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arXiv:2004.04829 · Physical Review A

Producing flow in racetrack atom circuits by stirring

Benjamin Eller, Olatunde Oladehin, Daniel Fogarty, Clayton H. Heller, Charles W. Clark, Mark Edwards

Published Dec 21, 2020• 10 citations
arXivHTMLPDF

Abstract

We present a study of how macroscopic flow can be produced in Bose-Einstein condensates confined in a ``racetrack'' potential by stirring with a wide rectangular barrier. This potential consists of two half-circle channels separated by straight channels of length $L$ and reduces to a ring potential if $L=0$. We present the results of a flow-production study where racetrack condensates were stirred with a barrier under varying conditions of barrier height, stir speed, racetrack geometry, and temperature. The result was that stirring was readily able to produce flow in ring and nonring geometries but that the exact amount of flow produced depended on all of the study parameters. We therefore investigated the mechanism by which flow was produced in the stirring process. The basic mechanism that we discovered was that when the sweeping barrier potential height reached a critical value a series of phase slip (i.e., a sudden change in the phase winding around the condensate midtrack) events occurred. Phase slipping stopped when the flow produced overtook the speed of the stirring barrier. Disturbances generated at each phase slip circulated around the channel and served to convert the initially localized velocity distribution into smooth macroscopic flow. This picture of the mechanism for making flow should facilitate the design of closed-channel atom circuits for creating a desired amount of quantized smooth flow on demand.

DOI
10.1103/physreva.102.063324

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We present a study of how macroscopic flow can be produced in Bose-Einstein condensates confined in a ``racetrack'' potential by stirring with a wide rectangular barrier. This potential consists of two half-circle channels separated by straight channels of length LLL and reduces to a ring potential if L=0L=0L=0. We present the results of a flow-production study where racetrack condensates were stirred with a barrier under varying conditions of barrier height, stir speed, racetrack geometry, and temperature. The result was that stirring was readily able to produce flow in ring and nonring geometries but that the exact amount of flow produced depended on all of the study parameters. We therefore investigated the mechanism by which flow was produced in the stirring process. The basic mechanism that we discovered was that when the sweeping barrier potential height reached a critical value a series of phase slip (i.e., a sudden change in the phase winding around the condensate midtrack) events occurred. Phase slipping stopped when the flow produced overtook the speed of the stirring barrier. Disturbances generated at each phase slip circulated around the channel and served to convert the initially localized velocity distribution into smooth macroscopic flow. This picture of the mechanism for making flow should facilitate the design of closed-channel atom circuits for creating a desired amount of quantized smooth flow on demand.
We have measured the threshold for creating long-lived excitations when a toroidal Bose-Einstein condensate is stirred by a rotating (optical) barrier of variable height. When the barrier height is on the order of or greater than half of the chemical potential, the critical barrier velocity at which we observe a change in the circulation state is much less than the speed for sound to propagate around the ring. In this regime we primarily observe discrete jumps (phase slips) from the noncirculating initial state to a simple, well-defined, persistent current state. For lower barrier heights, the critical barrier velocity at which we observe a change in the circulation state is higher, and approaches the effective sound speed for vanishing barrier height. The response of the condensate in this small-barrier regime is more complex, with vortex cores appearing in the bulk of the condensate. We find that the variation of the excitation threshold with barrier height is in qualitative agreement with the predictions of an effective one-dimensional hydrodynamic model.
Quantum phase slips are a dual process of particle tunneling in coherent networks.Besides being of central interest to condensed matter physics, quantum phase slips are resources that are sought to be manipulated in quantum circuits.Here, we devise a specific matter-wave circuit enlightening quantum phase slips.Specifically, we investigate the quantum many-body dynamics of two side-by-side ring-shaped neutral bosonic systems coupled through a weak link.By imparting a suitable magnetic flux, persistent currents flow in each ring with given winding numbers.We demonstrate that coherent phase slips occur as winding number transfer among the two rings, with the populations in each ring remaining nearly constant.Such a phenomenon occurs as a result of a specific entanglement of circulating states, that, as such, cannot be captured by a mean-field treatment of the system.Our work can be relevant for the observation of quantum phase slips in cold-atom experiments and their manipulation in matter-wave circuits.To make contact with the field, we show that the phenomenon has clear signatures in the momentum distribution of the system providing the time-of-flight image of the condensate.
Quantum fluids are able to flow past obstacles without creating drag and through channels without any resistance. This superfluidity is a consequence of Bose–Einstein condensation, a process in which all the particles gather in the same, lowest-energy quantum state. At low flow velocities, energy exchanges between the obstacle and the fluid are forbidden because of the twin requirements of energy and momentum conservation. As the flow speed is increased, however, the superfluidity breaks down at some critical velocity above which excitations in the fluid can occur. These excitations can be phonons (i.e. quantized vibrations), vortices or, in the case of superfluid liquid helium, rotons (see Rotons: a low-temperature puzzle by Russell Donnelly Physics World February 1997 p25)
Superfluidity is a remarkable phenomenon. Superfluidity was initially characterized by flow without friction, first seen in liquid helium in 1938, and has been studied extensively since. Superfluidity is believed to be related to, but not identical to Bose-Einstein condensation, a statistical mechanical phenomena predicted by Albert Einstein in 1924 based on the statistics of Satyendra Nath Bose, where bosonic atoms make a phase transition to form a Bose-Einstein condensate (BEC), a gas which has macroscopic occupation of a single quantum state. Developments in laser cooling of neutral atoms and the subsequent realization of Bose-Einstein condensates in ultracold gases have opened a new window into the study of superfluidity and its relation to Bose-Einstein condensation. In our atomic sodium BEC experiment, we studied superfluidity and dissipationless flow in an all-optical toroidal trap, constructed using the combination of a horizontal ``sheet''-like beam and vertical ``ring''-like beam, which, like a circuit loop, allows flow around the ring. On inducing a single quantum of circulation in the condensate, the smoothness and uniformity of the toroidal BEC enabled the sustaining of a persistent current lasting 40 seconds, limited by the lifetime of the BEC due to background gas pressure. This success set the stage for further experiments studying superfluidity. In a first set of experiments, we studied the stability of the persistent current by inserting a barrier in the flow path of the ring. The superflow stopped abruptly at a barrier strength such that the local flow velocity at the barrier exceeded a critical velocity, which supported decay via the creation of a vortex-antivortex pair. Our precise control in inducing and arresting superflow in the BEC is a first step toward studying other aspects of superfluidity, such as the effect of temperature and dimensionality. This thesis discusses these experiments and also details partial-transfer absorption imaging, an imaging technique developed in the course of this work.
We study why it is quite so hard to make a superposition of superfluid flows in a Bose–Einstein condensate. To do this we initially investigate the quantum states of N atoms trapped in a 1D ring with a barrier at one position and a phase applied around it. We show how macroscopic superpositions can in principle be produced and investigate factors which affect the superposition. We then use the Bose–Hubbard model to study an array of Bose–Einstein condensates trapped in optical potentials and coupled to one another to form a ring. We derive analytic expressions for the quality of the superposition for this system, which agrees well with direct diagonalization of the Hamiltonian for relatively small numbers of atoms. We show that for macroscopic superpositions to be realized there are essentially three straightforward requirements, other than an absence of decoherence, which become harder to achieve as the system size increases. Firstly, the energies of the two distinct superfluid states must be sufficiently close. Secondly, coupling between the two states must be sufficiently strong, and thirdly, other states must be well separated from those participating in the superposition.