Superoperator representation of nonlinear response: unifying quantum field and mode coupling theories

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.

Enhanced TEMPO Algorithm for Quantum Path Integrals with Off-Diagonal System-Bath Coupling: Applications to Photonic Quantum Networks

Multitime system correlation functions are relevant in various areas of physics and science, dealing with system-bath interaction including spectroscopy and quantum optics, where many of these schemes include an off-diagonal system bath interaction. Here we extend the enhanced time-evolving matrix product operator (eTEMPO) algorithm for quantum path integrals using tensor networks [Phys. Rev. Lett. 123, 240602 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.240602 to open quantum systems with off-diagonal coupling beyond a single two level system. We exemplify the approach on a coupled cavity waveguide system with spatially separated quantum two-state emitters, though many other applications in material science are possible, including entangled photon propagation, photosynthesis spectroscopy, and on-chip quantum optics with realistic dissipation.

Photonics and spectroscopy in nanojunctions: a theoretical insight

Green function methods for photonics and spectroscopy in nanojunctions.

On the Resolution Limit of Femtosecond Stimulated Raman Spectroscopy: Modelling Fifth-Order Signals with Overlapping Pulses

Femtosecond stimulated Raman scattering (FSRS) spectroscopy is a powerful pump-probe technique that can track electronic and vibrational dynamics with high spectral and temporal resolution. The investigation of extremely short-lived species, however, implies deciphering complex signals and is ultimately hampered by unwanted nonlinear effects once the time resolution limit is approached and the pulses overlap temporally. Using the loop diagrams formalism we calculate the fifth-order response of a model system and address the limiting case where the relevant dynamics timescale is comparable to the pump-pulse duration and, consequently, the pump and the probe overlap temporally. We find that in this regime, additional diagrams that do not contribute for temporally well separated pulses need to be taken into account, giving rise to new time-dependent features, even in the absence of photoinduced dynamics and for negative delays.

Generalized Kramers-Heisenberg expressions for stimulated Raman scattering and two-photon absorption

The frequency-domain pump-probe signal of a material system interacting with two quantum modes of the radiation field is recast in terms of products of scattering amplitudes (T matrix elements) rather than the third-order susceptibility Im chi((3)). The resulting expression offers a more intuitive physical picture for the optical process compared with the semiclassical approach which treats the radiation field as classical. It can be derived and interpreted using closed-time-path-loop diagrams which represent the joint state of the matter and the field for each contribution to the signal. The signal has two components representing stimulated Raman scattering omega(1) - omega(2) and two-photon absorption omega(1) + omega(2) two-photon resonances. Both are expressed as nonequi-librium steady-state photon and matter fluxes, as is common in the description of dissipative processes in open quantum systems.

Coherence and correlations in multitime quantum measurements of stochastic quantum trajectories

Quantum effects on multitime distributions and correlation functions of single objects, stemming from both the dynamics and repeated measurements, are calculated for a driven harmonic system using a superoperator generating functional formalism. Marked differences between multipoint observables associated with classical and quantum measurements are identified. The effects of quantum collapse and measurement resolution are discussed.

Nonequilibrium superoperator GW equations

Hedin's equations [Phys. Rev. 139, 796 (1965)] for the one-particle equilibrium Green's function of a many-electron system are generalized to nonequilibrium open systems using two fields that separately control the evolution of the bra and the ket of the density matrix. A closed hierarchy is derived for the Green's function, the self-energy, the screened potential, the polarization, and the vertex function, all expressed as Keldysh matrices in Liouville space.

QUANTUM MECHANICS OF DISSIPATIVE SYSTEMS

Quantum dissipation involves both energy relaxation and decoherence, leading toward quantum thermal equilibrium. There are several theoretical prescriptions of quantum dissipation but none of them is simple enough to be treated exactly in real applications. As a result, formulations in different prescriptions are practically used with different approximation schemes. This review examines both theoretical and application aspects on various perturbative formulations, especially those that are exact up to second-order but nonequivalent in high-order system-bath coupling contributions. Discrimination is made in favor of an unconventional formulation that in a sense combines the merits of both the conventional time-local and memory-kernel prescriptions, where the latter is least favorite in terms of the applicability range of parameters for system-bath coupling, non-Markovian, and temperature. Also highlighted is the importance of correlated driving and dissipation effects, not only on the dynamics under strong external field driving, but also in the calculation of field-free correlation and response functions.

Time- and frequency-resolved fluorescence spectra of nonadiabatic dissipative systems: What photons can tell us

The monitoring of the excited-state dynamics by time- and frequency-resolved spontaneous emission spectroscopy has been studied in detail for a model exhibiting an excited-state curve crossing. The model represents characteristic aspects of the photoinduced ultrafast dynamics in large molecules in the gas or condensed phases and accounts for strong nonadiabatic and electron-vibrational coupling effects, as well as for vibrational relaxation and optical dephasing. A comprehensive overview of the dependence of spontaneous emission spectra on the characteristics of the excitation and detection processes (such as carrier frequencies, pump/gate pulse durations, as well as optical dephasing) is presented. A systematic comparison of ideal spectra, which provide simultaneously perfect time and frequency resolution and thus contain maximal information on the system dynamics, with actually measurable time- and frequency-gated spectra has been carried out. The calculations of real time- and frequency-gated spectra demonstrate that complementary information on the excited-state dynamics can be extracted when the duration of the gate pulse is varied.

All-forward semiclassical simulations of nonlinear response functions

We propose a quantum trajectory algorithm for computing nonlinear response functions of condensed phase molecular systems based on a time-ordered expansion of the density matrix. The nth-order response function is expressed as a sum of 2(n) impulsive response pathways representing trajectories involving zero, one, and up to n interactions with short external pulses. These are evaluated using a forward propagation algorithm based upon a Liouville space extension of the Bohmian propagation method.