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arXiv:1309.2647 · Physical Review Letters

Kinetics of Mobile Impurities and Correlation Functions in One-Dimensional Superfluids at Finite Temperature

Maksims Arzamasovs, Filippo Bovo, Dimitri M. Gangardt

Published Apr 30, 2014• 27 citations
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Abstract

We examine the hydrodynamic approach to dynamical correlations in one-dimensional superfluids near integrability and calculate the characteristic time scale, τ, beyond which this approach is valid. For time scales shorter than τ, hydrodynamics fails, and we develop an approach based on kinetics of fermionic quasiparticles described as mobile impurities. New universal results for the dynamical structure factor relevant to experiments in ultracold atomic gases are obtained.

DOI
10.1103/physrevlett.112.170602

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We examine the hydrodynamic approach to dynamical correlations in one-dimensional superfluids near integrability and calculate the characteristic time scale, τ, beyond which this approach is valid. For time scales shorter than τ, hydrodynamics fails, and we develop an approach based on kinetics of fermionic quasiparticles described as mobile impurities. New universal results for the dynamical structure factor relevant to experiments in ultracold atomic gases are obtained.
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 integrable case, corresponding to the Yang-Gaudin model, the impurity becomes transparent for quasiparticles and thus the friction force is absent. Our results could be further generalized to study other kinetic phenomena.
This Thesis discusses approaches to calculating static and dynamic correlation functions in onedimensional gases of interacting bosons. The first part of the Thesis deals with the momentummomentum correlation function in the weakly interacting 1D Bose gas. In the regime of phase fluctuating quasicondensate this correlator is found to differ qualitatively from the form predicted by Bogoliubov theory of the true condensate in that correlations between any two values of momentum become finite. Linear hydrodynamics used to calculate the quasicondensate correlation function prove to be adequate. A classical field approximation is used to smoothly interpolate between the quasicondensate and strongly degenerate gas regimes. In the second part the focus is shifted to the dynamical structure factor and it is shown that hydrodynamics is generally inapplicable to calculating the dynamical correlators. The hydrodynamic treatment is enhanced using impurity theory and an exact model-dependent boundary is obtained for the region of applicability of hydrodynamics on the momentum-energy plane. Numerical estimates show that non-hydrodynamic behavior should be observable for the currently available values of experimental parameters.
The use of atomically sized quantum systems as highly sensitive measuring devices represents an exciting and quickly growing research field. Here we explore the properties of a quasiparticle formed by a mobile impurity interacting with a two-dimensional fermionic superfluid. The energy of the quasiparticle is shown to be lowered by superfluid pairing, as this increases the compressibility of the Fermi gas, thereby making it easier for the impurity to perturb its surroundings. We demonstrate that the fundamentally discontinuous nature of the superfluid-to-normal phase transition of a two-dimensional system leads to a rapid increase in the quasiparticle energy around the critical temperature. The magnitude of this increase exhibits a nonmonotonic behavior as a function of the pairing strength with a sizable maximum in the crossover region, where the spatial extend of the Cooper pairs is comparable to the interparticle spacing. Since the quasiparticle energy is measurable with present experimental techniques, our results illustrate how impurities entangled with their environment can serve as useful probes for nontrivial thermal and quantum correlations.
We use a mobile impurity or depleton model to study elementary excitations in one-dimensional integrable systems. For Lieb-Liniger and bosonic Yang-Gaudin models we express two phenomenological parameters characterising renormalised inter- actions of mobile impurities with superfluid background: the number of depleted particles, NNN and the superfluid phase drop πJ\pi JπJ in terms of the corresponding Bethe Ansatz solution and demonstrate, in the leading order, the absence of two-phonon scattering resulting in vanishing rates of inelastic processes such as viscosity experienced by the mobile impurities
We theoretically investigate the correlated decoherence dynamics of two mobile impurities trapped within a gas of ultracold fermionic atoms. We use a mean-field approximation to self-consistently describe the effect of impurity-gas collisions on impurity motion, while decoherence of the impurities' internal state is computed exactly within a functional determinant approach. At equilibrium, we find that the impurities undergo bath-induced localization as the impurity-gas interaction strength is increased. We then study the nonequilibrium dynamics induced by a sudden change of the impurities' internal state, which can be experimentally probed by Ramsey interferometry. Our theoretical approach allows us to investigate the effect of impurity motion on decoherence dynamics, finding strong deviations from the universal behavior associated with Anderson's orthogonality catastrophe when the mass imbalance between impurity and gas atoms is small. Finally, we show that mobile impurities can be used as thermometers of their environment, and that bath-mediated correlations can be beneficial for thermometric performance at low temperatures, even in the presence of nontrivial impurity motion. Our results showcase the interesting open quantum dynamics of mobile impurities dephasing in a common environment, and they can help to provide more precise temperature estimates of ultracold fermionic mixtures.
In this work we examine the dynamics of one-dimensional systems. We present a continuum approach to the construction of the non-equilibrium Keldysh functional integral and derive a relation between the classical and quantum fields of the Keldysh formalism and the occupation of a state. Using the Keldysh formalism, we give a self-contained presentation of bosonization and refermionisation of fermionic and bosonic interacting particles. We derive the first two non-linear corrections to linear bosonization due to the fermionic spectrum curvature using the functional integral formalism. Using the previous results, we study the thermal dynamics of one-dimensional systems. We consider both the phonons, coming from bosonization, and fermionic quasiparticles, coming from refermionisation, in a single theory. Having them in a single theory is justified by a scale separation between them. Studying the dynamical structure factor we find three regimes. From higher to lower energies we have a ballistic and a collisional regimes of fermionic quasiparticles and a hydrodynamical regime of non-linear phonons. The phase field of the non-linear bosons satisfies the Kardar-Parisi-Zhang equation, thereby linking the dynamics of one-dimensional quantum systems to the universality class of surface growth. The time-scale separating the phononic and fermionic quasiparticle regimes is very long for up-to-date experiments, meaning that the ballistic regime of fermionic quasiparticles is the only one likely to be observed. Since this approach has a limited range of validity for weakly interacting bosons, we derive their dynamical structure factor using a semiclassical approach.