We evaluate the relaxation rate of high-energy quasiparticles in a weakly interacting one-dimensional Bose gas. Unlike in higher dimensions, the rate is a nonmonotonic function of temperature, with a maximum at the crossover to the state of suppressed density fluctuations. At the maximum, the relaxation rate may significantly exceed its zero-temperature value. We also find the dependence of the differential inelastic scattering rate on the transferred energy. This rate yields information about temperature dependence of local pair correlations.
We analyze the excitation spectrum of a three-dimensional(3D) Bose-Fermi mixture with tunable resonant interaction parameters and high hyperfine spin multiplets. We focus on a 3-particle vertex describing fermionic and bosonic atoms which can scatter to create fermionic molecules or disassociate. For a single molecular level, in analogy to the single magnetic impurity problem we argue that the low lying excitations of the mean-field theory are described by the Fermi liquid picture with a quasiparticle weight and charge which is justified by a $1/N_ψ$ expansion, expected to be exact in the limi…
The peculiarities in the Bose-Einstein condensation of particles and quasiparticles are discussed. The difference between the condensation of conserved and unconserved particles is analyzed. A classification of quasiparticles is given. The emphasis is made on the ability of particles and quasiparticles to condense. Illustrations include: general Bose-condensed atomic systems, such as ensembles of trapped atoms, Bose gases with conserved and unconserved number of atoms, vibrating atoms in double-well lattices, Holstein-Primakoff magnons, Schwinger bosons, slave bosons, and the condensation of s…
We consider decay of a quasiparticle in a nearly-one-dimensional quasicondensate of trapped atoms, where virtual excitations of transverse modes break down one-dimensionality and integrability, giving rise to effective three-body elastic collisions. We calculate the matrix element for the process that involves one incoming quasiparticle and three outgoing quasiparticles. Scattering that involves low-frequency modes with high thermal population results in a diffusive dynamics of a bunch of quasiparticles created in the system.
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 perform a simulation of the experiment [1] where the temporal modification of the effective one dimensional interaction constant was used to create pairs of atoms with opposite velocities. The simulations clearly demonstrate huge impact of interaction between quasiparticles due to finite temperature on the pair production process, explaining relatively small atom pair production and the absence of the number squeezing in the experiment.
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 late-time relaxation following a quench in a driven-dissipative quantum many-body system. We consider the open Dicke model, describing the infinite-range interactions between $N$ atoms and a single, lossy electromagnetic mode. We show that the dynamical phase transition at a critical atom-light coupling is characterized by the interplay between reservoir-driven and intrinsic relaxation processes. Above the critical coupling, small fluctuations in the occupation of the dominant quasiparticle-mode start to grow in time while the quasiparticle lifetime remains finite due to losses. N…
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 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…
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…
Considering a two-dimensional Bose-Hubbard spinor lattice with weak nearest neighbour interactions and no particle transfer between sites, we theoretically study the transport of energy from one initially excited dimer, to the rest of the lattice. Beyond a critical interaction strength, low energy on-site excitations are quickly dispersed throughout the array, while stronger excitations are self trapped, resulting in localized energy breathers and solitons. These structures are quasiparticle analogues to the discrete 2D solitons in photonic lattices. Full many-body simulations additionally dem…
We study the relaxation of excitations in a system of one-dimensional weakly interacting bosons. Due to residual weak interactions, Bogoliubov quasiparticles in this system have finite lifetimes. As a result of the conservation laws in one dimension, at zero temperature the leading mechanism of decay of a quasiparticle is disintegration into three others. We focus on phonon quasiparticles and find that their decay rate is proportional to the seventh power of momentum. In the integrable case of contact interaction between the bosons, the decay rate vanishes.
