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arXiv:1504.01902 · Physical Review A

Some exact properties of the nonequilibrium response function for transient photoabsorption

Enrico Perfetto, Gianluca Stefanucci

Published Mar 30, 2015• 47 citations
arXivHTMLPDF

Abstract

The physical interpretation of time-resolved photoabsorption experiments is not as straightforward as for the more conventional photoabsorption experiments conducted on equilibrium systems. In fact, the relation between the transient photoabsorption spectrum and the properties of the examined sample can be rather intricate since the former is a complicated functional of both the driving pump and the feeble probe fields. In this work, we critically review the derivation of the time-resolved photoabsorption spectrum in terms of the nonequilibrium dipole response function $\ensuremath{\chi}$ and assess its domain of validity. We then analyze $\ensuremath{\chi}$ in detail and discuss a few exact properties useful to interpret the transient spectrum during (overlapping regime) and after (nonoverlapping regime) the action of the pump. The nonoverlapping regime is the simplest to address. The absorption energies are indeed independent of the delay between the pump and probe pulses and hence the transient spectrum can change only by a rearrangement of the spectral weights. We give a close expression of these spectral weights in two limiting cases (ultrashort and everlasting monochromatic probes) and highlight their strong dependence on coherence and probe envelope. In the overlapping regime, we obtain a Lehmann-type representation of $\ensuremath{\chi}$ in terms of light-dressed states and provide a unifying framework of various well-known effects in pump-driven systems. We also show the emergence of spectral substructures due to the finite duration of the pump pulse.

