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

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.

Quantum Interferometric Pathway Selectivity in Difference-Frequency-Generation Spectroscopy

Even-order spectroscopies such as sum-frequency generation (SFG) and difference-frequency generation (DFG) can serve as direct probes of molecular chirality. Such signals are usually given by the sum of several interaction pathways that carry different information about matter. Here we focus on DFG, involving impulsive optical-optical-IR interactions, where the last IR pulse probes vibrational transitions in the ground or excited electronic state manifolds, depending on the interaction pathway. Spectroscopy with classical light can use phase matching to select the two pathways. In this theoretical study, we propose a novel quantum interferometric protocol that uses entangled photons to isolate individual pathways. This additional selectivity originates from engineering the state of light using a Zou-Wang-Mandel interferometer combined with coincidence detection.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

Cavity Control of Molecular Spectroscopy and Photophysics

ConspectusOptical cavities have been established as a powerful platform for manipulating the spectroscopy and photophysics of molecules. Molecules placed inside an optical cavity will interact with the cavity field, even if the cavity is in the vacuum state with no photons. When the coupling strength between matter excitations, either electronic or vibrational, and a cavity photon mode surpasses all decay rates in the system, hybrid light-matter excitations known as cavity polaritons emerge. Originally studied in atomic systems, there has been growing interest in studying polaritons in molecules. Numerous studies, both experimental and theoretical, have demonstrated that the formation of molecular polaritons can significantly alter the optical, electronic, and chemical properties of molecules in a noninvasive manner.This Account focuses on novel studies that reveal how optical cavities can be employed to control electronic excitations, both valence and core, in molecules and the spectroscopic signatures of molecular polaritons. We first discuss the capacity of optical cavities to manipulate and control the intrinsic conical intersection dynamics in polyatomic molecules. Since conical intersections are responsible for a wide range of photochemical and photophysical processes such as internal conversion, photoisomerization, and singlet fission, this provides a practical strategy to control molecular photodynamics. Two examples are given for the internal conversion in pyrazine and singlet fission in a pentacene dimer. We further show how X-ray cavities can be exploited to control the core-level excitations of molecules. Core polaritons can be created from inequivalent core orbitals by exchanging X-ray cavity photons. The core polaritons can also alter the selection rules in nonlinear spectroscopy.Polaritonic states and dynamics can be monitored by nonlinear spectroscopy. Quantum light spectroscopy is a frontier in nonlinear spectroscopy that exploits the quantum-mechanical properties of light, such as entanglement and squeezing, to extract matter information inaccessible by classical light. We discuss how quantum spectroscopic techniques can be employed for probing polaritonic systems. In multimolecule polaritonic systems, there exist two-polariton states that are dark in the two-photon absorption spectrum due to destructive interference between transition pathways. We show that a time-frequency entangled photon pair can manipulate the interference between transition pathways in the two-photon absorption signal and thus capture classically dark two-polariton states. Finally, we discuss cooperative effects among molecules in spectroscopy and possibly in chemistry. When many molecules are involved in forming the polaritons, while the cooperative effects clearly manifest in the dependence of the Rabi splitting on the number of molecules, whether they can show up in chemical reactivity, which is intrinsically local, is an open question. We explore the cooperative nature of the charge migration process in a cavity and show that, unlike spectroscopy, polaritonic charge dynamics is intrinsically local and does not show collective many-molecule effects.

Modeling the space-time correlation of pulsed twin beams

Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications, due their multimodal nature in space and time. However, a satisfactory theoretical description is still lacking. In this work we propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory. The model is used to study the quantum correlation and the coherence in the angle-frequency domain of the parametric emission, and demonstrates a [Formula: see text] growth of their size as the gain g increases, with a corresponding contraction of the space-time distribution. These predictions are systematically compared with the results of stochastic numerical simulations, performed in the Wigner representation, of the full model equations: an excellent agreement is shown even for parameters well outside the expected limit of validity of the model.

Theoretical and experimental study of the 6S-8S two-photon absorption cross-section in cesium atoms

The probability of a two-photon absorption (TPA) process is quantified by means of the TPA cross-section. In this work the TPA cross-section for the 6S1/2 → 8S1/2 transition in cesium (Cs) atoms is obtained from a theoretical and experimental approach. It is calculated using second order perturbation theory including hyperfine structure and Doppler broadening for a thermal atomic vapor. The theoretical values for the TPA cross-sections of the two allowed hyperfine transitions are σ~3,3=3.10×10-24 cm4/W and σ~4,4=3.65×10-24 cm4/W. An experiment is set up to measure these cross-sections based on the quadratic dependence between the TPA transition rate and the intensity of the laser light. Values of σ~3,3=(3.6±1.1)×10-24 cm4/W and σ~4,4=(4.6±1.1)×10-24 cm4/W are obtained from the measurements. The results show an agreement between theory and experiment. To the best of our knowledge, this is the first time that these cross-sections are reported.

Probing exciton dynamics with spectral selectivity through the use of quantum entangled photons

Quantum light is increasingly recognized as a promising resource for developing optical measurement techniques. Particular attention has been paid to enhancing the precision of the measurements beyond classical techniques by using nonclassical correlations between quantum entangled photons. Recent advances in the quantum optics technology have made it possible to manipulate spectral and temporal properties of entangled photons, and photon correlations can facilitate the extraction of matter information with relatively simple optical systems compared to conventional schemes. In these respects, the applications of entangled photons to time-resolved spectroscopy can open new avenues for unambiguously extracting information on dynamical processes in complex molecular and materials systems. Here, we propose time-resolved spectroscopy in which specific signal contributions are selectively enhanced by harnessing nonclassical correlations of entangled photons. The entanglement time characterizes the mutual delay between an entangled twin and determines the spectral distribution of photon correlations. The entanglement time plays a dual role as the knob for controlling the accessible time region of dynamical processes and the degrees of spectral selectivity. In this sense, the role of the entanglement time is substantially equivalent to the temporal width of the classical laser pulse. The results demonstrate that the application of quantum entangled photons to time-resolved spectroscopy leads to monitoring dynamical processes in complex molecular and materials systems by selectively extracting desired signal contributions from congested spectra. We anticipate that more elaborately engineered photon states would broaden the availability of quantum light spectroscopy.

Emulating Quantum Entangled Biphoton Spectroscopy Using Classical Light Pulses

We show that for a class of quantum light spectroscopy (QLS) experiments using n = 0, 1, 2, ··· classical light pulses and an entangled photon pair (a biphoton state) where one photon acts as a reference without interacting with the matter sample, identical signals can be obtained by replacing the biphotons with classical-like coherent states of light, where these are defined explicitly in terms of the parameters of the biphoton states. An input-output formulation of quantum nonlinear spectroscopy is used to prove this equivalence. We demonstrate the equivalence numerically by comparing a classical pump-quantum probe experiment with the corresponding classical pump-classical probe experiment. This analysis shows that understanding the equivalence between entangled biphoton probes and carefully designed classical-like coherent state probes leads to quantum-inspired classical experiments that yield equivalent signals and provides insights for the future design of QLS experiments that could provide a true quantum advantage.

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.

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.

Quantized Fields for Optimal Control in the Strong Coupling Regime

We tailor the quantum statistics of a bosonic field to deterministically drive a quantum system into a target state. Experimentally accessible states of the field achieve good control of multilevel or multiqubit systems, notably also at coupling strengths beyond the rotating-wave approximation. This extends optimal control theory to the realm of fully quantized, strongly coupled control and target degrees of freedom.