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arXiv:quant-ph/0305186 · Physical Review A

Multiorder coherent Raman scattering of a quantum probe field

Fam Le Kien, Anil K. Patnaik, K. Hakuta

Published Dec 2, 2003• 10 citations

Abstract

We study the multiorder coherent Raman scattering of a quantum probe field in a far-off-resonance medium with a prepared coherence. Under the conditions of negligible dispersion and limited bandwidth, we derive a Bessel-function solution for the sideband field operators. We analytically and numerically calculate various quantum statistical characteristics of the sideband fields. We show that the multiorder coherent Raman process can replicate the statistical properties of a single-mode quantum probe field into a broad comb of generated Raman sidebands. We also study the mixing and modulation of photon statistical properties in the case of two-mode input. We show that the prepared Raman coherence and the medium length can be used as control parameters to switch a sideband field from one type of photon statistics to another type, or from a nonsqueezed state to a squeezed state and vice versa. We demonstrate that an even or odd coherent state of the quantum probe field can produce a multipartite entangled coherent state. We show that the concurrence reaches its maximal value at an optimal medium length that is determined by the magnitude of the Raman coherence and the orders of the Raman sidebands.

DOI: 10.1103/physreva.68.063803

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We study the multiorder coherent Raman scattering of a quantum probe field in a far-off-resonance medium with a prepared coherence. Under the conditions of negligible dispersion and limited bandwidth, we derive a Bessel-function solution for the sideband field operators. We analytically and numerically calculate various quantum statistical characteristics of the sideband fields. We show that the multiorder coherent Raman process can replicate the statistical properties of a single-mode quantum probe field into a broad comb of generated Raman sidebands. We also study the mixing and modulation of photon statistical properties in the case of two-mode input. We show that the prepared Raman coherence and the medium length can be used as control parameters to switch a sideband field from one type of photon statistics to another type, or from a nonsqueezed state to a squeezed state and vice versa. We demonstrate that an even or odd coherent state of the quantum probe field can produce a multipartite entangled coherent state. We show that the concurrence reaches its maximal value at an optimal medium length that is determined by the magnitude of the Raman coherence and the orders of the Raman sidebands.

We investigate the parametric beating of a quantum probe field with a prepared Raman coherence in a far-off-resonance medium, and describe the resulting multiplexing processes. We show that the normalized autocorrelation functions of the probe field are exactly reproduced in the Stokes and anti-Stokes sideband fields. We find that an initial coherent state of the probe field can be replicated to the Raman sidebands, and an initial squeezing of the probe field can be partially transferred to the sidebands. We show that a necessary condition for the output fields to be in an entangled state or, more generally, in a nonclassical state is that the input field state is a nonclassical state.

We investigate the parametric beating of a quantum probe field with a prepared Raman coherence in a far-off-resonance medium, and describe the resulting multiplexing processes. We show that the normalized autocorrelation functions of the probe field are exactly reproduced in the Stokes and anti-Stokes sideband fields. We find that an initial coherent state of the probe field can be replicated to the Raman sidebands, and an initial squeezing of the probe field can be partially transferred to the sidebands. We show that a necessary condition for the output fields to be in an entangled state or, more generally, in a nonclassical state is that the input field state is a nonclassical state.

We present a detailed experimental investigation into the off-resonant preparation of a vibrational coherence for multiorder Raman generation. In particular, the importance of the balance between the conflicting requirements for generating a strong coherence and for adiabatic evolution of the system are examined. For the parameters accessible in our experiment, we find that the strongest frequency modulation occurs under conditions for which there is some nonadiabatic behavior, and the coherence is less than the peak value obtainable. We investigate the modulation of a narrowband probe pulse, and an ultrashort probe pulse, in the coherently prepared medium, and demonstrate efficient modulation of both probe pulses resulting in the generation of

360\phantom{\rule{0.3em}{0ex}}\mathrm{THz}

bandwidth fields. This system therefore has an application in the field of subfemtosecond pulse generation.

The initially prepared coherent state coupled to a third-order nonlinear medium is responsible for stimulated Raman and spontaneous Raman processes. By exploiting the analytical solutions of field operators for various modes, we investigate the quantum statistical properties for pure and two modes of the input coherent light responsible for stimulated Raman and spontaneous Raman processes. For spontaneous Raman processes the photons are unbunched for the pure and two-mode cases. By a suitable choice of phase, we obtain the bunching and antibunching of photons for stimulated Raman processes.

We demonstrate the efficient generation of Raman sidebands in a medium coherently prepared in a dark state by continuous-wave low-intensity laser radiation. Our experiment is performed in sodium vapor excited in $\ensuremath{\Lambda}$ configuration on the

{D}_{1}

line by two laser fields of resonant frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2},$ and probed by a third field ${\ensuremath{\omega}}_{3}.$ First-order sidebands for frequencies ${\ensuremath{\omega}}_{1},$ ${\ensuremath{\omega}}_{2}$ and up to the third-order sidebands for frequency ${\ensuremath{\omega}}_{3}$ are observed. The generation starts at a power as low as 10 \ensuremath{\mu}W for each input field. Dependences of the intensities of both input and generated waves on the frequency difference $({\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}),$ on the frequency ${\ensuremath{\omega}}_{3},$ and on the optical density are investigated.

We investigate quantum phase properties of two-mode optical fields whose quasi distributions have Gaussian form. We show how to simplify calculation of the joint phase distribution defined via radial integration of the quasi distribution related to s-ordering of the field operators. Introducing hyper spherical coordinates, we can carry out analytically one of two required integrations. The second integral over a finite interval is then evaluated numerically. Analytical formula for the joint phase distribution can be obtained in special case of vanishing coherent components of both modes. The general results are applied to analysis of quantum phase properties of two-mode Stokes-anti-Stokes field generated by means of Raman scattering with broad reservoir phonon system and strong coherent laser pumping.