Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1507.01200 · Physical review. B./Physical review. B

Numerical method to compute optical conductivity based on pump-probe simulations

Can Shao, Takami Tohyama, Hong‐Gang Luo, Hantao Lu

Published May 23, 2016• 58 citations
arXivHTMLPDF

Abstract

A numerical method to calculate optical conductivity based on a pump-probe setup is presented. Its validity and limits are tested and demonstrated via concrete numerical simulations on the half-filled one-dimensional extended Hubbard model both in and out of equilibrium. By employing either a steplike or a Gaussian-like probing vector potential, it is found that in nonequilibrium, the method in the narrow-probe-pulse limit can be identified with variant types of linear-response theory, which, in equilibrium, produce identical results. The observation reveals the underlying probe-pulse dependence of the optical conductivity calculations in nonequilibrium, which may have applications in the theoretical analysis of ultrafast spectroscopy measurements.

DOI
10.1103/physrevb.93.195144

Related papers

Pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling

K. Sugimoto, Satoshi Ejima

By utilizing time-dependent tensor-network algorithms in the infinite matrix-product-state representation, we theoretically investigate the pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling. Our focus lies on nonequilibrium optical conductivity and single-particle excitation spectra. In the spin-density-wave (SDW) phase, we identify an in-gap state in the nonequilibrium optical conductivity due to the formation of excitons (or doublon-holon pairs), generated by the pulse through nonlocal interactions. In the strong-coupling regime, we discern additional multiple in-gap and out-of-gap states. In the charge-density-wave (CDW) phase, we detect not only an in-gap state but also a finite Drude weight, which results from the dissolution of charge order by photoexcitation. Analyzing time-dependent single-particle excitation spectra directly in the thermodynamic limit confirms the origin of these new states in the SDW and CDW phases as the excitation of newly emerged dispersions. We illustrate that the pump-probe spectroscopy simulations in the thermodynamic limit furnish unambiguous spectral structures that allow for direct comparison with experimental results, and the integration of nonequilibrium optical conductivity and time- and angle-resolved photoemission spectroscopy provides comprehensive insights into nonequilibrium states.

arXiv:2305.09909•Physical review. B./Physical review. B•Nov 14, 2023•7 citations

Nonequilibrium optical response of a one-dimensional Mott insulator

Julián Rincón, Adrian E. Feiguin

We define, compute, and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals (i) mid-gap states related to parity-forbidden optical states and (ii) strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.

arXiv:2012.15652•Physical review. B./Physical review. B•Aug 13, 2021•14 citations

Optical response of highly excited particles in a strongly correlated system

Zala Lenarčič, Denis Golež, J. Bonča +1 more

We present a linear-response formalism for a system of correlated electrons out of equilibrium, as relevant for the probe optical absorption in pump-probe experiments. We consider the time dependent optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega},t)$ and its nonequilibrium properties. As an application we numerically study a single highly excited charged particle in the spin background, as described within the two-dimensional $t$-$J$ model. Our results show that the optical sum rule approaches the equilibriumlike one very fast; however, the time evolution and the final asymptotic behavior of the absorption spectra in the finite systems considered still reveal dependence on the type of initial pump perturbation. This is observed in the evolution of its main features: the midinfrared peak and the Drude weight.

arXiv:1312.1962•Physical Review B•Mar 24, 2014•55 citations

Generalized linear response theory for pumped systems and its application to transient optical properties

Amir Eskandari-asl, Adolfo Avella

We derive the two-time linear response theory for out-of-equilibrium pumped systems, generic pump-probe delays, and probe frequencies. Such a theory enormously simplifies the numerical calculations, for instance, of the optical conductivity with respect to the actual procedure, which requires computing the effect of the probe pulse for each time delay with respect to the pump pulse. The theory is given for a generic observable and pumped Hamiltonian and then specialized for a system with a quadratic Hamiltonian and its transient optical properties, exploiting the dynamical projective operatorial approach (DPOA). The theory is complemented by a set of crucial numerical guidelines that help perform actual calculations in a computationally affordable way. The optical response (differential transient reflectivity and absorption) of a prototypical three-band (core, valence, and conduction) model in the extreme ultraviolet regime is analyzed in detail to illustrate the theory and its application. Using some generalizations of the density of states, we provide a systematic approach to exploring the optical properties in terms of the system band-structure features and the pump parameters. Such an analysis can be extremely helpful in understanding the actual results of experimental optical measurements. Moreover, we study the effects of interband and intraband transitions, the local dipole coupling, and single and multiphoton processes. The latter is further investigated by varying the central frequency of the pump pulse to have different regions of the first Brillouin zone in resonance with it. We also study the effect of varying the pump pulse intensity. Finally, we study and analyze the transient optical properties in the probe pulse regime of the infrared and visible.

arXiv:2404.10768•Physical Review A•Oct 25, 2024•9 citations

Theory of time-resolved optical spectroscopy on correlated electron systems

Martin Eckstein, Marcus Kollar

The real-time dynamics of interacting electrons out of equilibrium contains detailed microscopic information about electronically correlated materials, which can be read out with time-resolved optical spectroscopy. The reflectivity that is typically measured in pump-probe experiments is related to the nonequilibrium optical conductivity. We show how to express this quantity in terms of real-time Green's functions using dynamical mean-field theory. As an application we study the electrical response of the Falicov-Kimball model during the ultrafast buildup of the gapped phase at large interaction.

arXiv:0808.1005•Physical Review B•Nov 25, 2008•72 citations

Theory of Time-Resolved Optical Conductivity of Superconductors: Comparing Two Methods for Its Evaluation

