We explore the collective excitations of optical lattices filled with two-species Bose-Einstein condensates (TBECs). We use a set of coupled discrete nonlinear Schrödinger equations to describe the system, and employ Hartree-Fock-Bogoliubov (HFB) theory with the Popov approximation to analyze the quasiparticle spectra at zero temperature. The ground state geometry, evolution of quasiparticle energies, structure of quasiparticle amplitudes, and dispersion relations are examined in detail. The trends observed are in stark contrast to the case of TBECs only with a harmonic confining potential. One key observation is the quasiparticle energies are softened as the system is tuned towards phase separation, but harden after phase separation and mode degeneracies are lifted.
We analyze the uniform system of weakly interacting bosonic gas undergoing periodic oscillation of interaction constant. This, within Bogoliubov approximation, leads to creation of atom pairs with well defined opposite velocities. We show how interaction between quasiparticles, omitted in the Bogoliubov approximation, significantly changes the atom pair creation process and properties of scattered atoms.
We present a detailed study of the spectrum and dispersion of Bogoliubov quasiparticles in two coupled elongated Bose-Einstein condensates. We develop an analytically solvable model that approximates two infinite homogeneous condensates and compare its predictions to a numerical simulation of a realistic trapped system. While the comparisons show a reasonable agreement between the two models, they also manifest the existence of several anomalous Bogoliubov modes in the spectrum. These modes show degeneracy in both energy and momentum together with self-localization in the coordinate space.
We study the effects of quasiparticle interactions in a quasi-two dimensional (quasi-2D), zero-temperature Bose-Einstein condensate of dipolar atoms, which can exhibit a roton-maxon feature in its quasiparticle spectrum. Our focus is the Beliaev damping process, in which a quasiparticle collides with the condensate and resonantly decays into a pair of quasiparticles. Remarkably, the rate for this process exhibits a highly non-trivial dependence on the quasiparticle momentum and the dipolar interaction strength. For weak interactions, the low energy phonons experience no damping, and the higher…
We develop a systematic perturbation theory for the quasiparticle properties of a single impurity immersed in a Bose-Einstein condensate. Analytical results are derived for the impurity energy, the effective mass, and residue to third order in the impurity-boson scattering length. The energy is shown to depend logarithmically on the scattering length to third order, whereas the residue and effective mass are given by analytical power series. When the boson-boson scattering length equals the boson-impurity scattering length, the energy has the same structure as that of a weakly interacting Bose…
Landau's description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics. It provides an accurate description of otherwise prohibitively complex many-body systems, and has led to the development of several key technologies. In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, so-called Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC). In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for t…
The Nambu-Goldstone (NG) mode in a Bose-Einstein condensate (BEC) transmits a potential barrier with probability 1 in the zero-energy limit, which is known as the anomalous tunneling. In this paper, we investigate the tunneling properties of quasiparticles in a dynamically unstable BEC. We prepare a multi-component BEC (binary and spin-1 BEC) in a dynamically unstable state and solve the tunneling problem of the spin-wave excitation from the condensate. We find that the perfect transmission occurs even when the BEC is dynamically unstable if the spin-wave is the NG mode. Here, the mode that ex…
We explore the topological transformation of quasi-2D Bose-Einstein condensates of dilute atomic gases, and changes in the low-energy quasiparticles associated with the geometry of the confining potential. In particular, we show the density profile of the condensate and quantum fluctuation follow the transition from a multiply to a simply connected geometry of the confining potential. The thermal fluctuations, in contrast, remain multiply connected. The genesis of the key difference lies in the structure of the low-energy quasiparticles. For which we use the Hartree-Fock-Bogoliubov, and study …
We study the collisional dynamics of multiple dark solitons in a Bose-Einstein condensate confined by a toroidal trap. We assume a tight enough confinement in the radial direction to prevent possible dissipative effects due to the presence of solitonic vortices. Analytical expressions for the initial order parameters with imprinted phases are utilized to generate different initial arrays of solitons, for which the time-dependent Gross-Pitaevskii equation is numerically solved. Given that the soliton velocity is conserved due to the lack of dissipation, we are able to apply a simple quasipartic…
We study the dynamics of Bogoliubov excitations of a Bose-Einstein condensate in the quasiperiodic kicked rotor. In the weakly interacting regime, the condensate is stable and both the condensate and the excitations undergo a phase transition from a quasilocalized to a diffusive regime. The corresponding critical exponents are identical for the condensate and the excitations, and compare very well with the value $ν\approx1.6$ for non-interacting particles.
