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Physical Review A

Observation of extreme sensitivity to induced molecular coherence in stimulated Raman scattering

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

Published Aug 1, 1993• 23 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.48.1514

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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.
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.
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.
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.
We discuss a novel method to create maximum coherence in a two-level system that is selectively excited among many having similar frequencies by making use of two specifically chirped pulses in the Raman configuration. The feasibility of the method is analyzed in the presence of decoherence caused by vibrational energy relaxation and collisional dephasing. It has been demonstrated that a high value of coherence may be sustained by the implementation of two chirped pulse trains prepared in accordance with the proposed method and having the same period as the vibrational energy relaxation time. Maximum coherence between predetermined states in atoms and molecules is an important aspect of many problems in quantum optics. One possible example is the generation of optimal CARS signal in the CARS microscopy aiming to reveal structures constituted of particular molecular groups. Presently, in experiments on biological imaging, the CARS signal is generated with implementation of picosecond laser pulses (1), a narrow spectral bandwidth of which allows one to address a particular molecular group with a good accuracy. Aiming to improve chemical sensitivity and to get optimal CARS signal for given pulse intensity we propose to use the quantum control methods for selective excitation of required vibrations in complex molecular systems. We developed a novel method that allows one to achieve maximum coherence in a predetermined vibrational mode in a multimode mole- cular system via the Raman transitions induced by the pump and Stokes chirped pulses. According to the Maxwell-Bloch equations, maximum coherence is the condition for the CARS signal to acquire the highest intensity upon propagation through a molecular medium (2). The mechanism of creation of maximum coherence underlying the proposed method is based on the adiabatic passage. An important aspect in the investigations asso- ciated with a condense phase is decoherence. Two main sources of decoherence, the vibrational energy relaxa- tion and collisional dephasing, may significantly affect the CARS signal intensity. The phase control of molecular processes in the presence of collisions was