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Yu M, Liu K, Li M, Yan J, Cao C, Tan J, Liang J, Guo K, Cao W, Lan P, Zhang Q, Zhou Y, Lu P. Full experimental determination of tunneling time with attosecond-scale streaking method. LIGHT, SCIENCE & APPLICATIONS 2022; 11:215. [PMID: 35798716 PMCID: PMC9262890 DOI: 10.1038/s41377-022-00911-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/10/2022] [Revised: 06/13/2022] [Accepted: 06/23/2022] [Indexed: 06/15/2023]
Abstract
Tunneling is one of the most fundamental and ubiquitous processes in the quantum world. The question of how long a particle takes to tunnel through a potential barrier has sparked a long-standing debate since the early days of quantum mechanics. Here, we propose and demonstrate a novel scheme to accurately determine the tunneling time of an electron. In this scheme, a weak laser field is used to streak the tunneling current produced by a strong elliptically polarized laser field in an attoclock configuration, allowing us to retrieve the tunneling ionization time relative to the field maximum with a precision of a few attoseconds. This overcomes the difficulties in previous attoclock measurements wherein the Coulomb effect on the photoelectron momentum distribution has to be removed with theoretical models and it requires accurate information of the driving laser fields. We demonstrate that the tunneling time of an electron from an atom is close to zero within our experimental accuracy. Our study represents a straightforward approach toward attosecond time-resolved imaging of electron motion in atoms and molecules.
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Affiliation(s)
- Miao Yu
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Kun Liu
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Min Li
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China.
| | - Jiaqing Yan
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Chuanpeng Cao
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Jia Tan
- Jiangsu Key Laboratory of Micro and Nano Heat Fluid Flow Technology and Energy Application, School of Physical Science and Technology, Suzhou University of Science and Technology, 215009, Suzhou, China
| | - Jintai Liang
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Keyu Guo
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Wei Cao
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Pengfei Lan
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Qingbin Zhang
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Yueming Zhou
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China.
| | - Peixiang Lu
- Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China.
- Optics Valley Laboratory, 430074, Hubei, China.
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Attosecond angular streaking and tunnelling time in atomic hydrogen. Nature 2019; 568:75-77. [PMID: 30886392 DOI: 10.1038/s41586-019-1028-3] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2017] [Accepted: 01/07/2019] [Indexed: 11/08/2022]
Abstract
The tunnelling of a particle through a potential barrier is a key feature of quantum mechanics that goes to the core of wave-particle duality. The phenomenon has no counterpart in classical physics, and there are no well constructed dynamical observables that could be used to determine 'tunnelling times'. The resulting debate1-5 about whether a tunnelling quantum particle spends a finite and measurable time under a potential barrier was reignited in recent years by the advent of ultrafast lasers and attosecond metrology6. Particularly important is the attosecond angular streaking ('attoclock') technique7, which can time the release of electrons in strong-field ionization with a precision of a few attoseconds. Initial measurements7-10 confirmed the prevailing view that tunnelling is instantaneous, but later studies11,12 involving multi-electron atoms-which cannot be accurately modelled, complicating interpretation of the ionization dynamics-claimed evidence for finite tunnelling times. By contrast, the simplicity of the hydrogen atom enables precise experimental measurements and calculations13-15 and makes it a convenient benchmark. Here we report attoclock and momentum-space imaging16 experiments on atomic hydrogen and compare these results with accurate simulations based on the three-dimensional time-dependent Schrödinger equation and our experimental laser pulse parameters. We find excellent agreement between measured and simulated data, confirming the conclusions of an earlier theoretical study17 of the attoclock technique in atomic hydrogen that presented a compelling argument for instantaneous tunnelling. In addition, we identify the Coulomb potential as the sole cause of the measured angle between the directions of electron emission and peak electric field: this angle had been attributed11,12 to finite tunnelling times. We put an upper limit of 1.8 attoseconds on any tunnelling delay, in agreement with recent theoretical findings18 and ruling out the interpretation of all commonly used 'tunnelling times'19 as 'time spent by an electron under the potential barrier'20.
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Wells D, Quiney H. A fast and adaptable method for high accuracy integration of the time-dependent Schrödinger equation. Sci Rep 2019; 9:782. [PMID: 30692569 PMCID: PMC6349856 DOI: 10.1038/s41598-018-37382-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Accepted: 11/27/2018] [Indexed: 11/15/2022] Open
Abstract
We present an adaptable, fast, and robust method for integrating the time-dependent Schrödinger equation. We apply the method to calculations of High Harmonic (HHG) and Above Threshold Ionisation (ATI) spectra for a single atomic electron in an intense laser field. Our approach implements the stabilized bi-conjugate gradient method (BiCG-STAB) for solving a sparse linear system to evolve the electronic wavefunction in time. The use of this established method makes the propagation scheme less restrictive compared to other schemes which may have particular requirements for the form of the equation, such as use of a three-point finite-difference approximation for spatial derivatives. Our method produces converged solutions significantly faster than existing methods, particularly if high accuracy is required. We demonstrate that this approach is suitable for a range of different parameters and show that in many circumstances significant gains can be made with the use of a fourth-order time propagator as opposed to the more common second-order Crank-Nicolson (CN) method.
