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The long-range and anisotropic nature of the dipolar interaction provides the so-called supersolid phases in Bose-Einstein condensates (BECs) in an optical lattice. However, in a certain area of dipole interaction parameters, BECs can form into a droplet. In this paper, in order to qualitatively understand the droplet formations, we propose a toy model that allows us to estimate the size and shape of droplets in dipolar Bose-Hubbard system in the optical lattice. We compare results of the toy model with numerical solutions of the mean-field calculation., 7 pages, 3 figures

The phase difference of the macroscopic wave function is a unique structure of the soliton in an atomic Bose--Einstein condensate (BEC). However, experiments on ultracold atoms so far have observed the valley of the density profile to study the dynamics of solitons. We propose a method to observe the phase difference of a soliton in a BEC by using an interference technique with Raman and rf pulses. We introduce a phase jump factor, which is an indicator to measure the phase difference between two points. It is demonstrated by using the projected Gross--Pitaevskii equation that an interference density ratio, the density ratio of two-component BECs after the Raman and rf pulses, reproduces the phase jump factor well. This technique will become an alternative method to study the decay and breakdown of a phase imprinted soliton in atomic BECs., Comment: 10 pages, 9 figures

We investigate dipole modes in a trapped Bose--Fermi mixture gas in the normal phase, composed of single-species bosons and single-species fermions with $s$-wave scattering. In the extremely low temperature regime, Bose--Einstein statistics and Fermi--Dirac statistics may give rise to an interesting temperature dependence of collective modes. Applying the moment method to the linearized Boltzmann equation, we study the transition of the dipole modes between the hydrodynamic regime and the collisionless regime., Comment: 8 pages, 1 figure

We study phase-imprinted solitons of ultracold bosons in an optical lattice with a harmonic trap, which shows the superfluid (SF) and Mott-insulator (MI) shell structures. The earlier study [Konstantin V. Krutitsky, J. Larson, and M. Lewenstein, Phys. Rev. A 82, 033618 (2010).] reported three types of phase-imprinted solitons in the Bose-Hubbard model: in-phase soliton, out-of-phase soliton, and wavelet. In this paper, we uncover the dynamical phase diagram of these phase-imprinted solitons, and find another type of the phase-imprinted soliton namely, the hybrid soliton. In the harmonically trapped system, the solitonic excitations created at the SF core cannot penetrate into the outer SF shell. This repulsion at the surface of the outer SF shell can be cured by inposing a repulsive potential at the center of the trap. These results can be interpreted as a kind of the impedance matching of excitations in BECs in terms of the effective chemical potentials or the local particle numbers in the shell, and the analogous results can be observed also in the sound wave created by the local single-shot pulse potential.

We study relaxation dynamics of dark soliton, created by a phase-imprinted method, in a two-dimensional trapped Bose-Einstein condensate at non-zero temperatures by using the projected Gross-Pitaevskii equation. At absolute zero temperature, a dark soliton is known to decay with a snake instability. At non-zero temperature, as we expected, we find that this snake instability cannot be clearly seen as in the absolute zero temperature case because of the presence of thermal fluctuations. However, we find that the decay rate, the half width of the overlap integral with respect to the phase-imprinted initial state, shows a power low decay as a function of the energy and finally remains a non-zero value., Comment: 5pages, 4figures

Dipole oscillation is studied in a normal phase of a trapped Bose--Fermi-mixture gas composed of single-species bosons and single-species fermions. Applying the moment method to the linearized Boltzmann equation, we derive a closed set of equations of motion for the center-of-mass position and momentum of both components. By solving the coupled equations, we reveal the behavior of dipole modes in the transition between the collisionless regime and the hydrodynamic regime. We find that two oscillating modes in the collisionless regime have distinct fates in the hydrodynamic regime: one collisionless mode shows a crossover to a hydrodynamic in-phase mode, and the other collisionless mode shows a transition to two purely damped modes. The temperature dependence of these dipole modes are also discussed., 10 pages, 5 figures

This paper discusses exact relations in Bose--Einstein condensates (BECs), starting from basic properties of an ideal Bose gas. In particular, focused on are the Hugenholtz--Pines relation, Nepomnyashchii--Nepomnyashchii identity, and identities for the density response function. After introducing these exact relations, a few approaches of many-body approximations are discussed, which satisfy the exact relations in BECs. This paper will serve as a bridge between theories on exact relations and those on approximations in BECs., 10 pages

Strong connection between the single-particle and collective excitations stands out as one of the features of Bose-Einstein condensates (BECs). We discuss theoretically these excitations of BECs focusing on the exact properties of the one-body and two-body Green's functions developed by Gavoret and Nozi\`eres. 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 Nozi\`eres, involving the subsequent results given by Nepomnyashchii and Nepomnyashchii, in terms of the matrix formalism representation. This 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 and density excitations 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 using 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 and collective excitations in the low-energy and low-momentum regime., Comment: 63 pages, 24 figures

We investigate collective excitations of density fluctuations and a dynamic density structure factor in a mixture of Bose and Fermi gases in a normal phase. With decreasing temperature, we find that the frequency of the collective excitation deviates from that of the hydrodynamic sound mode. Even at temperature much lower than the Fermi temperature, the collective mode frequency does not reach the collisionless limit analogous to zero sound in a Fermi gas, because of collisions between bosons and fermions.

