In this paper we study the usefulness of photon statistics techniques in quantum beat spectroscopy when the intensity of the detected light beam is very small. It is concluded that accurate results can be obtained if the Fourier transform of the time-interval probability is measured.
There are many experiments in spectroscopy in which some quantity is swept as a linear function of time. For instance, the frequency is swept when a spectrum is recorded, the magnetic field is swept in a level-crossing experiment, etc. If the intensity of the resulting light beam is small the detected signal has a large nose component. One can reduce noise by repeating the experiment periodically and using a multichannel signal analyzer to process the signal and obtain the information contained in it.
Abstract Two-photon excitation spectroscopy is a nonlinear technique that has gained rapidly in interest and significance for studying the complex energy-level structure and transition probabilities of materials. While the conventional spectroscopy based on tunable classical light has been long established, quantum light provides an alternative way towards excitation spectroscopy with potential advantages in temporal and spectral resolution, as well as reduced photon fluxes. By using a quantum Fourier transform that connects the sum-frequency intensity and N00N-state temporal interference, we present an approach for quantum interferometric two-photon excitation spectroscopy. Our proposed protocol overcomes the difficulties of engineering two-photon joint spectral intensities and fine-tuned absorption-frequency selection. These results may significantly facilitate the use of quantum interferometric spectroscopy for extracting the information about the electronic structure of the two-photon excited-state manifold of atoms or molecules without any requirement for precise and complicated scanning in the spectral domain. This may be particularly relevant for photon-sensitive biological and chemical samples.
A photon-statistics technique that is based on the time-interval probability, W(θ), is studied. This technique consists of measuring the transform QR(X)=∫0∞W(θ)R(X,θ)dθ, where R(X, θ) is a square-wave function of frequency X. This function oscillates between one and zero as θ varies. The measurement of QR(X) can be carried out in a simple way. We study the error with which the period of a low-intensity square-wave-modulated light beam can be obtained by fitting a Lorentzian curve to the experimental values of QR(X). It is found that this technique is more accurate than the intensity-correlation technique when the intensity is small. The advantage increases as the intensity of the light beam decreases. This technique can be applied for those experiments in which oscillating-intensity light beams are obtained, the period providing the required information. For instance, it can be used in laser Doppler velocimetry and in quantum-beat spectroscopy.