A projection operator approach for ultracold bosons coupled to a cavity
Abstract
We employ a projection operator technique to study the equilibrium phases and the non-equilibrium quench and ramp dynamics of ultracold bosons described by a two-dimensional (2D) Bose-Hubbard model coupled to a high-finesse cavity with competing local short-range and cavity-mediated long-range interactions. Our analysis relies on a systematic elimination of high-energy virtual hopping processes; this enables us to capture the effects of short-range quantum fluctuations on the phase diagram of the model while treating the cavity-induced long-range interaction within mean-field theory. We find that the phase boundaries between the superfluid (SF), supersolid (SS), charge-density-wave (CDW) and Mott insulating (MI) phases are significantly modified by the presence of these fluctuations. We use this approach to study the dynamics of bosons following a quench/ramp from the CDW to the SS and SF phases; our analysis indicates the presence of oscillatory dynamics characterized by a single frequency due to a quench which takes the system near the critical point. In contrast, for a quench deep inside the SF phase, the dynamics involves multiple frequencies. An explicit comparison with Gutzwiller mean-field theory shows the importance of quantum fluctuations in shaping such post-quench dynamics; this feature may be tested experimentally as we discuss. We also study the ramp dynamics of these bosons and identify a bound on the ramp rate above which the present method is expected to produce accurate results.
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BibTeX
@misc{sen2026projection,
title = {{A projection operator approach for ultracold bosons coupled to a cavity}},
author = {Sarbarish Sen and Bimalendu Deb and K. Sengupta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34908},
eprint = {2609.34908},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34908},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A projection operator approach for ultracold bosons coupled to a cavity
AU - Sarbarish Sen
AU - Bimalendu Deb
AU - K. Sengupta
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34908
UR - https://arxiv.org/abs/2609.34908
AB - We employ a projection operator technique to study the equilibrium phases and the non-equilibrium quench and ramp dynamics of ultracold bosons described by a two-dimensional (2D) Bose-Hubbard model coupled to a high-finesse cavity with competing local short-range and cavity-mediated long-range interactions. Our analysis relies on a systematic elimination of high-energy virtual hopping processes; this enables us to capture the effects of short-range quantum fluctuations on the phase diagram of the model while treating the cavity-induced long-range interaction within mean-field theory. We find that the phase boundaries between the superfluid (SF), supersolid (SS), charge-density-wave (CDW) and Mott insulating (MI) phases are significantly modified by the presence of these fluctuations. We use this approach to study the dynamics of bosons following a quench/ramp from the CDW to the SS and SF phases; our analysis indicates the presence of oscillatory dynamics characterized by a single frequency due to a quench which takes the system near the critical point. In contrast, for a quench deep inside the SF phase, the dynamics involves multiple frequencies. An explicit comparison with Gutzwiller mean-field theory shows the importance of quantum fluctuations in shaping such post-quench dynamics; this feature may be tested experimentally as we discuss. We also study the ramp dynamics of these bosons and identify a bound on the ramp rate above which the present method is expected to produce accurate results.
ER -