We investigate multiparticle excitation effect on a collective density excitation as well as a single-particle excitation in a weakly interacting Bose--Einstein condensate (BEC). We find that although the weakly interacting BEC offers weak multiparticle excitation spectrum at low temperatures, this multiparticle excitation effect may not remain hidden, but emerges as bimodality in the density response function through the single-particle excitation. Identification of spectra in the BEC between the single-particle excitation and the density excitation is also assessed at nonzero temperatures, which has been known to be unique nature in the BEC at absolute zero temperature., 6 pages, 4 figures

The Hugenholtz-Pines (HP) theorem is derived for Bose-Einstein condensates (BECs) with internal degrees of freedom. The low-energy Ward-Takahashi identity is provided in the system with the linear and quadratic symmetry breaking terms. This identity serves to organize the HP theorem for multicomponent BECs, such as the binary BEC as well as the spin-$f$ spinor BEC in the presence of a magnetic field with broken U$(1)$$\times$SO$(3)$ symmetry. The experimental method based on the Stern-Gerlach experiment is proposed for studying the Ward-Takahashi identity., Comment: 14 pages, 1 figure

We study nonlinear mixing effects among quadrupole modes and scissors modes in a harmonically trapped Bose-Einstein condensate. Using a perturbative technique in conjunction with a variational approach with a Gaussian trial wave function for the Gross-Pitaevskii equation, we find that mode mixing selectively occurs. Our perturbative approach is useful in gaining qualitative understanding of the recent experiment [Yamazaki et al., J. Phys. Soc. Japan 84, 44001 (2015)], exhibiting a beating phenomenon of the scissors mode as well as a modulation phenomenon of the low-lying quadrupole mode by the high-lying quadrupole mode frequency. Within the second-order treatment of the nonlinear mode coupling terms, our approach predicts all the spectral peaks obtained by the numerical simulation of the Gross-Pitaevskii equation., Comment: 9pages, 5figures

We study mass and population imbalance effect on density (in-phase) and spin (out-of-phase) collective modes in a two-component normal Fermi gas. By calculating eigenmodes of the linearized Boltzmann equation as well as the density/spin dynamic structure factor, we show that mass and population imbalance effects offer a variety of collective mode crossover behaviors from collisionless to hydrodynamic regimes. The mass imbalance effect shifts the crossover regime to the higher-temperature, and a significant peak of the spin dynamic structure factor emerges only in the collisionless regime. This is in contrast to the case of mass and population balanced normal Fermi gases, where the spin dynamic response is always absent. Although the population imbalance effect does not shift the crossover regime, the spin dynamic structure factor survives both in the collisionless and hydrodynamic regimes., 9 pages, 6 figures

We study tunneling properties of collective excitations in spin-1 Bose-Einstein condensates. In the absence of magnetic fields, the total transmission in the long wavelength limit occurs in all kinds of excitations but the quadrupolar spin mode in the ferromagnetic state. The quadrupolar spin mode alone shows the total reflection. A difference between those excitations comes from whether the wavefunction of an excitation corresponds to that of the condensate in the long wavelength limit. The correspondence results in the total transmission as in the spinless BEC., Comment: 6 pages, 5 figures

We present a Green's function formalism for an interacting Bose-Einstein condensate (BEC) satisfying the two required conditions: (i) the infrared-divergent longitudinal susceptibility with respect to the BEC order parameter, and (ii) the Nepomnyashchii-Nepomnyashchii identity stating the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. These conditions cannot be described by the ordinary mean-field Bogoliubov theory, the many-body $T$-matrix theory, as well as the random-phase approximation with the vertex correction. In this paper, we show that these required conditions can be satisfied, when we divide many-body corrections into singular and non-singular parts, and separately treat them as different self-energy corrections. The resulting Green's function may be viewed as an extension of the Popov's hydrodynamic theory to the region at finite temperatures. Our results would be useful in constructing a consistent theory of BECs satisfying various required conditions, beyond the mean-field level., Comment: 31 pages, 9 figures

We study a stability criterion hypothesis for superfluids in terms of the the local density spectral function $I_n (r, \omega)$ applicable both to homogeneous and inhomogeneous systems. We evaluate the local density spectral function in the presence of a one-dimensional repulsive/attractive external potential within the Bogoliubov theory using solutions of the tunneling problem. We also evaluate the local density spectral function using an orthogonal basis, and calculate the autocorrelation function $C_n (r,t)$. When superfluids flow below a threshold, we find that in the $d$-dimensional system, $I_n (r, \omega) \propto \omega^{d}$ in the low-energy regime and $C_n (r, t) \propto 1/t^{d+1}$ in the long-time regime hold. When superfluids flow with the critical current, on the other hand, we find $I_n (r, \omega) \propto \omega^{\beta}$ in the low-energy regime and $C_n (r,t) \propto 1/t^{\beta+1}$ in the long-time regime with $\beta < d$. These results support the stability criterion hypothesis recently proposed., Comment: 18 pages, 10 figures

