Quantifying the enhancement of two-photon absorption due to spectral-temporal entanglement

Exploiting Quantum Light-Matter Interaction for Probing and Controlling Molecules

Quantum mechanical properties of light, such as time-energy entanglement, quadrature squeezing, and non-Poisson statistics, can be exploited to develop novel spectroscopic signals that enhance the signal strength and spectrotemporal resolution. Moreover, quantum light also provides nonclassical control knobs for controlling the outcome of a chemical reaction. Here, we provide a perspective on how quantum light-matter interaction can be exploited to probe and control molecular events.

Enhancing Two-Photon Absorption of Green Fluorescent Protein by Quantum Entanglement

Exploring the electronic states of molecules through excitation with entangled and classical photon pairs offers new insights into the nature of light-matter interactions and stimulates the development of quantum spectroscopy. Here, we address the importance of temporal entanglement of light in two-photon absorption (TPA) upon the S0 → S1 transition by the green fluorescent protein (GFP)─a key molecular unit in the bioimaging of living cells. By invoking a two-level model applicable when permanent dipole pathways dominate the two-photon transition, we derive a convenient closed-form analytical expression for the entangled TPA strength. For the first time, we disclose specific molecular properties that cause classical and entangled two-photon absorptions to be qualitatively different when exciting the same state. We reveal a new nonclassical contribution to the TPA strength, which is defined by the magnitude and directional alignment of permanent dipole moments in the initial and final states. Using high-level electronic structure theory, we show that the nonclassical contribution is intrinsically larger than the classical counterpart in GFP, leading to an enhancement of the TPA strength due to quantum entanglement by several orders of magnitude. We also present evidence that the classical and quantum TPA strengths can be modulated differently by the protein environment and demonstrate how to control the outcome by alterations in the local electric field of the protein caused by a single amino acid replacement. Our findings establish physical grounds for enhancing TPA in photoactive proteins by quantum entanglement, facilitating the rational design of high-efficiency biomarkers for future applications that utilize quantum light.

Impact of Classical and Quantum Light on Donor-Acceptor-Donor Molecules

Investigations of entangled and classical two-photon absorption have been carried out for six donor (D)-acceptor (A)-donor (D) compounds containing the dithieno pyrrole (DTP) unit as donor and acceptors with systematically varied electronic properties. Comparing ETPA (quantum) and TPA (classical) results reveals that the ETPA cross section decreases with increasing TPA cross section for molecules with highly off-resonant excited states for single-photon excitation. Theory (TDDFT) results are in semiquantitative agreement with this anticorrelated behavior due to the dependence of the ETPA cross section but not TPA on the two-photon excited state lifetime. The largest cross section is found for a DTP derivative that has a single photon excitation energy closest to resonance with half the two-photon excitation energy. These results are important for the possible use of quantum light for low-intensity energy-conversion applications.

Two-photon absorption cross sections of pulsed entangled beams

Entangled two-photon absorption (ETPA) could form the basis of nonlinear quantum spectroscopy at very low photon fluxes, since, at sufficiently low photon fluxes, ETPA scales linearly with the photon flux. When different pairs start to overlap temporally, accidental coincidences are thought to give rise to a "classical" quadratic scaling that dominates the signal at large photon fluxes and, thus, recovers a supposedly classical regime, where any quantum advantage is thought to be lost. Here, we scrutinize this assumption and demonstrate that quantum-enhanced absorption cross sections can persist even for very large photon numbers. To this end, we use a minimal model for quantum light, which can interpolate continuously between the entangled pair and a high-photon-flux limit, to analytically derive ETPA cross sections and the intensity crossover regime. We investigate the interplay between spectral and spatial degrees of freedom and how linewidth broadening of the sample impacts the experimentally achievable enhancement.

