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/0408503 · Physical Review A

Langevin analysis of fundamental noise limits in coherent anti-Stokes Raman spectroscopy

Kunal K. Das, G. S. Agarwal, Yu. M. Golubev, Marlan O. Scully

Published Jan 4, 2005• 4 citations
arXivHTMLPDF

Abstract

We use a Langevin approach to analyze the quantum noise in coherent anti-Stokes Raman spectroscopy in several experimental scenarios: with continuous-wave input fields acting simultaneously and with fast sequential pulsed lasers where one field scatters off the coherence generated by other fields and for interactions within a cavity and in free space. In all cases, the signal and quantum noise due to spontaneous decay and decoherence in the medium are shown to be described by the same general expression. Our theory in particular shows that for short interaction times, the medium noise is not important and the efficiency is limited only by the intrinsic quantum nature of the photon. We obtain fully analytic results without making an adiabatic approximation; the fluctuations of the medium and the fields are solved self-consistently.

DOI
10.1103/physreva.71.013802

Related papers

Role of noise operators on two-photon correlations in an extended coherent Raman medium

C. H. Raymond Ooi, Muhammad Suhail Zubairy

An extended medium driven in a double Raman configuration generates Stokes and anti-Stokes fields that are described by coupled parametric oscillator equations with solutions that depend on input boundary operators and quantum noise operators. We identify the conditions where the boundary operators can be the substitute to the noise operators for describing two-photon cross correlation in forward and backward geometries. These conditions include short sample and small decoherence between ground states ${\ensuremath{\gamma}}_{bc}$, and they are fulfilled by the spontaneous Raman electromagnetic induced transparency scheme (weak pump with large detuning). We verify the correspondence between the results from boundary and noise operators analytically and show that the correlation due to the boundary operators is typically smaller than that due to the noise operators. In general the noise operators are required to obtain the correct correlation, especially when the control laser field is weak and ${\ensuremath{\gamma}}_{bc}$ is finite. Explanations for the findings are given based on the physics represented by the boundary operators and noise operators. Similar conclusions are obtained for the Stokes and anti-Stokes intensities.

Physical Review A•May 29, 2007•9 citations

Cancellation of laser phase fluctuations in Stokes and anti-Stokes generation

Z. W. Li, Czesław Radzewicz, Michael G. Raymer

In the coherent anti-Stokes Raman scattering process, the spectrum of the generated optical phonon depends on the degree of temporal correlation between the pump laser field and the Stokes field. When the two fields are strongly correlated, such as when the Stokes field is generated with stimulated Raman scattering (SRS), the spectral shape of the optical phonon is found experimentally and theoretically to be the same as the gain-narrowed Raman line shape because the laser phase fluctuations cancel out totally, leaving only the collisional noise in the SRS process. When the two fields are uncorrelated, the shape of the optical-phonon spectrum is found to be the same as the Raman line shape without gain narrowing. When two fields are partially correlated, then the two spectral components appear together. We provide a method to measure the degree of correlation between two optical fields that have different central frequencies. The theory developed to interpret the experimental results is an extension of the quantum theory of SRS to include anti-Stokes scattering. We show that only in the high-gain limit can the quantum fluctuations be thought of as arising from a classical noise process.

Journal of the Optical Society of America B•Nov 1, 1988•13 citations

Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory

C. H. Raymond Ooi, Qingqing Sun, Muhammad Suhail Zubairy +1 more

We present a largely analytical theory for two-photon correlations ${G}^{(2)}$ between Stokes $(s)$ and anti-Stokes $(a)$ photon pairs from an extended medium (amplifier) composed of double-$\ensuremath{\Lambda}$ atoms in counterpropagating geometry. We generalize the parametric coupled equations with quantum Langevin noise given in a beautiful experimental paper of Balic et al. [Phys. Rev. Lett. 94, 183601 (2005)] beyond adiabatic approximation and valid for arbitrary strength and detuning of laser fields. We derive an analytical formula for cross correlation ${G}_{as}^{(2)}=⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{s}^{\ifmmode\dagger\else\textdagger\fi{}}(L){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{a}^{\ifmmode\dagger\else\textdagger\fi{}}(0,\ensuremath{\tau}){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{a}(0,\ensuremath{\tau}){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{s}(L)⟩$ and use it to obtain results that are in good quantitative agreement with the experimental data. Results for ${G}_{as}^{(2)}$ obtained using our coupled equations are in good quantitative agreement with the results using the equations of Balic et al., while perfect agreement is obtained for sufficiently large detuning. We also compute the reverse correlation ${G}_{sa}^{(2)}$ which turns out to be negligibly small and remains classical while the cross correlation violates the Cauchy-Schwartz inequality by a factor of more than a hundred.

