Effect of the Atomic Dipole-Dipole Interaction on the Phase Diagrams of Field-Matter Interactions I: Variational procedure

Abstract

We establish, within the second quantization method, the general dipole-dipole Hamiltonian interaction of a system of $n$-level atoms. The variational energy surface of the $n$-level atoms interacting with $\ell$-mode fields and under the Van Der Waals forces is calculated with respect the tensorial product of matter and electromagnetic field coherent states. This is used to determine the quantum phase diagram associated to the ground state of the system and quantify the effect of the dipole-dipole Hamiltonian interaction. By considering real induced electric dipole moments, we find the quantum phase transitions for $2$- and $3$-level atomic systems interacting with $1$- and $2$- modes of the electromagnetic field, respectively. The corresponding order of the transitions is established by means of Ehrenfest classification; for some undetermined cases, we propose two procedures: the difference of the expectation value of the Casimir operators of the $2$-level subsystems, and by maximizing the Bures distance between neighbor variational solutions.

arXiv comment17 pages, 9 figures

References in corpus (11)

• The physics of dipolar bosonic quantum gases
• Quo vadis, cold molecules? - Editorial review
• Super-Tonks-Girardeau regime in trapped one-dimensional dipolar gases
• Uniqueness of the Phase Transition in Many-Dipole Cavity Quantum Electrodynamical Systems
• Generalized Heisenberg algebra coherent states for Power-law potentials
• Long range dipole-dipole interaction in atomic vapors probed by double-quantum two-dimensional coherent spectroscopy
• Polychromatic phase diagram for $n$-level atoms interacting with $\ell$ modes of electromagnetic field
• A semi-classical versus quantum description of the ground state of three-level atoms interacting with a one-mode electromagnetic field
• Quantum Phase Diagrams of Matter-Field Hamiltonians II: Wigner Function Analysis
• Quantum Phase Diagrams of Matter-Field Hamiltonians I: Fidelity, Bures Distance, and Entanglement
• Variational Study of $\lambda$- and $N$-Atomic Configurations Interacting with an Electromagnetic Field of $2$ Modes