We study the decay of Bogoliubov quasiparticles in one-dimensional Bose gases. Starting from the hydrodynamic Hamiltonian, we develop a microscopic theory that enables one to systematically study both the excitations and their decay. At zero temperature, the leading mechanism of decay of a quasiparticle is disintegration into three others. We find that low-energy quasiparticles (phonons) decay with the rate that scales with the seventh power of momentum, whereas the rate of decay of the high-energy quasiparticles does not depend on momentum. In addition, our approach allows us to study analyti…
We use a momentum-space hole-burning technique implemented via stimulated Raman transitions to measure the momentum relaxation time for a gas of bosonic atoms trapped in an optical lattice. By changing the lattice potential depth, we observe a smooth crossover between relaxation times larger and smaller than the bandwidth. The latter condition violates the Mott-Ioffe-Regal bound and indicates a breakdown of the quasi-particle picture. We produce a simple kinetic model that quantitatively predicts these relaxation times. Finally, we introduce a cooling technique based upon our hole-burning tech…
In a one-dimensional weakly interacting Bose-Fermi mixture one branch of elementary excitations is well described by the Bogoliubov spectrum. Here we use the microscopic theory to study the decay of such quasiparticle excitations. The main scattering process which leads to their decay is the backscattering of a Bogoliubov quasiparticle off the Fermi sea, where a particle-hole pair is excited. For a low-momentum quasiparticle (phonon) of momentum $q$, we find that the decay rate scales as $q^3$ provided $q$ is smaller than the Fermi momentum $k_F$, while in the opposite case the decay behaves a…
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 …
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 study the properties of Bose polarons in two dimensions using quantum Monte Carlo techniques. Results for the binding energy, the effective mass, and the quasiparticle residue are reported for a typical strength of interactions in the gas and for a wide range of impurity-gas coupling strengths. A lower and an upper branch of the quasiparticle exist. The lower branch corresponds to an attractive polaron and spans from the regime of weak coupling where the impurity acts as a small density perturbation of the surrounding medium to deep bound states which involve many particles from the bath an…
The Bose polaron has attracted theoretical and experimental interest because the mobile impurity is surrounded by a bath that undergoes a superfluid-to-normal phase transition. Although many theoretical works have studied this system in its ground state, only few analyze its behavior at finite temperature. We have studied the effect of temperature on a Bose polaron system performing ab-initio Path Integral Monte Carlo simulations. This method is able to approach the critical temperature without losing accuracy, in contrast with perturbative approximations. We have calculated the polaron energy…
We investigate experimentally and theoretically the dynamical properties of a Mott insulator in decoupled one-dimensional chains. Using a theoretical analysis of the Bragg excitation scheme we show that the spectrum of inter-band transitions holds information on the single-particle Green's function of the insulator. In particular the existence of particle-hole coherence due to quantum fluctuations in the Mott state is clearly seen in the Bragg spectra and quantified. Finally we propose a scheme to directly measure the full, momentum resolved spectral function as obtained in angle-resolved phot…
The temperature dependence of a mobile impurity in a dilute Bose gas, the Bose polaron, is investigated for wide a range of impurity-bath interactions. Using a diagrammatic resummation scheme designed to include scattering processes important at finite temperature $T$, we show that the phase transition of the environment to a Bose-Einstein condensate at the critical temperature $T_c$ leads to several non-trivial effects. The attractive polaron present at $T=0$ fragments into two quasiparticle states for finite temperature whenever $|a|\gtrsim a_B$, with $a$ and $a_B$ the impurity-boson and bos…
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 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 the Anderson localization of Bogoliubov quasiparticles (elementary many-body excitations) in a weakly interacting Bose gas of chemical potential $μ$ subjected to a disordered potential $V$. We introduce a general mapping (valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov-de Gennes equations onto a single-particle Schrödinger-like equation with an effective potential. For disordered potentials, the Schrödinger-like equation accounts for the scattering and localization properties of the Bogoliubov quasiparticles. We derive analytically the localization lengths …
The emergence of quasiparticles in strongly interacting matter represents one of the cornerstones of modern physics. However, when different phases of matter compete near a quantum critical point, the very existence of quasiparticles comes under question. Here we create Bose polarons near quantum criticality by immersing atomic impurities in a Bose-Einstein condensate (BEC) with near-resonant interactions. Using locally-resolved radiofrequency spectroscopy, we probe the energy, spectral width, and short-range correlations of the impurities as a function of temperature. Far below the superfluid…
The properties of a Bose polaron immersed in a dilute two-dimensional medium at finite temperatures are discussed. Assuming that the impurity is weakly-coupled to the bath particles we have perturbatively calculated the polaron energy, effective mass, quasiparticle residue and damping rate. The parameters of impurity spectrum are found to be well-defined in the whole temperature region whereas the pole structure of the impurity Green's function is visible only at absolute zero. At any finite temperatures the quasiparticle residue is logarithmically divergent signalling of the branch-cut behavi…
We study the relaxation dynamics of quantum turbulence in a two-component Bose-Einstein condensate containing half-quantum vortices. We find a temporal scaling regime for the number of vortices and the correlation lengths that at early times is strongly dependent on the relative strength of the inter-species interaction. At later times we find that the scaling becomes universal, independent of the inter-species interaction, and approaches that numerically observed in a scalar Bose-Einstein condensate.
