Cooling by heating in the quantum optics domain

A class of Hamiltonians that are experimentally feasible in several contexts within quantum optics and lead to so-called cooling by heating for fermionic as well as for bosonic systems has been analyzed numerically. We have found a large range of parameters for which cooling by heating can be observed either for the fermionic system alone or for the combined fermionic and bosonic systems. Analyzing the experimental requirements, we conclude that cooling by heating is achievable with present-day technology, especially in the context of trapped-ion and cavity QED, thus contributing to the understanding of this interesting and counterintuitive effect.

Figure 1

(a) Average energy for the atomic $\langle H_a\rangle /{\omega }_0$ [dashed line ($\times 10$)] and bosonic $\langle H_f\rangle /\nu$ (solid line) systems versus a common mean number of thermal photons $n_{\text{th}}=m_{\text{th}}$ for the model $k=1$. (b) Response function versus mean number of thermal photons. The cooling by heating can occur for $m_{\text{th}}=n_{\text{th}}\lesssim 1.4$ for the bosonic system and $m_{\text{th}}=n_{\text{th}}\lesssim 0.9$ for the atomic system. The parameters used are $\kappa =0.1\gamma$ and $g_1=1.0\gamma$.

Figure 2

(a) Average energy for the atomic [dashed line ($\times 10$)] and bosonic (solid line) systems versus a common mean number of thermal photons $n_{\text{th}}=m_{\text{th}}$ for the model $k=2$. The mean value of the interaction Hamiltonian $H_I$ (not shown in this figure) is always zero. (b) Response function versus mean number of thermal photons. The cooling by heating can occur for $m_{\text{th}}=n_{\text{th}}\lesssim 1.2$ for the bosonic and $m_{\text{th}}=n_{\text{th}}\lesssim 0.4$ for the atomic system. The parameters used are $\kappa =0.1\gamma$ and $g_2=0.2\gamma$.

Figure 3

Response function to the atomic system versus the average photon number $m_{\text{th}}$ of its reservoir when fixing the average photon number of the bosonic reservoir: $n_{\text{th}}=0.0$ (solid line), $n_{\text{th}}=1.0$ (dashed line), and $n_{\text{th}}=2.0$ (dotted line), for model (a) $k=1$, using $\kappa =0.1\gamma$ and $g_1=1.0\gamma$, and (b) $k=2$, using $\kappa =0.1\gamma$ and $g_2=0.2\gamma$.