# Dispersion Properties of a Spin-Orbit-Coupled Bose-Einstein Condensate

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A Bose–Einstein condensate (BEC) is a state of matter in which a large fraction of the particles of a bosonic gas occupy the lowest-energy quantum state. For such a system, when the particle's spin couples to its orbital angular momentum, a so-called spin-orbit-coupled Bose–Einstein condensate (SOC-BEC) is formed. This state can be achieved experimentally by using Raman lasers to couple two internal states of an atomic BEC while transferring momentum [1]. In the limit of a homogeneous and noninteracting gas, the SOC-BEC can be described by the following momentum-space Hamiltonian:

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Contributed by: David Colas, Fabrice P. Laussy and Matthew J. Davis (September 2017)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The Snapshots show various configurations of the SOC-BEC dispersion.

Snapshot 1: the lower branch only exhibits a large negative mass for positive wavevectors,* *affecting the value of the velocity

Snapshot 2: the lower branch exhibits both negative mass and for positive wavevectors, affecting both the value and the sign of the velocity

Snapshot 3: the lower branch exhibits a broader range of wavevectors for which there is a negative mass ; this is obtained from Snapshot 2 by using the sliders to increase the Raman detuning and wavevector values

References

[1] Y.-J. Lin, K. Jiménez-Garcia and I. B. Spielman, "Spin–Orbit-Coupled Bose–Einstein Condensates," *Nature*, 471(7336), 2001 pp. 83–86. doi:10.1038/nature09887.

[2] D. Colas and F. P. Laussy, "Self-Interfering Wave Packets," *Physical Review Letters*,* *116, 2016 026401. doi:10.1103/PhysRevLett.116.026401.

## Permanent Citation

"Dispersion Properties of a Spin-Orbit-Coupled Bose-Einstein Condensate"

http://demonstrations.wolfram.com/DispersionPropertiesOfASpinOrbitCoupledBoseEinsteinCondensat/

Wolfram Demonstrations Project

Published: September 15 2017