Session Y6: Quantum Hydrodynamics

Matter-wave Interference in Bose-Einstein Condensates: a dispersive hydrodynamics perspective

Bose-Einstein condensates (BECs) can show striking nonlinear dynamics marked by the formation of dispersive shock waves and soliton trains, and by the existence of stable and unstable fluid flow regimes. These phenomena are readily observed in our experiments. For example, when two initially separate condensates with large atom numbers collide in a magnetic trap, dispersive shock waves can develop and spread out through the entire merged condensate. For sufficiently low particle numbers, the dynamics are markedly different and the merging of two condensates leads to a uniform train of dark solitons. The soliton train is closely related to the trigonometric interference patterns observed when two freely expanding, nearly non-interacting condensates overlap. Indeed, a uniform mathematical description can be found that identifies a smooth transition from solitons in the initial, low-density overlap region to the soliton trains observed in our in-trap merging experiments [1]. This leads to a hydrodynamic perspective on matterwave interference. In this talk I will present our recent and ongoing experiments studying nonlinear dynamics in ultracold quantum gases. In addition to creating solitons and shock waves by merging trapped BECs, we also observe soliton and shock wave formation when crossing the BEC phase transition rapidly. The results for the bosonic case will be contrasted to the behavior of ultracold quantum degenerate Fermi clouds where shock waves are predicted to exist but appear to be more difficult to observe experimentally. The results also have implications for the behavior of bosons and fermions in the presence of disordered potentials that we produce e.g. using speckle potentials. \\[4pt] [1] M. A. Hoefer, P. Engels and J. J. Chang, Physica D 238, 1311 (2009)   

Two-fluid hydrodynamics in strongly interacting Fermi gases

Landau's theory of two-fluid hydrodynamics provides an exact description of the finite-temperature, low-energy dynamics of all strongly interacting superfluids described by a two-component order parameter. Reliable solutions of the two-fluid equations in trapped Fermi gases through the BCS-BEC crossover are crucial for extracting information about the equation of state and transport coefficients from experiments in the superfluid phase. In this talk, I will present new accurate variational solutions for the first and second sound frequencies in a trapped Fermi gas at unitarity, highlighting similarities with superfluid Helium-4 as well as some surprising differences [1.]. I will also discuss proposals to detect these modes in experiments. For the uniform gas, we show that at temperatures of order $0.7T_c$ and higher, second sound enters with comparable weight to first sound in the dynamic structure factor, in agreement with the recent results of Arahata and Nikuni on the propagation of density pulses [2.].\newline [1.] E.~Taylor, H.~Hu, X.-J.~Liu, L.~P.~Pitaevskii, A.~Griffin, and S.~Stringari, Phys. Rev. A \textbf{80}, 053601 (2009).\newline [2.] E.~Arahata and T.~Nikuni, Phys. Rev. A \textbf{80}, 043613 (2009).   

Second sound in a collisionally hydrodynamic Bose gas

In 1995 Bose-Einstein condensation (BEC) in dilute Bose gases has been realized experimentally for the first time. Although the first condensates were created with a few million atoms or less, it has been speculated at that time that soon the number of atoms would increase considerably such that the sample becomes hydrodynamic. This would allow to enter the regime of the Landau two-fluid model for dilute Bose gases, where experiments in liquid helium below the $\lambda$-point have been very successful. Since that time a few experiments have been carried out where the sample was close to hydrodynamic, although most of the experiment using dilute Bose gases have been in the collisionless regime. We have been carrying out experiments, where for the first time the sample is fully hydrodynamic in the axial direction. We have displaced the condensate with respect to the thermal cloud and subsequently released the condensate, such that it moves through the thermal cloud~[1]. Contrary to the superfluid properties of the condensate we observe damping of the out-of-phase motion between condensate and thermal cloud. In another experiment we locally heat the sample of condensate and thermal cloud and observe the equilibration of the sample to a homogeneous temperature extending our work above $T_{\rm c}$~[2]. We observe two standing wave sound modes, where the mode in the condensate (thermal cloud) is associated with second (first) sound. In a final experiment we directly induce a wave by locally decreasing the density in the condensate and measure its propagation speed~[3]. The speed of sound, which is 5-10\% smaller compared to the Bogoliubov speed of sound, is compared to the speed of second sound in the Landau two-fluid hydrodynamics model. We observe excellent agreement between the model and experiment in a large range of temperatures. These experiments open the field of quantum hydrodynamics for dilute Bose gases and broadens our knowledge on second sound and superfluidity. \\[4pt] [1] R. Meppelink et al., {\em Damping of superfluid flow by a thermal cloud}, Phys. Rev. Lett. (accepted).\\[0pt] [2] R. Meppelink et al., {\em Enhanced Heat Flow in the Hydrodynamic Collisionless Regime}, Phys. Rev. Lett. {103}{095301}{2009}.\\[0pt] [3] R. Meppelink et al., {\em Sound propagation in a Bose-Einstein condensate at finite temperatures}, Phys. Rev. A 80 043605 2009.   

Exciting Bose-Condensate using oscillatory fields: Observation of turbulence and fragmentation

In this work we demonstrate nucleation of vortices in a BEC, where an oscillating field generated by a set of coils is superimposed to the trapping field creating displacement, rotation and deformation of the trap potential. As a function of the amplitude of oscillation we observe several different behaviors of the condensate cloud allowing the construction of a diagram for stable structures. Increasing the amplitude we observe the formation of one, two, three or more vortices in the cloud. Above certain amplitude of oscillation we observe uncountable vortices in every direction, producing a tangled vortices configuration which can be considered as the emergence of a turbulent regime in the cloud. Variations of behavior during TOF for the cloud seem to be a signature of the turbulent regime. In extremes conditions of oscillations, a fragmentation of the cloud is observed. A theoretical model for the fragmentation is offered. .   

The Discovery of the Two Fluid Theory and Second Sound in Helium II

Colleagues and friends recently celebrated the one hundredth birthday of Laszlo Tisza at MIT. Tisza's discovery of the two fluid model of Helium II and prediction of second sound were recalled on that occasion. We review the controversial discovery of second sound and its modern applications. The two fluid theory of Helium II and the prediction of the existence of two forms of sound propagation make Laszlo ``Laci'' Tisza one of the important figures of twentieth century physics. Tisza died on April 15, 2009, his obituary is in the July issue of Physics Today. In this talk we explore the remarkable story of the discovery of second sound and mention some of the ways in which second sound is enabling landmark studies in quantum turbulence and prospects for observing second sound in a uniform superfluid gas of ultracold Fermi atoms.