PT-Symmetry in Coupled Oscillators

A system may be considered PT-symmetric when, upon the action of both parity and time-reversal operators, it remains unchanged. In a system of two coupled oscillators, for instance, driving one oscillator and allowing comparable loss in the other consistutes a PT-symmetric system. For a pair of quantum oscillators, characterized by Rabi oscillations between discrete energy states, we find that the gain rate $\Gamma$ should not be exactly equal to the loss rate $\gamma$ to be PT-symmetric, but rather $\frac{\Gamma}{\gamma}=1+\frac{1}{\bar{n}}$, where $\bar{n}$ is the steady state excitation level. The $g^{\left( 1 \right)}$ correlation spectra under this condition show a central peak narrower than an ordinary Lorentzian, with a line-width inversely related to $\bar{n}$. Such oscillator systems come up in electromagnetically induced transparency (EIT), where electronic transition probabilities interfere, and stopped light, which utilizes EIT to store a pulse of light in an oscillator and release it at a later time.