Bypassing thermalization timescales in temperature estimation using prethermal probes

We introduce prethermal temperature probes for sensitive, fast and robust temperature estimation. While equilibrium thermal probes with a manifold of quasidegenerate excited states have been previously recognized for their maximal sensitivity, they suffer from long thermalization timescales. When considering time as a critical resource in thermometry, it becomes evident that these equilibrium probes fall short of ideal performance. Here, we propose a different paradigm for thermometry, where setups originally suggested for optimal equilibrium thermometry should instead be employed as prethermal probes, by making use of their long-lived quasiequilibrium state. This transient state emerges from the buildup of quantum coherences among quasidegenerate levels. For a class of physically-motivated initial conditions, we find that energy measurements of the prethermal state exhibit a similar sensitivity as the equilibrium state. However, they offer the distinct benefit of orders of magnitude reduction in the time required for the estimation protocol. Upon introducing a figure-of-merit that accounts for the estimation protocol time, prethermal probes surpass the corresponding equilibrium probes in terms of effective thermal sensitivity, opening avenues for rapid thermometry by harnessing the long-lived prethermal states.