Expectation values in the Lieb-Liniger Bose gas

Area of Science:

• Quantum physics
• Condensed matter physics
• Atomic, molecular, and optical physics

Background:

• The Lieb-Liniger model describes one-dimensional ultracold Bose gases.
• Calculating expectation values is essential for understanding Bose gas properties.
• The three-body recombination rate is a key factor in Bose gas dynamics.

Purpose of the Study:

• To introduce a novel computational method for expectation values in the Lieb-Liniger model.
• To enable calculations at both zero and finite temperatures.
• To determine the three-body expectation value at finite temperature.

Main Methods:

• Development of a novel series expansion for computing expectation values.
• Application of the method to the Lieb-Liniger model.
• Calculation of quantities at zero and finite temperatures.

Main Results:

• A new method for computing expectation values in the Lieb-Liniger model is presented.
• The method exhibits remarkable convergence properties.
• The three-body expectation value at finite temperature was successfully computed.

Conclusions:

• The novel method provides an accurate way to calculate crucial quantities for one-dimensional ultracold Bose gases.
• The computation of the three-body expectation value offers insights into Bose gas recombination rates.
• This work advances the theoretical understanding and computational capabilities for Bose-Einstein condensates.