Quantum limits of thermometry

The precision of typical thermometers consisting of $N$ particles scales as $~1/\sqrt{N}$. For high-precision thermometry and thermometric standards, this presents an important theoretical noise floor. Here it is demonstrated that thermometry may be mapped onto the problem of phase estimation, and using techniques from optimal phase estimation, it follows that the scaling of the precision of a thermometer may in principle be improved to $~1/N$, representing a Heisenberg limit to thermometry.

Figure 1

Energy per particle $\mathrm{\varepsilon ̄}$ and relative sample uncertainty in $\beta$, scaled by $\sqrt{N}$, given by Eq. (5), for a toy thermometer consisting of $N$ independent, two-level systems.

Figure 2

An atomic interferometer with the bath in one branch. Atoms from the thermometer are input into mode 1 and detected in modes 5 and 6. Mode 2 is the vacuum port.