Physical Review A

Electromagnetically-induced-transparency-based paired photon generation

Pavel Kolchin

Published Mar 26, 2007• 92 citations

Abstract

We describe the theory of paired photon generation in a double-$\ensuremath{\Lambda}$ atomic system. Using the Heisenberg-Langevin formalism we evaluate and analyze the spectral generation rates and intensity correlation function for the output fields. Different regimes of parametric down conversion are analyzed. We discuss the influence of the optical depth and Langevin noise fluctuations on the paired photon generation and predict that at the optical depth of 100 or more the contribution of Langevin noise fluctuations is small and therefore Stokes and anti-Stokes photons are generated mostly in pairs. Comparison between the theory and experiments shows good agreement.

DOI: 10.1103/physreva.75.033814

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Physical Review A

Electromagnetically-induced-transparency-based paired photon generation

Pavel Kolchin

Published Mar 26, 2007• 92 citations

Publisher

Abstract

We describe the theory of paired photon generation in a double-

\ensuremath{\Lambda}

atomic system. Using the Heisenberg-Langevin formalism we evaluate and analyze the spectral generation rates and intensity correlation function for the output fields. Different regimes of parametric down conversion are analyzed. We discuss the influence of the optical depth and Langevin noise fluctuations on the paired photon generation and predict that at the optical depth of 100 or more the contribution of Langevin noise fluctuations is small and therefore Stokes and anti-Stokes photons are generated mostly in pairs. Comparison between the theory and experiments shows good agreement.

DOI: 10.1103/physreva.75.033814

Related papers

Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. II. Beyond perturbation theory

Jianming Wen, Morton H. Rubin

Generation of counterpropagating paired Stokes and anti-Stokes photons in a double-$\ensuremath{\Lambda}$- (or $M$ -) type electromagnetically induced transparency (EIT) system is examined in quantum theory in the three-dimensional space. We use the Maxwell-Bloch equations to study the transverse effects of generated entangled photon pairs via such an EIT medium. We reexamine correlation measurements for both amplitude and intensity correlations. In the low parametric gain region $[\sqrt{{v}_{g}∕8{\ensuremath{\gamma}}_{31}L}\ensuremath{\gg}\sqrt{{k}_{s}∕{k}_{as}}(\ensuremath{\mid}{\ensuremath{\Omega}}_{p}\ensuremath{\mid}∕\ensuremath{\mid}{\ensuremath{\Gamma}}_{p}\ensuremath{\mid})]$, when the paired Stokes and anti-Stokes are at the single-photon level, we obtain the results shown in Wen and Rubin, Phys. Rev. A 74, 023807 (2006). If $\sqrt{{k}_{s}∕{k}_{as}}(\ensuremath{\mid}{\ensuremath{\Omega}}_{p}\ensuremath{\mid}∕\ensuremath{\mid}{\ensuremath{\Gamma}}_{p}\ensuremath{\mid})$ is comparable to or greater than $\sqrt{{v}_{g}∕8{\ensuremath{\gamma}}_{31}L}$, i.e., in the high parametric gain regime, the system may not reach the single-photon level, and accidental coincidences occur which cause loss of visibility in the interference experiments.Generation of counterpropagating paired Stokes and anti-Stokes photons in a double-$\ensuremath{\Lambda}$- (or $M$-) type electromagnetically induced transparency (EIT) system is examined in quantum theory in the three-dimensional space. We use the Maxwell-Bloch equations to study the transverse effects of generated entangled photon pairs via such an EIT medium. We reexamine correlation measurements for both amplitude and intensity correlations. In the low parametric gain region $[\sqrt{{v}_{g}∕8{\ensuremath{\gamma}}_{31}L}\ensuremath{\gg}\sqrt{{k}_{s}∕{k}_{as}}(\ensuremath{\mid}{\ensuremath{\Omega}}_{p}\ensuremath{\mid}∕\ensuremath{\mid}{\ensuremath{\Gamma}}_{p}\ensuremath{\mid})]$, when the paired Stokes and anti-Stokes are at the single-photon level, we obtain the results shown in Wen and Rubin, Phys. Rev. A 74, 023807 (2006). If $\sqrt{{k}_{s}∕{k}_{as}}(\ensuremath{\mid}{\ensuremath{\Omega}}_{p}\ensuremath{\mid}∕\ensuremath{\mid}{\ensuremath{\Gamma}}_{p}\ensuremath{\mid})$ is comparable to or greater than $\sqrt{{v}_{g}∕8{\ensuremath{\gamma}}_{31}L}$, i.e., in the high parametric gain regime, the system may not reach the single-photon level, and accidental coincidences occur which cause loss of visibility in the interference experiments.

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European Quantum Electronics Conference (EQEC)Jan 1, 20030 citations

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Hui-Min Zhao, Xiaojun Zhang, M. Artoni +2 more

Tunable Rydberg interactions in cold atoms can be used to generate strongly correlated photon pairs through a spontaneous four-wave-mixing process in which all driving fields are allowed to work on resonance. The scheme relies on electromagnetically induced transparency and an imbalanced dark state with most atoms trapped in a ground state and a weakly populated Rydberg state. We show in particular that the combination of these two effects results in negligible linear absorption and Raman gain at the Stokes and anti-Stokes frequencies of generated photon pairs, while the nonlocal (Rydberg) nonlinearities contribute significantly to the enhancement of photon-pair generation rates and cross correlations at very low pump strengths and optical depths.Tunable Rydberg interactions in cold atoms can be used to generate strongly correlated photon pairs through a spontaneous four-wave-mixing process in which all driving fields are allowed to work on resonance. The scheme relies on electromagnetically induced transparency and an imbalanced dark state with most atoms trapped in a ground state and a weakly populated Rydberg state. We show in particular that the combination of these two effects results in negligible linear absorption and Raman gain at the Stokes and anti-Stokes frequencies of generated photon pairs, while the nonlocal (Rydberg) nonlinearities contribute significantly to the enhancement of photon-pair generation rates and cross correlations at very low pump strengths and optical depths.

Physical Review AApr 16, 20248 citations

We describe the theory of paired photon generation in a double-

\ensuremath{\Lambda}

Generation of counterpropagating paired Stokes and anti-Stokes photons in a double-$\ensuremath{\Lambda}$- (or

M

-) type electromagnetically induced transparency (EIT) system is examined in quantum theory in the three-dimensional space. We use the Maxwell-Bloch equations to study the transverse effects of generated entangled photon pairs via such an EIT medium. We reexamine correlation measurements for both amplitude and intensity correlations. In the low parametric gain region $[\sqrt{{v}_{g}∕8{\ensuremath{\gamma}}_{31}L}\ensuremath{\gg}\sqrt{{k}_{s}∕{k}_{as}}(\ensuremath{\mid}{\ensuremath{\Omega}}_{p}\ensuremath{\mid}∕\ensuremath{\mid}{\ensuremath{\Gamma}}_{p}\ensuremath{\mid})]$, when the paired Stokes and anti-Stokes are at the single-photon level, we obtain the results shown in Wen and Rubin, Phys. Rev. A 74, 023807 (2006). If $\sqrt{{k}_{s}∕{k}_{as}}(\ensuremath{\mid}{\ensuremath{\Omega}}_{p}\ensuremath{\mid}∕\ensuremath{\mid}{\ensuremath{\Gamma}}_{p}\ensuremath{\mid})$ is comparable to or greater than $\sqrt{{v}_{g}∕8{\ensuremath{\gamma}}_{31}L}$, i.e., in the high parametric gain regime, the system may not reach the single-photon level, and accidental coincidences occur which cause loss of visibility in the interference experiments.

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.