Entropic costs of extracting classical ticks from a quantum clock

TL;DR

This paper experimentally investigates the thermodynamic costs of quantum timekeeping by measuring the entropy and precision of a quantum clock based on charge tunneling in a double quantum dot, highlighting the dominant role of measurement-induced entropy.

Contribution

It provides the first experimental analysis of the interplay between microscopic clock entropy and macroscopic measurement costs in a quantum clock system.

Findings

Measurement record enhances clock precision at equilibrium.

Measurement-induced entropy surpasses microscopic clock entropy.

Amplification and measurement are the main thermodynamic costs of quantum timekeeping.

Abstract

We experimentally realize a quantum clock by using a charge sensor to count charges tunneling through a double quantum dot (DQD). Individual tunneling events are used as the clock's ticks. We quantify the clock's precision while measuring the power dissipated by the DQD and, separately, the charge sensor in both direct-current and radio-frequency readout modes. This allows us to probe the thermodynamic cost of creating ticks microscopically and recording them macroscopically. Our experiment is the first to explore the interplay between the entropy produced by a microscopic clockwork and its macroscopic measurement apparatus. We show that the latter contribution not only dwarfs the former but also unlocks greatly increased precision, because the measurement record can be exploited to optimally estimate time even when the DQD is at equilibrium. Our results suggest that the entropy produced by the amplification and measurement of a clock's ticks, which has often been ignored in the literature, is the most important and fundamental thermodynamic cost of timekeeping at the quantum scale.