vortex is shown to be (meta)stable in a nonrotating trap even in the zero-temperature limit, thus confirming that weak particle interactions induce the condensed gas a fundamental property characterizing ``classical'' superfluids. We present the structure of the vortex at ultralow temperatures and discuss the crucial effect of the thermal gas component to its energetic stability.
We compute the critical temperature of Bose-Einstein condensation in dilute three-dimensional homogeneous Bose gases. Our method involves the models of spatial permutations and it should be exact to lowest order in the scattering length of the particle interactions. We find that the change in the critical temperature is proportional to a rho^{1/3} with constant c = -2.33; this contradicts the current consensus among physicists.
In terms of the s-wave phase shift of the two-body scattering at thermal wavelength, a systematic perturbative expansion of the virial coefficients is developed for a two-dimensional dilute system of bosons in its gaseous phase at low temperature. The thermodynamic functions are calculated to the second order of the expansion parameter. The observability of the universal low energy limit of the two-dimensional phase shift with a quasi-two dimensional atomic gas in an anisotropic trap is discussed.
Multiply quantized vortices in trapped Bose-Einstein condensates are studied using the Bogoliubov theory. Suitable combinations of a localized pinning potential and external rotation of the system are found to energetically stabilize, both locally and globally, vortices with multiple circulation quanta. We present a phase diagram for stable multiply quantized vortices in terms of the angular rotation frequency and the width of the pinning potential. We argue that multiquantum vortices could be experimentally created using these two expedients.
The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schroedinger equation; the condensation is 100% into the state that minimizes the Gross-Pitaevskii energy functional. This is the first rigorous proof of BEC in a physically realistic, continuum model.
For some time, the theoretical result for the transition temperature of a dilute three-dimensional Bose gas in an arbitrarily wide harmonic trap has been known to first order in the interaction strength. We extend that result to second order. The first-order result for a gas trapped in a harmonic potential can be computed in mean field theory (in contrast to the first order result for a uniform gas, which cannot). We show that, at second order, perturbation theory suffices for relating the transition temperature to the chemical potential at the transition, but the chemical potential is non-per…
We develop a diagrammatic perturbation treatment to calculate the zero-temperature equation of state of the dilute gas mixture of a single spin component Bose-Einstein condensate (BEC) and a normal Fermi gas of indistinguishable (single spin) fermion particles. We find that the mean-field description breaks down near the mechanical instability related to the phase separation phenomenon. Our analysis shows that the instability is caused by the competition of the usual short-range and fermion-mediated boson-boson interactions, which result in a boson compressibility that diverges. In the low BEC…
We study the dynamical phase diagram of a dilute Bose-Einstein condensate (BEC) trapped in a periodic potential. The dynamics is governed by a discrete non-linear Schrödinger equation: intrinsically localized excitations, including discrete solitons and breathers, can be created even if the BEC's interatomic potential is repulsive. Furthermore, we analyze the Anderson-Kasevich experiment [Science 282, 1686 (1998)], pointing out that mean field effects lead to a coherent destruction of the interwell Bloch oscillations.
Baym, Blaizot, and Zinn-Justin have recently used the large N approximation to calculate the effect of interactions on the transition temperature of dilute Bose gases. We extend their calculation to next-to-leading-order in 1/N and find a relatively small correction of -26% to the leading-order result. This suggests that the large N approximation works surprisingly well in this application.
We investigate the behavior of a dilute quasi two-dimensional, harmonically confined, weakly interacting Bose gas within the finite-temperature Thomas-Fermi approximation. We find that the thermodynamic properties of the system are markedly different for repulsive and attractive interactions. Specifically, in contrast to the repulsive case, there appears to be a phase transition when the atoms interact with an attractive pseudo-potential, in the sense that there is no self-consistent solution for the normal ground state below a certain temperature $T^{\star}$. These numerical findings are supp…
It was recently shown (A. Bulgac. Phys. Rev. Lett. {\bf 89}, 050402 (2002)) that an entirely new class of quantum liquids with widely tunable properties could be manufactured from bosons (boselets), fermions (fermilets) and their mixtures (ferbolets) by controlling their interaction properties by the means of a Feshbach resonance. We extend the previous mean--field analysis of these quantum liquids by computing the lowest order quantum corrections to the ground state energy and the depletion of the Bose--Einstein condensate and by estimating higher order corrections as well. We show that the q…
We calculate a force due to zero-temperature quantum fluctuations on a stationary object in a moving superfluid flow. We model the object by a localized potential varying only in the flow direction and model the flow by a three-dimensional weakly interacting Bose-Einstein condensate at zero temperature. We show that this force exists for any arbitrarily small flow velocity and discuss the implications for the stability of superfluid flow.
A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density $ρ$ and temperature $T$. In the dilute regime, i.e., when $a^3ρ\ll 1$, where $a$ denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term $4πa (2ρ^2 - [ρ-ρ_c]_+^2)$. Here, $ρ_c(T)$ denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and $[ ]_+$ denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critic…
We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a^2 ρis small and the temperature T satisfies T > 4 πρ/ \ln |\ln(a^2ρ). Here, a is the scattering length of the repulsive interaction potential and ρis the density. To leading order in a^2 ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when ΔT_c / T_c^0 > 5 \sqrt{a ρ^{1/3}}, where T_c^0 is the critical temperature of the ideal gas. While this condition is not expected to be sharp, it g…
We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $ρ$ and inverse temperature $β$ differs from the one of the non-interacting system by the correction term $4 πρ^2 |\ln a^2 ρ|^{-1} (2 - [1 - β_{\mathrm{c}}/β]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\cdot]_+ = \max\{ 0, \cdot \}$ and $β_{\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^2ρ\ll 1$ and if $βρ\gtr…
A dilute two-dimensional (2D) Bose gas at zero temperature is studied by the method developed earlier by the authors. Low density expansions are derived for the chemical potential, ground state energy, kinetic and interaction energies. The expansion parameter is found to be a dimensionless in-medium scattering amplitude u obeying the equation 1/u+\ln u=-\ln(na^2π)-2γ, where na^2 and γare the gas parameter and the Euler constant, respectively. It is shown that the ground state energy is mostly kinetic in the low density limit; this result does not depend on a specific form of the pairwise inter…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。