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Hysteresis in a quantized superfluid ‘atomtronic’ circuit

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Abstract

Atomtronics1,2 is an emerging interdisciplinary field that seeks to develop new functional methods by creating devices and circuits where ultracold atoms, often superfluids, have a role analogous to that of electrons in electronics. Hysteresis is widely used in electronic circuits—it is routinely observed in superconducting circuits3 and is essential in radio-frequency superconducting quantum interference devices4. Furthermore, it is as fundamental to superfluidity5 (and superconductivity) as quantized persistent currents6,7,8, critical velocity9,10,11,12,13,14 and Josephson effects15,16. Nevertheless, despite multiple theoretical predictions5,17,18,19, hysteresis has not been previously observed in any superfluid, atomic-gas Bose–Einstein condensate. Here we directly detect hysteresis between quantized circulation states in an atomtronic circuit formed from a ring of superfluid Bose–Einstein condensate obstructed by a rotating weak link (a region of low atomic density). This contrasts with previous experiments on superfluid liquid helium where hysteresis was observed directly in systems in which the quantization of flow could not be observed20, and indirectly in systems that showed quantized flow21,22. Our techniques allow us to tune the size of the hysteresis loop and to consider the fundamental excitations that accompany hysteresis. The results suggest that the relevant excitations involved in hysteresis are vortices, and indicate that dissipation has an important role in the dynamics. Controlled hysteresis in atomtronic circuits may prove to be a crucial feature for the development of practical devices, just as it has in electronic circuits such as memories, digital noise filters (for example Schmitt triggers) and magnetometers (for example superconducting quantum interference devices).

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Figure 1: Origin of hysteresis.
Figure 2: Experimental set-up and procedure.
Figure 3: Hysteresis data.
Figure 4: Extracted critical velocities versus U2.

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Acknowledgements

This work was partially supported by ONR, the ARO atomtronics MURI, and the NSF through the PFC at the JQI and grant PHY-1068761. S.E. is supported by a National Research Council postdoctoral fellowship. We wish to thank K. Wright, W. T. Hill III and A. Kumar for valuable discussions and experimental assistance.

Author information

Authors and Affiliations

Authors

Contributions

S.E., J.G.L. and F.J. took the experimental data. N.M., C.W.C. and M.E. developed and performed the GPE simulations. All authors were involved in analysis and discussions of the results, and contributed to writing the manuscript.

Corresponding author

Correspondence to Gretchen K. Campbell.

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Competing interests

The authors declare no competing financial interests.

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Supplementary information

Supplementary Information

This file contains Supplementary Methods (sections S1-S2) that describe in detail the calibration procedures and numerical calculations. The Supplementary Discussion (S3-S5) extends ideas contained within the main text in more detail, including non-zero temperature's effect on the broadening of the transitions, adiabaticity in our system, and speculation as to what occurs in the non-hysteretic regime. (PDF 297 kb)

Animation showing a numerical simulation of our ring condensate transitioning from n=0 to n=0.

The left panel shows the vorticity and the right panel the atomic density. The barrier stir rate is 1.2 Hz, just below the theoretical n=0 to n=1 transition frequency. See section S2 of the Supplementary Methods for more details. (MOV 95 kb)

Animation showing a numerical simulation of our ring condensate transitioning from n=0 to n=1.

The left panel shows the vorticity and the right panel the atomic density. The barrier stir rate is 1.4 Hz, just above the theoretical n=0 to n=1 transition frequency. See section S2 of the Supplementary Methods for more details. (MOV 96 kb)

Animation showing a numerical simulation of our ring condensate transitioning from n=1 to n=1.

The left panel shows the vorticity and the right panel the atomic density. The barrier stir rate is 0.0 Hz, just above the theoretical n=1 to n=0 transition frequency. See section S2 of the Supplementary Methods for more details. (MOV 69 kb)

Animation showing a numerical simulation of our ring condensate transitioning from n=1 to n=0.

The left panel shows the vorticity and the right panel the atomic density. The barrier stir rate is -0.2 Hz, just below the theoretical n=1 to n=0 transition frequency. See section S2 of the Supplementary Methods for more details. (MOV 74 kb)

Animation showing a numerical simulation of our ring condensate transitioning from n=0 to n=0.

The left panel shows the phase and the right panel the atomic density. The barrier stir rate is 1.2 Hz, just below the theoretical n=0 to n=1 transition frequency. See section S2 of the Supplementary Methods for more details. (MOV 1214 kb)

Animation showing a numerical simulation of our ring condensate transitioning from n=0 to n=1.

The left panel shows the phase and the right panel the atomic density. The barrier stir rate is 1.4 Hz, just above the theoretical n=0 to n=1 transition frequency. See section S2 of the Supplementary Methods for more details. (MOV 1296 kb)

Animation showing a numerical simulation of our ring condensate transitioning from n=1 to n=1.

The left panel shows the phase and the right panel the atomic density. The barrier stir rate is 0.0 Hz, just above the theoretical n=1 to n=0 transition frequency. See section S2 of the Supplementary Methods for more details. (MOV 1496 kb)

Animation showing a numerical simulation of our ring condensate transitioning from n=1 to n=0.

The left panel shows the phase and the right panel the atomic density. The barrier stir rate is -0.2 Hz, just below the theoretical n=1 to n=0 transition frequency. See section S2 of the Supplementary Methods for more details. (MOV 1481 kb)

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Eckel, S., Lee, J., Jendrzejewski, F. et al. Hysteresis in a quantized superfluid ‘atomtronic’ circuit. Nature 506, 200–203 (2014). https://doi.org/10.1038/nature12958

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