M. Khodas, M. Pustilnik, A. Kamenev, L. I. Glazman
We show that the dynamic structure factor of a one-dimensional Bose liquid has a power-law singularity defining the main mode of collective excitations. Using the Lieb-Liniger model, we evaluate the corresponding exponent as a function of the wave vector and the interaction strength.
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We study the properties of coreless vortices(skyrmion) in spinor Bose-Einstein condensate. We find that this excitation is always energetically unstable, it always decays to an uniform spin texture. We obtain the skyrmion energy as a function of its size and position, a key quantity in understanding the decay process. We also point out that the decay rate of a skyrmion with high winding number will be slower. The interaction between skyrmions and other excitation modes are also discussed.
The Ramsey fringes formation during the excitation of topological coherent modes of a Bose-Einstein condensate by an external modulating field is considered. The Ramsey fringes appear when a series of pulses of the excitation field is applied. In both Rabi and Ramsey interrogations, there is a shift of the population maximum transfer due to the strong non-linearity present in the system. It is found that the Ramsey pattern itself retains information about the accumulated relative phase between both ground and excited coherent modes.
A new approach developed by A. Shanenko [Phys. Lett. A 227 (1997) 367] for investigating the spatial boson correlations at low temperatures is considered in the particular case of the Coulomb interaction potential. This approach is based on integro-differential equations for the radial distribution function and can be used beyond the weak coupling regime.
The distinction between a classical liquid and a classical ordered solid is easy and depends on their different symmetries. The distinction between a classical glass and a classical liquid is more difficult, since the glass is also disordered. The difference is in the fact that a glass is frozen while the liquid is not. In this article an equilibrium measure is suggested that distinguishes between a glass and a liquid. The choice of this measure is based on the idea that in a system which is not frozen symmetry under permutation of particles is physically relevant, because particles can be per…
Realistic scenario can be represented by general canonical ensemble way better than the ideal one, with proper parameter sets involved. We study the Bose-Einstein condensation phenomena of liquid helium within the framework of Tsallis statistics. With a comparatively high value of the deformation parameter $q(\sim 1.4)$, the theoretically calculated value of the critical temperature($T_c$) of the phase transition of liquid helium is found to agree with the experimentally determined value ($T_c = 2.17~\rm{K}$), although they differs from each other for $q=1$ (undeformed scenario). This throws a…
Bose-Einstein condensation of the excitons in graphene is considered. We suggested the model spinor equation for neutral particles with short range interaction described the microscopic graphene excitons dynamic. Using this equation we derived quantum hydrodynamic equations for description of collective properties of excitons in graphene, particularly for the case when excitons being in the Bose-Einstein condensate (BEC) state. The dispersion of collective excitations in graphene excitons BEC is studied. We shown that frequency of collective excitations is proportional to the square root of th…
A phenomenological criterion for the superfluid transition is proposed, which is similar to the Lindemann criterion for the crystal melting. Then we derive a new formula for the critical temperature, relating $T_λ$ to the mean kinetic energy per particle above the transition. The suppression of the critical temperature in a sufficiently dense liquid is described as a result of the quantum decoherence phenomenon. The theory can account for the observed dependence of $T_λ$ on density in liquid helium and results in an estimate $T_λ \sim 1.1$ K for molecular hydrogen.
On the basis of gauge invariance, it is proven in an elementary and straightforward manner, but without invoking any {\it ad hoc} assumption, that the existence of off-diagonal long-range order in one-particle reduced density matrix in Bose liquids implies both the irrotational flow in a simply connected region and the quantization of circulation in a multiply connected region, the two fundamental properties of a Bose superfluid. The origin for both is the phase coherence of condensate wave-functions. Some relevant issues are also addressed.
General theory in case of homogenous Bose-Einstein condensed systems with spinor condensate is presented for the correlation functions of density and spin fluctuations and for the one-particle propagators as well. The random phase approximation is investigated and the damping of the modes is given in the intermediate temperature region. It is shown that the collective and the one-particle excitation spectra do not coincide fully.
We study emptiness formation probability (EFP) in interacting 1D Bose liquids. That is the probability that a snapshot of its ground state reveals exactly zero number of particles within the interval $|x|<R$. For a weakly interacting liquid there is parametrically wide regime $n^{-1} < R <ξ$ (here $n$ is the average density and $ξ$ is the healing length), where EFP exhibits a non-trivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [A. Abanov, 2004] to study quantitative details of these regime and compare it with previously reported limited cases.
We develop a theory to describe the damping of elementary excitations of a Bose-condensed gas in the hydrodynamic regime for the thermal cloud. We discuss second sound in a spatially homogeneous gas and the lowest excitations of a trapped condensate.