Physical Review A•Jan 31, 2007•58 citations

Noise figure and photon statistics in coherent anti-Stokes Raman scattering

Dimitrios Dimitropoulos, Daniel R. Solli, R. Claps +1 more

Coherent anti-Stokes Raman scattering (CARS) is a well-known Raman scattering process that occurs when Stokes, anti-Stokes and pump waves are properly phase-matched. Using a quantum-field approach with Langevin noise sources, we calculate the noise figure for wavelength conversion between the Stokes and anti-Stokes waves in CARS and show its dependence on phase mismatch. Under phase matched conditions, the minimum noise figure is approximately 3 dB, with a correction that depends on the pump frequency, Stokes shift, refractive indices, and nonlinear susceptibilities. We calculate the photon statistics of CARS and show that the photon number distribution is non-Gaussian. Our findings may be significant for currently pursued applications of CARS including wavelength conversion in data transmission and spectroscopic detection of dilute biochemical species.

arXiv:physics/0603004•Optics Express•Jan 1, 2006•5 citations

Quantum parametric double Raman oscillators with co- and counterpropagating fields: Relative intensity squeezing and spatial photon correlations

C. H. Raymond Ooi, Konstantin E. Dorfman

We present a comprehensive study of co- and counterpropagating Stokes and anti-Stokes quantum fields in double Raman four-wave mixing parametric oscillators using full quantum Heisenberg-Langevin framework with noise operators. General analytical solutions of the fields operators at any point in the Raman medium are obtained for four cases: two possible copropagating (forward) and two counterpropagating (backward) Stokes and anti-Stokes. We analyze the symmetrical properties of the complex linear and nonlinear susceptibilities spectra of the quantum fields, nonclassicality of two-photon correlation functions, spatial variations of the quantum fields, and the two-mode relative intensity squeezing. We compare the results of forward and backward cases for several limiting double Raman schemes. We find interesting resonant effects of medium length, laser detunings and laser field strengths (Rabi frequencies) for backward-propagating geometries. Analysis of the solutions provide insights on the resonant conditions while computation over multiple variables enables us to identify the values of laser detuning, field strength, and propagation length that give enhanced nonclassical intensity squeezing and persistent correlations. The present work sets the crucial foundations for optimization of the nonclassicality of photons in double Raman systems and would be useful for quantum information storage, quantum nonlinear optics, and quantum spectroscopy.

Physical Review A•Nov 7, 2022•3 citations

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

Peter A. Roos, Sytil Murphy, Lei S. Meng +4 more

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump $\ensuremath{\leftrightarrow}$ pump, Stokes $\ensuremath{\leftrightarrow}$ signal, and Raman coherence $\ensuremath{\leftrightarrow}$ idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

