Optimal phase control of a measurement-assisted quantum refrigerator

Jinkai Liu; Xian He; Jizhou He; Jianhui Wang

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arXiv · 2610.04237

Optimal phase control of a measurement-assisted quantum refrigerator

Jinkai Liu·Xian He·Jizhou He·Jianhui Wang

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Abstract

A tilted nonselective measurement can close the upper transition of a three-level quantum refrigerator, but it also generates coherence that feeds back on the populations and suppresses the cooling current. We formulate randomized open-loop control of the measurement azimuthal phase $α$, sampled independently at each event from a probability distribution $P(α)$, while keeping the event rate, polar angle, and single-event population-transfer probability fixed. Direct population transfer is phase independent, whereas the coherence source carries the factor $e^{-iα}$. Exact elimination of the stationary coherence gives $0\leq k_{\rm eff}[P]\leq A_m$, where $k_{\rm eff}[P]$ is the effective population-transfer rate between the upper levels and $A_m$ is the bare direct mixing rate. When the fixed measurement couples populations and coherence, the upper bound is attained if and only if $\langle e^{iα}\rangle_P=0$, where $\langle\cdot\rangle_P$ denotes an average over the phase distribution. The minimal realization uses two equally weighted phases separated by $π$: the population-to-coherence source and its return to the populations then vanish at the generator level, while the full direct mixing remains. Because the cold current increases strictly with $k_{\rm eff}$ in the refrigeration window, the same condition maximizes the stationary cooling power over the independent random-phase distributions considered here. For one representative parameter set, phase cycling increases the fixed-gap cooling power by about $32\%$ relative to a fixed-phase measurement, while leaving the ratio of extracted cold heat to supplied measurement energy unchanged.

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Jinkai Liu, Xian He, Jizhou He, Jianhui Wang. 2026-10-03. Optimal phase control of a measurement-assisted quantum refrigerator. https://arxiv.org/abs/2610.04237

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