The problem of estimating the frequency of a two-level atom in a noisy environment is studied. Our interest is to minimise both the energetic cost of the protocol and the statistical uncertainty of the estimate. In particular, we prepare a probe in a 'GHZ-diagonal' state by means of a sequence of qubit gates applied on an ensemble of n atoms in thermal equilibrium. Noise is introduced via a phenomenological time-non-local quantum master equation, which gives rise to a phase-covariant dissipative dynamics. After an interval of free evolution, the n-atom probe is globally measured at an interrogation time chosen to minimise the error bars of the final estimate. We model explicitly a measurement scheme which becomes optimal in a suitable parameter range, and are thus able to calculate the total energetic expenditure of the protocol. Interestingly, we observe that scaling up our multipartite entangled probes offers no precision enhancement when the total available energy  is limited. This is at stark contrast with standard frequency estimation, where larger probes-more sensitive but also more 'expensive' to prepare-are always preferred. Replacing  by the resource that places the most stringent limitation on each specific experimental setup, would thus help to formulate more realistic metrological prescriptions.

We devise experimental schemes able to mimic uniform and staggered magnetic fluxes acting on ultracold two-electron atoms, such as ytterbium atoms, propagating in a honeycomb lattice. The atoms are first trapped into two independent state-selective triangular lattices and are further exposed to a suitable configuration of resonant Raman laser beams. These beams induce hops between the two triangular lattices and make atoms move in a honeycomb lattice. Atoms traveling around each unit cell of this honeycomb lattice pick up a nonzero phase. In the uniform case, the artificial magnetic flux sustained by each cell can reach about two flux quanta, thereby realizing a cold atom analogue of the Harper model with its notorious Hofstadter's butterfly structure. Different condensed-matter phenomena such as the relativistic integer and fractional quantum Hall effects, as observed in graphene samples, could be targeted with this scheme.Comment: 12 pages, 14 figure

We present a quantitative method, utilising a highly sensitive quantum sensor, that extends applicability of magnetorelaxometry to biological samples at physiological temperature. The observed magnetic fields allow for non-invasive determination of physical properties of magnetic materials and their surrounding environment inside the specimen. The method is applied to American cockroaches and reveals magnetic deposits with strikingly different behaviour in alive and dead insects. We discuss consequences of this finding to cockroach magneto-reception. To our knowledge, this work represents the first characterisation of the magnetisation dynamics in live insects and helps to connect results from behavioural experiments on insects in magnetic fields with characterisation of magnetic materials in their corpses.