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Bruschi M, Gallina F, Fresch B. A Quantum Algorithm from Response Theory: Digital Quantum Simulation of Two-Dimensional Electronic Spectroscopy. J Phys Chem Lett 2024; 15:1484-1492. [PMID: 38295347 DOI: 10.1021/acs.jpclett.3c03499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2024]
Abstract
Multidimensional optical spectroscopies are powerful techniques to investigate energy transfer pathways in natural and artificial systems. Because of the high information content of the spectra, numerical simulations of the optical response are of primary importance to assist the interpretation of spectral features. However, the increasing complexity of the investigated systems and their quantum dynamics call for the development of novel simulation strategies. In this work, we consider using digital quantum computers. By combining quantum dynamical simulation and nonlinear response theory, we present a quantum algorithm for computing the optical response of molecular systems. The quantum advantage stems from the efficient quantum simulation of the dynamics governed by the molecular Hamiltonian, and it is demonstrated by explicitly considering exciton-vibrational coupling. The protocol is tested on a near-term quantum device, providing the digital quantum simulation of the linear and nonlinear response of simple molecular models.
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Affiliation(s)
- Matteo Bruschi
- Dipartimento di Scienze Chimiche, Università degli Studi di Padova, via Marzolo 1, Padua 35131, Italy
| | - Federico Gallina
- Dipartimento di Scienze Chimiche, Università degli Studi di Padova, via Marzolo 1, Padua 35131, Italy
| | - Barbara Fresch
- Dipartimento di Scienze Chimiche, Università degli Studi di Padova, via Marzolo 1, Padua 35131, Italy
- Padua Quantum Technologies Research Center, Università degli Studi di Padova, via Gradenigo 6/A, Padua 35131, Italy
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2
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Rose PA, Krich JJ. Interpretations of High-Order Transient Absorption Spectroscopies. J Phys Chem Lett 2023; 14:10849-10855. [PMID: 38032056 DOI: 10.1021/acs.jpclett.3c02491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2023]
Abstract
Transient absorption (TA) spectroscopy is an invaluable tool for determining the energetics and dynamics of excited states. When pump intensities are sufficiently high, TA spectra include both the generally desired third-order response and responses that are higher in order in the field amplitudes. Recent work demonstrated that pump-intensity-dependent TA measurements allow separating the orders of response, but the information content in those higher orders has not been described. We give a general framework for understanding high-order TA spectra. We extend to higher order the fundamental processes of standard TA: ground-state bleach (GSB), stimulated emission (SE), and excited-state absorption (ESA). Each order introduces two new processes: SE and ESA from previously inaccessible highly excited states and negations of lower-order processes. We show the new spectral and dynamical information at each order and show how the relative signs of the signals in different orders can be used to identify which processes dominate.
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Affiliation(s)
- Peter A Rose
- Department of Physics, University of Ottawa, Ottawa ON K1N 6N5, Canada
| | - Jacob J Krich
- Department of Physics, University of Ottawa, Ottawa ON K1N 6N5, Canada
- Nexus for Quantum Technologies, University of Ottawa, Ottawa ON K1N 6N5, Canada
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Lüttig J, Mueller S, Malý P, Krich JJ, Brixner T. Higher-Order Multidimensional and Pump-Probe Spectroscopies. J Phys Chem Lett 2023; 14:7556-7573. [PMID: 37589504 DOI: 10.1021/acs.jpclett.3c01694] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
Transient absorption and coherent two-dimensional spectroscopy are widely established methods for the investigation of ultrafast dynamics in quantum systems. Conventionally, they are interpreted in the framework of perturbation theory at the third order of interaction. Here, we discuss the potential of higher-(than-third-)order pump-probe and multidimensional spectroscopy to provide insight into excited multiparticle states and their dynamics. We focus on recent developments from our group. In particular, we demonstrate how phase cycling can be used in fluorescence-detected two-dimensional spectroscopy to isolate higher-order spectra that provide information about highly excited states such as the correlation of multiexciton states. We discuss coherently detected fifth-order 2D spectroscopy and its power to track exciton diffusion. Finally, we show how to extract higher-order signals even from ordinary pump-probe experiments, providing annihilation-free signals at high excitation densities and insight into multiexciton interactions.