Spontaneous Emergence of Phase Coherence in a quasiparticle Bose-Einstein Condensate
RPTU University Kaiserslautern-Landau（莱布尼茨技术大学凯泽斯劳滕-兰道）；University of Colorado Colorado Springs（科罗拉多大学科泉分校）；Fraunhofer Institute for Industrial Mathematics ITWM（弗劳恩霍夫工业数学研究所）
We study a two-species Bose-Einstein condensates confined in quasi-two-dimensional (quasi-2D) optical lattices at finite temperatures, employing the Hartree-Fock-Bogoliubov theory with the Popov approximation. We examine the role of thermal fluctuations on the ground-state density distributions, and the quasiparticle mode evolution. At zero temperature, the geometry of the ground-state in the immiscible domain is side-by-side. Our results show that the thermal fluctuations enhance the miscibility of the condensates, and at a characteristic temperature the system becomes miscible with rotationa…
We consider the propagation of quasiparticle excitations in a dipolar Bose-Einstein condensate, and derive a nonlocal field theory of quasiparticle scattering at a stepwise inhomogeneity of the sound speed, obtained by tuning the contact coupling part of the interaction on one side of the barrier. To solve this problem $ab$ $initio$, i.e., without prior assumptions on the form of the solutions, we reformulate the dipolar Bogoliubov-de Gennes equation as a singular integral equation. The latter is of a $novel$ $hypersingular$ type, in having a kernel which is hypersingular at only two isolated …
We study the condensate phase dynamics in a low-temperature equilibrium gas of weakly interacting bosons, harmonically trapped and isolated from the environment. We find that at long times, much longer than the collision time between Bogoliubov quasiparticles, the variance of the phase accumulated by the condensate grows with a ballistic term quadratic in time and a diffusive term affine in time. We give the corresponding analytical expressions in the limit of a large system, in the collisionless regime and in the ergodic approximation for the quasiparticle motion. When properly rescaled, they…
We have calculated low-lying quasiparticle excitation spectra of rotating three-dimensional Bose-Einstein condensates. As opposed to the prediction of hydrodynamic continuum theories, we find a minimum in the Tkachenko mode spectrum at intermediate rotation frequencies of the harmonic trap. Such a minimum can harbour a Tkachenko quasiparticle with zero excitation energy. We discuss the experimental signatures of such a zero mode.
We study an interacting spinless Bose-Einstein condensate to clarify theoretically whether the spectra of its quasiparticles (one-particle excitations) and collective modes (two-particle excitations) are identical, as concluded by Gavoret and Nozières [Ann. Phys. 28, 349 (1964)]. We derive analytic expressions for their first and second moments so as to extend the Bijl-Feynman formula for the peak of the collective-mode spectrum to its width (inverse lifetime) and also to the one-particle channel. The obtained formulas indicate that the width of the collective-mode spectrum manifestly vanishes…
A Bose gas in a double-well potential, exhibiting a true Bose-Einstein condensate (BEC) amplitude and initially performing Josephson oscillations, is a prototype of an isolated, non-equilibrium many-body system. We investigate the quasiparticle (QP) creation and thermalization dynamics of this system by solving the time-dependent Keldysh-Bogoliubov equations. We find avalanche-like QP creation due to a parametric resonance between BEC and QP oscillations, followed by slow, exponential relaxation to a thermal state at an elevated temperature, controlled by the initial excitation energy of the o…
We present a study for the dispersion relation and character of the excitations of a single and two component Bose Einstein Condensate (BEC). We study the single component dispersion for a finite BEC system and look at examples of quasiparticles to understand and characterize the dispersion relation. Next we present the dispersion relation for a two component BEC in both the miscible and immiscible parameter regimes. Then we present examples of the quasiparticles for both regimes.
