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Makhija V, Gupta R, Neville S, Schuurman M, Francisco J, Kais S. Time Resolved Quantum Tomography in Molecular Spectroscopy by the Maximal Entropy Approach. J Phys Chem Lett 2024; 15:9525-9534. [PMID: 39264357 DOI: 10.1021/acs.jpclett.4c02368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/13/2024]
Abstract
Attosecond science offers unprecedented precision in probing the initial moments of chemical reactions, revealing the dynamics of molecular electrons that shape reaction pathways. A fundamental question emerges: what role, if any, do quantum coherences between molecular electron states play in photochemical reactions? Answering this question necessitates quantum tomography─the determination of the electronic density matrix from experimental data, where the off-diagonal elements represent these coherences. The Maximal Entropy (MaxEnt) based Quantum State Tomography (QST) approach offers unique advantages in studying molecular dynamics, particularly with partial tomographic data. Here, we explore the application of MaxEnt-based QST on photoexcited ammonia, necessitating the operator form of observables specific to the performed measurements. We present two methodologies for constructing these operators: one leveraging Molecular Angular Distribution Moments (MADMs) which accurately capture the orientation-dependent vibronic dynamics of molecules and another utilizing Angular Momentum Coherence Operators to construct measurement operators for the full rovibronic density matrix in the symmetric top basis. A key revelation of our study is the direct link between Lagrange multipliers in the MaxEnt formalism and the unique set of MADMs. Additionally, we visualize the electron density within the molecular frame, demonstrating charge migration across the molecule. Furthermore, we achieve a groundbreaking milestone by constructing, for the first time, the entanglement entropy of the electronic subsystem─a metric that was previously inaccessible. The entropy vividly reveals and quantifies the effects of coupling between the excited electron and nuclear degrees of freedom. Consequently, our findings open new avenues for research in ultrafast molecular spectroscopy within the broader domain of quantum information science, offering profound implications for the study of molecular systems under excitation using quantum tomographic schemes.
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Affiliation(s)
- Varun Makhija
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, United States
| | - Rishabh Gupta
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Simon Neville
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Michael Schuurman
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Chemistry, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Joseph Francisco
- Department of Earth and Environmental Science and Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Sabre Kais
- Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27606, United States
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2
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Shobeiry F, Fross P, Srinivas H, Pfeifer T, Moshammer R, Harth A. Emission control of entangled electrons in photoionisation of a hydrogen molecule. Sci Rep 2024; 14:19630. [PMID: 39179641 PMCID: PMC11343767 DOI: 10.1038/s41598-024-67465-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2024] [Accepted: 07/11/2024] [Indexed: 08/26/2024] Open
Abstract
For photo-dissociation of a single hydrogen molecule ( H 2 ) with combined XUV and IR laser pulses, we demonstrate optical control of the emission direction of the photoelectron with respect to the outgoing neutral fragment (the H-atom). Depending on the relative delay between the two laser fields, adjustable with sub-femtosecond time resolution, the photoelectron is emitted into the same hemisphere as the H-atom or opposite. This emission asymmetry is a result of entanglement of the two-electron final-state involving the spatially separated bound and emitted electron.
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Affiliation(s)
- Farshad Shobeiry
- Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117, Heidelberg, Germany.
| | - Patrick Fross
- Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117, Heidelberg, Germany
| | - Hemkumar Srinivas
- Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117, Heidelberg, Germany
| | - Thomas Pfeifer
- Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117, Heidelberg, Germany.
| | - Robert Moshammer
- Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117, Heidelberg, Germany.
| | - Anne Harth
- Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117, Heidelberg, Germany.
- Center for Optical Technologies, Aalen University, Anton Huber Straße 1, 73430, Aalen, Germany.
