We present general first principles derivation of expression for current-induced forces. The expression is applicable in non-equilibrium molecular systems with arbitrary intra-molecular interactions and for any electron-nuclei coupling. It provides a controlled consistent way to account for quantum effects of nuclear motion, accounts for electronic non-Markov character of the friction tensor, and opens way to treatments beyond strictly adiabatic approximation. We show connection of the expression with previous studies, and discuss effective ways to evaluate the friction tensor.

We introduce auxiliary quantum master equation -dual fermion approach (QME-DF) and argue that it presents a convenient way to describe steady-states of correlated impurity systems. The combined scheme yields an expansion around a reference much closer to the true nonequilibrium state than in the original dual fermion formulation. In steady-state situations, the scheme is numerically cheaper and allows to avoid long time propagation of previous considerations. Anderson impurity is used as a test model. The QME-DF simulations are compared with numerically exact tdDMRG results.

Time-energy entangled photons produced by spontaneous parametric down-conversion (SPDC) are employed to calculate vibrational hyper-Raman (HR) signals of the conjugated organic chromophore Wu112. Compared with classical light, time-energy entanglement can provide selectivity of Liouvillespace pathways and thus suppress the strong broad electronic-Raman background arising from one-photon resonances of the intermediate states. The entangled-photon HR signal scales linearly with the SPDC pump field intensity rather than quadratically for classical light, which allows weak-field measurements on fragile samples.

In this theoretical study, we show how ultrafast electron–nuclear dynamics in a molecule can be monitored by two-photon absorption of time–energy entangled photon pairs generated by spontaneous parametric down-conversion with a narrow-band pump. The dynamics is tracked by a controllable signal-idler delay. Time correlation of the entangled photons enables an ultrafast measurement even with a monochromatic pump. The frequency anticorrelation of the photon pair allows the projection of the intermediate excited-state wavepacket onto an energy-selected vibrational level on a higher-lying electronic state with high energy resolution. Such joint high temporal and energy resolution is not possible with classical light. We demonstrate our scheme for a conical intersection model with four electronic states and two vibrational modes. The ultrafast nuclear wavepacket dynamics around the conical intersection is imprinted onto the time- and frequency-resolved entangled two-photon absorption signals. Electronic population dynamics is obtained by the frequency-integrated signal.

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.