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Physical Review

Intensity Correlations in Raman Scattering

Alexander L. Fetter

Published Aug 30, 1965• 7 citations
Publisher

Abstract

Correlated counting rates in Raman scattering are proposed as a means of studying optical phonons in crystals. This technique may be used to measure both the lifetime and spatial coherence of the vibrational states. Experimental counting times are estimated to be the order of 50 \ensuremath{\mu}sec for the case of a gas laser as a light source.

DOI
10.1103/physrev.139.a1616

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Correlated counting rates in Raman scattering are proposed as a means of studying optical phonons in crystals. This technique may be used to measure both the lifetime and spatial coherence of the vibrational states. Experimental counting times are estimated to be the order of 50 \ensuremath{\mu}sec for the case of a gas laser as a light source.
With the development of quantum optics, photon correlations acquired a prominent role as a tool to test our understanding of physics, and played a key role in verifying the validity of quantum mechanics. The spatial and temporal correlations in a light field also reveal information about its origin, and allow us to probe the nature of the physical systems interacting with it. Additionally, with the advent of quantum technologies, they have acquired technological relevance, as they are expected to play an important role in quantum communication and quantum information processing. This thesis develops techniques that combine spontaneous Raman scattering with Time Correlated Single Photon Counting, and uses them to study the quantum mechanical nature of high frequency vibrations in crystals and molecules. We demonstrate photon bunching in the Stokes and anti-Stokes fields scattered from two ultrafast laser pulses, and use their cross-correlation to measure the 3.9 ps decay time of the optical phonon in diamond. We then employ this method to measure molecular vibrations in CS2, where we are able to excite the respective vibrational modes of the two isotopic species present in the sample in a coherent superposition, and observe quantum beating between the two signals. Stokes scattering, when combined with a projective measurement, leads to a well defined quantum state. We demonstrate this by measuring the second order correlation function of the anti-Stokes field conditional on detecting one or more photons in the Stokes field, which allows us to observe a phonon modeâ s transition form a thermal state into the first excited Fock state, and measure its decay over the characteristic phonon lifetime. Finally, we use this technique to prepare a highly entangled photon-phonon state, which violates a Bell-type inequality. We measure S = 2.360 ± 0.025, violating the CHSH inequality, compatible with the non-locality of the state. The techniques we developed open the door to the study of a broad range of physical systems, where spectroscopic information is obtained with the preparation of specific quantum states. They also hold potential for future technological use, and promote vibrational Raman scattering to a resource in nonlinear quantum optics -- where it used to be considered as a source of noise instead.
We propose and demonstrate a versatile technique to measure the lifetime of the one-phonon Fock state using two-color pump-probe Raman scattering and spectrally resolved, time-correlated photon counting. Following pulsed laser excitation, the n=1 phonon Fock state is probabilistically prepared by projective measurement of a single Stokes photon. The detection of an anti-Stokes photon generated by a second, time-delayed laser pulse probes the phonon population with subpicosecond time resolution. We observe strongly nonclassical Stokes-anti-Stokes correlations, whose decay maps the single phonon dynamics. Our scheme can be applied to any Raman-active vibrational mode. It can be modified to measure the lifetime of n≥1 Fock states or the phonon quantum coherences through the preparation and detection of two-mode entangled vibrational states.
Time-resolved Raman spectroscopy techniques offer various ways to study the dynamics of molecular vibrations in liquids or gases and optical phonons in crystals. While these techniques give access to the coherence time of the vibrational modes, they are not able to reveal the fragile quantum correlations that are spontaneously created between light and vibration during the Raman interaction. Here, we present a scheme leveraging universal properties of spontaneous Raman scattering to demonstrate Bell correlations between light and a collective molecular vibration. We measure the decay of these hybrid photon-phonon Bell correlations with sub-picosecond time resolution and find that they survive over several hundred oscillations at ambient conditions. Our method offers a universal approach to generate entanglement between light and molecular vibrations. Moreover, our results pave the way for the study of quantum correlations in more complex solid-state and molecular systems in their natural state.
IMeasurements of space-time correlations in the intensity of a beam of scattereq particles yield information about the scatterer.Goldberger and Watson have developed a theory of such measl~ementG appropriate to the case of ne~rly elastic scattering; in this paper we extend their theory to the case of inelastic scattering.The main result of our work is that under certain experimental conditions the correlated counting rate in an inelastic scattering experiment is of a form equivalent to the correlated counting rate for an incoherent beam of particles emitted by a source.This result applies, in particular, to Raman or Brillouin scattering of light by phonons in an extended target.However, estimates of the signal to noise ratio for this case indicate that it may not be possible to observe intensity correlations in Raman or Brillouin lines using presently available light sources. ABSTRACT OF PART IIThe coherent excitation of several atomic status by inelastic electron' scattering and their subsequent radia ti ve decay is considered.General expressions for the photon counting rate in a quantum beat experiment, and the total number of photons counted. in a le,vel crossing experiment are d.erived.The general results are used to calculate the phase of the oscillatory part of the photon counting rate in the Radeishi-Nierenberg quantum beat experiment.
A theoretical description of the fifth-order coherent light scattering is presented. By calculating the corresponding radiative transition rate, it is found that the intensity of the fifth-order scattering light is proportional to the squares of the number density as well as to the thickness of the optical sample. The fifth-order coherent light scattering expression is a two-dimensional extension of the Kramers–Heisenberg expression for light scattering. The intensity of each peak in the two-dimensional spectrum is determined by the product of three Raman transition matrix elements. A detailed discussion on the relative intensities of the diagonal and off-diagonal peaks is presented.
The cross-correlation function between the pump and Stokes intensities in stimulated Raman scattering has been measured. It has previously been conjectured 1 and theoretically shown2 that the Stokes light generated in the presence of a multimode or broadband pump is generated with mode amplitudes and phases in perfect correlation with those of the pump. We present here experimental evidence of such cross correlations for scattering in hydrogen gas. The measurement technique used is the same as that previously used for measuring the intensity autocorrelation function of a multimode dye laser.3 This technique is based on detecting the frequency doubled light from a nonlinear crystal as a function of time delay between the pump and Stokes beams. We have performed cross-correlation measurements using as a pump the light from a multimode dye laser which is operated in two different cavity configurations: one in which the mode spacing Δυ is large compared with the spontaneous linewidth of the Raman transition Γ, Δυ > Γ; and one in which the mode spacing is small, Δυ < Γ.