We present a general theory for calculating the damping rate of elementary density wave excitations in a Bose-Einstein condensate strongly coupled to a single radiation field mode of an optical cavity. Thereby we give a detailed derivation of the huge resonant enhancement in the Beliaev damping of a density wave mode, predicted recently by Kónya et al., Phys.~Rev.~A 89, 051601(R) (2014). The given density-wave mode constitutes the polariton-like soft mode of the self-organization phase transition. The resonant enhancement takes place, both in the normal and ordered phases, outside the critical…
For most kinds of already known Bose-Einstein condensates experimental evidence for the existence of a macroscopic coherent quantum state has been provided, e.g., from the observation of interference phenomena, the formation vortices, the detection of Josephson effects, or even by the manifestation of superfluid behaviour. However, none of these hallmarks for a true, macroscopic phase-coherent state has ever been reported for any insulating spin system in a solid in which magnetic bosonic quasiparticles are thought to condense close to a quantum critical point. We describe an attempt to detect…
Heating induced by an oscillating modulation of the interaction strength in an atomic Fermion pair condensate is analyzed. The coupled fermion-boson model, generalized by incorporating a time-dependent intermode coupling through a magnetic Feshbach resonance, is applied. The dynamics is analytically characterized in a perturbative scheme. The results account for experimental findings which have uncovered a damped and delayed response of the condensate to the modulation. The delay is due to the variation of the quasiparticle energies and the subsequent relaxation of the condensate. The detected…
We study quasi-two-dimensional dipolar Bose-Einstein condensates, in which the Bogoliubov excitation spectrum displays, at sufficiently large gas density, a deep roton minimum due to the spatially anisotropic behavior of the dipolar two-body potential. A rapid quench, performed on the speed of sound of excitations propagating on the condensate background, leads to the dynamical Casimir effect, which can be characterized by measuring the density-density correlation function. It is shown, for both zero and finite initial temperatures, that the continuous-variable bipartite quantum state of the c…
Using two-photon Bragg spectroscopy, we study the energy of particle-like excitations in a strongly interacting homogeneous Bose-Einstein condensate, and observe dramatic deviations from Bogoliubov theory. In particular, at large scattering length $a$ the shift of the excitation resonance from the free-particle energy changes sign from positive to negative. For an excitation with wavenumber $q$, this sign change occurs at $a \approx 4/(πq)$, in agreement with the Feynman energy relation and the static structure factor expressed in terms of the two-body contact. For $a \gtrsim 3/q$ we also see …
We study the instability of a moving spinor Bose-Einstein condensate when the speed of flow reaches the critical velocity. This we identify on the basis of Landau's criterion, i.e. the velocity above which some elementary excitation energy becomes negative. We show that the first-to-become unstable excitations are spin-carrying quasiparticles. We also discuss the temperature dependence of the critical velocity in a more advanced mean-field approximation.
The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics. However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized. Here, we use radio frequency spectroscopy of ultracold bosonic $^{39}$K atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC. We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, …
We investigate the properties of a neutral impurity atom coupled with the Tkachenko modes of a two-dimensional vortex lattice Bose-Einstein condensate. In contrast with polarons in homogeneous condensates, the marginal impurity-boson interaction in the vortex lattice leads to infrared singularities in perturbation theory and to the breakdown of the quasiparticle picture in the low energy limit. These infrared singularities are interpreted in terms of a renormalization of the coupling constant, quasiparticle weight and effective impurity mass. The divergence of the effective mass in the low ene…
We characterise the properties of a vortex line in an elongated dipolar Bose-Einstein condensate. Increasing the strength of the dipole-dipole interactions (DDIs) relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes.
From a linear stability analysis of the Gross Pitaevskii equation for binary Bose Einstein condensates, it is found that the uniform state becomes unstable to a periodic perturbation of wave number k if k exceeds a critical value kc. However we find that a stationary spatially periodic state does not exist. We show the existence of pulse type solutions, when the pulse structure for one condensate is strongly influenced by the presence of the other condensate.
