Competition between Two-Photon Driving, Dissipation, and Interactions in Bosonic Lattice Models: An Exact Solution

Area of Science:

• Quantum optics
• Many-body physics
• Condensed matter theory

Background:

• Quantum systems often exhibit complex dynamics under external driving and dissipation.
• Understanding steady states is crucial for controlling quantum devices and exploring novel quantum phenomena.
• Traditional methods like mean-field theory struggle with strong correlations in driven-dissipative systems.

Purpose of the Study:

• To develop an exact analytical solution for a specific class of quantum driven-dissipative bosonic models.
• To investigate phenomena such as dissipative phase transitions, mode competition, and symmetry breaking.
• To explore the stabilization of many-body quantum states, specifically SU(1,1) pair-coherent states.

Main Methods:

• Derivation of an exact solution for the steady states of quantum driven-dissipative bosonic models.
• Analysis of models with two-photon driving, single-photon loss, and global Hubbard (Kerr) interactions.
• Extension of the solution to arbitrary dimensions.

Main Results:

• Exact solutions reveal the emergence of dissipative phase transitions.
• Demonstration of nontrivial mode competition and symmetry breaking phenomena.
• Identification of the stabilization of many-body SU(1,1) pair-coherent states.
• The exact solutions allow for the description of spatial correlations.

Conclusions:

• The developed exact solutions are valid in regimes where mean-field and semiclassical approaches fail.
• This work provides a powerful tool for studying complex quantum phenomena in driven-dissipative systems.
• The findings open new avenues for designing and controlling quantum systems with tailored properties.