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Physical Review A

Quantized phase slips with hysteresis in rotating spin-orbit-coupled Bose-Einstein condensates

Chuanyi Zhang

Published Mar 10, 2017• 1 citation
Publisher

Abstract

Recently, hysteresis has been observed experimentally in a quantized superfluid circuit [S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Nature (London) 506, 200 (2014)], which is a very important step for developing atomtronic devices. Here we find that quantized phase slips occur as the angular velocity rises, and the average angular momenta are quantized at special angular velocities, immune to the nonlinear interactions. When the spin and orbital angular momentum coupling is introduced, we find that two hysteresis loops could arise for each spin, and there exists a phase slip for spin up in one loop and spin down in the other loop. At the special angular velocities, a phase slip emerges for spin down in the lower state of the loop. Especially, multistability appears if the angular velocity is located in the hysteretic region. These results can promote experimental verification and pave the way for atomtronic devices.

DOI
10.1103/physreva.95.033612

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Recently, hysteresis has been observed experimentally in a quantized superfluid circuit [S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Nature (London) 506, 200 (2014)], which is a very important step for developing atomtronic devices. Here we find that quantized phase slips occur as the angular velocity rises, and the average angular momenta are quantized at special angular velocities, immune to the nonlinear interactions. When the spin and orbital angular momentum coupling is introduced, we find that two hysteresis loops could arise for each spin, and there exists a phase slip for spin up in one loop and spin down in the other loop. At the special angular velocities, a phase slip emerges for spin down in the lower state of the loop. Especially, multistability appears if the angular velocity is located in the hysteretic region. These results can promote experimental verification and pave the way for atomtronic devices.
We have observed well-defined phase slips between quantized persistent current states around a toroidal atomic (23Na) Bose-Einstein condensate. These phase slips are induced by a weak link (a localized region of reduced superfluid density) rotated slowly around the ring. This is analogous to the behavior of a superconducting loop with a weak link in the presence of an external magnetic field. When the weak link is rotated more rapidly, well-defined phase slips no longer occur, and vortices enter into the bulk of the condensate. A noteworthy feature of this system is the ability to dynamically vary the current-phase relation of the weak link, a feature which is difficult to implement in superconducting or superfluid helium circuits.
The ability to generate and tune quantized persistent supercurrents is crucial for building superconducting or atomtronic devices with novel functionalities. In ultracold atoms, previous methods for generating quantized supercurrents are generally based on dynamical processes to prepare atoms in metastable excited states. Here, we show that arbitrary quantized circulation states can be adiabatically prepared and tuned as the ground state of a ring-shaped Bose-Einstein condensate by utilizing spin--orbital-angular-momentum (SOAM) coupling and an external potential. There exists superfluid hysteresis for tuning supercurrents between different quantization values with nonlinear atomic interactions, which is explained by developing a nonlinear Landau-Zener theory. Our work will provide a powerful platform for studying SOAM-coupled ultracold atomic gases and building atomtronic circuits.
We analyze the nucleation of persistent currents in Bose-Einstein condensates of ultracold gases confined in a ring. This phenomenon has been recently investigated in an experiment [S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Nature (London) 506, 200 (2014)], where hysteresis loops have been observed in the activation of quantized persistent currents by rotating weak links. In this work, we demonstrate the existence of three-dimensional stationary currents with nonquantized angular momentum. They are generated by families of solitary waves that exhibit a continuous variation in the angular momentum and provide a bridge between different winding numbers. We show that the size of hysteresis loops is determined by the range of existence within the weak link region of solitary waves which configure the energy barrier preventing phase slips. The barrier vanishes when the critical rotation leads winding number and solitonic states to a matching configuration. At this point, Landau and Feynman criteria for phase slips meet: the fluid flow reaches the local speed of sound, and stationary vortex lines (which are the building blocks of multidimensional solitons) can be excited inside the system.
We study superfluid dissipation due to phase slips for a Bose-Einstein condensate flowing through a repulsive barrier inside a torus. The barrier is adiabatically raised across the annulus, while the condensate flows with a finite quantized angular momentum. At a critical height, a vortex moves from the inner region and reaches the barrier to eventually circulate around the annulus. At a higher critical height, an antivortex also enters into the torus from the outer region. Both vortex and antivortex decrease the total angular momentum by leaving behind a $2\ensuremath{\pi}$ phase slip. When they collide and annihilate or orbit along the same loop, the condensate suffers a global $2\ensuremath{\pi}$ phase slip, and the total angular momentum decreases by one quantum. In hydrodynamic regime, the instability sets in when the local superfluid velocity equals the sound speed inside the barrier region.
We explore the hysteretic dynamics of spinor Bose-Einstein condensates of ultracold atoms loaded in static 2D ring geometries and subjected to varying synthetic magnetic fields. Electrically neutral, pseudo-spin-1/2 condensates are probed by one-component weak-link potentials that make available paths for the transit of vortices into and out of the ring in both components, and thus can control the number of flux quanta threading the ring hole. For perpendicular fields, domain walls that are dynamically generated in the relative phase of the spin components are shown to play a key role in driving the hysteretic behavior of the whole system through changes in the net magnetic flux. In the presence of spin-orbit coupling, hysteresis is exhibited around the phase transitions found by the metastable current states for varying fields.
The interplay of quantum fluctuation through the Lee-Huang-Yang (LHY) correction and spin-orbit coupling can modify the stability of the ultradilute Bose-Bose mixtures and result in rich nonlinear physics. Here, under the action of spin-orbit coupling, LHY correction, and rotation, the ground state and vortex excitation of spin-orbit coupled Bose-Einstein condensates (BECs) with LHY correction trapped in a rotating potential are studied. Stable isotropic and anisotropic ground states with zero momentum (in the zero-momentum phase) and nonzero momentum (in the plane wave phase) are obtained. It is shown that anisotropic ground states are persistent near the phase boundary. Particularly, unpolarized and polarized vortex states are predicted. The phase transition condition, the effective mass and quadrupole surface mode describing the anisotropic (deformation) of the condensates, and the critical rotation frequency for vortex excitation are provided analytically. Owing to the action of spin-orbit coupling, the effective mass of the condensates is spatially dependent and asymmetric in two phases, resulting in distinct quadrupole modes, deformations, and vortex excitations in the two phases, especially when the LHY correction is present. The LHY correction promotes the system in the zero-momentum phase with unpolarized vortex states, while the spin-orbit coupling promotes the emergence of a plane wave phase with polarized vortex states. The phase transition and vortex excitation can be well manipulated by spin-orbit coupling, Raman coupling, LHY correction, and external potential.