Truncated correlation hierarchy schemes for driven-dissipative multimode quantum systems
Abstract
We present a method to describe driven-dissipative multi-mode systems by considering a truncated hierarchy of equations for the correlation functions. We consider two hierarchy truncation schemes with a global cutoff on the correlation order, which is the sum of the exponents of the operators involved in the correlation functions: a 'hard' cutoff corresponding to an expansion around the vacuum, which applies to a regime where the number of excitations per site is small; a 'soft' cutoff which corresponds to an expansion around coherent states, which can be applied for large excitation numbers per site. This approach is applied to describe the bunching-antibunching transition in the driven-dissipative Bose-Hubbard model for photonic systems. The results have been successfully benchmarked by comparison with calculations based on the corner-space renormalization method in 1D and 2D systems. The regime of validity and strengths of the present truncation methods are critically discussed.
Cite
@article{arxiv.1605.00882,
title = {Truncated correlation hierarchy schemes for driven-dissipative multimode quantum systems},
author = {Wim Casteels and Stefano Finazzi and Alexandre Le Boité and Florent Storme and Cristiano Ciuti},
journal= {arXiv preprint arXiv:1605.00882},
year = {2016}
}