Amplitude and phase mode in a Bose Einstein condensate
Aranya B. Bhattacherjee
TL;DR
This paper demonstrates how to decompose the Bogoliubov mode in Bose-Einstein condensates into amplitude and phase modes using Heisenberg equations, applicable to free gases and optical lattices.
Contribution
It introduces a method to split the Bogoliubov mode into amplitude and phase components through operator transformations.
Findings
Decomposition of Bogoliubov mode into amplitude and phase modes.
Applicable to both free Bose gases and optical lattice systems.
Provides a theoretical framework for analyzing collective excitations.
Abstract
We show that starting from the Heisenberg equations of motion for Bose annihilation and creation operators and using an appropriate transformation, we can split the Bogoliubov mode into a free particle mode and the amplitude mode. We show this for both the free Bose gas as well as the Bose gas in an optical lattice.
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Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Quantum Mechanics and Applications · Mechanical and Optical Resonators