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arXiv:1611.03430 · New Journal of Physics

Beyond superfluidity in non-equilibrium Bose–Einstein condensates

Florian Pinsker

Published Oct 23, 2017• 4 citations
arXivHTMLPDF

Abstract

The phenomenon of superfluidity in open Bose–Einstein condensates (BEC) is analysed numerically and analytically. It is found that a superfluid phase is feasible above the speed of sound, when forces due to inhomogeneous non-equilibrium processes oppose the contributions of homogeneous processes. Furthermore a regime of accelerating impurities can be observed for particular pumping/decay strategies. All findings are derived within the complex Gross–Pitaevskii (GP) theory extended to include creation and annihilation terms. Utilising this framework the effective force acting on an impurity as it moves with velocity v through the open condensate can be calculated. The result shows that the drag force is continuously increasing with increasing velocity starting from the state of zero motion at v = 0, a property that can be traced down to the additional homogeneous annihilation/creation term in the extended GP model. For very large velocities however we observe a reversion of the drag force. Our findings stand in stark contrast to the concept of a topological phase transition to frictionless flow below a critical velocity as observed for equilibrium BEC analytically (Astrakharchik and Pitaevskii 2004 Phys. Rev. A 70 013608; Pinsker 2017 Physica B 521 36–42), numerically (Winiecki et al 1999 Phys. Rev. Lett. 82 26) and for trapped atoms experimentally (Desbuquois et al 2012 Nat. Phys. 8 645; Zwierlein et al 2006 Nature 442 54–58).

DOI
10.1088/1367-2630/aa9561

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The phenomenon of superfluidity in open Bose–Einstein condensates (BEC) is analysed numerically and analytically. It is found that a superfluid phase is feasible above the speed of sound, when forces due to inhomogeneous non-equilibrium processes oppose the contributions of homogeneous processes. Furthermore a regime of accelerating impurities can be observed for particular pumping/decay strategies. All findings are derived within the complex Gross–Pitaevskii (GP) theory extended to include creation and annihilation terms. Utilising this framework the effective force acting on an impurity as it moves with velocity v through the open condensate can be calculated. The result shows that the drag force is continuously increasing with increasing velocity starting from the state of zero motion at v = 0, a property that can be traced down to the additional homogeneous annihilation/creation term in the extended GP model. For very large velocities however we observe a reversion of the drag force. Our findings stand in stark contrast to the concept of a topological phase transition to frictionless flow below a critical velocity as observed for equilibrium BEC analytically (Astrakharchik and Pitaevskii 2004 Phys. Rev. A 70 013608; Pinsker 2017 Physica B 521 36–42), numerically (Winiecki et al 1999 Phys. Rev. Lett. 82 26) and for trapped atoms experimentally (Desbuquois et al 2012 Nat. Phys. 8 645; Zwierlein et al 2006 Nature 442 54–58).
This thesis examines the manifestation of the critical velocity for superfluidity in dilute gas Bose-Einstein condensates (BECs). Superfluidity is a macroscopic quantum phenomenon characterised by unique properties such as frictionless flow, high thermal conductivity and the presence of quantised vortices. Our study focuses on what is arguably the most well-known attribute: the ability for an object to move through a superfluid without experiencing a drag force when travelling below a threshold critical velocity.The Landau criterion for superfluidity predicts the critical velocity in a BEC is equal to the speed of sound, and this conclusion is supported by a large body of theoretical work. However, a number of experiments have observed lower critical velocities than theory predicts. In the first part of this thesis, we numerically model experiments on the superfluid critical velocity of an elongated, harmonically trapped Bose-Einstein condensate as reported by [P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)]. These experiments swept a repulsive obstacle, formed by a optical dipole potential, through the long axis of a condensate at constant velocity. Their results found an increase in the resulting density fluctuations of the condensate above an obstacle velocity of v _ 0:3 mm s
It has been proposed in recent years that an impurity moving in a superfluid will experience drag forces even below the Landau critical velocity [1–3]. Quantum fluctuations that are present in superfluid systems at zero temperature can scatter from impurities present in the fluid. If the impurity is moving, there will be an asymmetric Doppler shift associated with the scattered waves, which will result in a net drag force. This challenges the long-accepted notion of dissipationless flow in superfluids. Analytical estimates of this drag force in superfluid Bose-Einstein condensates using Bogoliubov methods have found a non-zero drag force, resulting from the most sensible choice of boundary conditions in an infinite system. Through stochastic simulations of the 1D Bose gas under the truncated Wigner formalism, we verify the existence of this sub-critical drag force and quantify the drag forces present. We will also determine whether dissipationless flow can be recovered in finite sized systems.
We derive a theoretical model which describes Bose-Einstein condensation in an open driven-dissipative system. It includes external pumping of a thermal reservoir, finite life time of the condensed particles and energy relaxation. The coupling between the reservoir and the condensate is described with semi-classical Boltzmann rates. This results in a dissipative term in the Gross-Pitaevskii equation for the condensate, which is proportional to the energy of the elementary excitations of the system. We analyse the main properties of a condensate described by this hybrid Boltzmann Gross-Pitaevskii model, namely, dispersion of the elementary excitations, bogolon distribution function, first order coherence, dynamic and energetic stability, drag force created by a disorder potential. We find that the dispersion of the elementary excitations of a condensed state fulfils the Landau criterion of superfluidity. The condensate is dynamically and energetically stable as longs it moves at a velocity smaller than the speed of excitations. First order spatial coherence of the condensate is found to decay exponentially in 1D and with a power law in 2D, similarly with the case of conservative systems. The coherence lengths are found to be longer due to the finite life time of the condensate excitations. We compare these properties with the ones of a condensate described by the popular models in which the dissipative term is proportional to the local condensate density. In the latter, the dispersion of excitations is diffusive which as soon as the condensate is put into motion implies finite mechanical friction and can lead to an energetic instability.
We theoretically study the superfluidity properties of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity under incoherent pumping. The dynamics of the condensate is described at mean-field level in terms of a generalized Gross-Pitaevskii equation. The drag force on a small moving object and the onset of fringes in the density profile are shown to have a sharp threshold as a function of the velocity; a generalized Landau criterion is developed to explain this behavior in terms of the dispersion of elementary excitations. Metastability of supercurrents in multiply-connected geometries is shown to persist up to higher flow speeds.
The motion of a body through a superfluid can generate phenomena distinct from a normal viscous fluid. This includes the absence of drag below a critical body speed with the shedding of quantised vortices and non-zero drag above this speed. These phenomena are often modelled using the Gross–Pitaevskii (GP) equation, which describes the wavefunction of a weakly interacting Bose–Einstein condensate and its superfluid dynamics. We study the drag experienced by a penetrable circular disk of radius, aaa , in the form of a two-dimensional potential barrier of height, V0V_0V0​ , that is moving in a superfluid of bulk density, n∞n_\inftyn∞​ , by solving the GP equation. The drag is found to exhibit a unimodal dependence on the disk speed for a fixed value of its barrier height. This behaviour is quantified analytically and confirmed using direct numerical solution. The maximum drag per unit length of Fdragmax≈5an∞V0F_{\textit{drag}}^{\textit{max}} \approx 5 a n_\infty V_0Fdragmax​≈5an∞​V0​ occurs when the barrier height coincides with the relative kinetic energy of the fluid particles. Flow excitations are diminished at a high particle kinetic energy with a commensurate reduction in the drag. This generates a saddle-node bifurcation in the dynamics of a moving disk under an applied force. These results advance understanding of the motion of bodies with finite penetrability, which is relevant to laser experiments probing the superfluidity of Bose–Einstein condensates.