We use a nonperturbative theoretical approach to the parametric down-conversion (PDC) process, which generates an entangled-photon field for an arbitrarily strong pump-pulse. This approach can be used to evaluate multipoint field correlation functions to compute nonlinear spectroscopic signals induced by a strong pump. The entangled-photon statistics is studied using Glauber’s g (2) function, which helps understand the significance of the photon entanglement-time and the pump-pulse intensity on spectroscopic signals. Under the nonperturbative treatment of the entangled field, the two-photon absorption (TPA) signal shows linear to strongly nonlinear growth with the pump intensity, rather than the linear to quadratic scaling reported previously. An increase in the range of pump intensity for the linear scaling is observed as the pump bandwidth is increased. We propose an experimental scheme that can select contributions to the TPA signal that arise solely from interactions with the entangled photons, and filter out unentangled-photon contributions, which are dominant at higher pump intensities, paving a way to explore the entanglement effects at higher intensities.
We use a nonperturbative theoretical approach to the parametric down-conversion (PDC) process, which generates an entangled-photon field for an arbitrarily strong pump-pulse. This approach can be used to evaluate multipoint field correlation functions to compute nonlinear spectroscopic signals induced by a strong pump. The entangled-photon statistics is studied using Glauber’s g (2) function, which helps understand the significance of the photon entanglement-time and the pump-pulse intensity on spectroscopic signals. Under the nonperturbative treatment of the entangled field, the two-photon absorption (TPA) signal shows linear to strongly nonlinear growth with the pump intensity, rather than the linear to quadratic scaling reported previously. An increase in the range of pump intensity for the linear scaling is observed as the pump bandwidth is increased. We propose an experimental scheme that can select contributions to the TPA signal that arise solely from interactions with the entangled photons, and filter out unentangled-photon contributions, which are dominant at higher pump intensities, paving a way to explore the entanglement effects at higher intensities.
Time- and frequency-gated two-photon counting is given by a four-time correlation function of the electric field. This reduces to two times with purely time gating. We calculate this function for entangled photon pulses generated by parametric down-conversion. At low intensity, the pulses consist of well-separated photon pairs, and crossover to squeezed light as the intensity is increased. This is illustrated by the two-photon absorption signal of a three-level model, which scales linearly for a weak pump intensity where both photons come from the same pair, and gradually becomes nonlinear as the intensity is increased. We find that the strong frequency correlations of entangled photon pairs persist even for higher photon numbers. This could help facilitate the application of these pulses to nonlinear spectroscopy, where these correlations can be used to manipulate congested signals.
The application of quantum states of light such as entangled photons, for example, created by parametric down conversion, has experienced tremendous progress in the almost 40 years since their first experimental realization. Initially, they were employed in the investigation of the foundations of quantum physics, such as the violation of Bell's inequalities and studies of quantum entanglement. They later emerged as basic platforms for quantum communication protocols and, in the recent experiments on single-photon interactions, in photonic quantum computation. These applications aim at the controlled manipulation of the photonic degrees of freedom, and therefore rely on simple models of matter, where the analysis is simpler. Furthermore, quantum imaging with entangled light can achieve enhanced resolution, and quantum metrology can overcome the shot noise limit for classical light. This Account focuses on an entirely different emerging class of applications using quantum light as a powerful spectroscopic tool to reveal novel information about complex molecules. These applications utilize two appealing properties of quantum light: its distinct intensity fluctuations and its nonclassical bandwidth properties. These give rise to new and surprising behavior of nonlinear optical signals. Nonclassical intensity fluctuations can enhance nonlinear optical signals relative to linear absorption. For instance, the two-photon absorption of entangled photon pairs scales linearly (rather than quadratically) in the photon flux, just like a single photon absorption. This enables nonlinear quantum spectroscopy of photosensitive, for example, biological, samples at low light intensities. We will discuss how the two-photon absorption cross section becomes a function of the photonic quantum state, which can be manipulated by properties of the entangled photon pairs. In addition, the quantum correlations in entangled photon states further influence the nonlinear signals in a variety of ways. Apart from affecting the signal's scaling with intensity, they also constitute an entirely new approach to shaping and controlling excitation pathways in molecular aggregates in a way that cannot be achieved with shaped classical pulses. This is because between the two absorption events in entangled two-photon absorption, the light and material system are entangled. Classical constraints for the simultaneous time and frequency resolution can thus be circumvented, since the two are not Fourier conjugates. Here we review the simplest manifestation of quantum light spectroscopy, two-photon absorption spectroscopy with entangled photons. This will allow us to discuss exemplarily the impact of quantum properties of light on a nonlinear optical signal and explore the opportunities for future applications.