John P. Revelle, Ankit Kumar, Alexander F. Kemper

Time-resolved optical conductivity is an often used tool to interrogate quantum materials driven out of equilibrium. Theoretically calculating this observable is a complex topic with several approaches discussed in the literature. Using a nonequilibrium Keldysh formalism and a functional derivative approach to the conductivity, we present a comparison of two particular approaches to the calculation of the optical conductivity and their distinguishing features, as applied to a pumped superconductor. The two methods are distinguished by the relative motion of the probe and gate times; either the probe or gate time is kept fixed while the other is swept. We find that both the methods result in same qualitative features of the time-resolved conductivity after pump is over. However, calculating the conductivity by keeping the gate fixed removes artifacts inherent to the other method. We provide software that, based on data for the first method, is able to construct the second approach.

arXiv:1909.04669•Condensed Matter•Aug 27, 2019•5 citations
A numerical method to calculate optical conductivity based on a pump-probe setup is presented. Its validity and limits are tested and demonstrated via concrete numerical simulations on the half-filled one-dimensional extended Hubbard model both in and out of equilibrium. By employing either a steplike or a Gaussian-like probing vector potential, it is found that in nonequilibrium, the method in the narrow-probe-pulse limit can be identified with variant types of linear-response theory, which, in equilibrium, produce identical results. The observation reveals the underlying probe-pulse dependence of the optical conductivity calculations in nonequilibrium, which may have applications in the theoretical analysis of ultrafast spectroscopy measurements.
By utilizing time-dependent tensor-network algorithms in the infinite matrix-product-state representation, we theoretically investigate the pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling. Our focus lies on nonequilibrium optical conductivity and single-particle excitation spectra. In the spin-density-wave (SDW) phase, we identify an in-gap state in the nonequilibrium optical conductivity due to the formation of excitons (or doublon-holon pairs), generated by the pulse through nonlocal interactions. In the strong-coupling regime, we discern additional multiple in-gap and out-of-gap states. In the charge-density-wave (CDW) phase, we detect not only an in-gap state but also a finite Drude weight, which results from the dissolution of charge order by photoexcitation. Analyzing time-dependent single-particle excitation spectra directly in the thermodynamic limit confirms the origin of these new states in the SDW and CDW phases as the excitation of newly emerged dispersions. We illustrate that the pump-probe spectroscopy simulations in the thermodynamic limit furnish unambiguous spectral structures that allow for direct comparison with experimental results, and the integration of nonequilibrium optical conductivity and time- and angle-resolved photoemission spectroscopy provides comprehensive insights into nonequilibrium states.
We define, compute, and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals (i) mid-gap states related to parity-forbidden optical states and (ii) strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.
We present a linear-response formalism for a system of correlated electrons out of equilibrium, as relevant for the probe optical absorption in pump-probe experiments. We consider the time dependent optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega},t)$ and its nonequilibrium properties. As an application we numerically study a single highly excited charged particle in the spin background, as described within the two-dimensional ttt-JJJ model. Our results show that the optical sum rule approaches the equilibriumlike one very fast; however, the time evolution and the final asymptotic behavior of the absorption spectra in the finite systems considered still reveal dependence on the type of initial pump perturbation. This is observed in the evolution of its main features: the midinfrared peak and the Drude weight.
We derive the two-time linear response theory for out-of-equilibrium pumped systems, generic pump-probe delays, and probe frequencies. Such a theory enormously simplifies the numerical calculations, for instance, of the optical conductivity with respect to the actual procedure, which requires computing the effect of the probe pulse for each time delay with respect to the pump pulse. The theory is given for a generic observable and pumped Hamiltonian and then specialized for a system with a quadratic Hamiltonian and its transient optical properties, exploiting the dynamical projective operatorial approach (DPOA). The theory is complemented by a set of crucial numerical guidelines that help perform actual calculations in a computationally affordable way. The optical response (differential transient reflectivity and absorption) of a prototypical three-band (core, valence, and conduction) model in the extreme ultraviolet regime is analyzed in detail to illustrate the theory and its application. Using some generalizations of the density of states, we provide a systematic approach to exploring the optical properties in terms of the system band-structure features and the pump parameters. Such an analysis can be extremely helpful in understanding the actual results of experimental optical measurements. Moreover, we study the effects of interband and intraband transitions, the local dipole coupling, and single and multiphoton processes. The latter is further investigated by varying the central frequency of the pump pulse to have different regions of the first Brillouin zone in resonance with it. We also study the effect of varying the pump pulse intensity. Finally, we study and analyze the transient optical properties in the probe pulse regime of the infrared and visible.
The real-time dynamics of interacting electrons out of equilibrium contains detailed microscopic information about electronically correlated materials, which can be read out with time-resolved optical spectroscopy. The reflectivity that is typically measured in pump-probe experiments is related to the nonequilibrium optical conductivity. We show how to express this quantity in terms of real-time Green's functions using dynamical mean-field theory. As an application we study the electrical response of the Falicov-Kimball model during the ultrafast buildup of the gapped phase at large interaction.
Time-resolved optical conductivity is an often used tool to interrogate quantum materials driven out of equilibrium. Theoretically calculating this observable is a complex topic with several approaches discussed in the literature. Using a nonequilibrium Keldysh formalism and a functional derivative approach to the conductivity, we present a comparison of two particular approaches to the calculation of the optical conductivity and their distinguishing features, as applied to a pumped superconductor. The two methods are distinguished by the relative motion of the probe and gate times; either the probe or gate time is kept fixed while the other is swept. We find that both the methods result in same qualitative features of the time-resolved conductivity after pump is over. However, calculating the conductivity by keeping the gate fixed removes artifacts inherent to the other method. We provide software that, based on data for the first method, is able to construct the second approach.