Electromagnetically induced transparency and quantum heat engines

We describe how electromagnetically induced transparency may be used to construct a nontraditional near-ideal quantum heat engine as constrained by the second law. The engine is pumped by a thermal reservoir that may be either hotter or colder than that of an exhaust reservoir, and also by a monochromatic laser. As output, it produces a bright narrow emission at line center of an otherwise absorbing transition.

Figure 1

(a) An ensemble of atoms is pumped by blackbody radiation. (b) The pumping temperature is $T_{13}$ on the $\left|1\right.〉\to \left|3\right.〉$ transition and $T_{23}$ on the $\left|2\right.〉\to \left|3\right.〉$ transition. A monochromatic “coupling” laser with Rabi frequency ${\mathrm{\Omega }}_c$ is tuned to resonance of the $\left|2\right.〉\to \left|3\right.〉$ transition. As a result of EIT there is a spectrally narrow and bright emission in the $z$ direction. This emission will generally have a higher temperature than that of either of the pertinent reservoirs.

Figure 2

(a) Absorptive (dashed line) and emissive (solid line) cross sections as a function of the detuning from resonance $\mathrm{\Delta }\omega$. (b) Spectral brightness $B_{\text{black}}\left(\mathrm{\Delta }\omega \right)$ normalized to the modal number ${\overline{n}}_{13}$. At peak the normalized brightness is 64.9 times larger than that of Kirchhoff's law. Parameters are ${\mathrm{\Gamma }}_{31}={10}^7,{\mathrm{\Gamma }}_{32}=6\times {10}^7,{\mathrm{\Omega }}_c=5\times {10}^7,{\omega }_{13}=4\times {10}^{15},{\omega }_{12}={10}^{15}$, and $T_0=5778\text{K}$. The population ratio $\mathrm{\Lambda }$ is 0.019.

Figure 3

(a) $B_{\text{black}}(\mathrm{\Delta }\omega =0)$ versus $\mathrm{\Omega }/{\gamma }_{31}$ normalized to ${\overline{n}}_{13}$ and (b) the same quantity in units of normalized temperature. The parameters are the same as those of Fig. 2. The dashed line is the temperature $T_B$ predicted by the second law.