Quantum Measurement Cooling

Invasiveness of quantum measurements is a genuinely quantum mechanical feature that is not necessarily detrimental: Here we show how quantum measurements can be used to fuel a cooling engine. We illustrate quantum measurement cooling (QMC) by means of a prototypical two-stroke two-qubit engine which interacts with a measurement apparatus and two heat reservoirs at different temperatures. We show that feedback control is not necessary for operation while entanglement must be present in the measurement projectors. We quantify the probability that QMC occurs when the measurement basis is chosen randomly, and find that it can be very large as compared to the probability of extracting energy (heat engine operation), while remaining always smaller than the most useless operation, namely, dumping heat in both baths. These results show that QMC can be very robust to experimental noise. A possible low-temperature solid-state implementation that integrates circuit QED technology with circuit quantum thermodynamics technology is presented.

Figure 1

Various ways to pump a heat current from a cold to a hot reservoir. (a) In standard refrigeration the heat current is powered by energy injected by a time dependent driving force $f(t)$. (b) In Maxwell demon refrigeration heat current is generated by a feedback loop where various driving forces $f_n(t)$ are applied depending on the outcome $n$ of noninvasive measurements on the working substance, without energy injection. (c) In quantum measurement cooling, put forward here, the heat current is powered by energy provided via invasive measurements on an appropriate measurement basis $\{|{\psi }_k⟩\}$, without performing feedback control. Solid arrows represent flow of energy.

Figure 2

Left panel: Two-stroke two-qubit quantum measurement cooling. During the first stroke (top) the two qubits interact with the measurement apparatus, as a consequence qubit 1 receives energy ($⟨\mathrm{\Delta }{E}_1⟩\ge 0$), while qubit 2 loses energy ($⟨\mathrm{\Delta }{E}_2⟩\le 0$) with an overall positive energy injection ($⟨\mathrm{\Delta }{E}_1⟩+⟨\mathrm{\Delta }{E}_2⟩=⟨\mathrm{\Delta }E⟩\ge 0$). During the second stroke qubit 1 releases energy to the hot bath while qubit 2 withdraws energy from the cold bath. Right panel: the four possible operations allowed by the second law of thermodynamics, Eq. (5), and energy conservation.

Figure 3

Probability $P_x$ of the various operations $x=[A],[H],[E],[R]$ as a function of level spacing ratio ${\omega }_2/{\omega }_1$, at two fixed values of temperature ratios ${\beta }_1/{\beta }_2$.