We present a theory describing the lambda transition and the Bose-Einstein condensation (BEC) in a liquid ${\rm ^4He}$ based on the diatomic quasiparticle concept. It is shown that in liquid ${\rm ^4He}$ for the temperature region $1~{\rm K}\leq{\rm T}\leq {\rm T}_λ$ the diatomic quasiparticles macroscopically populate the ground state which leads to BEC in liquid ${\rm ^4He}$. The approach yields the lambda transition temperature as ${\rm T}_λ=2.16~{\rm K}$ which is in excellent agreement with the experimental lambda temperature ${\rm T}_λ=2.17~{\rm K}$. The concept of diatomic quasiparticles…
We numerically examine slow and hierarchical relaxation dynamics of interacting bosons described by a tilted two-band Bose-Hubbard model. The system is found to exhibit signatures of quantum chaos within the spectrum and the validity of the eigenstate thermalization hypothesis for relevant physical observables is demonstrated for certain parameter regimes. Using the truncated Wigner representation in the semiclassical limit of the system, dynamics of relevant observables reveal hierarchical relaxation and the appearance of prethermalized states is studied from the perspective of statistics of …
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…
Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $ \mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $ \mathcal{G}^{22}$ and $ \mathcal{G}^{12}$. In this work, we show that the third collision integral $ \mathcal{G}^…
In this work we study the time evolution of soft core bosons on a one-dimensional lattice, where the particles are initially quenched into a atomic density wave. At time $t=0$ the particles are released from the quench and can evolve under the dynamics of a soft-core Bose-Hubbard Hamiltonian on a lattice including a confining trap.
We consider a simple realization of an event horizon in the flow of a one-dimensional two-component Bose-Einstein condensate. Such a condensate has two types of quasiparticles; In the system we study, one corresponds to density fluctuations and the other to polarization fluctuations. We treat the case where a horizon occurs only for one type of quasiparticles (the polarization ones). We study the one- and two-body signal associated to the analog of spontaneous Hawking radiation and demonstrate by explicit computation that it consists only in the emission of polarization waves. We discuss the e…
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 spin-dependent heat transport in quantum gases, focusing on transport phenomena related to pure spin currents and spin-dependent temperatures. Using the Boltzmann equation, we compute the coupled spin and heat transport coefficients as a function of temperature and interaction strength for energy dependent $s$-wave scattering. We address the issue of whether spin-dependent temperatures can be sustained on a time and length scale relevant for experiments by computing the spin-heat relaxation time and diffusion length. We find that the time scale for spin-heat relaxation time diverges a…
The disordered Bose-Hubbard model in two dimensions at non-integer filling admits a superfluid to Bose-glass transition at weak disorder. Less understood are the properties of this system at strong disorder and energy densities corresponding to excited states. In this work we study the Bose-glass transition of the ground state and the related finite energy localization transition, the mobility edge of the quasiparticle spectrum, a critical energy separating extended from localized quasiparticle excitations. To study these the fluctuation operator expansion is used. The level spacing statistics…
We study elementary excitations of a system of one-dimensional bosons with weak contact repulsion. We show that the Gross-Pitaevskii regime, in which the excitations are the well-known Bogoliubov quasiparticles and dark solitons, does not extend to the low energy limit. Instead, the spectra of both excitations have finite curvatures at zero momentum, in agreement with the phenomenological picture of fermionic quasiparticles. We describe analytically the crossover between the Gross-Pitaevskii and the low-energy regimes, and discuss implications of our results for the behavior of the dynamic str…
In this work we report preliminary results on the relaxational dynamics of one dimensional Bose gases, as described by the Lieb-Liniger model, upon release from a parabolic trap. We explore the effects of integrability and integrability breaking upon these dynamics by placing the gas post-release in an integrability breaking one-body cosine potential of variable amplitude. By studying the post-quench evolution of the conserved charges that would exist in the purely integrable limit, we begin to quantify the effects of the weak breaking of integrability on the long time thermalization of the ga…
The interaction between a mobile quantum impurity and a bosonic bath leads to the formation of quasiparticles, termed Bose polarons. The elementary properties of Bose polarons, such as their mutual interactions, can differ drastically from those of the bare impurities. Here, we explore Bose polaron physics in a two-dimensional nonequilibrium setting by injecting $σ^-$ polarised exciton-polariton impurities into a bath of coherent $σ^+$ polarised polaritons generated by resonant laser excitation of monolayer MoSe$_2$ embedded in an optical cavity. By exploiting a biexciton Feshbach resonance be…
The concept of quantum plasmonic excitations in plasmonic lattices, which similarly to Frenkel excitons in molecular crystals propagate by hopping from one nanoparticle to another, is introduced. A consistent quantum theory of such plasmonic excitons, beginning with the quantization of localized surface plasmons in a metal nanoparticle and including the radiative relaxation in both 1D and 2D lattices near a reflective substrate surface, is developed. A possible room-temperature Bose-Einstein condensation in the quantum gas of plasmonic excitons is also discussed.