DOI
10.1103/physreva.91.033416

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The physical interpretation of time-resolved photoabsorption experiments is not as straightforward as for the more conventional photoabsorption experiments conducted on equilibrium systems. In fact, the relation between the transient photoabsorption spectrum and the properties of the examined sample can be rather intricate since the former is a complicated functional of both the driving pump and the feeble probe fields. In this work, we critically review the derivation of the time-resolved photoabsorption spectrum in terms of the nonequilibrium dipole response function \ensuremathχ\ensuremath{\chi}\ensuremathχ and assess its domain of validity. We then analyze \ensuremathχ\ensuremath{\chi}\ensuremathχ in detail and discuss a few exact properties useful to interpret the transient spectrum during (overlapping regime) and after (nonoverlapping regime) the action of the pump. The nonoverlapping regime is the simplest to address. The absorption energies are indeed independent of the delay between the pump and probe pulses and hence the transient spectrum can change only by a rearrangement of the spectral weights. We give a close expression of these spectral weights in two limiting cases (ultrashort and everlasting monochromatic probes) and highlight their strong dependence on coherence and probe envelope. In the overlapping regime, we obtain a Lehmann-type representation of \ensuremathχ\ensuremath{\chi}\ensuremathχ in terms of light-dressed states and provide a unifying framework of various well-known effects in pump-driven systems. We also show the emergence of spectral substructures due to the finite duration of the pump pulse.
We put forward a first-principle nonequilibrium Green's-function (NEGF) approach to calculate the transient photoabsorption spectrum of optically thin systems. The method can deal with pump fields of arbitrary strength, frequency, and duration as well as overlapping and nonoverlapping pump and probe pulses. The electron-electron repulsion is accounted for by the correlation self-energy, and the resulting numerical scheme deals with matrices that scale quadratically with the system size. Two recent experiments, the first on helium and the second on krypton, are addressed. For the first experiment we explain the bending of the Autler-Townes absorption peaks with increasing pump-probe delay $\ensuremath{\tau}$ and relate the bending to the thickness and density of the gas. For the second experiment we find that sizable spectral structures of the pump-generated admixture of Kr ions are fingerprints of dynamical correlation effects, and hence they cannot be reproduced by time-local self-energy approximations. Remarkably, the NEGF approach also captures the retardation of the absorption onset of Kr2+{\mathrm{Kr}}^{2+}Kr2+ with respect to Kr1+{\mathrm{Kr}}^{1+}Kr1+ as a function of $\ensuremath{\tau}$.
We derive the two-time linear response theory for out-of-equilibrium pumped systems, generic pump-probe delays, and probe frequencies. Such a theory enormously simplifies the numerical calculations, for instance, of the optical conductivity with respect to the actual procedure, which requires computing the effect of the probe pulse for each time delay with respect to the pump pulse. The theory is given for a generic observable and pumped Hamiltonian and then specialized for a system with a quadratic Hamiltonian and its transient optical properties, exploiting the dynamical projective operatorial approach (DPOA). The theory is complemented by a set of crucial numerical guidelines that help perform actual calculations in a computationally affordable way. The optical response (differential transient reflectivity and absorption) of a prototypical three-band (core, valence, and conduction) model in the extreme ultraviolet regime is analyzed in detail to illustrate the theory and its application. Using some generalizations of the density of states, we provide a systematic approach to exploring the optical properties in terms of the system band-structure features and the pump parameters. Such an analysis can be extremely helpful in understanding the actual results of experimental optical measurements. Moreover, we study the effects of interband and intraband transitions, the local dipole coupling, and single and multiphoton processes. The latter is further investigated by varying the central frequency of the pump pulse to have different regions of the first Brillouin zone in resonance with it. We also study the effect of varying the pump pulse intensity. Finally, we study and analyze the transient optical properties in the probe pulse regime of the infrared and visible.
We present a fully quantum theory of time-resolved transient absorption spectroscopy, providing a general framework for describing the linear response of a nonequilibrium target to quantum probe fields beyond the semiclassical approximation. We elucidate how quantum correlations between probe-field frequency modes couple to coherences in the target and derive a simple expression for computing the resulting spectroscopic signals. We identify conditions under which quantum light can modify transient absorption spectra beyond the limits achievable with classical fields. Our work establishes a theoretical foundation for exploiting quantum light in ultrafast spectroscopy and suggests new routes for resolving dynamics in matter on timescales shorter than the duration of the probe pulse.
We describe the temporal evolution of the time-resolved photoemission response of the spinless Falicov-Kimball model driven out of equilibrium by strong applied fields. The model is one of the few possessing a metal-insulator transition and admitting an exact solution in the time domain. The nonequilibrium dynamics, evaluated using an extension of dynamical mean-field theory, show how the driven system differs from two common viewpoints---a quasiequilibrium system at an elevated effective temperature (the ``hot'' electron model) or a rapid interaction quench (``melting'' of the Mott gap)---due to the rearrangement of electronic states and redistribution of spectral weight. The results demonstrate the inherent trade-off between energy and time resolution accompanying the finite width probe pulses, characteristic of those employed in pump-probe time-domain experiments, which can be used to focus attention on different aspects of the dynamics near the transition.
The transient-absorption spectrum of a VVV-type three-level system is investigated, when this is periodically excited by a train of equally spaced, $\ensuremath{\delta}$-like pump pulses as, e.g., from an optical-frequency-comb laser. We show that, even though the probe pulse is not assumed to be much shorter than the pump pulses, light-induced states appear in the absorption spectrum. The frequency- and time-delay-dependent features of the absorption spectra are investigated as a function of several laser control parameters, such as the number of pump pulses used, their pulse area, and the pulse-to-pulse phase shift. We show that the frequencies of the light-induced states and the time-delay-dependent features of the spectra contain information on the action of the intense pulses exciting the system, which can thus complement the information on light-imposed amplitude and phase changes encoded in the absorption line shapes.
Abstract The quantum dynamics of a system of Rb atoms, modeled by a V -type three-level system interacting with intense probe and pump pulses, are studied. The time-delay-dependent transient-absorption spectrum of an intense probe pulse is thus predicted, simulating pump-probe experiments in which this is preceded or followed by a strong pump pulse. Numerical results are interpreted in terms of an analytical model based on interaction operators , which quantify the transformation undergone by the system under the action of an intense pulse. The oscillating features of the resulting transient-absorption spectra, due to the coupling of several excited states, are thus interpreted in terms of the atomic population and phase changes imposed by the pump and probe pulses. Strong-field-induced phases and their influence on the resulting transient-absorption spectra are thereby investigated for different values of pump and probe intensities and frequencies, focusing on the atomic properties which are encoded in the absorption line shapes for positive and negative time delays.