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Physical Review A

Quantum theory of phase correlations in optical frequency combs generated by stimulated Raman scattering

Chunbai Wu, M. G. Raymer, Yingying Wang, Fetah Benabid

Published Nov 29, 2010• 17 citations
Publisher

Abstract

We explore theoretically the phase correlation between multiple generated sidebands in a Raman optical frequency comb under conditions of spontaneous initiation from quantum zero-point noise. We show that there is a near-deterministic correlation between sideband phases in each laser shot which may lead to synthesis of attosecond pulse trains.

DOI
10.1103/physreva.82.053834

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We explore theoretically the phase correlation between multiple generated sidebands in a Raman optical frequency comb under conditions of spontaneous initiation from quantum zero-point noise. We show that there is a near-deterministic correlation between sideband phases in each laser shot which may lead to synthesis of attosecond pulse trains.
In this work, we theoretically and numerically investigate nonclassical phonon states created in the collective vibration of a Raman medium by the generation of a dual-pumped Raman optical frequency comb in an optical cavity. This frequency comb is generated by cascaded Raman scattering driven by two phase-locked pump lasers that are separated in frequency by three times the Raman phonon frequency. We characterize the variety of conditioned phonon states that are created when the number of photons in all optical frequency modes except the pump modes are measured. Almost all of these conditioned phonon states are extremely well approximated as three-phonon-squeezed states or Schrödinger-cat states, depending on the outcomes of the photon number measurements. We show how the combinations of first-, second-, and third-order Raman scattering that correspond to each set of measured photon numbers determine the fidelity of the conditioned phonon state with model three-phonon-squeezed states and Schrödinger-cat states. All of the conditioned phonon states demonstrate preferential growth of the phonon mode along three directions in phase space. That is, there are three preferred phase values that the phonon state takes on as a result of Raman scattering. We show that the combination of Raman processes that produces a given set of measured photon numbers always produces phonons in multiples of three. In the quantum number-state representation, these multiples of three are responsible for the threefold phase-space symmetry seen in the conditioned phonon states. \n \nWith a semiclassical model, we show how this three-phase preference can also be understood in light of phase correlations that are known to spontaneously arise in single-pumped Raman frequency combs. Additionally, our semiclassical model predicts that the optical modes also grow preferentially along three phases, suggesting that the dual-pumped Raman optical frequency comb is partially phase-stabilized.
In our studies of soliton formation in stimulated Raman scattering (SRS), we have discovered that a fully quantum mechanical theory predicts large shot-to-shot fluctuations in the SRS power spectrum, which leads to soliton decay. This theory, which includes a Langevin operator to simulate collision-induced fluctuations and maintain operator consistency, can be used to generate the statistics of the macroscopic SRS output. We have also studied a simpler model which uses a random vacuum field as an input to the semiclassical SRS equations. The vacuum field was numerically generated by summing a set of electromagnetic field modes that spanned the collisional Raman linewidth. Each mode was separated in frequency by less than the resolution of the system and given a random phase for each shot. Despite the lack of Langevin terms, the shot-to-shot variations and two-frequency correlation function from the simple approach were essentially indistinguishable from the fully quantum mechanical theory. This suggests that a simulation of SRS from spontaneous emission does not always require Langevin terms in the quantum noise.
The generation of a multifrequency continuous-wave laser through stimulated Raman scattering and phase-matched four-wave mixing in a medium-filled optical cavity is demonstrated. Three different quantum pathways for the four-wave mixing, two of them degenerate and one of them nondegenerate, can be excited independently by tuning the intracavity dispersion. The results suggest that phase-matched Raman sidebands were generated on the longer wavelength side as well as on the shorter wavelength side, which can be used for the Fourier synthesis of a train of ultrashort optical pulses.
Theoretical and experimental details of initiating and amplifying a Stokes pulse using stimulated Raman scattering in H2 are presented.Statistics associated with the spectral fluctuations of a Stokes seed pulse have been measured and theoretically calculated.The spectral fluctuations are shown to result from quantum noise associated with spontaneous initiation.These spectral fluctuations are an example of an easily measurable macroscopic fluctuation of quantum origin.The effects of frequency fluctuations on the generation of solitons in the nonlinear regime of stimulated Raman scattering are calculated and measured.A detailed derivation of the fully quantum mechanical stimulated Raman scattering equations is given along with their solution for various approximations.The driven Maxwell's equation for the Raman system is derived from the system Hamiltonian.For treating the quantum initiation of stimulated Raman scattering, the radiation field is expanded in localized coherent modes.The details of calculating and using these modes to generate an ensemble of Stokes pulses are presented along with specific examples and ensemble average statistics.The use of localized modes for treating the pulsed cavityless Raman laser gives insight into the spontaneous initiation of Stokes pulses.iv ACKNOWLEDGMENTS I feel very fortunate to have had Dr. John Carlsten for my thesis adviser.I would like to thank John for making graduate school an enjoyable part of life and for the many hours o f stimulating discussions on fundamental physics.I am also greatly indebted to my wife, Susie, for filling my big lunch bag every morning and for her many hours spent typing this thesis