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3
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Nandi S, Stenquist A, Papoulia A, Olofsson E, Badano L, Bertolino M, Busto D, Callegari C, Carlström S, Danailov MB, Demekhin PV, Di Fraia M, Eng-Johnsson P, Feifel R, Gallician G, Giannessi L, Gisselbrecht M, Manfredda M, Meyer M, Miron C, Peschel J, Plekan O, Prince KC, Squibb RJ, Zangrando M, Zapata F, Zhong S, Dahlström JM. Generation of entanglement using a short-wavelength seeded free-electron laser. SCIENCE ADVANCES 2024; 10:eado0668. [PMID: 38630815 PMCID: PMC11023495 DOI: 10.1126/sciadv.ado0668] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Accepted: 03/14/2024] [Indexed: 04/19/2024]
Abstract
Quantum entanglement between the degrees of freedom encountered in the classical world is challenging to observe due to the surrounding environment. To elucidate this issue, we investigate the entanglement generated over ultrafast timescales in a bipartite quantum system comprising two massive particles: a free-moving photoelectron, which expands to a mesoscopic length scale, and a light-dressed atomic ion, which represents a hybrid state of light and matter. Although the photoelectron spectra are measured classically, the entanglement allows us to reveal information about the dressed-state dynamics of the ion and the femtosecond extreme ultraviolet pulses delivered by a seeded free-electron laser. The observed generation of entanglement is interpreted using the time-dependent von Neumann entropy. Our results unveil the potential for using short-wavelength coherent light pulses from free-electron lasers to generate entangled photoelectron and ion systems for studying spooky action at a distance.
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Affiliation(s)
- Saikat Nandi
- Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, 69622, Villeurbanne, France
| | - Axel Stenquist
- Department of Physics, Lund University, 22100 Lund, Sweden
| | | | - Edvin Olofsson
- Department of Physics, Lund University, 22100 Lund, Sweden
| | - Laura Badano
- Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy
| | | | - David Busto
- Department of Physics, Lund University, 22100 Lund, Sweden
| | - Carlo Callegari
- Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy
| | | | | | - Philipp V. Demekhin
- Institute of Physics and CINSaT, University of Kassel, 34132 Kassel, Germany
| | | | | | - Raimund Feifel
- Department of Physics, University of Gothenburg, 41258 Gothenburg, Sweden
| | | | - Luca Giannessi
- Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy
- INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy
| | | | | | | | - Catalin Miron
- Université Paris-Saclay, CEA, CNRS, LIDYL, 91191 Gif-sur-Yvette, France
- ELI-NP, “Horia Hulubei” National Institute for Physics and Nuclear Engineering, 077125 Mǎgurele, Romania
| | - Jasper Peschel
- Department of Physics, Lund University, 22100 Lund, Sweden
| | - Oksana Plekan
- Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy
| | - Kevin C. Prince
- Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy
| | - Richard J. Squibb
- Department of Physics, University of Gothenburg, 41258 Gothenburg, Sweden
| | - Marco Zangrando
- Elettra-Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy
- IOM-CNR, Istituto Officina dei Materiali, 34149 Basovizza, Trieste, Italy
| | - Felipe Zapata
- Department of Physics, Lund University, 22100 Lund, Sweden
| | - Shiyang Zhong
- Department of Physics, Lund University, 22100 Lund, Sweden
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4
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Kretschmar M, Svirplys E, Volkov M, Witting T, Nagy T, Vrakking MJJ, Schütte B. Compact realization of all-attosecond pump-probe spectroscopy. SCIENCE ADVANCES 2024; 10:eadk9605. [PMID: 38381830 PMCID: PMC10881040 DOI: 10.1126/sciadv.adk9605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 01/17/2024] [Indexed: 02/23/2024]
Abstract
The ability to perform attosecond-pump attosecond-probe spectroscopy (APAPS) is a longstanding goal in ultrafast science. While first pioneering experiments demonstrated the feasibility of APAPS, the low repetition rates (10 to 120 Hz) and the large footprints of existing setups have so far hindered the widespread exploitation of APAPS. Here, we demonstrate two-color APAPS using a commercial laser system at 1 kHz, straightforward post-compression in a hollow-core fiber, and a compact high-harmonic generation (HHG) setup. The latter enables the generation of intense extreme-ultraviolet (XUV) pulses by using an out-of-focus HHG geometry and by exploiting a transient blueshift of the driving laser in the HHG medium. Near-isolated attosecond pulses are generated, as demonstrated by one-color and two-color XUV-pump XUV-probe experiments. Our concept allows selective pumping and probing on extremely short timescales in many laboratories and permits investigations of fundamental processes that are not accessible by other pump-probe techniques.
