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:cond-mat/0307768 · Physical Review A

Photon statistics: Nonlinear spectroscopy of single quantum systems

Shaul Mukamel

Published Dec 24, 2003• 60 citations
arXivHTMLPDF

Abstract

A unified description of multitime correlation functions, nonlinear response functions, and quantum measurements is developed using a common generating function which allows a direct comparison of their information content. A general formal expression for photon counting statistics from single quantum objects is derived in terms of Liouville-space correlation functions of the material system by making a single assumption that a spontaneous emission is described by a master equation.

DOI
10.1103/physreva.68.063821

Related papers

Photon Statistics for Single-Molecule Nonlinear Spectroscopy

F. Shikerman, Eli Barkai

We develop the theory of nonlinear spectroscopy for a single molecule undergoing stochastic dynamics and interacting with a sequence of two laser pulses. We find general expressions for the photon counting statistics and the exact solution to the problem for the Kubo-Anderson process. In the limit of impulsive pulses the information on the photon statistics is contained in the molecule's dipole correlation function. The selective limit, the semiclassical approximation, and the fast modulation limit exhibit rich general behaviors of this new type of spectroscopy. We show how the design of external fields leads to insights on ultrafast dynamics of individual molecules that are different from those found for an ensemble.

arXiv:0705.4028•Physical Review Letters•Nov 15, 2007•14 citations

Single-Molecule Photon Counting Statistics via Generalized Optical Bloch Equations

Yujun Zheng, Frank L. H. Brown

We derive the generating function for single molecule photon emission events within the context of the stochastically modulated optical Bloch equations. Statistical properties of single molecule photon counting experiments are deduced from a set of coupled differential equations only slightly more complicated than the Bloch equations themselves. This formulation allows for the study of photon bunching and antibunching within a single theoretical framework and provides a description of these behaviors that emphasizes the connection with single molecule experiments. Application is made to the spectroscopy of a chromophore coupled to a single two level system.

Physical Review Letters•Jun 13, 2003•129 citations

Liouville-space pathways for spectral diffusion in photon statistics from single molecules

František Šanda, Shaul Mukamel

The factorial moments of photon counting statistics from a single molecule coupled to a quantum bath are expressed in terms of multipoint quantum correlation functions and represented by double-sided Feynman diagrams, in close formal analogy with nonlinear spectroscopy. At infinite temperature we recover the results of stochastic models of spectral diffusion where the bath dynamics is independent on the state of the system and the moments are described by lower-order correlation functions.

Physical Review A•Mar 11, 2005•25 citations

Principles of Nonlinear Optical Spectroscopy

Shaul Mukamel

1. Introduction 2. Quantum Dynamics in Hilbert Space 3. The Density Operator and Quantum Dynamics in Liouville Space 4. Quantum Electrodynamics, Optical Polarization, and Nonlinear Spectroscopy 5. Nonlinear Response Functions and Optical Susceptibilities 6. The Optical Response Functions of a Multilevel System with Relaxation 7. Semiclassical Simulation of the Optical Response Functions 8. The Cumulant Expansion and the Multimode Brownian Oscillator Model 9. Fluorescence, Spontaneous-Raman and Coherent-Raman Spectroscopy 10. Selective Elimination of Inhomogeneous Broadening Photon Echoes 11. Resonant Gratings, Pump-Probe, and Hole Burning Spectroscopy 12. Wavepacket Dynamics in Liouville Space The Wigner Representation 13. Wavepacket Analysis of Nonimpulsive Measurements 14. Off-Resonance Raman Scattering 15. Polarization Spectroscopy Birefringence and Dichroism 16. Nonlinear Response of Molecular Assemblies The Local-Field Approximation 17. Many Body and Cooperative Effects in the Nonlinear Response

•Jan 15, 1995•4,534 citations

Multipoint Correlation Functions for Photon Statistics in Single-Molecule Spectroscopy: Stochastic Dynamics in Liouville Space

František Šanda, Shaul Mukamel

WORLD SCIENTIFIC eBooks•Oct 1, 2008•0 citations

Photon statistics: Nonlinear spectroscopy of single quantum systems (8 pages)

Shaul Mukamel

Physical Review A•Jan 1, 2003•0 citations
A unified description of multitime correlation functions, nonlinear response functions, and quantum measurements is developed using a common generating function which allows a direct comparison of their information content. A general formal expression for photon counting statistics from single quantum objects is derived in terms of Liouville-space correlation functions of the material system by making a single assumption that a spontaneous emission is described by a master equation.
We develop the theory of nonlinear spectroscopy for a single molecule undergoing stochastic dynamics and interacting with a sequence of two laser pulses. We find general expressions for the photon counting statistics and the exact solution to the problem for the Kubo-Anderson process. In the limit of impulsive pulses the information on the photon statistics is contained in the molecule's dipole correlation function. The selective limit, the semiclassical approximation, and the fast modulation limit exhibit rich general behaviors of this new type of spectroscopy. We show how the design of external fields leads to insights on ultrafast dynamics of individual molecules that are different from those found for an ensemble.
We derive the generating function for single molecule photon emission events within the context of the stochastically modulated optical Bloch equations. Statistical properties of single molecule photon counting experiments are deduced from a set of coupled differential equations only slightly more complicated than the Bloch equations themselves. This formulation allows for the study of photon bunching and antibunching within a single theoretical framework and provides a description of these behaviors that emphasizes the connection with single molecule experiments. Application is made to the spectroscopy of a chromophore coupled to a single two level system.
1. Introduction 2. Quantum Dynamics in Hilbert Space 3. The Density Operator and Quantum Dynamics in Liouville Space 4. Quantum Electrodynamics, Optical Polarization, and Nonlinear Spectroscopy 5. Nonlinear Response Functions and Optical Susceptibilities 6. The Optical Response Functions of a Multilevel System with Relaxation 7. Semiclassical Simulation of the Optical Response Functions 8. The Cumulant Expansion and the Multimode Brownian Oscillator Model 9. Fluorescence, Spontaneous-Raman and Coherent-Raman Spectroscopy 10. Selective Elimination of Inhomogeneous Broadening Photon Echoes 11. Resonant Gratings, Pump-Probe, and Hole Burning Spectroscopy 12. Wavepacket Dynamics in Liouville Space The Wigner Representation 13. Wavepacket Analysis of Nonimpulsive Measurements 14. Off-Resonance Raman Scattering 15. Polarization Spectroscopy Birefringence and Dichroism 16. Nonlinear Response of Molecular Assemblies The Local-Field Approximation 17. Many Body and Cooperative Effects in the Nonlinear Response