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arXiv:0809.4282 · Physical Review B

Measuring correlated electron dynamics with time-resolved photoemission spectroscopy

Martin Eckstein, Marcus Kollar

Published Dec 16, 2008• 53 citations
arXivHTMLPDF

Abstract

Time-resolved photoemission experiments can reveal fascinating quantum dynamics of correlated electrons. However, the thermalization of the electronic system is typically so fast that very short probe pulses are necessary to resolve the time evolution of the quantum state, and this leads to poor energy resolution due to the energy-time uncertainty relation. Although the photoemission intensity can be calculated from the nonequilibrium electronic Green's functions, the converse procedure is therefore difficult. We analyze a hypothetical time-resolved photoemission experiment on a correlated electronic system, described by the Falicov-Kimball model in dynamical mean-field theory, which relaxes between metallic and insulating phases. We find that the real-time Green's function which describes the transient behavior during the buildup of the metallic state cannot be determined directly from the photoemission signal. On the other hand, the characteristic collapse-and-revival oscillations of an excited Mott insulator can be observed as oscillating weight in the center of the Mott gap in the time-dependent photoemission spectrum.

DOI
10.1103/physrevb.78.245113

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Time-resolved photoemission experiments can reveal fascinating quantum dynamics of correlated electrons. However, the thermalization of the electronic system is typically so fast that very short probe pulses are necessary to resolve the time evolution of the quantum state, and this leads to poor energy resolution due to the energy-time uncertainty relation. Although the photoemission intensity can be calculated from the nonequilibrium electronic Green's functions, the converse procedure is therefore difficult. We analyze a hypothetical time-resolved photoemission experiment on a correlated electronic system, described by the Falicov-Kimball model in dynamical mean-field theory, which relaxes between metallic and insulating phases. We find that the real-time Green's function which describes the transient behavior during the buildup of the metallic state cannot be determined directly from the photoemission signal. On the other hand, the characteristic collapse-and-revival oscillations of an excited Mott insulator can be observed as oscillating weight in the center of the Mott gap in the time-dependent photoemission spectrum.
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.
Emergent properties of solids, such as long range order or quasiparticle states, often become manifest on small energy scales in the electronic spectrum. The time-frequency uncertainty therefore puts an intrinsic limit on how accurately their nonequilibrium properties can be studied with standard time-resolved photoemission experiments, although the real dynamics of the system can be much faster than this spectral uncertainty limit. Here we theoretically demonstrate that dynamical information on all timescales can nevertheless be retrieved from photoemission experiments, using suitably shaped light pulses of quantum or classical nature. This may provide a route to use arbitrarily short pulses to probe the dynamics of low energy degrees of freedom in solids. As a particular example, we analyze the real-time buildup of a Kondo resonance.
The real-time dynamics of interacting electrons out of equilibrium contains detailed microscopic information about electronically correlated materials, which can be read out with time-resolved optical spectroscopy. The reflectivity that is typically measured in pump-probe experiments is related to the nonequilibrium optical conductivity. We show how to express this quantity in terms of real-time Green's functions using dynamical mean-field theory. As an application we study the electrical response of the Falicov-Kimball model during the ultrafast buildup of the gapped phase at large interaction.
In time-resolved photoemission experiments, more than one electron can be emitted from the solid by a single ultrashort pulse. We theoretically demonstrate how correlations between the momenta of outgoing electrons relate to time-dependent two-particle correlations in the solid. This can extend the scope of time- and angle-resolved photoemission spectroscopy to probe superconducting and charge density fluctuations in systems without long-range order, and to reveal their dynamics independent of the electronic gap and thus unrestricted by the energy-time uncertainty. The proposal is illustrated for superconductivity in a BCS model. An impulsive perturbation can quench the gap on ultrafast timescales, while nonequilibrium pairing correlations persist much longer, even when electron-electron scattering beyond mean-field theory is taken into account. There is thus a clear distinction between a dephasing of the Cooper pairs and the thermalization into the normal state. While a measurement of the gap would be blind to such pairing correlations, they can be revealed by the angular correlations in photoemission.
We determine the exact time-resolved photoemission spectroscopy for a nesting driven charge density wave (described by the spinless Falicov-Kimball model within dynamical mean-field theory). The pump-probe experiment involves two light pulses: the first is an ultrashort intense pump pulse that excites the system into nonequilibrium, and the second is a lower amplitude, higher frequency probe pulse that photoexcites electrons. We examine three different cases: the strongly correlated metal, the quantum-critical charge density wave, and the critical Mott insulator. Our results show that the quantum critical charge density wave has an ultraefficient relaxation channel that allows electrons to be de-excited during the pump pulse, resulting in little net excitation. In contrast, the metal and the Mott insulator show excitations that are closer to what one expects from these systems. In addition, the pump field produces spectral band narrowing, peak sharpening, and a spectral gap reduction, all of which rapidly return to their field free values after the pump is over.
The energy-time uncertainty is an intrinsic limit for time-resolved experiments imposing a tradeoff between the duration of the light pulses used in experiments and their frequency content. In standard time-resolved photoemission, this limitation maps directly onto a tradeoff between the time resolution of the experiment and the energy resolution that can be achieved on the electronic spectral function. Here we propose a protocol to disentangle the energy and time resolutions in photoemission. We demonstrate that dynamical information on all time scales can be retrieved from time-resolved photoemission experiments using suitably shaped light pulses of quantum or classical nature. As a paradigmatic example, we study the dynamical buildup of the Kondo peak, a narrow feature in the electronic response function arising from the screening of a magnetic impurity by the conduction electrons. After a quench, the electronic screening builds up on timescales shorter than the inverse width of the Kondo peak and we demonstrate that the proposed experimental scheme could be used to measure the intrinsic time scales of such electronic screening. The proposed approach provides an experimental framework to access the nonequilibrium response of collective electronic properties beyond the spectral uncertainty limit and will enable the direct measurement of phenomena such as excited Higgs modes and, possibly, the retarded interactions in superconducting systems.