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Affiliation(s)
| | | | - Mikhail Volkov
- Max-Born-Institut, Max-Born-Strasse 2A, 12489 Berlin, Germany
| | - Tobias Witting
- Max-Born-Institut, Max-Born-Strasse 2A, 12489 Berlin, Germany
| | - Tamás Nagy
- Max-Born-Institut, Max-Born-Strasse 2A, 12489 Berlin, Germany
| | | | - Bernd Schütte
- Max-Born-Institut, Max-Born-Strasse 2A, 12489 Berlin, Germany
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5
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Ishikawa KL, Prince KC, Ueda K. Control of Ion-Photoelectron Entanglement and Coherence Via Rabi Oscillations. J Phys Chem A 2023; 127:10638-10646. [PMID: 38084843 DOI: 10.1021/acs.jpca.3c06781] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2023]
Abstract
We report a theoretical investigation of photoionization by a pair of coherent, ultrashort, fundamental and second-harmonic extreme-ultraviolet pulses, where the photon energies are selected to yield the same photoelectron energy for ionization of two different subshells. This choice implies that the fundamental energy is equal to the difference in energy of the ionic states and that they are therefore coupled by the fundamental photon. By deriving analytical expressions using the essential-states approach, we show that this Rabi coupling creates coherence between the two photoelectron wave packets, which would otherwise be incoherent. We analyze how the coupling is affected by the parameters, such as relative phase, pulse width, delay between the two pulses, Rabi coupling strength, and photoelectron energy. Our discussion mostly considers Ne 2p and 2s photoionization, but it is generally valid for many other quantum systems where photoionization from two different shells is observed.
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Affiliation(s)
- Kenichi L Ishikawa
- Department of Nuclear Engineering and Management, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Photon Science Center, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
- Research Institute for Photon Science and Laser Technology, The University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
- Institute for Attosecond Laser Facility, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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6
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Morrigan L, Neville SP, Gregory M, Boguslavskiy AE, Forbes R, Wilkinson I, Lausten R, Stolow A, Schuurman MS, Hockett P, Makhija V. Ultrafast Molecular Frame Quantum Tomography. PHYSICAL REVIEW LETTERS 2023; 131:193001. [PMID: 38000424 DOI: 10.1103/physrevlett.131.193001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Revised: 09/05/2023] [Accepted: 10/03/2023] [Indexed: 11/26/2023]
Abstract
We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically nonadiabatic wave packet in ammonia (NH_{3}). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH_{3}, we observe that electronic coherences are induced by nuclear dynamics which nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.
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Affiliation(s)
- Luna Morrigan
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, USA
| | - Simon P Neville
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Margaret Gregory
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, USA
| | - Andrey E Boguslavskiy
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Ruaridh Forbes
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Iain Wilkinson
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Institute for Electronic Structure Dynamics, Helmholtz-Zentrum für Materialien und Energie, Hahn-Meitner-Platz 1, 14109 Berlin, Germany
| | - Rune Lausten
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Albert Stolow
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- NRC-uOttawa Joint Centre for Extreme and Quantum Photonics (JCEP), Ottawa, Ontario K1A 0R6, Canada
| | - Michael S Schuurman
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Paul Hockett
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Varun Makhija
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, USA
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7
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Eckart S, Trabert D, Rist J, Geyer A, Schmidt LPH, Fehre K, Kunitski M. Ultrafast preparation and detection of entangled atoms. SCIENCE ADVANCES 2023; 9:eabq8227. [PMID: 37683006 PMCID: PMC10491222 DOI: 10.1126/sciadv.abq8227] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 08/08/2023] [Indexed: 09/10/2023]
Abstract
Atoms can form a molecule by sharing their electrons in binding orbitals. These electrons are entangled. Is there a way to break a molecular bond and obtain atoms in their ground state that are spatially separated and still entangled? Here, we show that it is possible to prepare these spatially separated, entangled atoms on femtosecond time scales from single oxygen molecules. The two neutral atoms are entangled in the magnetic quantum number of their valence electrons. In a time-delayed probe step, we use nonadiabatic tunneling, which is a magnetic quantum number-sensitive ionization mechanism. We find a fingerprint of entanglement in the measured ionization probability as a function of the angle between the light's quantization axis and the molecular axis. This establishes a platform for further experiments that harness the time resolution of strong-field experiments to investigate spatially separated, entangled atoms on femtosecond time scales.
