Time-Stretched Spectroscopy by the Quantum Zeno Effect: The Case of Auger Decay

E. Viñas Boström, M. Gisselbrecht, T. Brage, C.-O. Almbladh, A. Mikkelsen, and C. Verdozzi

Phys. Rev. Lett. 121, 233201 – Published 7 December 2018

Abstract

A tenet of time-resolved spectroscopy is “faster laser pulses for shorter timescales”. Here, we suggest turning this paradigm around, and slowing down the system dynamics via repeated measurements, to do spectroscopy on longer timescales. This is the principle of the quantum Zeno effect. We exemplify our approach with the Auger process, and find that repeated measurements increase the core-hole lifetime, redistribute the kinetic energy of Auger electrons, and alter entanglement formation. We further provide an explicit experimental protocol for atomic Li, to make our proposal concrete.

Received 16 April 2018
Revised 10 September 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.233201

Physics Subject Headings (PhySH)

Atomic, optical & lattice clocks Autoionization & Auger processes Coherent control Quantum Zeno dynamics Quantum control Quantum entanglement Ultrafast phenomena

Atomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

E. Viñas Boström^1,*, M. Gisselbrecht², T. Brage², C.-O. Almbladh¹, A. Mikkelsen², and C. Verdozzi^1,†

¹Lund University, Department of Physics and ETSF, P.O. Box 118, 221 00 Lund, Sweden
²Lund University, Department of Physics, P.O. Box 118, 221 00 Lund, Sweden

^*emil.vinas_bostrom@teorfys.lu.se
^†claudio.verdozzi@teorfys.lu.se

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Vol. 121, Iss. 23 — 7 December 2018

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Images

Figure 1
Pictorial rendering of an experiment on the quantum Zeno effect (QZE) in Auger decay. Isolated core-hole atoms are prepared by an x-ray source arising, e.g., from an accelerator based source or high harmonic generation. A pair of $π$ pulses separated by a time $t_{m}$ perform a measurement of valence electrons in the Auger-decaying states and can be repeated periodically with a delay $Δ t$ until Auger decay occurs (left panel). Provided that Auger decay dominates over competing processes, QZE should be observable as a slowing down of the Auger recombination time, i.e., a spectral narrowing of the Auger electron with kinetic energy, $ε_{A}$ (right panel). Auger electron readout can be carried out by electron spectroscopy allowing us, hence, to monitor the decay either in the energy domain (regardless of the temporal characteristics of the x-ray source), or in the time domain with attosecond pulses and a third laser field (not shown).
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Figure 2
Auger decay and the quantum Zeno effect with measurement time $t_{m} = 0.32 fs$ . Left: electron orbital occupations $n_{c}$ , $n_{v_{1}}$ , and $n_{v_{2}}$ in a model description of Li as a function of time, for field intensities $I = 0$ , 5.1, and ${20.4 TW / cm}^{2}$ (blue, green, and red curves, respectively) pertaining to Rabi frequencies $ℏ Ω = 0$ , 0.3, and 0.6 eV. The black lines indicate the lifetime $τ_{1}$ of the core level, and the correspondence between orbitals and curves for $ℏ Ω = 0.6 eV$ applies to all intensities. Center: Schematics of system and driving field. Right: Occupation $A (ε_{k}, t)$ in the continuum levels $| ε_{k} ⟩$ as a function of time and energy for $I = 20.4 TW / {cm}^{2}$ . The long time limit spectral line for $I = 0$ is shown in black.
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Figure 3
Parameter dependence of the QZE protocol. Top panel: Effective lifetime as a function of the squared Rabi frequency $(ℏ Ω)^{2} \propto I$ . The circles show a system with unperturbed lifetimes $τ_{1} = 100 fs$ and $τ_{2} = \infty$ , from RWA (green), full field dynamics for $ℏ ω = 10 eV$ (red) and $ℏ ω = 3 eV$ (blue). The lines are a guide to the eye. Squares: same as circles, but with $τ_{2} = 300 fs$ . Bottom panel: Orbital occupations $n_{c}$ and $n_{1}$ as a function of time for $τ_{2} = \infty$ and within RWA. The boundaries of such areas are the cases with no field and $ℏ Ω = \sqrt{10} eV$ .
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Figure 4
Concurrence matrix $C$ . Left: snapshots of $C_{ε_{k} ε_{k^{'}}}$ at $t = 12 fs$ and 380 fs, for no-field Auger decay with $ℏ ω = 10 eV$ , $τ_{1} = 100 fs$ , and $τ_{2} = 300 fs$ . Right: same, but for field intensity $I = 210 TW / {cm}^{2}$ and measurement time $t_{m} = 0.32 fs$ . The $C$ profiles are shown on linear vertical scales, and colored according to their value on the log-scale color bar.
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