Entangled Two-Photon Absorption in Transmission-Based Experiments: Deleterious Effects from Linear Optical Losses

Recently different experimental schemes have been proposed to study the elusive phenomenon of entangled two-photon absorption (ETPA) in nonlinear materials. The attempts to detect ETPA using transmission-based schemes have led to results whose validity is currently under debate because the ETPA signal can be corrupted or emulated by artifacts associated with linear optical losses. The present work addresses the issue of linear losses and the corresponding artifacts in transmission-based ETPA experiments through a new approach that exploits the properties of a Hong-Ou-Mandel (HOM) interferogram. Here, we analyze solutions of rhodamine B (RhB), commonly used as a model of a nonlinear medium in ETPA studies. Then, by using the HOM interferometer as a sensing device, we first demonstrate the equivalence of the standard transmission vs pump power ETPA experiments, presented in many reports, with our novel approach of transmission vs two-photon temporal delay. Second, a detailed study of the effects of optical losses, unrelated to ETPA, over the HOM interferogram is carried out by: (1) characterizing RhB in solutions prepared with different solvents and (2) considering scattering losses introduced by silica nanoparticles used as a controlled linear loss mechanism. Our results clearly expose the deleterious effects of linear optical losses over the ETPA signal when standard transmission experiments are employed and show how, by using the HOM interferogram as a sensing device, it is possible to detect the presence of such losses. Finally, once we showed that the HOM interferogram discriminates properly linear losses, our study also reveals that under the specific experimental conditions considered here, which are the same as those employed in many reported works, the ETPA was not unequivocally detected.

Experimental upper bounds for resonance-enhanced entangled two-photon absorption cross section of indocyanine green

Resonant intermediate states have been proposed to increase the efficiency of entangled two-photon absorption (ETPA). Although resonance-enhanced ETPA (r-ETPA) has been demonstrated in atomic systems using bright squeezed vacuum, it has not been studied in organic molecules. We investigate for the first time r-ETPA in an organic molecular dye, indocyanine green (ICG), when excited by broadband entangled photons in near-IR. Similar to many reported virtual state mediated ETPA (v-ETPA) measurements, no r-ETPA signals are measured, with an experimental upper bound for the cross section placed at 6(±2) × 10-23 cm2. In addition, the classical resonance-enhanced two-photon absorption (r-TPA) cross section of ICG at 800 nm is measured for the first time to be 20(±13) GM, where 1 GM equals 10-50 cm4 s, suggesting that having a resonant intermediate state does not significantly enhance two-photon processes in ICG. The spectrotemporally resolved emission signatures of ICG excited by entangled photons are also presented to support this conclusion.

Photoelectron spectroscopy with entangled photons; enhanced spectrotemporal resolution

In this theoretical study, we show how photoelectron signals generated by time-energy entangled photon pairs can monitor ultrafast excited state dynamics of molecules with high joint spectral and temporal resolutions, not limited by the Fourier uncertainty of classical light. This technique scales linearly, rather than quadratically, with the pump intensity, allowing the study of fragile biological samples with low photon fluxes. Since the spectral resolution is achieved by electron detection and the temporal resolution by a variable phase delay, this technique does not require scanning the pump frequency and the entanglement times, which significantly simplifies the experimental setup, making it feasible with current instrumentation. Application is made to the photodissociation dynamics of pyrrole calculated by exact nonadiabatic wave packet simulations in a reduced two nuclear coordinate space. This study demonstrates the unique advantages of ultrafast quantum light spectroscopy.

Nonlinear Interferometry for Quantum-Enhanced Measurements of Multiphoton Absorption

Multiphoton absorption is of vital importance in many spectroscopic, microscopic, or lithographic applications. However, given that it is an inherently weak process, the detection of multiphoton absorption signals typically requires large field intensities, hindering its applicability in many practical situations. In this Letter, we show that placing a multiphoton absorbent inside an imbalanced nonlinear interferometer can enhance the precision of multiphoton cross section estimation with respect to strategies based on photon-number measurements using coherent or even squeezed light directly transmitted through the medium. In particular, the power scaling of the sensitivity with photon flux can be increased by 1 order compared with transmission measurements of the sample with coherent light, such that the measurement precision at any given intensity can be greatly enhanced. Furthermore, we show that this enhanced measurement precision is robust against experimental imperfections leading to photon losses, which usually tend to degrade the detection sensitivity. We trace the origin of this enhancement to an optimal degree of squeezing which has to be generated in a nonlinear SU(1,1) interferometer.