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Affiliation(s)
| | - Daniel Trabert
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
| | | | - Angelina Geyer
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
| | - Lothar Ph. H. Schmidt
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
| | | | - Maksim Kunitski
- Institut für Kernphysik, Goethe-Universität Frankfurt am Main, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
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8
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He PL, Hatsagortsyan KZ, Keitel CH. Double-Slit Interference in the Ion Dynamics of Dissociative Photoionization. PHYSICAL REVIEW LETTERS 2023; 131:013201. [PMID: 37478442 DOI: 10.1103/physrevlett.131.013201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 04/03/2023] [Accepted: 06/13/2023] [Indexed: 07/23/2023]
Abstract
The ion momentum distribution in the x-ray-induced dissociative photoionization of molecules is investigated, treating the ionization analytically under the Born-Oppenheimer approximation and simulating numerically the ion motion via the Schrödinger equation. The ion-photoelectron entanglement transfers information of the electronic interference to the ion dynamics. As a consequence, the ion momentum distributions of dissociative molecular photoionization present Young's double-slit interference when the photoelectron emission angle is fixed. We demonstrate that double-slit interference signatures persist in the ion longitudinal momentum shift even when the information of the correlated photoelectron is lost, which is the case for heteronuclear molecules when an additional photoelectron recoil momentum arises due to the different ion masses. For the case of sequential double ionization, we show that double-slit interference in the ion dynamics can be utilized for coherent control of the molecular dynamics.
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Affiliation(s)
- Pei-Lun He
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
| | | | - Christoph H Keitel
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
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9
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Flórez-Angarita MF, Pérez-Torres JF. Photoionization of Oriented HD( 1Σ +) Yields Vibrating HD +( 2Σ +) with Charge Breathing and Small Charge Transfer. J Phys Chem A 2022; 126:8918-8929. [DOI: 10.1021/acs.jpca.2c05050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Affiliation(s)
| | - J. F. Pérez-Torres
- Universidad Industrial de Santander, carrera 27 calle 9, 680002Bucaramanga, Colombia
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10
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Kobayashi Y, Leone SR. Characterizing coherences in chemical dynamics with attosecond time-resolved x-ray absorption spectroscopy. J Chem Phys 2022; 157:180901. [DOI: 10.1063/5.0119942] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Coherence can drive wave-like motion of electrons and nuclei in photoexcited systems, which can yield fast and efficient ways to exert materials’ functionalities beyond the thermodynamic limit. The search for coherent phenomena has been a central topic in chemical physics although their direct characterization is often elusive. Here, we highlight recent advances in time-resolved x-ray absorption spectroscopy (tr-XAS) to investigate coherent phenomena, especially those that utilize the eminent light source of isolated attosecond pulses. The unparalleled time and state sensitivities of tr-XAS in tandem with the unique element specificity render the method suitable to study valence electronic dynamics in a wide variety of materials. The latest studies have demonstrated the capabilities of tr-XAS to characterize coupled electronic–structural coherence in small molecules and coherent light–matter interactions of core-excited excitons in solids. We address current opportunities and challenges in the exploration of coherent phenomena, with potential applications for energy- and bio-related systems, potential crossings, strongly driven solids, and quantum materials. With the ongoing developments in both theory and light sources, tr-XAS holds great promise for revealing the role of coherences in chemical dynamics.
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Affiliation(s)
- Yuki Kobayashi
- Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Stephen R. Leone
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Physics, University of California, Berkeley, California 94720, USA
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11
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Gregory M, Neville S, Schuurman M, Makhija V. A laboratory frame density matrix for ultrafast quantum molecular dynamics. J Chem Phys 2022; 157:164301. [DOI: 10.1063/5.0109607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In most cases, the ultrafast dynamics of resonantly excited molecules are considered and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here, we provide a formalism in terms of a lab frame density matrix, which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences, which are potentially experimentally accessible, are rejected by the orientation-averaged reduced vibronic density matrix. Instead, molecular angular distribution moments are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame.
