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Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two
Mateus C P Dos Santos1, Boris A Malomed2,3, Wesley B Cardoso1
1Instituto de Física, Universidade Federal de Goiás 74.690-970, Goiânia, Goiás, Brazil.
Physical Review. E
|November 20, 2020
Summary
We demonstrate a method to accurately reduce 3D Bose-Einstein condensate dynamics to 2D equations using a singular potential. This approach accurately predicts ground states, vortex states, and collapse thresholds, simplifying complex quantum system analysis.
Area of Science:
- Quantum physics
- Atomic physics
- Condensed matter physics
Background:
- Bose-Einstein condensates (BECs) exhibit complex 3D dynamics.
- Dimensional reduction simplifies theoretical models but requires validation.
- Singular potentials can induce unique quantum phenomena like superselection.
Purpose of the Study:
- To investigate the reduction of 3D Bose-Einstein condensate dynamics to a 2D mean-field equation using a specific singular potential.
- To analyze the accuracy of the reduced 2D model (nonpolynomial Schrödinger equation) against the full 3D Gross-Pitaevskii equation.
- To explore quantum phase transitions and the behavior of ground and vortex states within this reduced framework.
Main Methods:
- Utilizing a factorized ansatz for dimensional reduction.
- Solving the 1D Schrödinger equation with a singular potential V_{z}(z)=2z^{2}+ζ^{2}/z^{2} to obtain the z-dependent multiplier.
- Comparing numerical solutions of the 2D nonpolynomial Schrödinger equation (NPSE) with the 3D Gross-Pitaevskii equation (GPE).
Main Results:
- The 2D NPSE accurately reproduces ground states and vortex states for both repulsive and attractive interactions.
- The predicted collapse threshold in the attractive regime closely matches the 3D GPE results.
- Stability analysis of vortices with topological charges S=1, 2, and 3 was performed.
Conclusions:
- The spatial-dimension reduction from 3D to 2D using the factorized ansatz and singular potential is highly accurate.
- This method provides a reliable simplification for studying complex BEC dynamics.
- The approach is potentially applicable to other physical systems requiring dimensional reduction.
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