  We study the role of bath-induced correlations in temperature estimation of
cold bosonic baths. Our protocol includes multiple probes, that are not
interacting, nor are they initially correlated to each other. They interact
with a bosonic sample and reach a nonthermal steady state, which is measured to
estimate the temperature of the sample. It is well known that in the steady
state such noninteracting probes may get correlated to each other and even
entangled. Nonetheless, the impact of these correlations in metrology has not
been deeply investigated yet. Here, we examine their role for thermometry of
cold bosonic gases and show that, although being classical, bath-induced
correlations can lead to significant enhancement of precision for thermometry.
The improvement is especially important at low temperatures, where attaining
high precision thermometry is particularly demanding. The proposed thermometry
scheme does not require any precise dynamical control of the probes and tuning
the parameters and is robust to noise in initial preparation, as it is built
upon the steady state generated by the natural dissipative dynamics of the
system. Therefore, our results put forward new possibilities in thermometry at
low temperatures, of relevance, for instance, in cold gases and Bose-Einstein
condensates.
