Beating standard quantum limit via two-axis magnetic susceptibility measurement

We report a metrology scheme which measures magnetic susceptibility of an atomic spin ensemble along the x and z direction and produces parameter estimation with precision beating the standard quantum limit. The atomic ensemble is initialized via one-axis spin squeezing with optimized squeezing time and parameter φ to be estimated is assumed as uniformly distributed between 0 and 2π, while fixed in each estimation. One estimation of φ can be produced with every two magnetic susceptibility data measured along the two axis respectively, which has imprecision scaling (1.43 ± 0.02)/N 0.687±0.003 with respect to the number N of atomic spins. The measurement scheme is easy to implement and is robust against measurement fluctuation caused by environment noise and measurement defects.

Indistinguishability of Temporally Separated Pairwise Two- Photon State of Thermal Photons in Franson-Type Interferometry

The phenomenon of Franson interference with time–energy entangled photon pairs beyond the single-photon coherence length observed upon nonlocal measurement at two space-like separated locations is of particular research interest. Herein, we determine the coherence length of temporally separated pairwise two-photon (TSPT) states of thermal photons emitted from a warm atomic ensemble in Franson-type interferometry, with the setup consisting of two spatially separated unbalanced Michelson interferometers beyond the coherence length of a thermal photon. Using a novel method of square-modulated thermal photons, we show that the sinusoidal Franson-type interference fringe of thermal photons is determined by the presence or absence of TSPT states (corresponding to the time delay between the long and short paths in Franson-type interferometry). We find that the indistinguishability of the TSPT state in the Franson-type interference is independent of the temporal separation of the thermal photons in the TSPT states.