Probing the energy reactance with adiabatically driven quantum dots

The tunneling Hamiltonian describes a particle transfer from one region to another. Although there is no particle storage in the tunneling region itself, it has an associated amount of energy. The corresponding energy flux was named reactance since, such as an electrical reactance, it manifests itself in time-dependent transport only. We show here that the existence of the energy reactance leads to the universal response of a mesoscopic thermometer, a floating contact coupled to an adiabatically driven quantum dot.

Figure 1

Schematic of our proposal. The quantum RC circuit consists of a quantum dot (the dark blue disk in the middle) coupled to a fermionic reservoir (the light blue region in the left) with well-defined temperature $T$ and chemical potential $\mu$. Electrons can be transferred between the dot and the reservoir (the black curve). The dot is capacitively coupled to a gate terminal where an ac potential of amplitude $V$ and frequency $\mathrm{\Omega }$ is applied. A floating contact is also attached to the dot. For every time snapshot, the temperature $T_c^t$ and chemical potential ${\mu }_c^t$ of the floating contact adjust themselves to cancel both the charge and the heat currents flowing through it. This instantaneous reaction allows for an experimental test of the energy reactance, namely, the variation of the stored energy at the tunneling region between the floating contact and the dot (the gray line).

Figure 2

Deviation of the temperature of the floating contact $\delta {\tilde{T}}_c^t$ as a function of time for different background temperatures $T$. The ac potential is $20\mathrm{\Gamma }cos\left(\mathrm{\Omega }t\right)$ with $\hslash \mathrm{\Omega }=0.07\mathrm{\Gamma }$. The hybridization between the floating contact and the quantum level is ${\mathrm{\Gamma }}_c=0.6\mathrm{\Gamma }$. All energies are expressed in units of the hybridization $\mathrm{\Gamma }$ with the reservoir. The temperature of the floating contact displays oscillations that depend on the background temperature. As $T$ increases, the oscillations become less pronounced, and the maxima positions deviate from the moment when the level is aligned with the chemical potential of the reservoir, which in this case corresponds to $t\mathrm{\Omega }/2\pi =0.25$ and $t\mathrm{\Omega }/2\pi =0.75$.