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Annual Meeting Optical Society of America

Near quantum-limited phase memory in an optical amplifier

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

Published Jan 1, 1991• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1991.thr3

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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.
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.
We have studied the phase pulling and locking of an injected Stokes pulse in a transient Raman amplifier both experimentally and theoretically. In addition, we have investigated the pulse energy statistics and related spatial modes of a high gain amplified Stokes pulse. Experiments reported here show that in the unsaturated case, the phase of the amplified Stokes is pulled almost instantaneously to that of the pump, as soon as integrated gain levels of slightly greater than unity are reached. For higher input seed-Stokes levels, such that the amplified Stokes energy is saturated, the phase locking is completed early, and the phase of the amplified Stokes then follows the phase excursion of the pump. The phase pulling has been modelled theoretically for the specific parameters of our experiment. We have also used the pulse energy statistics to study the seed-Stokes control of a high gain Raman amplifier. For an input seed-Stokes beam to control a transient, high gain Raman amplifier, operated near threshold, it must dominate the self-generated Raman which builds from quantum noise. For a near-unity-Fresnel-number Raman amplifier we have measured the number of input seed-Stokes photons needed to produce an unchanged statistical signature on the amplified Stokes pulse and have found that a surprisingly large number (109) were needed. For a larger Fresnel number Raman amplifier, a near-field camera was used to study the level at which the seed-Stokes pulse controlled the spatial output of the amplifier. Control of the spatial modes seems to have a sharp threshold with input Stokes energy and was fully established with an input of 2x103 photons per mode.
We have previously reported experimental results of Raman amplification of a low-light-level seed-Stokes beam in the transient limit.1 Here we present results of measurements which used a 10-nsec seed-injected Nd:YAG laser. The 532-nm frequency-doubled output had a duration of 8.5 ns and was used both to generate a 4.5-ns duration seed-Stokes pulse at 683 nm and to pump the 1-m long Raman amplifier. The seed-Stokes beam was spatially filtered, apertured at the Airy minimum, and collimated before the amplifier at a diameter of 5.2 mm. Likewise, the spatial mode of the pump was optimized to be as smooth as possible and was collimated into the Raman amplifier at a diameter of 3.4 mm. With no seed Stokes incident in the amplifier, random spatial patterns characteristic of the quantum-noise initiated, self­generated Stokes light were observed over a spatially gain-narrowed beam size supporting ~ 12 spatial modes. For the Raman gains of ~105 used in these experiments the number of temporal modes was 1.8. The seed-Stokes light was used to illuminate a bar chart of line-width 0.315 mm, and either a direct image of the bar chart, or its Fourier transform, was amplified in the Raman amplifier. The original bar chart image was then observed using an intensified camera. As the level of seed-Stokes was reduced to that approaching one photon per spatial-temporal mode, we were able to observe intensity modulations approaching 100% within the amplified bar chart images. Modulation levels of a few percent persist out to input levels of ~103 photons per mode. This observation is consistent with an interpretation of interference between electric field of the seed-Stokes beam and the vacuum fluctuations present in the amplifier but is inconsistent with a photon number description where the maximum predicted modulation would be only 50%.
A pencil shaped region of a Raman-active medium forms a source for Stokes-shifted light via stimulated Raman Scattering (SRS) when driven by an intense laser pulse. Stokes photons are scattered spontaneously at first, and then amplified during propagation through the medium. Since the scattering is initiated by quantum noise, the actual number of photons produced in any given pulse will be highly uncertain, even if the pulse energy of the driving laser is constant1. As the Stokes light propagates through such an extended region, it's coherence properties will be changed. The spatial coherence is determined by the size and shape of the region, which may be characterized by its Fresnel number F, defined as F= A/λSL, where A is the cross-sectional area of the interaction region, which has length L, and λS is the Stokes wavelength. The rate at which the microscopic scatterers (atoms or molecules) are dephased by collisions affects the temporal coherence of the Stokes light, characterised by the temporal coherence parameter Γτ /gL, where Γ is the collisional dephasing rate, τ is the laser pulse duration and g is the steady-state Raman gain coefficient.
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.