Making the Virtual Real: Measurement-Powered Tunneling Engines

TL;DR

By leveraging continuous measurement of the central dot in a detuned triple quantum dot, the authors convert virtual tunneling processes into real transport and energy exchange with a detector, enabling measurement-powered engines, refrigerators, and hybrid energetics. The core approach combines a global eigenbasis treatment with a detector-induced Lindbladian, revealing that measurement backaction can drive the system into a dark state $|D\rangle$ and even purify it into a pure steady state via purification-by-noise. The work demonstrates two refrigeration mechanisms—energy-exchange with the detector (absorption-like) and checkpoint cooling from localization of barrier transmission—operating alongside autonomous, detector-assisted power generation and energy conversion. These results establish measurement as a thermodynamic resource and purity engine in quantum transport, with potential realizations in solid-state devices and circuit QED platforms.

Abstract

Quantum tunneling allows electrons to be transferred between two regions separated by an energetically forbidden barrier. Performing a position measurement that finds a particle in the barrier forces the tunneling electrons to transition from having a classically forbidden energy to an energy above the barrier height. We exploit this effect to define quantum tunneling engines that can use the unconditioned detection of virtually occupied states as a resource for power generation and cooling. Leveraging energy exchange with the detector, we show that the device can operate in a hybrid regime, enabling simultaneous cooling and power generation. Furthermore, we demonstrate measurement-assisted autonomous refrigeration and "checkpoint" cooling driven purely by a thermal bias, without the need for an applied potential. We also find a "purification-by-noise" effect when the measurement drives the system into a stationary dark state. These results underscore the intriguing dual role of measurement as a thermodynamic resource and a dark state generator.

Figures (7)

• Figure 1: Triple quantum dot engine fueled by a quantum point contact detector. Each dot is coupled to a different reservoir $l$=L,C,R via tunneling rates $\Gamma_l$. Electrons tunneling between the left and right quantum dots with energies $\varepsilon$ are detected when virtually occupying the central one detuned by an energy $\Delta$ and absorbed by reservoir C. Interdot tunneling is given by $\Omega$. The electrochemical potential of C can be either tuned to have a power-generating engine or a quantum state purifier, or grounded to have a refrigerator.
• Figure 2: (a) Zero bias generated current $I_{\rm C}$ in units of $e\Gamma$ as a function of the position of the outer quantum dot levels, $\varepsilon$ and the splitting of the central dot with respect to them, $\Delta$, with $\gamma=5\Gamma$, and (b) as a function of the bias $\mu_{\rm C}-\mu$ for different detection strengths, with $\varepsilon-\mu=-k_{\rm B}T$ and $\Delta=10k_{\rm B}T$. Other parameters: $\Omega=k_{\rm B}T$, $\Gamma=0.1k_{\rm B}T/\hbar$, and $\mu_L=\mu_R=\mu=0$. The black star in panel (b) denotes the potential bias where the current becomes independent of the detector strength. A finite measurement-induced current is observed even in the absence of potential bias ($\mu_{\rm C} = \mu$).
• Figure 3: (a) Generated power, $P$, as a function of $\mu_{\rm C}$ for different detection strengths $\gamma/\Gamma$. Contour plots of (b) $(P)$, (c) the heat current exchanged with the detector, $J_{\rm d}$, and (d) the efficiency, $\eta$, as functions of the measurement strength $\gamma$ and the potential bias $\mu_{\rm C} - \mu$. Negative values in (b), indicating dissipated power, are shown in gray for clarity. The same parameters as in Fig. \ref{['fig:current_3t_gating']} are used.
• Figure 4: Operations of the device for different couplings to the detector: (a) $\gamma\to0$, (b) $\gamma=\Gamma/5$ and (c) $\gamma=\Gamma$, with parameters as given in Fig. \ref{['fig:current_3t_gating']}. The operational regimes are classified as follows: ${\rm R}_l$ denotes the region where the system operates as a refrigerator for reservoir $l$$(J_l<0)$; E corresponds to power generation ($P > 0$); and ${\rm ER}_l$ identifies hybrid regions where refrigeration and power generation coexist.
• Figure 5: Autonomous refrigerator: Heat currents in reservoirs (a), (b) $R$ and (c), (d) $C$ for different couplings to the detector: (a), (c) $\gamma=\Gamma$ and (b), (d) $\gamma=10\Gamma$, as functions of the position of the quantum dot levels. Parameters: $\Omega/k_{\rm B}T=1$, $T_R=T_C=T$, $T_L=1.1T$, $\Gamma/k_{\rm B}T=0.1$ and $\mu_L=\mu_R=\mu=0$. Schematic descriptions of the involved processes are shown in (e) for the absorption refrigeration and in (f) for checkpoint cooling.