Revealing the fuel of a quantum continuous measurement-based refrigerator

TL;DR

The paper tackles the question of whether energy provided by quantum measurements manifests as heat or work, arguing that a microscopic model of the measuring device is essential. It studies a measurement-powered refrigerator built from two tunnel-coupled quantum dots with continuous measurement of the right dot, described by a global Lindblad master equation and a realistic QPC detector model; steady-state energy currents $J_L$, $J_R$, and the energy input $\dot E_M$ determine refrigeration when $J_L>0$. The authors show that the refrigerating device can operate in heat-fueled or work-fueled modes by tuning apparatus parameters such as the QPC bias $\mu_M$ and temperature $T_M$, with a trade-off between thermodynamic efficiency $\eta$ and measurement efficiency quantified by SNR; a microscopic framework clarifies energy accounting in measurement-based quantum machines. This work provides a pathway for energetic optimization of quantum measurement protocols and suggests feasible nanoelectronic experiments to validate the predictions.

Abstract

While quantum measurements have been shown to constitute a resource for operating quantum thermal machines, the nature of the energy exchanges involved in the interaction between system and measurement apparatus is still under debate. In this work, we show that a microscopic model of the apparatus is necessary to unambiguously determine whether quantum measurements provide energy in the form of heat or work. We illustrate this result by considering a measurement-based refrigerator, made of a double quantum dot embedded in a two-terminal device, with the charge of one of the dots being continuously monitored. Tuning the parameters of the measurement device interpolates between a heat- and a work-fueled regimes with very different thermodynamic efficiency. Notably, we demonstrate a trade-off between a maximal thermodynamic efficiency when the measurement-based refrigerator is fueled by heat and a maximal measurement efficiency quantified by the signal-to-noise ratio in the work-fueled regime. Our analysis offers a new perspective on the nature of the energy exchanges occurring during a quantum measurement, paving the way for energy optimization in quantum protocols and quantum machines.

Figures (3)

• Figure 1: Principle of the continuous measurement-powered refrigerator. The charge in the right quantum dot is continuously monitored by an apparatus at rate $\gamma_M$. As this measurement does not commute with the dot Hamiltonians, it results in an energy flow $\dot{E}_M$, which in turn powers heat transfer from the cold (left) to the hot (right) lead, that is $J_L < 0 < J_S$. On general grounds, the measuring apparatus can be powered either by a source of work providing power $P_M$ and/or a source of heat at temperature $T_M$ providing heat flow $J_M$.
• Figure 2: a): Stationary cooling power $J_L$ (blue), heat flow received from the hot lead $J_R$ (orange) and energy flow provided by the measuring apparatus $\dot{E}_M$ (green) in unit of $\gamma g$ as a function of the measurement strength $\gamma_M$. b) Cooling power $J_L$ in units of $\gamma g$ as a function of the ratio of the hot over cold lead temperatures $T_R/T_L$ and the measurement strength $\gamma/g$. c) Efficiency of conversion of measurement energy into cooling power $\eta_\text{id}=J_L/\dot{E}_M$ as a function of the ratio of the hot over cold lead temperatures $T_R/T_L$ and the measurement strength $\gamma/g$. In a) and b) and c), other parameters are set as follows: $\gamma/g= 0.01$, $\Delta/g = 4.3$, $\mu/g = 10$, $\epsilon/g = 5.4$, $\gamma_M/g = 1$, $T_L/g = 2$, and for a): $T_R/T_L =2$. The red dots indicate the parameter values considered in the QPC model.
• Figure 3: a): Realistic measuring apparatus model based on a tunnel junction (QPC) capacitively coupled to the right QD. b): Cooling power $J_L/\gamma g$, c): Coefficient of performance $\eta$ of the hybrid machine, defined in Eq. \ref{['eq:COP']} and d): Signal-to-noise ratio, as a function of the measuring apparatus temperature $T_M$ and electric bias $\mu_M$. The dashed black line delimits the area $J_L \leq 0$ in which refrigeration is not possible. e): Ratio $\xi = J_M/P_M$ of the heat and power flows used to fuel the measuring apparatus as a function of the electric bias $\mu_M$, for different values of the measuring apparatus temperature $T_M$. The other parameters are the same as in Fig.