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Time-resolved photoemission beyond the energy-time uncertainty

Francesco Randi, Daniele Fausti, Martin Eckstein

Published Apr 28, 2016• 0 citations
OpenAlex

Abstract

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.

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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 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.
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.
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.
Quantum materials are systems in which electronic ground states emerge from strong interactions between charge, spin, lattice, and orbital degrees of freedom. These interactions may be enhanced by reduced dimensionality or geometric frustration, and may also result in topologically protected electronic states. Noninteracting single band models fail to adequately describe these systems. Time-resolved optical measurements using femtosecond laser pulses can be used to study strongly interacting degrees of freedom on their natural timescales. By photoexciting the samples gently, it is possible to study these dynamics without disturbing the underlying order. In this work, the relaxation dynamics of photoexcited quasiparticles are studied in several quantum materials in which Coulomb repulsion and spin-orbit coupling are both strong. The relaxation dynamics reveal information about the low energy energy electronic structure as well as the nature of the strong interactions that govern the emergent properties of the system.
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 theoretically study time-resolved photoemission in atoms as probed by attosecond streaking. We review recent advances in the study of the photoelectric efect in the time domain and show that the experimentally accessible time shifts can be decomposed into distinct contributions that stem from the feld-free photoionization process itself and from probe-field induced corrections. We perform accurate quantum-mechanical as well as classical simulations of attosecond streaking for efective one-electron systems and determine all relevant contributions to the time delay with attosecond precision. In particular, we investigate the properties and limitations of attosecond streaking for the transition from short-ranged potentials (photodetachment) to long-ranged Coulomb potentials (photoionization). As an example for a more complex system, we study time-resolved photoionization for endohedral fullerenes A @C 60 and discuss how streaking time shifts are modifed due to the interaction of the C 60 cage with the probing infrared streaking field.