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Affiliation(s)
- Julian Lüttig
- Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Stefan Mueller
- Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Pavel Malý
- Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague, Czech Republic
| | - Jacob J Krich
- Department of Physics, University of Ottawa, Ottawa K1N 6N5, Canada
- School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa K1N 6N5, Canada
| | - Tobias Brixner
- Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Center for Nanosystems Chemistry (CNC), Universität Würzburg, Theodor-Boveri-Weg, 97074 Würzburg, Germany
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4
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Segatta F, Ruiz DA, Aleotti F, Yaghoubi M, Mukamel S, Garavelli M, Santoro F, Nenov A. Nonlinear Molecular Electronic Spectroscopy via MCTDH Quantum Dynamics: From Exact to Approximate Expressions. J Chem Theory Comput 2023; 19:2075-2091. [PMID: 36961952 PMCID: PMC10100531 DOI: 10.1021/acs.jctc.2c01059] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/26/2023]
Abstract
We present an accurate and efficient approach to computing the linear and nonlinear optical spectroscopy of a closed quantum system subject to impulsive interactions with an incident electromagnetic field. It incorporates the effect of ultrafast nonadiabatic dynamics by means of explicit numerical propagation of the nuclear wave packet. The fundamental expressions for the evaluation of first- and higher-order response functions are recast in a general form that can be used with any quantum dynamics code capable of computing the overlap of nuclear wave packets evolving in different states. Here we present the evaluation of these expressions with the multiconfiguration time-dependent Hartree (MCTDH) method. Application is made to pyrene, excited to its lowest bright excited state S2 which exhibits a sub-100-fs nonadiabatic decay to a dark state S1. The system is described by a linear vibronic coupling Hamiltonian, parametrized with multiconfiguration electronic structure methods. We show that the ultrafast nonadiabatic dynamics can have a remarkable effect on the spectral line shapes that goes beyond simple lifetime broadening. Furthermore, a widely employed approximate expression based on the time scale separation of dephasing and population relaxation is recast in the same theoretical framework. Application to pyrene shows the range of validity of such approximations.
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Affiliation(s)
- Francesco Segatta
- Dipartimento di Chimica Industriale "Toso Montanari", University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
| | - Daniel Aranda Ruiz
- ICMol, Universidad de Valencia, Catedrático José Beltrán Martínez, 2, 46980 Paterna, Spain
- Istituto di Chimica dei Composti Organometallici (ICCOM-CNR), Area della Ricerca del CNR, Via Moruzzi 1, I-56124 Pisa, Italy
| | - Flavia Aleotti
- Dipartimento di Chimica Industriale "Toso Montanari", University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
| | - Martha Yaghoubi
- Istituto di Chimica dei Composti Organometallici (ICCOM-CNR), Area della Ricerca del CNR, Via Moruzzi 1, I-56124 Pisa, Italy
| | - Shaul Mukamel
- Department of Chemistry and Department of Physics and Astronomy, University of California, Irvine, California 92697, United States
| | - Marco Garavelli
- Dipartimento di Chimica Industriale "Toso Montanari", University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
| | - Fabrizio Santoro
- Istituto di Chimica dei Composti Organometallici (ICCOM-CNR), Area della Ricerca del CNR, Via Moruzzi 1, I-56124 Pisa, Italy
| | - Artur Nenov
- Dipartimento di Chimica Industriale "Toso Montanari", University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
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Gelin MF, Chen L, Domcke W. Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals. Chem Rev 2022; 122:17339-17396. [PMID: 36278801 DOI: 10.1021/acs.chemrev.2c00329] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.
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Affiliation(s)
- Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Lipeng Chen
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching,Germany
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Anda A, Cole JH. Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes. J Chem Phys 2021; 154:114113. [PMID: 33752354 DOI: 10.1063/5.0038550] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Abstract
Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.