We investigate the properties a mobile ion immersed in a Bose-Einstein condensate (BEC) using different theoretical approaches. A coherent state variational ansatz predicts that the ion spectral function exhibits several branches in addition to polaronic quasiparticle states, and we employ a diagrammatic analysis of the ion-atom scattering in the BEC to identify them as arising from the binding of an increasing number of bosons to the ion. We develop a simplified model describing the formation of these molecular ions showing that their spectral weight scales with the number of bound atoms. The…
Using the time-dependent Bogoliubov approach, we study adiabaticity for a two-component Bose-Einstein condensate in a 3D time-dependent optical lattice with unit filling, in the superfluid and weakly interacting regime. We show that raising the lattice potential height can couple the ground state of the Bogoliubov Hamiltonian to excited states with two quasiparticles of opposite quasi-momenta. In the symmetric case for interactions and density in the two components these represent sound waves where the two components oscillate out of phase. We find an analytic expression of the adiabatic time,…
Recently, magnons, which are quasiparticles describing the collective motion of spins, were found to undergo Bose-Einstein condensation (BEC) at room temperature in films of Yttrium Iron Garnet (YIG). Unlike other quasiparticle BEC systems, this system has a spectrum with two degenerate minima, which makes it possible for the system to have two condensates in momentum space. Recent Brillouin Light scattering studies for a microwave-pumped YIG film of thickness d=5 $μ$m and field H=1 kOe find a low-contrast interference pattern at the characteristic wavevector $Q$ of the magnon energy minimum. …
Solid state quantum condensates often differ from previous examples of condensates (such as Helium, ultra-cold atomic gases, and superconductors) in that the quasiparticles condensing have relatively short lifetimes, and so as for lasers, external pumping is required to maintain a steady state. On the other hand, compared to lasers, the quasiparticles are generally more strongly interacting, and therefore better able to thermalise. This leads to questions of how to describe such non-equilibrium condensates, and their relation to equilibrium condensates and lasers. This chapter discusses in det…
We propose a feasible way of engineering Majorana-type quasiparticles in ultracold fermionic gases on a one-dimensional (1D) optical lattice. For this purpose, imbalanced ultracold atoms interacting by the spin-orbit coupling should be hybridized with a three-dimensional Bose-Einstein condensate (BEC) molecular cloud. By constraining the profile of an internal defect potential we show that the Majorana-type excitations can be created or annihilated. This process is modelled within the Bogoliubov-de Gennes approach. This study is relevant also to nanoscopic 1D superconductors where modification…
Recent experimental progress has produced Molecular Superfluids (MSF) in thermal equilibrium; this opens the door to a new class of experiments investigating the associated thermodynamic and dynamical responses. We review the theoretical picture of the phase diagram and quasiparticle spectrum in the Atomic Superfluid (ASF) and MSF phases. We further compute the parametric dependence of the quasiparticle lifetimes at one-loop order. In the MSF phase, the $U(1)$ particle number symmetry breaks to $\mathbb{Z}_2$ and the spectrum exhibits a gapless Goldstone mode in addition to a gapped $\mathbb{Z…
We study systematically the quantum corrections to a weakly interacting Bose-Einstein condensate with spin-orbit coupling. We show that quantum fluctuations, enhanced by the spin-orbit coupling, modify quantitatively the mean-field properties such as the superfluid density, spin polarizability, and sound velocity. We find that the phase boundary between the plane wave and zero momentum phases is shifted to a smaller transverse field. We also calculate the Beliaev and Landau damping rates and find that the Landau process dominates the quasiparticle decay even at low temperature.
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schroedinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.
We find a first order transition driven by the strength of non-equilibrium conditions of one-dimensional driven open condensates. Associated with this transition is a new stable non-equilibrium phase, space-time vortex turbulence, whose vortex density and quasiparticle distribution show strongly non-thermal behavior. Below the transition, we identify a new time scale associated with noise activated unbound space-time vortices, beyond which the temporal coherence function changes from a Kardar-Parisi-Zhang type subexponential to a disordered exponential decay. Experimental realization of the no…
We explore the formation and collective modes of Bose-Einstein condensate of Dirac magnons (Dirac BEC). While we focus on two-dimensional Dirac magnons, an employed approach is general and could be used to describe Bose-Einstein condensates with linear quasiparticle spectrum in various systems. By using a phenomenological multicomponent model of pumped boson population together with bosons residing at Dirac nodes, the formation and time evolution of condensates of Dirac bosons is investigated. The condensate coherence and its multicomponent nature are manifested in the Rabi oscillations whose …
Ferroelectricity in a magnon Bose-Einstein condensate: Nonreciprocal superfluidity, exceptional points, and Majorana bosons
The University of Osaka（大阪大学）；Kyoto University（京都大学）；Fukushima Medical University（福岛医科大学）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）
