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Quantum lattice Boltzmann simulation of expanding Bose-Einstein condensates in random potentials
1Dipartimento di Matematica, Università Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy.
Summary
Anderson localization in expanding Bose-Einstein condensates is observed using a quantum lattice Boltzmann method. While localized states are metastable, they degrade slowly over time, following a specific decay law.
Area of Science:
- Quantum physics
- Condensed matter physics
- Nonlinear dynamics
Background:
- Bose-Einstein condensates (BECs) exhibit quantum phenomena.
- Anderson localization describes wave function confinement in disordered systems.
- One-dimensional BECs provide a platform to study localization effects.
Purpose of the Study:
- Investigate Anderson localization in expanding 1D BECs.
- Numerically solve the Gross-Pitaevskii equation with a random potential.
- Compare quantum lattice Boltzmann (QLB) with Crank-Nicolson methods.
Main Methods:
- Numerical simulations of the Gross-Pitaevskii equation.
- Implementation of a random speckle potential.
- Application of the quantum lattice Boltzmann (QLB) method.
- Comparison with the Crank-Nicolson numerical scheme.
Main Results:
- Evidence of Anderson localization in low-energy condensates.
- Healing length found to be one-tenth of the Thomas-Fermi length.
- Observed slow degradation of Anderson localization over long-time simulations (15,000 periods).
- Inverse localization length decay follows a t^{-1/3} law.
Conclusions:
- Localized wave functions in expanding BECs are extremely long-lived metastable states.
- The QLB method effectively captures Anderson localization phenomena.
- The observed slow degradation supports the metastable nature of localized states.
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