Dissipation-induced Tonks-Girardeau gas of polaritons

A scheme for the generation of a Tonks-Girardeau (TG) gas of polaritons with purely dissipative interaction is described. We put forward a master equation approach for the description of stationary light in atomic four-level media and show that, under suitable conditions, two-particle decays are the dominant photon loss mechanism. These dissipative two-photon losses increase the interaction strength by at least one order of magnitude as compared to dispersive two-photon processes and can drive the polaritons into the TG regime. Characteristic correlations of the TG gas, including quantities that distinguish it from free fermions, can be measured via standard quantum optical techniques. Our scheme thus allows one to feasibly generate highly correlated photon states, which can be of considerable use in quantum-information processing and precision measurements.

Figure 1

(a) Considered setup of $N$ atoms confined to an interaction volume of length $L$ and transverse area $A$. ${\Omega }_{\pm }$ are the Rabi frequencies of the classical control fields, and ${\mathrm{Ê}}_{\pm }$ are the quantum probe fields. (b) Atomic level scheme. ${\gamma }_{\mathit{ij}}$ is the full decay rate on the $|i\rangle \leftrightarrow |j\rangle$ transition, $\delta$ and $\Delta$ label the detuning of the probe fields with states $|3\rangle$ and $|4\rangle$, respectively, and $\varepsilon$ is the two-photon detuning.