We construct the hydrodynamic theory for spin 1/2 Bose gases at arbitrary temperatures. This theory describes the coupling between the magnetization, and the normal and superfluid components of the gas. In particular, our theory contains the geometric forces on the particles that arise from their spin's adiabatic following of the magnetization texture. The phenomenological parameters of the hydrodynamic theory are calculated in the Bogoliubov approximation and using the Boltzmann equation in the relaxation-time approximation. We consider the topological Hall effect due to the presence of a sky…
We consider an impurity immersed in a Bose-Einstein condensate with tunable boson-impurity interactions. Such a Bose polaron has recently been predicted to exhibit an intriguing energy spectrum at finite temperature, where the ground-state quasiparticle evenly splits into two branches as the temperature is increased from zero [Guenther et al., Phys. Rev. Lett. 120, 050405 (2018)]. To investigate this theoretical prediction, we employ a recently developed variational approach that systematically includes multi-body correlations between the impurity and the finite-temperature medium, thus allowi…
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）
The dynamics of a weakly interacting Bose gas at low temperatures is close to integrable due to the approximate quadratic nature of the many-body Hamiltonian. While the short-time physics after an abrupt ramp of the interaction constant is dominated by the integrable dynamics, integrability is broken at longer times by higher-order interaction terms in the Bogoliubov Hamiltonian, in particular by Beliaev-Landau scatterings involving three quasiparticles. The two-stage relaxation process is highlighted in the evolution of local observables such as the density-density correlation function: a dep…
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…
Decay of a high-energy double occupancy state, doublon, in a narrow-band lattice requires creation of a coherent many-particle excitation. This leads to an exponentially long relaxation time of such a state. We show that, if the average occupation number is sufficiently small, the corresponding exponent may be evaluated exactly. To this end we develop the quasiclassical approach to calculation of the high-order tree-level decay amplitudes.
We develop a microscopic theory of a quantum impurity propagating in a one-dimensional Bose liquid. As a result of scattering off thermally excited quasiparticles, the impurity experiences the friction. We find that, at low temperatures, the resulting force scales either as the fourth or the eighth power of temperature, depending on the system parameters. For temperatures higher than the chemical potential of the Bose liquid, the friction force is a linear function of temperature. Our approach enables us to find the friction force in the crossover region between the two limiting cases. In the …
The temporal evolution of a perturbation of the equilibrium distribution of a condensed Bose gas is investigated using the kinetic equation which describes collision between condensate and noncondensate atoms. The dynamics is studied in the low momentum limit where an analytical treatment is feasible. Explicit results are given for the behavior at large times in different temperature regimes.
We investigate thermal relaxation of superfluid turbulence in a highly oblate Bose-Einstein condensate. We generate turbulent flow in the condensate by sweeping the center region of the condensate with a repulsive optical potential. The turbulent condensate shows a spatially disordered distribution of quantized vortices and the vortex number of the condensate exhibits nonexponential decay behavior which we attribute to the vortex pair annihilation. The vortex-antivortex collisions in the condensate are identified with crescent-shaped, coalesced vortex cores. We observe that the nonexponential …
Starting from a phenomenological standard energy functional to describe the condensation of a dilute gas of bosonic quasiparticles in magnetic insulators, we find that the inclusion of a perturbation term that explicitly violates the axial symmetry significantly modifies the details of the resulting Bose Einstein condensation. Systems with an originally axial symmetry must show an intrinsic tendency to spontaneously violate this symmetry as soon as the condensation sets in, and the phase transition at the respective critical field may even become of first order. We can explain a number of feat…
By using simple and efficient method we discuss properties of a single impurity immersed in three-dimensional Bose gas with the interaction between particles tuned to unitary limit. Particularly, adopting the mean-field-like approximation we present the first estimations for the low-momentum parameters of the impurity spectrum, namely, the binding energy, the effective mass and the quasiparticle residue both for repulsive and attractive Bose polarons in the unitary gas.
