We show that the two-photon temporal (longitudinal) correlation of light is limited by its classical optical spectral width. We present examples of the sources of two-photon light approaching this limit.
Although light quanta were known since the works by Planck and Einstein, for several decades after these works, there was no need to treat light quantum mechanically, and all experiments could be well explained using the quantum description of matter and classical description of light (the semiclassical approach). The situation changed with the development of sources of so-called nonclassical light, i.e., light whose properties cannot be understood in the framework of the semiclassical approach. Two simple examples can be given here. The first one is the suppression of shot noise in optical detectors. Shot noise, i.e., fluctuations of photocurrent scaling as the square root of the photocurrent mean value, can be, in principle, attributed to the discrete nature of the charge generated by the detector. At the same time, the effect of shot-noise suppression, which is observed with certain light sources (squeezed light) is clearly related to the statistics of light, and quantum mechanics is completely necessary for its description. Another example, which brings us closer to the subject of the present paper, is two-photon light. This type of light contains only pairs of photons (often called biphotons), and hence, a pair of properly aligned photon-counting detectors registering two-photon light, in an ideal case, will produce only simultaneous photocounts. This behavior, again, can only be explained in terms of a quantum-mechanical description for the light.
In this talk, I will discuss the growing field of entangled-photon spectroscopy as related to mol. systems. An entangled \nstate is represented by a wavefunction, describing a group of particles, which cannot be factored into sep. states of \nindividual particles. For photons, these correlations lead to non-classical light-matter interactions, potentially creating new opportunities for spectroscopic techniques. For example, second-order processes with two entangled photons, such as two-photon absorption or sum frequency generation, occur at a linear rate with a cross section that should be close to that of one-photon classical processes. However, early results in the field have produced conflicting measurements as to its magnitude. I will discuss the role of excited state dephasing and time-ordering for entangled photon interactions. I will also briefly remark on other interesting prospects of entangled photons, such as their ability to break the temporal-spectral Fourier transform limit. For instance, few-femtosecond spectroscopy is predicted to be possible with entangled light sources of MHz linewidths. Given the entangled photons quantum correlations, this property may lead to interesting opportunities in directing quantum coupled quantum states, although the techniques are still at an early stage.
Spectroscopy based on individual-photon-level light sources brings new variables to both spectroscopy and imaging. We refer to this approach as quantum-light spectroscopy (QLS). The photon statistics of different types of photon sources and photon entanglements are briefly described. We then illustrate the potential of QLS by means of some current experimental examples including time-resolved spectroscopy performed with single photons and quantum-enhanced optical imaging, showing how all the methods rely on correlations between entangled photons in the pair. We then ask: how might physical chemists exploit QLSs to expose new physical insights? For example, can we address fundamental questions in interactions between light and molecules or materials that are very difficult to address with classical light sources? Does QLS open up techniques to study highly congested spectra with higher combined spectral and temporal resolution than is possible with classical light? The concept of QLS also opens the potential study of fundamental questions such as what initial excited states are produced by individual photon absorption? We also point out the experimental challenges in extending QLS to more complex spectroscopies, such as multidimensional spectroscopies. We conclude with a brief selection of recent theoretical proposals to extend the capabilities of the QLS.
Theoretical analysis shows that the correlation time of a photon pair is closely related to the spectrum of two-photon light. This entails limitations on the shortest achievable two-photon correlation time. These limitations are important for quantum optical metrology and information processing applications, especially those involving quasi-monochromatic light. In this paper we present a more rigorous proof of the fact that the shortest possible two-photon correlation time is limited by approximately the inverse width of the optical spectrum. We further show that this limit can be closely approached with Type-I spontaneous parametric down-conversion at a specific pump wavelength. This study also results in the prediction of very unusual parametric down-conversion spectra, suggesting a method for engineering of frequency-entangled two-photon states.
A concept for an ultra-broad-band optical parametric amplifier or oscillator has emerged as a by-product of a theoretical study in fundamental quantum optics. The study was originally intended to address the question of whether the two-photon temporal correlation function of light [in particular, light produced by spontaneous parametric down conversion (SPDC)] can be considerably narrower than the inverse of the spectral width (bandwidth) of the light. The answer to the question was found to be negative. More specifically, on the basis of the universal integral relations between the quantum two-photon temporal correlation and the classical spectrum of light, it was found that the lower limit of two-photon correlation time is set approximately by the inverse of the bandwidth. The mathematical solution for the minimum two-photon correlation time also provides the minimum relative frequency dispersion of the down-converted light components; in turn, the minimum relative frequency dispersion translates to the maximum bandwidth, which is important for the design of an ultra-broad-band optical parametric oscillator or amplifier. In the study, results of an analysis of the general integral relations were applied in the case of an optically nonlinear, frequency-dispersive crystal in which SPDC produces collinear photons. Equations were found for the crystal orientation and pump wavelength, specific for each parametric-down-converting crystal, that eliminate the relative frequency dispersion of collinear degenerate (equal-frequency) signal and idler components up to the fourth order in the frequency-detuning parameter