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Affiliation(s)
- André Anda
- ARC Centre of Excellence in Exciton Science and Chemical and Quantum Physics, School of Science, RMIT University, Melbourne, Australia
| | - Jared H Cole
- ARC Centre of Excellence in Exciton Science and Chemical and Quantum Physics, School of Science, RMIT University, Melbourne, Australia
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Rose PA, Krich JJ. Automatic Feynman diagram generation for nonlinear optical spectroscopies and application to fifth-order spectroscopy with pulse overlaps. J Chem Phys 2021; 154:034109. [PMID: 33499626 DOI: 10.1063/5.0024105] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Abstract
Perturbative nonlinear optical spectroscopies are powerful methods to understand the dynamics of excitonic and other condensed phase systems. Feynman diagrams have long provided the essential tool to understand and interpret experimental spectra and to organize the calculation of spectra for model systems. When optical pulses are strictly time ordered, only a small number of diagrams contribute, but in many experiments, pulse-overlap effects are important for interpreting results. When pulses overlap, the number of contributing diagrams can increase rapidly, especially with higher order spectroscopies, and human error is especially likely when attempting to write down all the diagrams. We present an automated Diagram Generator (DG) that generates all the Feynman diagrams needed to calculate any nth-order spectroscopic signal. We characterize all perturbative nonlinear spectroscopies by their associated phase-discrimination condition as well as the time intervals where pulse amplitudes are nonzero. Although the DG can be used to automate impulsive calculations, its greatest strength lies in automating finite pulse calculations where pulse overlaps are important. We consider third-order transient absorption spectroscopy and fifth-order exciton-exciton interaction 2D (EEI2D) spectroscopy, which are described by six or seven diagrams in the impulsive limit, respectively, but 16 or 240 diagrams, respectively, when pulses overlap. The DG allows users to automatically include all relevant diagrams at a relatively low computational cost, since the extra diagrams are only generated for the inter-pulse delays where they are relevant. For EEI2D spectroscopy, we show the important effects of including the overlap diagrams.
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Affiliation(s)
- Peter A Rose
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Jacob J Krich
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
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Rose PA, Krich JJ. Efficient numerical method for predicting nonlinear optical spectroscopies of open systems. J Chem Phys 2021; 154:034108. [PMID: 33499622 DOI: 10.1063/5.0024104] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
Nonlinear optical spectroscopies are powerful tools for probing quantum dynamics in molecular and nanoscale systems. While intuition about ultrafast spectroscopies is often built by considering impulsive optical pulses, actual experiments have finite-duration pulses, which can be important for interpreting and predicting experimental results. We present a new freely available open source method for spectroscopic modeling, called Ultrafast Ultrafast (UF2) spectroscopy, which enables computationally efficient and convenient prediction of nonlinear spectra, such as treatment of arbitrary finite duration pulse shapes. UF2 is a Fourier-based method that requires diagonalization of the Liouvillian propagator of the system density matrix. We also present a Runge-Kutta-Euler (RKE) direct propagation method. We include open system dynamics in the secular Redfield, full Redfield, and Lindblad formalisms with Markovian baths. For non-Markovian systems, the degrees of freedom corresponding to memory effects are brought into the system and treated nonperturbatively. We analyze the computational complexity of the algorithms and demonstrate numerically that, including the cost of diagonalizing the propagator, UF2 is 20-200 times faster than the direct propagation method for secular Redfield models with arbitrary Hilbert space dimension; it is similarly faster for full Redfield models at least up to system dimensions where the propagator requires more than 20 GB to store; and for Lindblad models, it is faster up to Hilbert space dimension near 100 with speedups for small systems by factors of over 500. UF2 and RKE are part of a larger open source Ultrafast Software Suite, which includes tools for automatic generation and calculation of Feynman diagrams.
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Affiliation(s)
- Peter A Rose
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Jacob J Krich
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
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