Gaussian impurity moving through a Bose-Einstein superfluid

Abstract

In this paper a Gaussian impurity moving through an equilibrium Bose-Einstein condensate at T = 0 is studied. The problem can be described by a Gross-Pitaevskii equation, which is solved perturbatively. The analysis is done for systems of 2 and 3 spatial dimensions and generalises the work by [G.E. Astrakharchik and L.P. Pitaevskii, Phys. Rev. A 70, 013608 (2004)]. The Bogoliubov equation solutions for the condensate perturbed by a finite impurity are calculated in the co-moving frame, which are formally equivalent up to a dimension dependent form factor for general dimensions. From those solutions the total energy of the perturbed system is determined as a function of the width and the amplitude of the moving Gaussian impurity and its velocity. Finally we derive the drag force the Gaussian impurity approximately experiences as it moves through the superfluid, which proofs the existence of a superfluid phase for finite extensions of the impurities below the speed of sound and that the force increases monotonically with velocity until it decreases again

Beyond superfluidity in non-equilibrium Bose–Einstein condensates

“…This analysis confirmed the existence of a superfluid phase in the leading order contribution-the drag force vanishes below the non-zero critical velocity that is equal the speed of sound for weakly-interacting obstacles. This holds as well quantum mechanically [25], while geometric features significantly alter the drag force's magnitude [6]. The analytical insights made for non-equilibrium systems presented here build on this type of analysis and will be supported by numerical integration.…”

“…Even when the line e = pv intersects the energy spectrum of the fluid in its ground state, transition probabilities to these states can be strongly suppressed due to Boson interactions or due to the nature of the external perturbing potential [4]. For all scenarios the drag force experienced by the impurity gives us a quantitative measure of the state of the fluid and below a critical velocity, if the fluid cannot be excited, the impurity experiences no drag [5,6] a phenomenon already envisaged in the classic papers in the beginning of the 20th century [7][8][9][10][11].…”

“…Experimentally superfluidity has been unambiguously observed for the condensed state in various weakly interacting and dilute effectively Bose gases of atoms or molecules at ultra-low temperatures in the nano Kelvin range [12,13,[14][15][16] and even in strongly interacting gases of 6 Li fermions [13]. On the other hand, theoretically, the ideal Bose gas, i.e.…”

“…Superfluidity can be tested experimentally and proven in a wider sense by considering the dissipationless flow around impurities [17,[18][19][20]27], even in the presence of quantum fluctuations [21,25,26]. This has been done theoretically in the semiclassical Gross-Pitaevskii (GP) framework by the means of a Bogoliubov analysis for point-like [5] and subsequently Gaussian [6] weakly-interacting impurities. This analysis confirmed the existence of a superfluid phase in the leading order contribution-the drag force vanishes below the non-zero critical velocity that is equal the speed of sound for weakly-interacting obstacles.…”

“…truly non-equilibrium phenomena without one to one analogy to equilibrium condensates. While by naively applying the analogy to conserved BE condensed systems a superfluid phase aka absence of drag would be expected for small velocities below the speed of sound of the fluid due to particle interactions, while above a critical velocity a drag force would arise due to the possibility of emission of elementary excitations [5,6,29,30]. The continuous flow of particles into the condensate phase and the corresponding balancing drain may alter the scenario as studied numerically in [30] and thus superfluidity could be suppressed [50,51].…”