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Physical Review Letters

Near quantum-limited phase memory in a Raman amplifier

D. T. Smithey, Michael Scott Belsley, K. Wedding, M. G. Raymer

Published Oct 28, 1991• 20 citations
Publisher

Abstract

We have detected molecular coherence lasting nearly 9 times the collisional dephasing time in a Raman amplifier. Two laser pulses, separated in time, pumped a common set of hydrogen molecules, producing two Stokes pulses whose relative phase was measured interferometrically. The variance of this phase is a direct measure of the memory of the molecular coherence induced by the first scattering process. This experiment is capable of detecting a level of molecular coherence equivalent to between 15 and 50 vibrational phonons in the most strongly excited mode.

DOI
10.1103/physrevlett.67.2446

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We have detected molecular coherence lasting nearly 9 times the collisional dephasing time in a Raman amplifier. Two laser pulses, separated in time, pumped a common set of hydrogen molecules, producing two Stokes pulses whose relative phase was measured interferometrically. The variance of this phase is a direct measure of the memory of the molecular coherence induced by the first scattering process. This experiment is capable of detecting a level of molecular coherence equivalent to between 15 and 50 vibrational phonons in the most strongly excited mode.
We have detected molecular coherence lasting nearly nine times the collisional dephasing time in a Raman generator. Two laser pulses, separated in time, pumped a common set of hydrogen molecules, producing two Stokes pulses whose relative phase was measured interferometrically. By making repeated measurements, the probability distribution of the relative phase was obtained. The variance of this phase distribution is a direct measure of the memory of the molecular coherence induced by the first scattering process. A one-dimensional theoretical model is developed which implies that the technique is capable of measuring a level of molecular coherence equivalent to between 15 and 50 phonons (delocalized vibrational quanta) in the most strongly excited mode.
Probing the quantum noise level with respect to a coherent input has recently received much attention. Several researchers have probed this question by examining the level of external optical input needed to influence the output field of a quantum noise amplifier. For example, it has been found that it takes, on average, about one photon per (temporal) mode to control the phase of the output field of a Raman amplifier.1 A similar result has been seen in optical parametric amplification.2 In contrast to using light to seed the amplification, we have investigated the level of initial molecular coherence needed to control the phase of the output field of a Raman amplifier. Two laser pulses, separated in time, were used to pump a common set of hydrogen molecules producing two Stokes pulses via stimulated Raman scattering. The relative phase of the two Stokes pulses was measured interferometrically. The variance of this relative phase is a direct measure of the memory of the molecular coherence that was induced by the first scattering process. Correlations between the two Stokes phases were observed even after nine molecular dephasing times, when the level of coherence had decayed by a factor of e−9. We show that this extraordinarily long-lived phase memory comes about because a molecular coherence corresponding to order ten vibrational photons per mode is sufficient to influence the phase of the output field.
Stimulated Raman scattering is conventionally employed to probe vibrational dynamics by inducing a coherent oscillation within a molecular ensemble. In contrast, spontaneous Raman scattering is considered as an incoherent process because the scattered field lacks any predictable phase relationship with the incoming laser pulse. It raises questions about the nature of the quantum state of a molecular ensemble following spontaneous Stokes scattering: should it be described as a statistical mixture of vibrationally excited molecules, where collective coherence is absent? Here, we measure time-resolved Stokes--anti-Stokes two-photon coincidences on a molecular liquid and find that a coherent superposition of two collective vibrational modes from two isotopic sub-ensembles is generated under spontaneous Raman scattering. Our results confirm that a spatially extended vibrational coherence emerges when a single collective excitation is spontaneously scattered and detected in a single spatiotemporal mode.
A model of two-level weakly interacting quantum systems is used to demonstrate that the phase of molecular vibrations excited through stimulated Raman scattering can be controlled by the relative phase of time-separated laser pulses, allowing synchronization and amplitude control of coherence excitation in a medium. For transients with a phase relaxation time less than the field cycle, the field half-cycle can serve as a subfemtosecond probe of coherent vibrations. In this regime, the high-frequency field-induced modulation of molecular dipole moments gives rise to a detectable modulation of the optical response of a medium at the frequency $2\ensuremath{\omega}$, $\ensuremath{\omega}$ being the frequency of the laser field.
Spontaneous vibrational Raman scattering is a ubiquitous form of light-matter interaction whose description necessitates quantization of the electromagnetic field. It is usually considered as an incoherent process because the scattered field lacks any predictable phase relationship with the incoming field. When probing an ensemble of molecules, the question therefore arises: What quantum state should be used to describe the molecular ensemble following spontaneous Stokes scattering? We experimentally address this question by measuring time-resolved Stokes-anti-Stokes two-photon coincidences on a molecular liquid consisting of several sub-ensembles with slightly different vibrational frequencies. When spontaneously scattered Stokes photons and subsequent anti-Stokes photons are detected into a single spatiotemporal mode, the observed dynamics is inconsistent with a statistical mixture of individually excited molecules. Instead, we show that the data are reproduced if Stokes-anti-Stokes correlations are mediated by a collective vibrational quantum, i.e. a coherent superposition of all molecules interacting with light. Our results demonstrate that the degree of coherence in the vibrational state of the liquid is not an intrinsic property of the material system, but rather depends on the optical excitation and detection geometry.
A new method to measure picosecond or subpicosecond vibrational-dephasing dynamics with the use of incoherent or broadband light is presented theoretically and experimentally. It is based on a transient coherent Raman process with three beams. In our experimental scheme, two of them are incoherent light from a single source, and a delay time between the two is variable. A third beam has a higher frequency than the incoherent light by a vibrational energy in a molecule of interest, and is coherent in the delay-time range of the measurement. The delay-time dependence of coherent Stokes Raman scattering (CSRS) intensity offers the information about the coherence dynamics of the vibrational transition with a resolution time determined only by the correlation time of the incoherent light. For the theoretical calculation, a three-level model of the molecular system with homogeneous broadening is used, and delay-time dependences of the CSRS signal are calculated for off-resonance and resonance cases. Dephasing dynamics of the 2915-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ mode in dimethylsulfoxide was observed experimentally by the new method with the use of nanosecond laser pulses, and the result agrees well with that obtained with picosecond pulses.