Gas-liquid condensation (GLC) in an attractive Bose gas is studied on the basis of statistical mechanics. Using some results in combinatorial mathematics, the following are derived: (1) With decreasing temperature, the Bose-statistical coherence grows in the many-body wave function, which gives rise to the divergence of the grand partition function prior to Bose-Einstein condensation. It is a quantum-mechanical analogue to the GLC in a classical gas (quantum GLC). (2) This GLC is triggered by the bosons with zero momentum. Compared with the classical GLC, an incomparably weaker attractive forc…
Pair wave functions (PWF) which are eigenfunctions of the reduced density 2-matrix are considered for a homogeneous Bose liquid. With the Bogoliubov principle of the correlation weakening it is proved that the distribution of the "dissociated" pair states over momenta is exactly the product of the single-particle distribution functions. Thus, the "dissociated" pair states are naturally classified as condensate-condensate, condensate-supracondensate and supracondensate-supracondensate ones provided the Bose-Einstein condensate exists. The condensate-condensate as well as condensate-supracondens…
We study the Bose-Einstein condensate in the MIT double-well trap. We calculate the ground state density profile of $^{23}$Na atoms and the Bogoliubov spectrum of the elementary excitations as function of the strength of the double-well barrier. In particular, we analyze the behavior of quantum-mechanical collective excitations. Finally, we discuss the observability criteria for macroscopic quantum tunneling and macroscopic quantum self-trapping.
We have studied the collective excitation of Bose-Einstein condensate of short range weak interacting atoms with spin-orbit coupling (SOC) in two dimension in liquid phase. In our study, we have included Rashba, Dresselhaus SOC as well as Raman SOC. The study of Bogoliubov excitation shows that in small interaction case only phonon modes are present and for higher interactions roton modes start to appear. Energy spectra contain two roton modes in the system relatively strong interacting atomic system.
It is found that combining an excitation-energy sum rule with Fetter's trial wave function gives almost exact low-lying collective-mode frequencies of a trapped Bose-Einstein condensate at zero temperature.
We have studied excitation spectrum of the specfic 2D model of strongly interacting Bose particles via mapping of the many-body Schrodinger equation in imaginary time to the classical stochastic dynamics. In a broad range of coupling strength $α$ a roton-like spectrum is found, with the roton gap being extremely small in natural units. A single quantum phase transition between strongly correlated supefluid and quantum Berezinsky crystal is found.
We present precision neutron scattering measurements of the Bose-Einstein condensate fraction, n0(T), and the atomic momentum distribution, n\star(k), of liquid 4He at pressure p =24 bar. Both the temperature dependence of n0(T) and of the width of n\star(k) are determined. The n0(T) can be represented by n0(T) = n0(0)[1-(T/Tλ)γ] with a small n0(0) = 2.80\pm0.20% and large γ = 13\pm2 for T < Tλ indicating strong interaction. The onset of BEC is accompanied by a significant narrowing of the n\star(k). The narrowing accounts for 65% of the drop in kinetic energy below Tλ and reveals an important…
The model recently proposed by A.A. Shanenko [Phys. Lett. A 227 (1997) 367] is used to derive linear integro-differential equations whose solutions provide reasonable estimates for the momentum distribution and condensate fraction in interacting many-boson system at zero temperature. An advantage of these equations is that they can be employed in the weak coupling regime and beyond. As an example, analytical treatment of the weak coupling case is given.
We investigate collective excitations of an atomic Bose-Einstein condensate in a recently discovered regime [D.O'Dell et al., Phys. Rev. Lett. 84, 5687 (2000)] of a balance between electromagnetically induced $1/r$ attraction and a short-range interatomic repulsion. The corresponding frequencies for monopole, dipole, and quadrupole modes are calculated numerically in the zero temperature case.
Surface modes in a Bose-Einstein condensate of sodium atoms have been studied. We observed excitations of standing and rotating quadrupolar and octopolar modes. The modes were excited with high spatial and temporal resolution using the optical dipole force of a rapidly scanning laser beam. This novel technique is very flexible and should be useful for the study of rotating Bose-Einstein condensates and vortices.
We study the energies and decay of elementary excitations in weakly interacting Bose-Einstein condensates within a finite-temperature gapless second-order theory. The energy shifts for the high-lying collective modes turn out to be systematically negative compared with the Hartree-Fock-Bogoliubov-Popov approximation and the decay of the low-lying modes is found to exhibit collapse and revival effects. In addition, perturbation theory is used to qualitatively explain the experimentally observed Beliaev decay process of the scissors mode.
A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-deGennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, is extremely efficient in our implementation with parallel FFT methods, and produces highly accurate results. The method is suitable for general …
Starting from the Bogoliubov diagonalization for the Hamiltonian of a weakly interacting Bose gas under the presence of a Bose-Enstein Condensate, we derive the kinetic equation for the Bogoliubov excitations. Without dropping any of the commutators, we find three collisional processes. One of them describes the $1\leftrightarrow2$ interactions between the condensate and the excited atoms. The other two describe the $2\leftrightarrow2$ and $1\leftrightarrow3$ interactions between the excited atoms themselves.
