Quantum Thermal Machine as a Thermometer

We propose the use of a quantum thermal machine for low-temperature thermometry. A hot thermal reservoir coupled to the machine allows for simultaneously cooling the sample while determining its temperature without knowing the model-dependent coupling constants. In its most simple form, the proposed scheme works for all thermal machines which perform at Otto efficiency and can reach Carnot efficiency. We consider a circuit QED implementation which allows for precise thermometry down to $\sim$15 mK with realistic parameters. Based on the quantum Fisher information, this is close to the optimal achievable performance. This implementation demonstrates that our proposal is particularly promising in systems where thermalization between different components of an experimental setup cannot be guaranteed.Comment: Main text: 5 pages, 4 figures; Supplement: 5 page

On the Generality of Refined Algebraic Quantization

The Dirac quantization `procedure' for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as refined algebraic quantization. We find technical conditions under which refined algebraic quantization can reproduce the general implementation of the Dirac scheme for systems whose constraints form a Lie algebra with structure constants. The main result is that, under appropriate conditions, the choice of an inner product on the physical states is equivalent to the choice of a ``rigging map'' in refined algebraic quantization.Comment: 12 pages, no figures, ReVTeX, some changes in presentation, some references adde