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Affiliation(s)
- Margaret Gregory
- Department of Chemistry and Physics, University of Mary Washington, 1301 College Avenue, Fredericksburg, Virginia 22401, USA
| | - Simon Neville
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Michael Schuurman
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
| | - Varun Makhija
- Department of Chemistry and Physics, University of Mary Washington, 1301 College Avenue, Fredericksburg, Virginia 22401, USA
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12
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Mayer N, Beaulieu S, Jiménez-Galán Á, Patchkovskii S, Kornilov O, Descamps D, Petit S, Smirnova O, Mairesse Y, Ivanov MY. Role of Spin-Orbit Coupling in High-Order Harmonic Generation Revealed by Supercycle Rydberg Trajectories. PHYSICAL REVIEW LETTERS 2022; 129:173202. [PMID: 36332250 DOI: 10.1103/physrevlett.129.173202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Revised: 07/26/2022] [Accepted: 09/08/2022] [Indexed: 06/16/2023]
Abstract
High-harmonic generation is typically thought of as a sub-laser-cycle process, with the electron's excursion in the continuum lasting a fraction of the optical cycle. However, it was recently suggested that long-lived Rydberg states can play a particularly important role in high harmonic generation by atoms driven by the combination of the counterrotating circularly polarized fundamental light field and its second harmonic. Here we report direct experimental evidence of very long and stable Rydberg trajectories contributing to high-harmonic generation in such fields. We track their dynamics inside the laser pulse using the spin-orbit evolution in the ionic core, utilizing the spin-orbit Larmor clock. We confirm their effect on harmonic emission both via microscopic simulations and by showing how this radiation can lead to a well-collimated macroscopic far-field signal. Our observations contrast sharply with the general view that long-lived Rydberg orbits should generate negligible contribution to the macroscopic far-field high harmonic response of the medium.
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Affiliation(s)
- N Mayer
- Max-Born-Institute, Max-Born Straße 2A, 12489 Berlin, Germany
| | - S Beaulieu
- Université de Bordeaux-CNRS-CEA, Centre Lasers Intenses et Applications (CELIA), UMR5107, F33405 Talence, France
| | - Á Jiménez-Galán
- Max-Born-Institute, Max-Born Straße 2A, 12489 Berlin, Germany
- Joint Attosecond Science Laboratory, National Research Council of Canada and University of Ottawa, Ottawa, Canada
| | - S Patchkovskii
- Max-Born-Institute, Max-Born Straße 2A, 12489 Berlin, Germany
| | - O Kornilov
- Max-Born-Institute, Max-Born Straße 2A, 12489 Berlin, Germany
| | - D Descamps
- Université de Bordeaux-CNRS-CEA, Centre Lasers Intenses et Applications (CELIA), UMR5107, F33405 Talence, France
| | - S Petit
- Université de Bordeaux-CNRS-CEA, Centre Lasers Intenses et Applications (CELIA), UMR5107, F33405 Talence, France
| | - O Smirnova
- Max-Born-Institute, Max-Born Straße 2A, 12489 Berlin, Germany
| | - Y Mairesse
- Université de Bordeaux-CNRS-CEA, Centre Lasers Intenses et Applications (CELIA), UMR5107, F33405 Talence, France
| | - M Y Ivanov
- Max-Born-Institute, Max-Born Straße 2A, 12489 Berlin, Germany
- Department of Physics, Humboldt University, Newtonstraße 15, D-12489 Berlin, Germany
- Blackett Laboratory, Imperial College London, SW7 2AZ London, United Kingdom
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13
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Blavier M, Gelfand N, Levine R, Remacle F. Entanglement of electrons and nuclei: A most compact representation of the molecular wave function. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2022.139885] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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14
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Maxwell AS, Madsen LB, Lewenstein M. Entanglement of orbital angular momentum in non-sequential double ionization. Nat Commun 2022; 13:4706. [PMID: 35948552 PMCID: PMC9365801 DOI: 10.1038/s41467-022-32128-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 07/19/2022] [Indexed: 11/30/2022] Open
Abstract
Entanglement has a capacity to enhance imaging procedures, but this remains unexplored for attosecond imaging. Here, we elucidate that possibility, addressing orbital angular momentum (OAM) entanglement in ultrafast processes. In the correlated process non-sequential double ionization (NSDI) we demonstrate robust photoelectron entanglement. In contrast to commonly considered continuous variables, the discrete OAM allows for a simpler interpretation, computation, and measurement of entanglement. The logarithmic negativity reveals that the entanglement is robust to incoherence and an entanglement witness minimizes the number of measurements to detect the entanglement, both quantities are related to OAM coherence terms. We quantify the entanglement for a range of targets and field parameters to find the most entangled photoelectron pairs. This methodology provides a general way to use OAM to quantify and measure entanglement, well-suited to attosecond processes, and can be exploited to enhance imaging capabilities through correlated measurements, or for generation of OAM-entangled electrons.
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Affiliation(s)
- Andrew S Maxwell
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels, Barcelona, Spain.
