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arXiv:2304.06199 · Physical Review A

Optimizing persistent currents in a ring-shaped Bose-Einstein condensate using machine learning

Simeon Simjanovski, Guillaume Gauthier, Matthew J. Davis, Halina H. Rubinsztein-Dunlop, Tyler W. Neely

Published Dec 6, 2023• 10 citations
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Abstract

We demonstrate a method for generating persistent currents in Bose-Einstein condensates by using a Gaussian process learner to experimentally control the stirring of the superfluid. The learner optimizes four different outcomes of the stirring process: (O.I) targeting and (O.II) maximization of the persistent current winding number and (O.III) targeting and (O.IV) maximization with time constraints. The learner optimizations are determined based on the achieved winding number and the number of spurious vortices introduced by stirring. We find that the learner is successful in optimizing the stirring protocols, although the optimal stirring profiles vary significantly depending strongly on the choice of cost function and scenario. These results suggest that stirring is robust and persistent currents can be reliably generated through a variety of stirring approaches.

DOI
10.1103/physreva.108.063306

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We demonstrate a method for generating persistent currents in Bose-Einstein condensates by using a Gaussian process learner to experimentally control the stirring of the superfluid. The learner optimizes four different outcomes of the stirring process: (O.I) targeting and (O.II) maximization of the persistent current winding number and (O.III) targeting and (O.IV) maximization with time constraints. The learner optimizations are determined based on the achieved winding number and the number of spurious vortices introduced by stirring. We find that the learner is successful in optimizing the stirring protocols, although the optimal stirring profiles vary significantly depending strongly on the choice of cost function and scenario. These results suggest that stirring is robust and persistent currents can be reliably generated through a variety of stirring approaches.
Persistent current, or "flow without friction", as well as quantum vortices are the hallmarks of superfluidity. Recently a very long-lived persistent flow of atoms has been experimentally observed in Bose-Einstein condensates trapped in a ring-shaped potential. This enables fundamental studies of superfluidity and may lead to applications in high-precision metrology and atomtronics. We overview our recent theoretical studies of the generation of the persistent current in a stirred toroidal atomic Bose-Einstein condensate, and discuss our new investigation of the hysteresis in the atomtronic circuit.
We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates (BEC). BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our 'learner' discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of the relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system.
Abstract We apply three machine learning strategies to optimize the atomic cooling processes utilized in the production of a Bose–Einstein condensate (BEC). For the first time, we optimize both laser cooling and evaporative cooling mechanisms simultaneously. We present the results of an evolutionary optimization method (differential evolution), a method based on non-parametric inference (Gaussian process regression) and a gradient-based function approximator (artificial neural network). Online optimization is performed using no prior knowledge of the apparatus, and the learner succeeds in creating a BEC from completely randomized initial parameters. Optimizing these cooling processes results in a factor of four increase in BEC atom number compared to our manually-optimized parameters. This automated approach can maintain close-to-optimal performance in long-term operation. Furthermore, we show that machine learning techniques can be used to identify the main sources of instability within the apparatus.
Dissipating of disorder quantum vortices in an annular two-dimensional Bose-Einstein condensate can form a macroscopic persistent flow of atoms. We propose a protocol to create persistent flow with high winding number based on a double concentric ring-shaped configuration. We find that a sudden geometric quench of the trap from single ring-shape into double concentric ring-shape will enhance the circulation flow in the outer ring-shaped region of the trap when the initial state of the condensate is with randomly distributed vortices of the same charge. The circulation flows that we created are with high stability and good uniformity free from topological excitations. Our study is promising for new atomtronic designing, and is also helpful for quantitatively understanding quantum tunneling and interacting quantum systems driven far from equilibrium.
The surface excitations, shape deformation, and the formation of persistent current for a Gaussian obstacle potential rotating in a highly oblate Bose–Einstein condensate (BEC) are investigated. A vortex dipole can be produced and trapped in the center of the stirrer even for the slow motion of the stirring beam. When the angular velocity of the obstacle is above some critical value, the condensate shape can be deformed remarkably at the corresponding rotation frequency followed by surface wave excitations. After a long enough time, a small number of vortices are found to be either trapped in the condensate or pinned by the obstacle, and a vortex dipole or several vortices can be trapped at the beam center, which provides another way to manipulate the vortex.
We propose a simple stirring experiment to generate quantized ring currents and solitary excitations in Bose-Einstein condensates in a toroidal trap geometry. Simulations of the three-dimensional Gross-Pitaevskii equation show that pure ring current states can be generated efficiently by adiabatic manipulation of the condensate, which can be realized on experimental timescales. This is illustrated by simulated generation of a ring current with winding number two. While solitons can be generated in quasi-one-dimensional tori, we show the even more robust generation of hybrid, solitonic vortices (svortices) in a regime of wider confinement. Svortices are vortices confined to essentially one-dimensional dynamics, which obey a similar phase-offset-velocity relationship as solitons. Marking the transition between solitons and vortices, svortices are a distinct class of symmetry-breaking stationary and uniformly rotating excited solutions of the two-dimensional and three-dimensional Gross-Pitaevskii equation in a toroidal trapping potential. Svortices should be observable in dilute-gas experiments.