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Abstract The authors demonstrate a form of two‐photon‐counting interferometry by measuring the coincidence counts between single‐photon‐counting detectors at an output port of a Mach–Zehnder Interferometer (MZI) following injection of broad‐band time‐frequency‐entangled photon pairs (EPP) generated from collinear spontaneous parametric down conversion into a single input port. Spectroscopy and refractometry are performed on a sample inserted in one internal path of the MZI by scanning the other path in length, which acquires phase and amplitude information about the sample's linear response. Phase modulation and lock‐in detection are introduced to increase detection signal‐to‐noise ratio and implement a “down‐sampling” technique for scanning the interferometer delay, which reduces the sampling requirements needed to reproduce fully the temporal interference pattern. The phase‐modulation technique also allows the contributions of various quantum‐state pathways leading to the final detection outcomes to be extracted individually. Feynman diagrams frequently used in the context of molecular spectroscopy are used to describe the interferences resulting from the coherence properties of time‐frequency EPPs passing through the MZI. These results are an important step toward the implementation of a proposed method for molecular spectroscopy—quantum‐light‐enhanced 2D spectroscopy. 

Two-photon absorption (TPA) and other nonlinear interactions of molecules with time–frequency-entangled photon pairs have been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This Tutorial presents a detailed theoretical study of one- and two-photon absorption by molecules, focusing on how to treat the quantum nature of light. We review some basic quantum optics theory and then we review the density-matrix (Liouville) derivation of molecular optical response, emphasizing how to incorporate quantum states of light into the treatment. For illustration, we treat in detail the TPA of photon pairs created by spontaneous parametric down conversion, with an emphasis on how quantum light TPA differs from that with classical light. In particular, we treat the question of how much enhancement of the TPA rate can be achieved using entangled states. This Tutorial includes a review of known theoretical methods and results as well as some extensions, especially the comparison of TPA processes that occur via far-off-resonant intermediate states only and those that involve off-resonant intermediate states by virtue of dephasing processes. A brief discussion of the main challenges facing experimental studies of entangled two-photon absorption is also given. 

When a low flux of time-frequency-entangled photon pairs (EPP) illuminates a two-photon transition, the rate of two-photon absorption (TPA) can be enhanced considerably by the quantum nature of photon number correlations and frequency correlations. We use a quantum-theoretic derivation of entangled TPA (ETPA) and calculate an upper bound on the amount of quantum enhancement that is possible in such systems. The derived bounds indicate that in order to observe ETPA the experiments would need to operate at a combination of significantly higher rates of EPP illumination, molecular concentrations, and conventional TPA cross sections than are achieved in typical experiments. 

The theory of sum-frequency generation (SFG) as a two-photon measurement process is used to infer the role of two-photon entanglement in this process, and an experimental setup and preliminary data are presented as a way towards quantifying the dependence of SFG on entanglement. 

Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process affects a generalized measurement on the input two-photon state. We describe the positive operator-valued measure (POVM) associated with such a measurement and show that its elements are proportional to the two-photon states produced by the time-reversed PDC process. Such a detection acts as a joint measurement on two photons and is thus an important component of many quantum information processing protocols relying on photonic entanglement. Using the retrodictive approach, we analyze the properties of the two-photon POVM that are relevant for quantum protocols exploiting two-photon states and measurements. 

We present a theoretical proof that the “quantum enhancement” of two-photon absorption, thought to be a means to improve molecular spectroscopy and imaging, is tightly bounded by the physics of photonic entanglement and nonlinear response. 

Fluorescence-detected Fourier transform (FT) spectroscopy is a technique in which the relative paths of an optical interferometer are controlled to excite a material sample, and the ensuing fluorescence is detected as a function of the interferometer path delay and relative phase. A common approach to enhance the signal-to-noise ratio in these experiments is to apply a continuous phase sweep to the relative optical path, and to detect the resulting modulated fluorescence using a phase-sensitive lock-in amplifier. In many important situations, the fluorescence signal is too weak to be measured using a lock-in amplifier, so that photon counting techniques are preferred. Here we introduce an approach to low-signal fluorescence-detected FT spectroscopy, in which individual photon counts are assigned to a modulated interferometer phase (‘phase-tagged photon counting,’ or PTPC), and the resulting data are processed to construct optical spectra. We studied the fluorescence signals of a molecular sample excited resonantly by a pulsed coherent laser over a range of photon flux and visibility levels. We compare the performance of PTPC to standard lock-in detection methods and establish the range of signal parameters over which meaningful measurements can be carried out. We find that PTPC generally outperforms the lock-in detection method, with the dominant source of measurement uncertainty being associated with the statistics of the finite number of samples of the photon detection rate.