Electronic Coherence and Coherent Dephasing in the Optical Control of Electrons in Graphene - Heide, Christian; Eckstein, Timo; Boolakee, Tobias; Gerner, Constanze; Weber, Heiko B.; Franco, Ignacio; Hommelhoff, Peter (Nano Letters, 2021)
Electronic coherence is of utmost importance for the access and control of quantum-mechanical solid-state properties. Using a purely electronic observable, the photocurrent, we measure a lower bound of the electronic coherence time of 22 ± 4 fs in graphene. The photocurrent is ideally suited to measure electronic coherence, as it is a direct result of coherent quantum-path interference, controlled by the delay between two ultrashort two-color laser pulses. The maximum delay for which interference between the population amplitude injected by the first pulse interferes with that generated by the second pulse determines the electronic coherence time. In particular, numerical simulations reveal that the experimental data yields a lower bound on the electronic coherence time, masked by coherent dephasing due to the broadband absorption in graphene. We expect that our results will significantly advance the understanding of coherent quantum control in solid-state systems ranging from excitation with weak fields to strongly driven system
Keywords: graphene; quantum-path interference; electronic coherence time; quantum control

From strong-field physics in and at nanoscale matter to photonics-based laser accelerators - Kozak, Martin; Higuchi, Takuya; McNeur, Joshua; Shiloh, Roy; Heide, Christian; Paschen, Timo; Yousefi, Peyman; Sturm, Constanze; Li, Ang; Illmer, Johannes; Meier, Stefan; Schönenberger, Norbert; et al. (205, 2019)
New ways of controlling quasi-free and free electrons by means of phase-controlled ultrashort laser pulses are demonstrated: from strong-field physics in the conducting 2-d material graphene and at the surface of nanostructures, to laser acceleration of free electrons with a nanophotonic structure, and the demonstration of the longitudinal Kapitza-Dirac effec

Inelastic ponderomotive scattering of electrons at a high-intensity optical travelling wave in vacuum - Kozak, Martin; Eckstein, Timo; Schönenberger, Norbert; Hommelhoff, Peter (Nature Physics, 2018)
In the early days of quantum mechanics Kapitza and Dirac predicted that matter waves would scatter off the optical intensity grating formed by two counter-propagating light waves1. This interaction, driven by the ponderomotive potential of the optical standing wave, was both studied theoretically and demonstrated experimentally for atoms<a href="https://www.nature.com/articles/nphys4282#ref2" title="Gould, P. L., Ruff, G. A. & Pritchard, D. E. Diffraction of atoms by light: the near-resonant Kapitza–Dirac effect. Phys. Rev. Lett. 56, 827–830 (1986).">2 and electrons3,4,5. In the original version of the experiment1,5, only the transverse momentum of particles was varied, but their energy and longitudinal momentum remained unchanged after the interaction. Here, we report on the generalization of the Kapitza–Dirac effect. We demonstrate that the energy of sub-relativistic electrons is strongly modulated on the few-femtosecond timescale via the interaction with a travelling wave created in vacuum by two colliding laser pulses at different frequencies. This effect extends the possibilities of temporal control of freely propagating particles with coherent light and can serve the attosecond ballistic bunching of electrons6, or for the acceleration of neutral atoms or molecules by ligh
Keywords: attosecond bunching; Kapitza-Dirac effect; few-femtosecond laser pulses; temporal control of freely propagating particles

Large-scale simulations of Floquet physics on near-term quantum computers - Eckstein, Timo; Mansuroglu, Refik; Czarnik, Piotr; Zhu, Jian Xin; Hartmann, Michael; Cincio, Lukasz; Sornborger, Andrew T.; Holmes, Zoë (npj Quantum Information, 2024)
Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum’s trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency ω but also a linear advantage in simulation time t compared to Trotterization.
CRIS-Team Scopus Importer:2024-09-20
Keywords: Quantum Computing; Floquet physics; NISQ