Interference experiments with independent condensates provide a powerful tool for analyzing correlation functions. Scaling of the average fringe contrast with the system size is determined by the two-point correlation function and can be used to study the Luttinger liquid liquid behavior in one-dimensional systems and to observe the Kosterlitz-Thouless transition in two-dimensional quasicondensates. Additionally, higher moments of the fringe contrast can be used to determine the higher order correlation functions. In this article we focus on interference experiments with one-dimensional Bose l…
We discuss a sympathetic cooling strategy that can successfully mitigate fermion-hole heating in a dilute atomic Fermi-Bose mixture and access the temperature regime in which the fermions behave as a Fermi liquid. We introduce an energy-based formalism to describe the temperature dynamics with which we study a specific and promising mixture composed of 6Li and 87Rb. Analyzing the harmonically trapped mixture, we find that the favourable features of this mixture are further enhanced by using different trapping frequencies for the two species.
The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this theory fails in dimensions d less than or equal to 2, and we propose the appropriate low-dimensional modifications. For d=1 we analyze density profiles in confining potentials, superfluid properties, solitons, and self-similar solutions.
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…
Model of the degenerated weakly non-ideal Bose gas is considered without suggestion on C-number representation of the creation and annihilation operators with zero momentum. The "density-density" correlation function and the one-particle Green function are calculated on basis of the suggestion about C-number representation of the operator of particle density in the Bose condensate. It is shown, that the pole in the "density-density" Green function determines the Bogolyubov's spectrum of the collective excitations, which have the phonon-roton form. At the same time the spectrum of the one-parti…
The $ν$-component two-dimensional (2D) Bose liquid is considered. It is shown that the finite temperature phase transition exists in this 2D continuously degenerate multicomponent system. The new type of quasi-long-range order occurs as a result of this transition. The correlation function in ordered state is a product of the power-law XY-universality class type function and the exponential function corresponding to the $SU(ν)$ invariant model. The transition temperature is calculated for the diluted system. It is found that the physical mechanism of the phase transition is changed when $ν$ ex…
An appropriate, time-dependent modification of the trapping potential may be sufficient to create effectively collective excitations in a cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions and should allow the creation of both dark solitons and vortices.
Properties of the weakly non-ideal Bose gas are considered without suggestion on C-number representation of the creation and annihilation operators with zero momentum. The "density-density" correlation function and the one-particle Green function of the degenerated Bose gas are calculated on the basis of the self-consistent Hartree-Fock approximation. It is shown that the spectrum of the one-particle excitations possesses a gap whose value is connected with the density of particles in the "condensate". At the same time, the pole in the "density-density" Green function determines the phonon-rot…
It is shown that by an appropriate modification of the trapping potential one may create collective excitation in cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions. It seems to be feasible experimentally --- it requires only a proper change in time of the potential in atomic traps, as realized in laboratories already.
Excitation spectrum and momentum distribution of the ionic Bose-Hubbard model
该研究用标准基算符方法计算离子玻色-哈伯德模型的激发谱和动量分布，发现超固体和近边界电荷密度波相在区域角点有动量峰，且可由空穴模式的谱权重解释。
Recent progress in the field of ultracold gases has allowed the creation of phase-segregated Bose-Fermi systems. We present a theoretical study of their collective excitations at zero temperature. As the fraction of fermion to boson particle number increases, the collective mode frequencies take values between those for a fully bosonic and those for a fully fermionic cloud, with damping in the intermediate region. This damping is caused by fermions which are resonantly driven at the interface.
We discuss the tunneling of phonon excitations across a potential barrier separating two condensate bulks. It is shown that the strong barrier proves to be transparent for the excitations at low energy $ε$. Moreover, the transmission is reduced with increasing $ε$ in contrast to the standard dependence. This anomalous behavior is due to an existence of the quasiresonance interaction. The origin of this interaction is a result of the formation of the special well determined by the density distribution of condensate in the vicinity of a high barrier.
Using path integral Monte Carlo we simulate a 3D system of up to 1000 magnetic flux lines by mapping it onto a system of interacting bosons in (2+1)D. With increasing temperature we find a first order melting of flux lines from an ordered solid to an entangled liquid signalled by a finite entropy jump and sharp discontinuities in the defect density and the structure factor $S({\bf G})$ at the first reciprocal lattice vector. In the presence of a small number of strong columnar pins, we find that the crystal is transformed into a Bose glass phase with patches of crystalline order nucleated arou…
Attractive Solution of Binary Bose Mixtures: Liquid-Vapor Coexistence and Critical Point
本文用路径积分蒙特卡洛方法研究吸引性二元玻色混合物的液-汽共存与临界行为，揭示密度跃变处玻色-爱因斯坦凝聚的不连续发生，并指出该现象可在陷阱实验中被观测。
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