- Department of Physics and Astronomy, Aarhus University, DK-8000, Aarhus C, Denmark.
| | - Lars Bojer Madsen
- Department of Physics and Astronomy, Aarhus University, DK-8000, Aarhus C, Denmark
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels, Barcelona, Spain
- ICREA, Pg. Lluís Companys 23, 08010, Barcelona, Spain
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15
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Blavier M, Levine RD, Remacle F. Time evolution of entanglement of electrons and nuclei and partial traces in ultrafast photochemistry. Phys Chem Chem Phys 2022; 24:17516-17525. [PMID: 35838986 DOI: 10.1039/d2cp01440h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Broad in energy optical pulses induce ultrafast molecular dynamics where nuclear degrees of freedom are entangled with electronic ones. We discuss a matrix representation of wave functions of such entangled systems. Singular Value Decomposition (SVD) of this matrix provides a representation as a sum of separable terms. Their weights can be arranged in decreasing order. The representation provided by the SVD is equivalent to a Schmidt decomposition. If there is only one term or if one term is already a good approximation, the system is not entangled. The SVD also provides either an exact or a few term approximation for the partial traces. A simple example, the dynamics of LiH upon ultrafast excitation to several non-adiabatically coupled electronic states, is provided. The major contribution to the entanglement is created during the exit from the Franck Condon region. An additional contribution is the entanglement due to the nuclear motion induced non-adiabatic transitions.
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Affiliation(s)
- Martin Blavier
- Theoretical Physical Chemistry, University of Liège, 4000 Liège, Belgium. .,The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
| | - R D Levine
- The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel.,Department of Chemistry and Biochemistry and Department of Molecular and Medical Pharmacology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095, USA
| | - F Remacle
- Theoretical Physical Chemistry, University of Liège, 4000 Liège, Belgium. .,The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
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16
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Koll LM, Maikowski L, Drescher L, Vrakking MJJ, Witting T. Phase-locking of time-delayed attosecond XUV pulse pairs. OPTICS EXPRESS 2022; 30:7082-7095. [PMID: 35299479 DOI: 10.1364/oe.452018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 02/08/2022] [Indexed: 06/14/2023]
Abstract
We present a setup for the generation of phase-locked attosecond extreme ultraviolet (XUV) pulse pairs. The attosecond pulse pairs are generated by high harmonic generation (HHG) driven by two phase-locked near-infrared (NIR) pulses that are produced using an actively stabilized Mach-Zehnder interferometer compatible with near-single cycle pulses. The attosecond XUV pulses can be delayed over a range of 400 fs with a sub-10-as delay jitter. We validate the precision and the accuracy of the setup by XUV optical interferometry and by retrieving the energies of Rydberg states of helium in an XUV pump-NIR probe photoelectron spectroscopy experiment.
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17
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Koll LM, Maikowski L, Drescher L, Witting T, Vrakking MJJ. Experimental Control of Quantum-Mechanical Entanglement in an Attosecond Pump-Probe Experiment. PHYSICAL REVIEW LETTERS 2022; 128:043201. [PMID: 35148151 DOI: 10.1103/physrevlett.128.043201] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 12/07/2021] [Indexed: 06/14/2023]
Abstract
Entanglement is one of the most intriguing aspects of quantum mechanics and lies at the heart of the ongoing second quantum revolution, where it is a resource that is used in quantum key distribution, quantum computing, and quantum teleportation. We report experiments demonstrating the crucial role that entanglement plays in pump-probe experiments involving ionization, which are a hallmark of the novel research field of attosecond science. We demonstrate that the degree of entanglement in a bipartite ion + photoelectron system, and, as a consequence, the degree of vibrational coherence in the ion, can be controlled by tailoring the spectral properties of the attosecond extreme ultraviolet laser pulses that are used to create them.
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Affiliation(s)
- Lisa-Marie Koll
- Max-Born-Institut, Max-Born-Strasse 2A, 12x489 Berlin, Germany
| | - Laura Maikowski
- Max-Born-Institut, Max-Born-Strasse 2A, 12x489 Berlin, Germany
| | - Lorenz Drescher
- Max-Born-Institut, Max-Born-Strasse 2A, 12x489 Berlin, Germany
| | - Tobias Witting
- Max-Born-Institut, Max-Born-Strasse 2A, 12x489 Berlin, Germany
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