Quantum metrology using time-frequency as quantum continuous variables: Resources, sub shot-noise precision and phase space representation

We study the role of the electromagnetic field's frequency in time precision measurements using single photons as a paradigmatic system. For such, we independently identify the contributions of intensity and spectral resources and show that both can play a role on the scaling of the precision of parameter estimation with the number of probes. We show in particular that it is possible to observe a quadratic scaling using quantum mode correlations only and explicit the mathematical expression of states saturating the Heisenberg limit. We also provide a geometrical and phase space interpretation of our results, and observe a curious quantum-to-classical-like transition on scaling by modifying the spectral variance of states. Our results connect discrete and continuous aspects of single photons and quantum optics by considering from a quantum mechanical perspective the role of frequency.Comment: 15 pages, 3 figure

Fundamental limitations of time measurement precision in Hong-Ou-Mandel interferometry

In quantum mechanics, the precision achieved in parameter estimation using a quantum state as a probe is determined by the measurement strategy employed. The ultimate quantum limit of precision is bounded by a value set by the state and its dynamics. Theoretical results have revealed that in interference measurements with two possible outcomes, this limit can be reached under ideal conditions of perfect visibility and zero losses. However, in practice, this cannot be achieved, so precision {\it never} reaches the quantum limit. But how do experimental setups approach precision limits under realistic circumstances? In this work we provide a general model for precision limits in two-photon Hong-Ou-Mandel interferometry for non-perfect visibility. We show that the scaling of precision with visibility depends on the effective area in time-frequency phase space occupied by the state used as a probe, and we find that an optimal scaling exists. We demonstrate our results experimentally for different states in a set-up where the visibility can be controlled and reaches up to $99.5\%$. In the optimal scenario, a ratio of $0.97$ is observed between the experimental precision and the quantum limit, establishing a new benchmark in the field