Physical Review A•Jul 2, 2003•9 citations
We use a Langevin approach to analyze the quantum noise in coherent anti-Stokes Raman spectroscopy in several experimental scenarios: with continuous-wave input fields acting simultaneously and with fast sequential pulsed lasers where one field scatters off the coherence generated by other fields and for interactions within a cavity and in free space. In all cases, the signal and quantum noise due to spontaneous decay and decoherence in the medium are shown to be described by the same general expression. Our theory in particular shows that for short interaction times, the medium noise is not important and the efficiency is limited only by the intrinsic quantum nature of the photon. We obtain fully analytic results without making an adiabatic approximation; the fluctuations of the medium and the fields are solved self-consistently.
An extended medium driven in a double Raman configuration generates Stokes and anti-Stokes fields that are described by coupled parametric oscillator equations with solutions that depend on input boundary operators and quantum noise operators. We identify the conditions where the boundary operators can be the substitute to the noise operators for describing two-photon cross correlation in forward and backward geometries. These conditions include short sample and small decoherence between ground states ${\ensuremath{\gamma}}_{bc}$, and they are fulfilled by the spontaneous Raman electromagnetic induced transparency scheme (weak pump with large detuning). We verify the correspondence between the results from boundary and noise operators analytically and show that the correlation due to the boundary operators is typically smaller than that due to the noise operators. In general the noise operators are required to obtain the correct correlation, especially when the control laser field is weak and ${\ensuremath{\gamma}}_{bc}$ is finite. Explanations for the findings are given based on the physics represented by the boundary operators and noise operators. Similar conclusions are obtained for the Stokes and anti-Stokes intensities.
In the coherent anti-Stokes Raman scattering process, the spectrum of the generated optical phonon depends on the degree of temporal correlation between the pump laser field and the Stokes field. When the two fields are strongly correlated, such as when the Stokes field is generated with stimulated Raman scattering (SRS), the spectral shape of the optical phonon is found experimentally and theoretically to be the same as the gain-narrowed Raman line shape because the laser phase fluctuations cancel out totally, leaving only the collisional noise in the SRS process. When the two fields are uncorrelated, the shape of the optical-phonon spectrum is found to be the same as the Raman line shape without gain narrowing. When two fields are partially correlated, then the two spectral components appear together. We provide a method to measure the degree of correlation between two optical fields that have different central frequencies. The theory developed to interpret the experimental results is an extension of the quantum theory of SRS to include anti-Stokes scattering. We show that only in the high-gain limit can the quantum fluctuations be thought of as arising from a classical noise process.
We present a largely analytical theory for two-photon correlations G(2){G}^{(2)}G(2) between Stokes (s)(s)(s) and anti-Stokes (a)(a)(a) photon pairs from an extended medium (amplifier) composed of double-$\ensuremath{\Lambda}$ atoms in counterpropagating geometry. We generalize the parametric coupled equations with quantum Langevin noise given in a beautiful experimental paper of Balic et al. [Phys. Rev. Lett. 94, 183601 (2005)] beyond adiabatic approximation and valid for arbitrary strength and detuning of laser fields. We derive an analytical formula for cross correlation ${G}_{as}^{(2)}=⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{s}^{\ifmmode\dagger\else\textdagger\fi{}}(L){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{a}^{\ifmmode\dagger\else\textdagger\fi{}}(0,\ensuremath{\tau}){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{a}(0,\ensuremath{\tau}){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{E}}_{s}(L)⟩$ and use it to obtain results that are in good quantitative agreement with the experimental data. Results for Gas(2){G}_{as}^{(2)}Gas(2)​ obtained using our coupled equations are in good quantitative agreement with the results using the equations of Balic et al., while perfect agreement is obtained for sufficiently large detuning. We also compute the reverse correlation Gsa(2){G}_{sa}^{(2)}Gsa(2)​ which turns out to be negligibly small and remains classical while the cross correlation violates the Cauchy-Schwartz inequality by a factor of more than a hundred.
Coherent anti-Stokes Raman scattering (CARS) is a well-known Raman scattering process that occurs when Stokes, anti-Stokes and pump waves are properly phase-matched. Using a quantum-field approach with Langevin noise sources, we calculate the noise figure for wavelength conversion between the Stokes and anti-Stokes waves in CARS and show its dependence on phase mismatch. Under phase matched conditions, the minimum noise figure is approximately 3 dB, with a correction that depends on the pump frequency, Stokes shift, refractive indices, and nonlinear susceptibilities. We calculate the photon statistics of CARS and show that the photon number distribution is non-Gaussian. Our findings may be significant for currently pursued applications of CARS including wavelength conversion in data transmission and spectroscopic detection of dilute biochemical species.
We present a comprehensive study of co- and counterpropagating Stokes and anti-Stokes quantum fields in double Raman four-wave mixing parametric oscillators using full quantum Heisenberg-Langevin framework with noise operators. General analytical solutions of the fields operators at any point in the Raman medium are obtained for four cases: two possible copropagating (forward) and two counterpropagating (backward) Stokes and anti-Stokes. We analyze the symmetrical properties of the complex linear and nonlinear susceptibilities spectra of the quantum fields, nonclassicality of two-photon correlation functions, spatial variations of the quantum fields, and the two-mode relative intensity squeezing. We compare the results of forward and backward cases for several limiting double Raman schemes. We find interesting resonant effects of medium length, laser detunings and laser field strengths (Rabi frequencies) for backward-propagating geometries. Analysis of the solutions provide insights on the resonant conditions while computation over multiple variables enables us to identify the values of laser detuning, field strength, and propagation length that give enhanced nonclassical intensity squeezing and persistent correlations. The present work sets the crucial foundations for optimization of the nonclassicality of photons in double Raman systems and would be useful for quantum information storage, quantum nonlinear optics, and quantum spectroscopy.
We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump $\ensuremath{\leftrightarrow}$ pump, Stokes $\ensuremath{\leftrightarrow}$ signal, and Raman coherence $\ensuremath{\leftrightarrow}$ idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.