Mean Field Theory for Ground State of Superradiance

実 木村, Minoru Kimura

L. Bakemeier, Andreas Alvermann, Holger Fehske

We introduce a variational ansatz for the Dicke model that extends mean-field theory through the inclusion of spin–oscillator correlations. The correlated variational state is obtained from the mean-field product state via a unitary transformation. The ansatz becomes correct in the limit of large oscillator frequency and in the limit of a large spin, for which it captures the leading quantum corrections to the classical limit exactly including the spin–oscillator entanglement entropy. We explain the origin of the unitary transformation before we show that the ansatz improves substantially upon mean-field theory, giving near exact results for the ground state energy and very good results for other observables. We then discuss why the ansatz still encounters problems in the transition regime at moderate spin lengths, where it fails to capture the precursors of the superradiant quantum phase transition faithfully. This observation illustrates the principal limits of semi-classical formulations, even after they are extended with correlations and entanglement.

Toshihico Arimitsu, Masuo Suzuki

Xiaofan Zhou, Jingtao Fan, Gang Chen +1 more

Using a state-of-the-art numerical method density-matrix renormalization-group, we study the ground states of one-dimensional spinless Bose-Hubbard model inside a red-detuned cavity. By calculating the superfluid order, density distribution, second and third-order correlation functions, we find that there exist two novel supersolid phases with diagonal, off-diagonal orders beyond mean-field theory. One has package type density modulation along the lattice axis, another exhibits uniform density distribution. Moreover, by calculating the superradiant order parameter and the number of photon inside the cavity, we find that the novel supersolid phases are highly related to cavity-field fluctuation. Our work gives the physics beyond the mean-field theory of the Bose-Hubbard model inside an optical cavity, and provides the complete approach to fully explore the collective state of light and matter inside an optical cavity.

Vincenzo Gino Benza, E. Montaldi, Mikael Ciftan

Noe Salmeron, Marin Bukov, Markus Schmitt

Recent advances in cold atom manipulation enable the study of many-body systems where short-range interactions between neighboring atoms coexist with long-range interactions mediated by photons. Such a combination of interactions makes a theoretical approach challenging beyond mean-field methods. In this work, we develop a neural quantum state based approach to study these systems numerically. We introduce a neural-network architecture capable of handling hybrid Hilbert spaces with large local bosonic dimensions in strongly interacting spin-photon systems. We benchmark this approach on a model of a two-dimensional lattice of Rydberg atoms coupled to a photon mode. The superradiant ground states found in the large spin-photon coupling regime allow us to demonstrate the efficiency of the method in the presence of high photon occupation. Furthermore, the ability to capture spin-spin and spin-photon correlations leads us to observe quantitative deviations in the ground state phase boundaries with respect to mean-field theory. The method extends to other systems with a similar hybrid Hilbert space structure, such as spin-phonon systems, and provides a scalable framework for investigating their ground state properties.