We investigate the tunneling properties of collective excitations through a domain wall in the ferromagnetic phase of a spin-1 spinor Bose--Einstein condensate. Within the mean-field theory at T=0, we show that the transverse spin wave undergoes perfect reflection in the low-energy limit. This reflection property differs considerably from that of a domain wall in a Heisenberg ferromagnet where spin-wave excitations exhibit perfect transmission at arbitrary energy. When the Bogoliubov mode is scattered from this domain wall soliton, the transmission and reflection coefficients exhibit pronounced non-monotonicity. In particular, we find perfect reflection of the Bogoliubov mode at energies where bound states appear. This is in stark contrast to the perfect transmission of the Bogoliubov mode with arbitrary energy through a dark soliton in a scalar Bose--Einstein condensate., Comment: 10 pages, 7 figures

We investigate tunneling properties of collective modes in the polar phase of a spin-1 spinor Bose-Einstein condensate. This spinor BEC state has two kinds of gapless modes, i.e., Bogoliubov mode and spin-wave. Within the framework of the mean-field theory at T=0, we show that these Goldstone modes exhibit the perfect transmission in the low-energy limit. Their anomalous tunneling behaviors still hold in the presence of superflow, except in the critical current state. In the critical current state, while the tunneling of Bogoliubov mode is accompanied by finite reflection, the spin-wave still exhibit the perfect transmission, unless the strengths of a spin-dependent and spin-independent interactions take the same value., 8 pages, 3 figures

We investigate tunneling properties of collective excitations in the ferromagnetic phase of a spin-1 spinor Bose-Einstein condensate (BEC). In addition to the Bogoliubov mode, this superfluid phase has two spin excitations, namely, the gapless transverse spin wave and the quadrupolar mode with a finite excitation gap. In the mean-field theory at T=0, we examine how these collective modes tunnel through a barrier potential that couples to the local density of particles. In the presence of supercurrent with a finite momentum $q$, while the Bogoliubov mode shows the so-called anomalous tunneling behavior (which is characterized by perfect transmission) in the low energy limit, the transverse spin-wave transmits perfectly only when the momentum $k$ of this mode coincides with $\pm q$. At $k=\pm q$, the wave function of this spin wave has the same form as the condensate wave function in the current carrying state, so that the mechanism of this perfect transmission is found to be the same as tunneling of supercurrent. Using this fact, the perfect transmission of the spin wave is proved for a generic barrier potential. We show that such perfect transmission does not occur in the quadrupolar mode. Further, we consider the effects of potentials breaking U(1) and spin rotation symmetries on the transmission properties of excitations. Our results would be useful for understanding excitation properties of spinor BECs, as well as the anomalous tunneling phenomenon in Bose superfluids., Comment: 28pages, 7figures

We investigate tunneling of excitations across a potential barrier separating two spin-1 Bose-Einstein condensates. Using the mean-field theory at the absolute zero temperature, we determine transmission coefficients of excitations in the saturated magnetization state and unsaturated magnetization states. All excitations except the quadrupolar spin mode in the saturated magnetization state show the anomalous tunneling phenomenon characterized as perfect tunneling in the low momentum limit through a potential barrier. The quadrupolar spin mode in the saturated magnetization state, whose spectrum is massive, shows total reflection. We discuss properties common between excitations showing the anomalous tunneling phenomenon. Excitations showing perfect tunneling have gapless spectrum in the absence of the magnetic field, and their wave functions in the low energy limit are the same as the condensate wave function., Comment: 45 pages, 16 figures

We present the simplest theory of perfect tunneling of an excitation in a Bose-Einstein condensate (BEC) through an impurity potential with an arbitrary shape in the low-momentum limit. That is for the transverse spin wave in the ferromagnetic phase of a spin-1 BEC. This mode obeys a Schr\"odinger-type equation; yet, effects of the potential on its transmission coefficient $T$ and on its scattering cross section $sigma$ vanish in that limit. The order parameter determines $T$, and the momentum $p$-dependence of $sigma$ exhibits a Rayleigh scattering type ($sigma propto p^{4}$). These properties are common between two types of Nambu-Goldstone modes: this spin wave and the Bogoliubov mode., Comment: 5 pages

On the basis of a moment method, general solutions of a linearized Boltzmann equation for a normal Fermi system are investigated. In particular, we study the sound velocities and damping rates as functions of the temperature and the coupling constant. In the extreme limits of collisionless and hydrodynamic regimes, eigenfrequency of sound mode obtained from the moment equations reproduces the well-known results of zero sound and first sound. In addition, the moment method can describe crossover between those extreme limits at finite temperatures. Solutions of the moment equations also involve a thermal diffusion mode. From solutions of these equations, we discuss excitation spectra corresponding to the particle-hole continuum as well as collective excitations. We also discuss a collective mode in a weak coupling case., 38 pages, 5 figures