Entangled Two-photon Absorption Research Articles

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.

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 800nm 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.

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.

Linear and Nonlinear Optical Properties of All-cis and All-trans Poly(p-phenylenevinylene).

Poly(p-phenylenevinylene) (PPV) is a staple of the family of conjugated polymers with desirable optoelectronic properties for applications including light-emitting diodes (LEDs) and photovoltaic devices. Although the significant impact of olefin geometry on the steady-state optical properties of PPVs has been extensively studied, PPVs with precise stereochemistry have yet to be investigated using nonlinear optical spectroscopy for quantum sensing, as well as light harvesting for biological applications. Herein, we report our investigation of the influence of olefin stereochemistry on both linear and nonlinear optical properties through the synthesis of all-cis and all-trans PPV copolymers. We performed two-photon absorption (TPA) using a classical and entangled light source and compared both classical TPA and entangled two-photon absorption (ETPA) cross sections of these stereodefined PPVs. Whereas the TPA cross section of the all-trans PPV was expectedly higher than that of all-cis PPV, presumably because of the larger transition dipole moment, the opposite trend was measured via ETPA, with the all-cis PPV exhibiting the highest ETPA cross section. DFT calculations suggest that this difference might stem from the interaction of entangled photons with lower-lying electronic states in the all-cis PPV variant. Additionally, we explored the photoinduced processes for both cis and trans PPVs through time-resolved fluorescence upconversion and femtosecond transient absorption techniques. This study revealed that the sensitivity of PPVs in two-photon absorption varies with classical versus quantum light and can be modulated through the control of the geometry of the repeating alkenes, which is a key stepping stone toward their use in quantum sensing, bioimaging, and the design of polymer-based light-harvesting systems.

Multichromatic quantum superpositions in entangled two-photon absorption spectroscopy

Quantum information science is driving progress in a vast number of scientific and technological areas that cover molecular spectroscopy and matter-light interactions in general. In these fields, the ability to generate quantum mechanically-entangled photons is opening avenues to explore the interaction of molecules with quantum light. This work considers an alternative way of correlating photons by including energy superpositions. We study how the multichromatic quantum superposition, or color superposition of photon-pair states, influences the optical properties of organic chromophores. This work uses electronic structure calculations based on time-dependent density functional theory, and a simple modification of the standard entangled two-photon absorption theory. Our calculations show that it is possible to substantially modify the optical absorption cross section of molecules, where constructive and destructive interferences are computed. The quantum interference effects are more pronounced than the constructive ones. These quantum effects, or related ones, could be observed in quantum spectroscopic experiments where qudit photon states are generated.

Colors of entangled two-photon absorption

Multiphoton absorption of entangled photons offers ways for obtaining unique information about chemical and biological processes. Measurements with entangled photons may enable sensing biological signatures with high selectivity and at very low light levels to protect against photodamage. In this paper, we present a theoretical and experimental study of the excitation wavelength dependence of the entangled two-photon absorption (ETPA) process in a molecular system, which provides insights into how entanglement affects molecular spectra. We demonstrate that the ETPA excitation spectrum can be different from that of classical TPA as well as that for one-photon resonant absorption (OPA) with photons of doubled frequency. These results are modeled by assuming the ETPA cross-section is governed by a two-photon excited state radiative linewidth rather than by electron-phonon interactions, and this leads to excitation spectra that match the observed results. Further, we find that the two-photon-allowed states with highest TPA and ETPA intensities have high electronic entanglements, with ETPA especially favoring states with the longest radiative lifetimes. These results provide concepts for the development of quantum light-based spectroscopy and microscopy that will lead to much higher efficiency of ETPA sensors and low-intensity detection schemes.

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 Te and the relative position of just two electronic states. Moreover, the dependency on Te is periodic. These predictions are confirmed by molecular quantum mechanical calculations for several chromophores.

Witnessing entangled two-photon absorption via quantum interferometry

Recent investigations have suggested that the use of non-classical states of light, such as entangled photon pairs, may open new and exciting avenues in experimental two-photon absorption spectroscopy. Despite several experimental studies of entangled two-photon absorption (eTPA), there is still a heated debate on whether eTPA has truly been observed. This interesting debate has arisen mainly because it has recently been argued that single-photon-loss mechanisms, such as scattering or hot-band absorption, may mimic the expected entangled-photon linear absorption behavior. In this work, we focus on transmission measurements of eTPA and explore three different two-photon quantum interferometers in the context of assessing eTPA. We demonstrate that the so-called N00N-state configuration is the only one among those considered insensitive to linear (single-photon) losses. Remarkably, our results show that N00N states may become a potentially powerful tool for quantum spectroscopy, placing them as a strong candidate for the certification of eTPA in an arbitrary sample.

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.

Manipulating Two-Photon Absorption of Molecules through Efficient Optimization of Entangled Light.

We report how the unique temporal and spectral features of pulsed entangled photons from a parametric downconversion source can be utilized for manipulating electronic excitations through the optimization of their spectral phase. A new comprehensive optimization protocol based on Bayesian optimization has been developed in this work to selectively excite electronic states accessible by two-photon absorption. Using our optimization method, the entangled two-photon absorption probability for a thiophene dendrimer can be enhanced by up to a factor of 20, while classical light turns out to be nonoptimizable. Moreover, the optimization involving photon entanglement enables selective excitation that would not be possible otherwise. In addition to optimization, we have explored entangled two-photon absorption in the small entanglement time limit showing that entangled light can excite molecular electronic states that are vanishingly small for classical light. We demonstrate these opportunities with an application to a thiophene dendrimer.