Studies of Local DNA Backbone Conformation and Conformational Disorder Using Site-Specific Exciton-Coupled Dimer Probe Spectroscopy

The processes of genome expression, regulation, and repair require direct interactions between proteins and DNA at specific sites located at and near single-stranded-double-stranded DNA (ssDNA-dsDNA) junctions. Here, we review the application of recently developed spectroscopic methods and analyses that combine linear absorbance and circular dichroism spectroscopy with nonlinear 2D fluorescence spectroscopy to study the local conformations and conformational disorder of the sugar-phosphate backbones of ssDNA-dsDNA fork constructs that have been internally labeled with exciton-coupled cyanine (iCy3)2 dimer probes. With the application of these methods, the (iCy3)2 dimer can serve as a reliable probe of the mean local conformations and conformational distributions of the sugar-phosphate backbones of dsDNA at various critical positions. The results of our studies suggest a possible structural framework for understanding the roles of DNA breathing in driving the processes of protein-DNA complex assembly and function.

Spectral Considerations of Entangled Two-Photon Absorption Effects in Hong-Ou-Mandel Interference Experiments

Recently, different experimental methods intended to detect the entangled two-photon absorption (ETPA) phenomenon in a variety of materials have been reported. The present work explores a different approach in which the ETPA process is studied based on the changes induced in the visibility of a Hong-Ou-Mandel (HOM) interferogram. By using an organic solution of Rhodamine B as a model of nonlinear material interacting with entangled photons at ∼800 nm region produced by spontaneous parametric down-conversion (SPDC) Type-II, the conditions that make possible to detect changes in the visibility of a HOM interferogram upon ETPA are investigated. We support the discussion of our results by presenting a model in which the sample is considered as a spectral filtering function which fulfills the energy conservation conditions required by ETPA, allowing us to explain the experimental observations with good agreement. We believe that this work represents a new perspective to studying the ETPA interaction, by using an ultrasensitive quantum interference technique and a detailed mathematical model of the process.

Fine-Tuning of Entangled Two-Photon Absorption by Controlling the One-Photon Absorption Properties of the Chromophore

The detailed analysis of the sum-over-state formula for the entanglement-induced two-photon absorption (ETPA) transition moment shows that the magnitude of the ETPA cross-section is expected to vary significantly depending on the coherence time T_e and the relative position of just two electronic states. Moreover, the dependency on T_e is periodic. These predictions are confirmed by molecular quantum mechanical calculations for several chromophores.

Spatial Properties of Entangled Two-Photon Absorption

We experimentally study entangled two-photon absorption in rhodamine 6G as a function of the spatial properties of a high flux of broadband entangled photon pairs. We first demonstrate a key signature dependence of the entangled two-photon absorption rate on the type of entangled pair flux attenuation: linear, when the laser pump power is attenuated, and quadratic, when the pair flux itself experiences linear loss. We then perform a fluorescence-based Z-scan measurement to study the influence of beam waist size on the entangled two-photon absorption process and compare this to classical single- and two-photon absorption processes. We demonstrate that the entangled two-photon absorption shares a beam waist dependence similar to that of classical two-photon absorption. This result presents an additional argument for the wide range of contrasting values of quoted entangled two-photon absorption cross sections of dyes in literature.

Single-Photon Scattering Can Account for the Discrepancies among Entangled Two-Photon Measurement Techniques

Entangled photon pairs are predicted to linearize and increase the efficiency of two-photon absorption, allowing continuous wave laser diodes to drive ultrafast time-resolved spectroscopy and nonlinear processes. Despite a range of theoretical studies and experimental measurements, inconsistencies in the value of the entanglement-enhanced interaction cross section persist. A spectrometer that can temporally and spectrally characterize the entangled photon state before, during, and after any potential two-photon excitation event is constructed. For the molecule rhodamine 6G, which has a virtual state pathway, any entangled two-photon interaction is found to be equal to or weaker than classical, single-photon scattering events. This result can account for the discrepancies among the wide variety of entangled two-photon absorption cross sections reported from different measurement techniques. The reported instrumentation can unambiguously separate classical and entangled effects and therefore is important for the growing field of nonlinear and multiphoton entangled spectroscopy.