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Affiliation(s)
- Daniel Wells
- ARC Centre of Excellence for Advanced Molecular Imaging, Theoretical Condensed Matter Physics Group, School of Physics, University of Melbourne, Victoria, 3010, Australia.
| | - Harry Quiney
- ARC Centre of Excellence for Advanced Molecular Imaging, Theoretical Condensed Matter Physics Group, School of Physics, University of Melbourne, Victoria, 3010, Australia
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Zeller S, Kunitski M, Voigtsberger J, Waitz M, Trinter F, Eckart S, Kalinin A, Czasch A, Schmidt LPH, Weber T, Schöffler M, Jahnke T, Dörner R. Determination of Interatomic Potentials of He_{2}, Ne_{2}, Ar_{2}, and H_{2} by Wave Function Imaging. PHYSICAL REVIEW LETTERS 2018; 121:083002. [PMID: 30192586 DOI: 10.1103/physrevlett.121.083002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2018] [Indexed: 06/08/2023]
Abstract
We report on a direct method to measure the interatomic potential energy curve of diatomic systems. A cold target recoil ion momentum spectroscopy reaction microscope was used to measure the squares of the vibrational wave functions of H_{2}, He_{2}, Ne_{2}, and Ar_{2}. The Schrödinger equation relates the curvature of the wave function to the potential V(R) and therefore offers a simple but elegant way to extract the shape of the potential.
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Affiliation(s)
- S Zeller
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, 64291 Darmstadt, Germany
| | - M Kunitski
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - J Voigtsberger
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - M Waitz
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - F Trinter
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - S Eckart
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - A Kalinin
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - A Czasch
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - L Ph H Schmidt
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - T Weber
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - M Schöffler
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - T Jahnke
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - R Dörner
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
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Wahlstrand JK, Zahedpour S, Bahl A, Kolesik M, Milchberg HM. Bound-Electron Nonlinearity Beyond the Ionization Threshold. PHYSICAL REVIEW LETTERS 2018; 120:183901. [PMID: 29775376 PMCID: PMC6074032 DOI: 10.1103/physrevlett.120.183901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2018] [Indexed: 05/25/2023]
Abstract
We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.
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Affiliation(s)
- J. K. Wahlstrand
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742
- Engineering Physics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899
| | - S. Zahedpour
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742
| | - A. Bahl
- College of Optical Sciences, University of Arizona, Tucson, AZ 85712
| | - M. Kolesik
- College of Optical Sciences, University of Arizona, Tucson, AZ 85712
| | - H. M. Milchberg
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742
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Luo S, Hu W, Yu J, Li X, He L, Wang C, Liu F, Ding D. Multielectron Effects in the Strong Field Sequential Ionization of Aligned CH3I Molecules. J Phys Chem A 2017; 121:6547-6553. [DOI: 10.1021/acs.jpca.7b05588] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sizuo Luo
- Institute of Atomic
and Molecular Physics, and Jilin Provincial
Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, China
| | - Wenhui Hu
- Institute of Atomic
and Molecular Physics, and Jilin Provincial
Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, China
| | - Jiaqi Yu
- Institute of Atomic
and Molecular Physics, and Jilin Provincial
Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, China
| | - Xiaokai Li
- Institute of Atomic
and Molecular Physics, and Jilin Provincial
Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, China
| | - Lanhai He
- Institute of Atomic
and Molecular Physics, and Jilin Provincial
Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, China
| | - Chuncheng Wang
- Institute of Atomic
and Molecular Physics, and Jilin Provincial
Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, China
| | - Fuchun Liu
- Institute of Atomic
and Molecular Physics, and Jilin Provincial
Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, China
| | - Dajun Ding
- Institute of Atomic
and Molecular Physics, and Jilin Provincial
Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, China
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Summers AM, Yu X, Wang X, Raoul M, Nelson J, Todd D, Zigo S, Lei S, Trallero-Herrero CA. Spatial characterization of Bessel-like beams for strong-field physics. OPTICS EXPRESS 2017; 25:1646-1655. [PMID: 29519019 DOI: 10.1364/oe.25.001646] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
We present a compact, simple design for the generation and tuning of both the spot size and effective focal length of Bessel-like beams. In particular, this setup provides an important tool for the use of Bessel-like beams with high-power, femtosecond laser systems. Using a shallow angle axicon in conjunction with a spherical lens, we show that it is possible to focus Bessel-like modes to comparable focal spot sizes to sharp axicons while maintaining a long effective focal length. The resulting focal profiles are characterized in detail using an accurate high dynamic range imaging technique. Quantitatively, we introduce a metric (R0.8) which defines the spot-size containing 80% of the total energy. Our setup overcomes the typical compromise between long working distances and small spot sizes. This is particularly relevant for strong-field physics where most experiments must operate in vacuum.
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