Monitoring Wavepacket Dynamics at Conical Intersections by Entangled Two-Photon Absorption

Monitoring Wavepacket Dynamics at Conical Intersections by Entangled Two-Photon Absorption

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.

Two-Photon Absorption in Electron Donor–Acceptor Dyads and Triads Using Classical and Entangled Photons: Potential Systems for Photon-to-Spin Quantum Transduction

Photon-to-spin quantum transduction, i.e., the exchange of coherence between photons and spins, is important for establishing links between localized molecular qubit systems performing logic and/or sensing operations and similar systems at different physical locations. We are developing molecular systems to explore how transduction can be implemented by using entangled photons to produce entangled spin pairs by ultrafast electron transfer leading to spin-correlated radical pairs (SCRPs). We have prepared and systematically evaluated electron transfer dyads and triads based on a 9-(N-piperidinyl)perylene-3,4-dicarboximide (6PMI) donor, a naphthalene-1,8:4,5-bis(dicarboximide) (NDI) acceptor, and a tetrathiofulvalene (TTF) secondary donor, which are prepared with and without a phenyl spacer between the 6PMI and NDI to give 6PMI-NDI, 6PMI-Ph-NDI, TTF-6PMI-NDI, and TTF-6PMI-Ph-NDI. We used transient absorption, fluorescence-detected classical two-photon-absorption, and entangled two-photon-absorption (ETPA) spectroscopies to characterize the optical properties of these systems, while time-resolved EPR spectroscopy was used to characterize their photogenerated SCRPs. The results show that the ETPA cross section depends entirely on the presence of 6PMI and NDI in the 6PMI-NDI and 6PMI-Ph-NDI dyads, but in the triads TTF-6PMI-NDI and TTF-6PMI-Ph-NDI, the presence of the Ph spacer significantly affects the ETPA cross section. These results provide important information for designing molecular systems to implement photon-to-spin quantum transduction using entangled photons.

Entangled two-photon absorption with Brownian-oscillator fluctuations.

We theoretically investigate the two-photon absorption signals of a three-band (g, e, f) system diagonally coupled to an over-damped Brownian oscillator bath, which induces random Gaussian modulations of energy levels with an arbitrary degree of correlation. For fast modulation, extra 2ωeg and 2ωfe peaks may obscure the g-f transitions in the classical two-photon absorption (CTPA) spectra for nearly resonant e states. These peaks arise from one-photon resonant g-e or e-f transitions. In the slow modulation limit, these peaks vanish because of the short tails of the Gaussian line shape. CTPA strongly depends on the correlations between energy fluctuations. In entangled two-photon absorption, the extra peaks are eliminated because of the broad one-photon but narrow two-photon spectrum of the twin photons. The variation of the coherences between f states with the correlation between energy fluctuations is explored.

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.

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.

Enhancing Entangled Two-Photon Absorption for Picosecond Quantum Spectroscopy

Entangled two-photon absorption (ETPA) is known to create photoinduced transitions with extremely low light intensity, reducing the risk of phototoxicity compared to classical two-photon absorption. Previous works have predicted the ETPA cross-section, σe, to vary inversely with the product of entanglement time (Te) and entanglement area (Ae), i.e., σe ∼ 1/AeTe. The decreasing σe with increasing Te has limited ETPA to fs-scale Te, while ETPA applications for ps-scale spectroscopy have been unexplored. However, we show that spectral-spatial coupling, which reduces Ae as the SPDC bandwidth (σf) decreases, plays a significant role in determining σe when Te > ∼100 fs. We experimentally measured σe for zinc tetraphenylporphyrin at several σf values. For type-I ETPA, σe increases as σf decreases down to 0.1 ps-1. For type-II SPDC, σe is constant for a wide range of σf. With a theoretical analysis of the data, the maximum type-I σe would occur at σf = 0.1 ps-1 (Te = 10 ps). At this maximum, σe is 1 order of magnitude larger than fs-scale σe and 3 orders of magnitude larger than previous predictions of ps-scale σe. By utilizing this spectral-spatial coupling, narrowband type-I ETPA provides a new opportunity to increase the efficiency of measuring nonlinear optical signals and to control photochemical reactions requiring ps temporal precision.

Experimental requirements for entangled two-photon spectroscopy.

Coherently controlling the spectral properties of energy-entangled photons is a key component of future entangled two-photon spectroscopy schemes that are expected to provide advantages with respect to classical methods. We present here an experimental setup based on a grating compressor. It allows for the spectral shaping of entangled photons with a sevenfold increase in resolution, compared to previous setups with a prism compressor. We evaluate the performances of the shaper by detecting sum frequency generation in a nonlinear crystal with both classical pulses and entangled photon pairs. The efficiency of both processes is experimentally compared and is in accordance with a simple model relating the classical and entangled two-photon absorption coefficients. Finally, the entangled two-photon shaping capability is demonstrated by implementing an interferometric transfer function.

Entangled two-photon absorption spectroscopy with varying pump wavelengths

In entangled two-photon absorption (eTPA) spectroscopy, information about the energy-level structure of an arbitrary sample is retrieved by Fourier transforming sets of measured two-photon absorption probabilities of entangled photon pairs where the degree of entanglement and the delay time between the photons are varied. This works well for simple systems but quickly becomes rather difficult when many intermediate states are involved. We propose and discuss an extension of eTPA spectroscopy that solves this problem by means of repeated measurements at different pump wavelengths, thus reducing the experimental complexity of eTPA spectroscopy by removing the need to control the correlations of the entangled photons. Specifically, we demonstrate that our extension works well for a variety of realistic experimental setups.