When two-photon interactions are induced by down-converted light with a bandwidth that exceeds the pump bandwidth, they can obtain a behavior that is pulselike temporally, yet spectrally narrow. At low photon fluxes this behavior reflects the time and energy entanglement between the down-converted photons. However, two-photon interactions such as two-photon absorption (TPA) and sum-frequency generation (SFG) can exhibit such a behavior even at high power levels, as long as the final state (i.e., the atomic level in TPA, or the generated light in SFG) is narrow-band enough. This behavior does not depend on the squeezing properties of the light, is insensitive to linear losses, and has potential applications. In this paper we describe analytically this behavior for traveling-wave down conversion with continuous or pulsed pumping, both for high- and low-power regimes. For this we derive a quantum-mechanical expression for the down-converted amplitude generated by an arbitrary pump, and formulate operators that represent various two-photon interactions induced by broadband light. This model is in excellent agreement with experimental results of TPA and SFG with high-power down-converted light and with entangled photons [Dayan et al., Phys. Rev. Lett. 93, 023005 (2004); 94, 043602 (2005); Pe'er et al., ibid. 94, 073601 (2005)].
The linear intensity scaling of entangled two-photon absorption (ETPA) offers a fundamental mechanism to enable nonlinear optical spectroscopy and microscopy under a substantially lower excitation power than is currently feasible. However, the long data acquisition time and low signal-to-noise ratio in reported ETPA-based spectroscopic and microscopic studies prevent its widespread application. To gain the full potential of this novel quantum light approach, it is essential to optimize entangled photon generation for significantly enhanced ETPA responses. Here, we report a new quantum light source by combining entangled photon generation with free-space femtosecond pump-pulse shaping. Through measurements of singles and coincidence counts by varying the patterns applied to a spatial light modulator to control the spectral widths of the pump pulses, we reveal strong dependence of the singles and coincidence count rates as well as their ratios on the spectral widths of pump pulses. An optimal spectral width for the highest ratios between the coincidence photon and the signal or idler photon count rates is also determined. Identification of such optimal spectral widths for entangled photon generation in the presence of postgeneration spectral selection makes this quantum light source a promising choice for ETPA-based spectroscopy and imaging.
We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statistical information of the pump field. In situations in which the pump is a Gaussian Schell-model field, we derive explicit expressions for the coherence functions. Finally, we show that the concurrence of time-energy-entangled two-qubit states is bounded by the degree of temporal coherence of the pump field. This study can have important implications for understanding how correlations of the pump field manifest as two-particle entanglement as well as for harnessing energy-time entanglement for long-distance quantum communication protocols.
Optical technologies based on two-photon absorption can provide high resolution and deep tissue penetration but require very high peak power intensities because of the extremely small absorption cross sections associated with this phenomenon. The use of quantum-entangled photon pairs has been reported to increase the two-photon absorption rate compared with that obtainable using classical coherent laser sources. However, the enhancement that can possibly be obtained using entangled two-photon absorption (ETPA) has thus far been realized only at low photon rates, typically ranging from 107 (on the pW level) to 1013 (on the μW level) photons/s. For this reason, ETPA has been regarded as impractical. The present work demonstrates an experimental evaluation of ETPA-excited fluorescence at both low (μW) and relatively high (mW) pump power levels, using a high-gain parametric down-conversion source. Both an increase in the absorption rate and a linear correlation between rate and power were observed within both power ranges. This work also compared quantum and coherent sources. Assessments of the crossover photon flux suggest that the larger spatial-mode diameter of the present quantum source at the focal point (relative to values used in prior research) may have contributed to the rate enhancement seen at high-power levels. The results presented herein are expected to provide a new route to the mitigation of damage often associated with two-photon imaging and photodynamic therapies.