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

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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:
[more]
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