Mesoscopic Photon Heat Transistor

We show that the heat transport between two bodies, mediated by electromagnetic fluctuations, can be controlled with an intermediate quantum circuit—leading to the device concept of a mesoscopic photon heat transistor (MPHT). Our theoretical analysis is based on a novel Meir-Wingreen-Landauer-type of conductance formula, which gives the photonic heat current through an arbitrary circuit element coupled to two dissipative reservoirs at finite temperatures. As an illustration we present an exact solution for the case when the intermediate circuit can be described as an electromagnetic resonator. We discuss in detail how the MPHT can be implemented experimentally in terms of a flux-controlled SQUID circuit.

Figure 1

Temperature gradient between the left and right reservoirs induces photonic heat current through an arbitrary quantum circuit coupled to them. Heat flows from left to right when $T_L>T_R$. The reservoirs are assumed to behave as linear dissipative elements and they couple only through the middle circuit. In principle a direct coupling between the reservoirs always exists but in practice it can be made negligible by an appropriate sample design.

Figure 2

An electromagnetic resonator as the intermediate circuit (a). In (b) the mediate resonator circuit with a tunable inductance is realized by a dc SQUID with an external magnetic flux bias $\Phi$. The external flux can be used to modulate the heat current through the structure and plays an analogous role to the gate voltage in electronic transistor.

Figure 3

Heat flow through the SQUID structure as a function of applied flux $\Phi$, corresponding to parameters $M^2{\omega }_0/LR=1$, ${\omega }_0/{\omega }_R=1$ and $T_R=T_L/2=\hslash {\omega }_0$. The different curves correspond to different reservoir $Q$ values (from top to bottom), $Q=0$, $Q=0.1$, $Q=0.5$, $Q=2$, and $Q=10$. The heat flux is normalized with respect to the universal single-channel maximum value $J_{\max }=\frac{{\pi }^2{k}_B^2}{6h}(T_L^2-T_R^2)$. In the inset the heat flux is plotted as a function of the temperature of the right reservoir corresponding to the parameters ${\omega }_0/{\omega }_R=1$, $T_L=2\hslash {\omega }_0$, $Q=0.1$, and $\Phi =0$ mod ${\Phi }_0$. The different curves correspond to parameter values (from bottom to top) $M^2{\omega }_0/LR=0.5$, $M^2{\omega }_0/LR=1$, $M^2{\omega }_0/LR=3$, $M^2{\omega }_0/LR=5$, and $M^2{\omega }_0/LR=10$.