Sensing ultrashort electronic coherent beating at conical intersections by single-electron pulses.

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.

Nonlinear quantum interferometric spectroscopy with entangled photon pairs.

We develop closed expressions for a time-resolved photon counting signal induced by an entangled photon pair in an interferometric spectroscopy setup. Superoperator expressions in Liouville-space are derived that can account for relaxation and dephasing induced by coupling to a bath. Interferometric setups mix matter and light variables non-trivially, which complicates their interpretation. We provide an intuitive modular framework for this setup that simplifies its description. Based on the separation between the detection stage and the light-matter interaction processes, we show that the pair entanglement time and the interferometric time-variables control the observed physics time scale. Only a few processes contribute in the limiting case of small entanglement time with respect to the sample response, and specific contributions can be singled out.

Distinguishability and "which pathway" information in multidimensional interferometric spectroscopy with a single entangled photon-pair.

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.

Interferometric spectroscopy with quantum light: Revealing out-of-time-ordering correlators.

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.

Investigations of Molecular Optical Properties Using Quantum Light and Hong-Ou-Mandel Interferometry.

Entangled photon pairs have been used for molecular spectroscopy in the form of entangled two-photon absorption and in quantum interferometry for precise measurements of light source properties and time delays. We present an experiment that combines molecular spectroscopy and quantum interferometry by utilizing the correlations of entangled photons in a Hong-Ou-Mandel (HOM) interferometer to study molecular properties. We find that the HOM signal is sensitive to the presence of a resonant organic sample placed in one arm of the interferometer, and the resulting signal contains information pertaining to the light-matter interaction. We can extract the dephasing time of the coherent response induced by the excitation on a femtosecond time scale. A dephasing time of 102 fs is obtained, which is relatively short compared to times found with similar methods and considering line width broadening and the instrument entanglement time As the measurement is done with coincidence counts as opposed to simply intensity, it is unaffected by even-order dispersion effects, and because interactions with the molecular state affect the photon correlation, the observed measurement contains only these effects and no other classical losses. The experiments are accompanied by theory that predicts the observed temporal shift and captures the entangled photon joint spectral amplitude and the molecule's transmission in the coincidence counting rate. Thus, we present a proof-of-concept experimental method based of entangled photon interferometry that can be used to characterize optical properties in organic molecules and can in the future be expanded on for more complex spectroscopic studies of nonlinear optical properties.

Frequency-, Time-, and Wavevector-Resolved Ultrafast Incoherent Diffraction of Noisy X-ray Pulses.

We study theoretically incoherent time-resolved X-ray diffraction of fluctuating sources such as free electron lasers, as well as coherent sources with controllably added randomness. We find that the temporal resolution is strongly eroded by the noise. By considering frequency resolution of the signal, we find that the statistical properties of the noise carry important information allowing us to restore the temporal resolution. We propose a multidimensional stochastic resonance treatment to shape the optical window and extract this information from signals. Using the frequency-dependent stochastic phase as a frequency marker allows to improve the spectral resolution as well via intensity correlations. Frequency-tuned field correlation functions are used to modify the effective frequency gating and extract specific charge density contributions to the diffraction pattern while maintaining temporal resolution.

Probing Molecular Chirality by Orbital-Angular-Momentum-Carrying X-ray Pulses.

A twisted X-ray beam with orbital angular momentum is employed in a theoretical study to probe molecular chirality. A nonlocal response description of the matter-field coupling is adopted to account for the field short wavelength and the structured spatial profile. We use the minimal-coupling Hamiltonian, which implicitly takes into account the multipole contributions to all orders. The combined interactions of the spin and orbital angular momentum of the X-ray beam give rise to circular-helical dichroism signals, which are stronger than ordinary circular dichroism signals, and may serve as a useful tool for the study of molecular chirality in the X-ray regime.

Quantum phase-sensitive diffraction and imaging using entangled photons.

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.

Femtosecond covariance spectroscopy.

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.

Monitoring Spontaneous Charge-Density Fluctuations by Single-Molecule Diffraction of Quantum Light.

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.

Scattering-Based Geometric Shaping of Photon-Photon Interactions.

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.

Nonequilibrium free-energy estimation conditioned on measurement outcomes.

The Jarzynski equality is one of the most influential results in the field of nonequilibrium statistical mechanics. This celebrated equality allow the calculation of equilibrium free-energy differences from work distributions of nonequilibrium processes. In practice, such calculations often suffer from poor convergence due to the need to sample rare events. Here we examine if the inclusion of measurement and feedback can improve the convergence of nonequilibrium free-energy calculations. A modified version of the Jarzynski equality in which realizations with a given outcome are kept, while others are discarded, is used. We find that discarding realizations with unwanted outcomes can result in improved convergence compared to calculations based on the Jarzynski equality. We argue that the observed improved convergence is closely related to Bennett's acceptance ratio method, which was developed without any reference to measurements or feedback.

No-pumping theorem for many particle stochastic pumps.

Stochastic pumps are models of artificial molecular machines which are driven by periodic time variation of parameters, such as site and barrier energies. The no-pumping theorem states that no directed motion is generated by variation of only site or barrier energies [S. Rahav, J. Horowitz, and C. Jarzynski, Phys. Rev. Lett. 101, 140602 (2008)]. We study stochastic pumps of several interacting particles and demonstrate that the net current of particles satisfies an additional no-pumping theorem.