  The ultrastrong coupling between the elementary excitations of matter and
microcavity modes is studied in a fully analytical quantum-mechanical
theoretical framework. The elementary excitation could be phonons, excitons,
plasmons, etc. From the diagonalization of the Hamiltonian, we obtain the
ground state of the polariton Hamiltonian. The ground state belongs to the
Gaussian class. Using the Gaussian property we calculate the quantum
entanglement in the ground state. We use two different measures for quantum
entanglement -- entanglement entropy and the logarithmic negativity parameter
and obtain rather simple analytical expressions for the entanglement measures.
Our findings show that the amount of quantum entanglement in the ground state
is quite significant in the ultrastrong coupling regime. It can be obtained
from the measurement of the polariton frequencies.

Quantum Physics