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arXiv:2201.11887 · Physical Review A

Critical velocity and arrest of a superfluid in a pointlike disordered potential

R. Doran, Andrew J. Groszek, T. P. Billam

Published Jan 5, 2024• 1 citation
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Abstract

Superfluid flow past a potential barrier is a well studied problem in ultracold Bose gases, however, fewer studies have considered the case of flow through a disordered potential. Here we consider the case of a superfluid flowing through a channel containing multiple point-like barriers, randomly placed to form a disordered potential. We begin by identifying the relationship between the relative position of two point-like barriers and the critical velocity of such an arrangement. We then show that there is a mapping between the critical velocity of a system with two obstacles, and a system with a large number of obstacles. By establishing an initial superflow through a point-like disordered potential, moving faster than the critical velocity, we study how the superflow is arrested through the nucleation of vortices and the breakdown of superfluidity, a problem with interesting connections to quantum turbulence and coarsening. We calculate the vortex decay rate as the width of the barriers is increased, and show that vortex pinning becomes a more important effect for these larger barriers. Published by the American Physical Society 2024

DOI
10.1103/physreva.109.013306

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Superfluid flow past a potential barrier is a well studied problem in ultracold Bose gases, however, fewer studies have considered the case of flow through a disordered potential. Here we consider the case of a superfluid flowing through a channel containing multiple point-like barriers, randomly placed to form a disordered potential. We begin by identifying the relationship between the relative position of two point-like barriers and the critical velocity of such an arrangement. We then show that there is a mapping between the critical velocity of a system with two obstacles, and a system with a large number of obstacles. By establishing an initial superflow through a point-like disordered potential, moving faster than the critical velocity, we study how the superflow is arrested through the nucleation of vortices and the breakdown of superfluidity, a problem with interesting connections to quantum turbulence and coarsening. We calculate the vortex decay rate as the width of the barriers is increased, and show that vortex pinning becomes a more important effect for these larger barriers. Published by the American Physical Society 2024
When a superfluid flows past an obstacle, quantized vortices can be created in the wake above a certain critical velocity. In the experiment by Kwon et al. [Phys. Rev. A 91, 053615 (2015)], the critical velocity vc{v}_{c}vc​ was measured for atomic Bose-Einstein condensates (BECs) using a moving repulsive Gaussian potential, and vc{v}_{c}vc​ was minimized when the potential height V0{V}_{0}V0​ of the obstacle was close to the condensate chemical potential $\ensuremath{\mu}$. Here we numerically investigate the evolution of the critical vortex shedding in a two-dimensional BEC with increasing V0{V}_{0}V0​ and show that the minimum vc{v}_{c}vc​ at the critical strength ${V}_{0c}\ensuremath{\approx}\ensuremath{\mu}$ results from the local density reduction and vortex-pinning effect of the repulsive obstacle. The spatial distribution of the superflow around the moving obstacle just below vc{v}_{c}vc​ is examined. The particle density at the tip of the obstacle decreases as V0{V}_{0}V0​ increases to Vc0{V}_{c0}Vc0​, and at the critical strength, a vortex dipole is suddenly formed and dragged by the moving obstacle, indicating the onset of vortex pinning. The minimum vc{v}_{c}vc​ exhibits power-law scaling with the obstacle size $\ensuremath{\sigma}$ as ${v}_{c}\ensuremath{\sim}{\ensuremath{\sigma}}^{\ensuremath{-}\ensuremath{\gamma}}$ with $\ensuremath{\gamma}\ensuremath{\approx}1/2$.
© The Author(s) 2024. We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.
The effect of disorder on many-body physics is important for our understanding of real-world systems. In particular, the behaviour of phase transitions between superfluid, normal and insulating phases is an area with many unanswered questions and experimental evidence remains scarce in certain important cases. In this thesis, we focus on systems of two-dimensional (2D) Bose gases subjected to a pointlike disorder potential. We trap atoms in radiofrequency dressed potentials and apply the technique of multiple-radiofrequency dressing to create a double-well potential into which we load the ultracold atoms. Matter-wave interferometry allows us to directly probe the local relative phase and its fluctuations between the clouds in the two potential wells. A pointlike disordered optical potential is produced by a high-intensity laser beam which is shaped by a programmable mirror array and passes through clouds in both of the wells. We adiabatically apply disordered potentials of increasing strength to observe their effect on the superfluids in equilibrium in a double-well. We observe that above a critical disorder strength the superfluid undergoes a transition to the normal phase at a lower temperature than that of the disorder-free case, and we characterise this disorder-induced transition. We also study the flow of a 2D superfluid cloud around both a single defect and a random potential and measure the dissipation induced by the obstacles. The absence of dissipation is observed below a critical velocity in the case of a single defect but we find no such dissipationless regime for the disordered potential. We describe the development of a software simulation package for modelling cold-atom systems and the implementation of particle collisions, magnetic trapping and evaporative cooling. Finally, we report on the initial work towards construction of a new cold-atom apparatus, capable of faster sequence times and greater atom numbers, to continue our investigation of many-body physics.
We use classical field simulations of the homogeneous Bose gas to study the breakdown of superflow due to vortex nucleation past a cylindrical obstacle at finite temperature. Thermal fluctuations modify the vortex nucleation from the obstacle, turning antiparallel vortex lines (which would be nucleated at zero temperature) into wiggly lines, vortex rings, and even vortex tangles. We find that the critical velocity for vortex nucleation decreases with increasing temperature and scales with the speed of sound of the condensate, becoming zero at the critical temperature for condensation.
Abstract We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.
We consider the setup employed in a recent experiment (Ramanathan et al 2011 Phys. Rev. Lett. 106 130401) devoted to the study of the instability of the superfluid flow of a toroidal Bose–Einstein condensate in the presence of a repulsive optical barrier. Using the Gross–Pitaevskii mean-field equation, we observe, consistently with what we found in Piazza et al (2009 Phys. Rev. A 80 021601), that the superflow with one unit of angular momentum becomes unstable at a critical strength of the barrier and decays through the mechanism of phase slippage performed by pairs of vortex–antivortex lines annihilating. While this picture qualitatively agrees with the experimental findings, the measured critical barrier height is not very well reproduced by the Gross–Pitaevskii equation, indicating that thermal fluctuations can play an important role (Mathey et al 2012 arXiv:1207.0501). As an alternative explanation of the discrepancy, we consider the effect of the finite resolution of the imaging system. At the critical point, the superfluid velocity in the vicinity of the obstacle is always of the order of the sound speed in that region, v barr = c l . In particular, in the hydrodynamic regime (not reached in the above experiment), the critical point is determined by applying the Landau criterion inside the barrier region. On the other hand, the Feynman critical velocity v f is much lower than the observed critical velocity. We argue that this is a general feature of the Gross–Pitaevskii equation, where we have v f = c l with being a small parameter of the model. Given these observations, the question still remains open about the nature of the superfluid instability.