Experimental Study of the Validity of Entangled Two-Photon Absorption Measurements in Organic Compounds

Entangled two-photon absorption (ETPA) has recently become a topic of lively debate, mainly due to the apparent inconsistencies in the experimentally reported ETPA cross sections of organic molecules obtained by a number of groups. In this work, we provide a thorough experimental study of ETPA in the organic molecules Rhodamine B (RhB) and zinc tetraphenylporphirin (ZnTPP). Our contribution is 3-fold: first, we reproduce previous results from other groups; second, we on the one hand determine the effects of different temporal correlations─introduced as a controllable temporal delay between the signal and idler photons to be absorbed─on the strength of the ETPA signal, and on the other hand, we introduce two concurrent and equivalent detection systems with and without the sample in place as a useful experimental check; third, we introduce, and apply to our data, a novel method to quantify the ETPA rate based on taking into account the full photon-pair behavior rather than focusing on singles or coincidence counts independently. Through this experimental setup we find that, surprisingly, the purported ETPA signal is not suppressed for a temporal delay much greater than the characteristic photon-pair temporal correlation time. While our results reproduce the previous findings from other authors, our full analysis indicates that the signal observed is not actually due to ETPA but simply to linear losses. Interestingly, for higher RhB concentrations, we find a two-photon signal that, contrary to expectations, likewise does not correspond to ETPA.

Hot-Band Absorption Can Mimic Entangled Two-Photon Absorption

It has been proposed that entangled two-photon absorption (E2PA) can be observed with up to 10¹⁰ lower photon flux than its classical counterpart, therefore enabling ultralow-power two-photon fluorescence microscopy. However, there is a significant controversy regarding the magnitude of this quantum enhancement in excitation efficiency. We investigated the fluorescence signals from Rhodamine 6G and LDS798 excited with a CW laser or an entangled photon pair source at ∼1060 nm. We observed a signal that originates from hot-band absorption (HBA), which is one-photon absorption from thermally populated vibrational levels of the ground electronic state. This mechanism, which has not been previously discussed in the context of E2PA, produces a signal with a linear power dependence, as would be expected for E2PA. For the typical conditions under which E2PA measurements are performed, contributions from the HBA process could lead to a several orders of magnitude overestimate of the quantum advantage.

Is Heralded Two-Photon Excited Fluorescence with Single Absorbers Possible with Current Technology?

The interaction between single or a fixed number of photons with a single absorber is of fundamental interest in quantum technology. The harnessing of light matter interactions at the single particle limit has several potential applications ranging from quantum communication and quantum metrology to quantum imaging. In this perspective, a setup for heralded two-photon excited fluorescence at the single absorber level is proposed. The setup is based on a heralded two-photon source utilizing spontaneous parametric down-conversion, entanglement swapping and sum frequency generation for joint detection. This perspective aimed at triggering a discussion about the study of TPA and TPEF with only very few photons. The feasibility of the scheme is assessed by estimating the performance based on state-of-the-art technologies and losses, with the conclusion that the realization appears to be very challenging, but not completely impossible.

Wave Packet Control and Simulation Protocol for Entangled Two-Photon Absorption of Molecules

Quantum light spectroscopy, providing novel molecular information nonaccessible by classical light, necessitates new computational tools when applied to complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce an entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two time distribution characteristics of the entangled photon state. The other protocol involves a Schmidt decomposition of the entangled light and requires summing over the Schmidt modes. We demonstrate how photon entanglement can be used to control and manipulate the two-photon excited nuclear wave packets in a displaced harmonic oscillator model.

Photoisomerization transition state manipulation by entangled two-photon absorption

We demonstrate how two-photon excitation with quantum light can influence elementary photochemical events. The azobenzene trans → cis isomerization following entangled two-photon excitation is simulated using quantum nuclear wave packet dynamics. Photon entanglement modulates the nuclear wave packets by coherently controlling the transition pathways. The photochemical transition state during passage of the reactive conical intersection in azobenzene photoisomerization is strongly affected with a noticeable alteration of the product yield. Quantum entanglement thus provides a novel control knob for photochemical reactions. The distribution of the vibronic coherences during the conical intersection passage strongly depends on the shape of the initial wave packet created upon quantum light excitation. X-ray signals that can experimentally monitor this coherence are simulated.

Entangled two-photon absorption by atoms and molecules: A quantum optics tutorial

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.