Abstract
Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero. The bound can be saturated by monitoring the non-equilibrium dynamics of a single-qubit probe. We support this finding by accurate numerical simulations of a spin-boson model. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantum thermometry, and practically, in guiding the development of sensitive thermometric techniques applicable at ultracold temperatures.
Highlights
Sensitive measurements of temperature are essential throughout natural science and modern technology
This scaling can be saturated by monitoring the nonequilibrium dynamics of a single-qubit probe. We support this finding by numerical simulations of a spin-boson model. This shows that thermometry with a vanishing absolute error at low temperature is possible with finite resolution, answering an interesting question left open by previous work
This indicates that the predicted precision scaling is experimentally relevant, even without the requirement of being able to probe the nonequilibrium qubit dynamics at very short-times
Summary
Sensitive measurements of temperature are essential throughout natural science and modern technology. Detailed studies of biological, chemical, and physical processes, the miniaturization of electronics, and emerging quantum technology drive a need for new thermometry techniques applicable at the nanoscale and in regimes where quantum effects become important. We determine a tight bound on the best possible precision with which temperature can be estimated in cold quantum systems, which accounts for limitations due to imperfect measurements. The classical picture of thermometry is that of a thermometer which is brought into thermal contact with a sample. A similar picture can be applied in the quantum regime, where an individual quantum probe, e.g. a two-level system, may interact with a sample system in a thermal state, and subsequently be measured to estimate the temperature. If the probe reaches thermal equilibrium with the sample, or a nonequilibrium
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