(| ω 1 > 1 | ω 2 > 2 +| ω 2 > 1 | ω 1 > 2), precision
decreases slower with visibility than for states with a Gaussian spectral distribution is ∫dωp( ω)| ω > 1 | ω + δ > 2, where is a Gaussian distribution and is a constant frequency. The experimental results are shown in Figure 2.
LIGHT AND COLOR FOCUS
FPC2), which allow for arbitrary polarization transformations. The temporal delay between the photons is controlled using an optical delay line( MDL) placed in arm 1. The two paths are recombined and separated by a 50 / 50 beam-splitter( BS). Finally, the photons are sent to superconducting nanowire single photon detectors( SNSPD)- the“ measurement” step in Box 1. Temporal correlations between the detected photons are analyzed by a time-to-digital converter( TDC).
The experimental results display an excellent agreement with the theoretical predictions: a quadratic behavior is observed for the ratio between the maximal Fisher information F ~ V and the QFI, F ~ V /. The curvature of the parabola depends on the state, and we confirm experimentally that for spectral distributions corresponding to Schrödinger cat-like states( states of the type
1
— √
– 2
(| ω 1 > 1 | ω 2 > 2 +| ω 2 > 1 | ω 1 > 2), precision
decreases slower with visibility than for states with a Gaussian spectral distribution is ∫dωp( ω)| ω > 1 | ω + δ > 2, where is a Gaussian distribution and is a constant frequency. The experimental results are shown in Figure 2.
Figure 2 illustrates the evolution of the ratio between the maximum of the Fisher Information F ~ V and the quantum Fisher Information as a function of visibility V for four engineered states. The results reveal that the Schrödinger Cat( SC)-like state exhibits the most favorable scaling behavior, outperforming the Gaussian state. For instance, at a visibility of approximately 99.4 %, the F ~ V / ratio is 0.97 for the SC-like state and 0.85 for the Gaussian state. Notably, the experimentally achieved ratio of 0.97 relative to the quantum limit is the highest ever reported, establishing a new benchmark in the field.
CONCLUSION In conclusion, we have presented the fundamental ideas and concepts of quantum metrology in quantum optics, along with recent efforts to establish a unified framework for quantum metrology ranging from single photons in different modes to many photons in a single mode. This approach highlights the respective roles of field statistics and of modes of the field, which vary depending on the specific quantum state. Additionally, we have described an experiment that explores the metrological potential of a two-photon system, along with its limitations. A careful analysis of these limitations has led to a strategy for optimizing the ratio between the Fisher information and the quantum Fisher information in this type of experiment. Quantum metrology in quantum optics remains a rapidly evolving field. A more comprehensive understanding of the interplay between modes and states will be essential for fully harnessing the capabilities of quantum optics to reach ultimate precision limits.
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