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arXiv:1604.08511 · Physical review. B./Physical review. B

Bypassing the energy-time uncertainty in time-resolved photoemission

Francesco Randi, Daniele Fausti, Martin Eckstein

Published Mar 16, 2017• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.95.115132

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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.
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.
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.
We show that the complete photoemission dynamics in situations of electron-ion entanglement can be retrieved from photoelectron spectral measurements without information on the ion. To this end, we develop an energy-time analysis of the photoelectron's reduced density matrix based on first principles. We test and assess our approach with numerical simulations on a low dimensional model molecule in interaction with broadband composite pulses occulting the vibrational resolution. Our method is directly applicable to recent experimental schemes measuring the photoelectron reduced density matrices in atomic and molecular photoemission. Therefore, it opens a new window on the dynamics of decoherence and entanglement at the attosecond timescale.
Recent advances in time-resolved spectroscopies have enabled direct access to the momentum-selective nonequilibrium dynamics of correlated quantum materials, revealing a strongly momentum-dependent response of electrons and collective excitations. Interpreting these observations requires a real-time theoretical framework that consistently captures the interplay between strong local electronic correlations and nonlocal collective fluctuations, a capability that remains beyond state-of-the-art nonequilibrium approaches. Using a recently developed real-time many-body framework, we resolve the momentum-selective ultrafast dynamics of a photoexcited correlated electron system. We predict a transient nodal-antinodal anisotropy in electronic heating, providing a microscopic explanation for the momentum-dependent response debated in time-resolved photoemission and Raman experiments, and identify the nonthermal spectral-weight transfer responsible for the transient antinodal in-gap states observed in ultrafast photoemission. We further uncover a momentum-selective magnetic response, in which antiferromagnetic fluctuations undergo a strongly nonthermal, quench-like excitation far above the electronic temperature while preserving their correlation length, before relaxing through a momentum-space magnon cascade toward lower-momentum modes. Finally, by tracking the real-time local spin susceptibility, we identify a dynamical, experimentally accessible signature of local-moment formation and its photoinduced melting. Our results establish a unified microscopic picture of ultrafast electronic and magnetic dynamics, providing a framework for interpreting momentum-resolved pump-probe experiments.
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.