We construct an effective Hamiltonian of interacting bosons, based on scattered radiation off vibrational modes of designed molecular architectures. Making use of the infinite yet countable set of spatial modes representing the scattering of light, we obtain a variable photon-photon interaction in this basis. The effective Hamiltonian Hermiticity is controlled by a geometric factor set by the overlaps of spatial modes. Using this mapping, we relate intensity measurements of the light to correlation functions of the interacting bosons evolving according to the effective Hamiltonian, rendering local as well as nonlocal observables accessible. This architecture may be used to simulate the dynamics of interacting bosons, as well as a designing tool for multiqubit photonic gates in quantum computing applications. Variable hopping, interaction, and confinement of the active space of the bosons are demonstrated on a model system.

Correlated photons inspire abundance of metrology-related platforms, which benefit from quantum (anti-) correlations and outperform their classical counterparts. While these mainly focus on entanglement, the role of photon exchange phase and degree of distinguishability has not been widely used in quantum applications. Using an interferometric setup, we theoretically show that, when a two-photon wave function is coupled to matter, it is encoded with “which pathway?” information even at low-degree of entanglement. An interferometric protocol, which enables phase-sensitive discrimination between microscopic interaction histories (pathways), is developed. We find that quantum light interferometry facilitates utterly different set of time delay variables, which are unbound by uncertainty to the inverse bandwidth of the wave packet. We illustrate our findings on an exciton model system and demonstrate how to probe intraband dephasing in the time domain without temporally resolved detection. The unusual scaling of multiphoton coincidence signals with the applied pump intensity is discussed.

We survey the inclusion of interferometric elements in nonlinear spectroscopy performed with quantum light. Controlled interference of electromagnetic fields coupled to matter can induce constructive or destructive contributions of microscopic coupling sequences (histories) of matter. Since quantum fields do not commute, quantum light signals are sensitive to the order of light-matter coupling sequences. Matter correlation functions are thus imprinted by different field factors, which depend on that order. We identify the associated quantum information obtained by controlling the weights of different contributing pathways and offer several experimental schemes for recovering it. Nonlinear quantum response functions include out-of-time-ordering matter correlators (OTOCs), which reveal how perturbations spread throughout a quantum system (information scrambling). Their effect becomes most notable when using ultrafast pulse sequences with respect to the path difference induced by the interferometer. OTOCs appear in quantum-informatics studies in other fields, including black hole, high energy, and condensed matter physics.

We propose a quantum diffraction imaging technique whereby one photon of an entangled pair is diffracted off a sample and detected in coincidence with its twin. The image is obtained by scanning the photon that did not interact with matter. We show that when a dynamical quantum system interacts with an external field, the phase information is imprinted in the state of the field in a detectable way. The contribution to the signal from photons that interact with the sample scales as [Formula: see text], where [Formula: see text] is the source intensity, compared with [Formula: see text] of classical diffraction. This makes imaging with weak fields possible, providing high signal-to-noise ratio, avoiding damage to delicate samples. A Schmidt decomposition of the state of the field can be used for image enhancement by reweighting the Schmidt modes contributions.

SignificanceIn a theoretical study, we present an ultrafast technique for probing time-dependent molecular charge densities. An ultrafast optical pump first brings the molecule into an electronic nonstationary state. This is followed by coherent inelastic scattering of a broadband single-electron probe pulse with a variable delay T, which is detected spectrally. The technique is applied to reveal phase-sensitive background-free coherent electron beating in the conical intersection passage in uracil and reveals the otherwise elusive coherent beating of strongly coupled electrons and nuclei.

Optical interferometry has been a long-standing setup for characterization of quantum states of light. Both linear and the nonlinear interferences can provide information regarding the light statistics and underlying detail of the light-matter interactions. Here we demonstrate how interferometric detection of nonlinear spectroscopic signals may be used to improve the measurement accuracy of matter susceptibilities. Light-matter interactions change the photon statistics of quantum light, which are encoded in the field correlation functions. Application is made to the Hong-Ou-Mandel two-photon interferometer that reveals entanglement-enhanced resolution that can be achieved with existing optical technology.

Homodyne X-ray diffraction signals produced by classical light and classical detectors are given by the modulus square of the charge density in momentum space |σ(q)|², missing its phase, which is required in order to invert the signal to real space. We show that quantum detection of the radiation field yields a linear diffraction pattern that reveals σ(q) itself, including the phase. We further show that repeated diffraction measurements with variable delays constitute a novel multidimensional measure of spontaneous charge-density fluctuations. Classical diffraction, in contrast, only reveals a subclass of even-order correlation functions. Simulations of two-dimensional signals obtained by two diffraction events are presented for the amino acid cysteine.

The success of nonlinear optics relies largely on pulse-to-pulse consistency. In contrast, covariance-based techniques used in photoionization electron spectroscopy and mass spectrometry have shown that a wealth of information can be extracted from noise that is lost when averaging multiple measurements. Here, we apply covariance-based detection to nonlinear optical spectroscopy, and show that noise in a femtosecond laser is not necessarily a liability to be mitigated, but can act as a unique and powerful asset. As a proof of principle we apply this approach to the process of stimulated Raman scattering in α-quartz. Our results demonstrate how nonlinear processes in the sample can encode correlations between the spectral components of ultrashort pulses with uncorrelated stochastic fluctuations. This in turn provides richer information compared with the standard nonlinear optics techniques that are based on averages over many repetitions with well-behaved laser pulses. These proof-of-principle results suggest that covariance-based nonlinear spectroscopy will improve the applicability of fs nonlinear spectroscopy in wavelength ranges where stable, transform-limited pulses are not available, such as X-ray free-electron lasers which naturally have spectrally noisy pulses ideally suited for this approach.