Optical current generation in graphene: CEP control vs. ω + 2ω control - Heide, Christian; Boolakee, Tobias; Eckstein, Timo; Hommelhoff, Peter (Nanophotonics, 2021)
The injection of directional currents in solids with strong optical fields has attracted tremendous attention as a route to realize ultrafast electronics based on the quantum-mechanical nature of electrons at femto- to attosecond timescales. Such currents are usually the result of an asymmetric population distribution imprinted by the temporal symmetry of the driving field. Here we compare two experimental schemes that allow control over the amplitude and direction of light-field-driven currents excited in graphene. Both schemes rely on shaping the incident laser field with one parameter only: either the carrier-envelope phase (CEP) of a single laser pulse or the relative phase between pulses oscillating at angular frequencies ω and 2ω, both for comparable laser parameters. We observe that the efficiency in generating a current via two-color-control exceeds that of CEP control by more than two orders of magnitude (7 nA vs. 18 pA), as the ω + 2ω field exhibits significantly more asymmetry in its temporal shape. We support this finding with numerical simulations that clearly show that two-color current control in graphene is superior, even down to single-cycle pulse durations. We expect our results to be relevant to experimentally access fundamental properties of any solid at ultrafast timescales, as well as for the emerging field of petahertz electronics.<br

Solving an industrially relevant quantum chemistry problem on quantum hardware - Nützel, Ludwig; Gresch, Alexander; Hehn, Lukas; Marti, Lucas; Freund, Robert; Steiner, Alex; Marciniak, Christian D.; Eckstein, Timo; Stockinger, Nina; Wolf, Stefan; Monz, Thomas; Kühn, Michael; et al. (Quantum Science and Technology, 2025)
Quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. Here we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs.
CRIS-Team Scopus Importer:2025-01-31
Keywords: quantum algorithms for chemical calculations; quantum chemistry; quantum computing; trapped ions

Ultrafast scanning electron microscope applied for studying the interaction between free electrons and optical near-fields of periodic nanostructures - Kozak, Martin; McNeur, Joshua; Schönenberger, Norbert; Illmer, Johannes; Li, Ang; Tafel, Alexander; Yousefi, Peyman; Eckstein, Timo; Hommelhoff, Peter (Journal of Applied Physics, 2018)
In this paper, we describe an ultrafast scanning electron microscope setup developed for the research of inelastic scattering of electrons at optical near-fields of periodic dielectric nanostructures. Electron emission from the Schottky cathode is controlled by ultraviolet femtosecond laser pulses. The electron pulse duration at the interaction site is characterized via cross-correlation of the electrons with an infrared laser pulse that excites a synchronous periodic near-field on the surface of a silicon nanostructure. The lower limit of 410 fs is found in the regime of a single electron per pulse. The role of pulse broadening due to Coulomb interaction in multielectron pulses is investigated. The setup is used to demonstrate an increase in the interaction distance between the electrons and the optical near-fields by introducing a pulse-front-tilt to the infrared laser beam. Furthermore, we show the dependence of the final electron spectra on the resonance condition between the phase velocity of the optical near-field and the electron propagation velocity. The resonance is controlled by adjusting the initial electron energy/velocity and by introducing a linear chirp to the structure period allowing the increase of the final electron energy gain up to a demonstrated value of 3.8 ke

Variational Hamiltonian simulation for translational invariant systems via classical pre-processing - Mansuroglu, Refik; Eckstein, Timo; Nützel, Ludwig; Wilkinson, Samuel; Hartmann, Michael (Quantum Science and Technology, 2023)
The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation thereof, where a higher approximation accuracy can be traded for an increased gate count. In this work, we introduce a variational algorithm which uses solutions of classical optimizations to predict efficient quantum circuits for time evolution of translationally invariant quantum systems. Our strategy can improve upon the Trotter-Suzuki accuracy by several orders of magnitude. It translates into a reduction in gate count and hence gain in overall fidelity at the same algorithmic accuracy. This is important in noisy intermediate scale quantum-applications where the fidelity of the output state decays exponentially with the number of gates. The performance advantage of our classical assisted strategy can be extended to open boundaries with translational symmetry in the bulk. We can extrapolate our method to beyond classically simulatable system sizes, maintaining its total fidelity advantage over a Trotter-Suzuki approximation making it an interesting candidate for beyond classical time evolution.
CRIS-Team Scopus Importer:2023-02-17
Keywords: Hamiltonian simulation; noisy intermediate scale quantum; time evolution; translational invariance; Trotter-Suzuki decomposition; variational algorithms