One qubit and one photon: The simplest polaritonic heat engine

Hybrid quantum systems can often be described in terms of polaritons. These are quasiparticles formed of superpositions of their constituents, with relative weights depending on some control parameter in their interaction. In many cases, these constituents are coupled to reservoirs at different temperatures. This suggests a general approach to the realization of polaritonic heat engines where a thermodynamic cycle is realized by tuning this control parameter. Here we discuss what is arguably the simplest such engine, a single qubit coupled to a single photon. We show that this system can extract work from feeble thermal microwave fields. We also propose a quantum measurement scheme of the work and evaluate its backaction on the operation of the engine.

Figure 1

Solid lines: dressed qubit energy levels as a function of the qubit-field detuning $\mathrm{\Delta }=\omega -{\omega }_L$ with $\omega$ being the qubit transition frequency and ${\omega }_L$ being the cavity field frequency for $g=0.1{\omega }_L$. Dashed lines: corresponding energy eigenvalues in the absence of interaction, $g=0$. The dressed and bare states are labeled beside the lines. ${\mathrm{\Delta }}_{1,2}$ denote the working frequency range of the quantum heat engine.

Figure 2

Dressed states picture for the two-qubit case. See the text for the definitions of the states $|{\varphi }_0^{(+)}\rangle$ and $|{\varphi }_0^{(-)}\rangle$. Other parameters as in Fig. 1.

Figure 3

Upper plot: Dressed states' and bare states' population dynamics during the isentropic stroke 3 in the absence of measurements ($\lambda =0$), and for measurement strengths $\lambda ={10}^{-4}{\omega }_L$ and $\lambda ={10}^{-3}{\omega }_L$. Here the qubit frequency $\omega \left(t\right)$ varies linearly in time from $1.2{\omega }_L$ to $0.8{\omega }_L$ and $g=0.013{\omega }_L$. Lower plot: Log-scale probability distribution $P\left(W\right)$ of the measured work obtained from 1000 stochastic quantum trajectories for the same measurement strengths.

Figure 4

Same plots as Fig. 3 but for the resonant absorptive measurement.