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Theory of Line Narrowing by Deep Nano-Trap Lattice in Raman Gas

Anton Husakou, M. Alharbi, Matthieu Chafer, Benoît Debord, Frédéric Gérôme, Fetah Benabid

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

Recently we demonstrated a system for light-trapping molecules and stimulated Raman \nscattering based on a lattice of ultra-deep traps created by spatially modulated Raman \nsaturation, where Raman-active molecules are strongly localized in a one-dimensional array \nof nanometre-wide sections, resulting in a central line with a sub-recoil linewidth as low as 14 \nkHz. Here the theoretical modelling of such a process is presented in detail. The numerical \nformalism is presented on both microscopic and macroscopic scale. The field distribution \nin the fiber is discussed, and the predictions regarding the line narrowing, sidebands, and \nlattice motion are provided

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Summary form only given. A new way to reach the Lamb-Dicke regime in molecular gases has been reported in [1]. This is achieved by trapping H2molecule during Stimulated Raman Scattering (SRS) in a photonic band gap hollow-core fiber (PBG HC-PCF) pumped with a high power CW laser [1]. The molecular trapping process occurs in a self-assembled manner, whereby the Raman active molecules are confined in nanometer-wide sections by a periodic and ultra-deep potential thanks to a spatially modulated Raman saturation. It has permitted to obtain sub-recoil linewidths as low as 14 kHz which is 5 orders of magnitude lower than the expected H2Doppler-broadened linewidth for a product of the input power and the pressure below 1000 W.bar. Above this threshold the linewidth broadens due to the generation of the second-order Stokes.Here, we report a further linewidth narrowing down to 2.7 kHz by increasing the length and decreasing the gas pressure. Longer fiber lowers the pump power required for the SRS generation and enables formation of the trapping potential for lower gas pressure, which in turn reduces the molecular collision rate. The Stokes generation was obtained using a set-up similar to the one used in [1]. The PBG fiber has been tailored in order to have a spectral window between 1000 and 1200 nm in order to filter out any other Raman generation except the first rotational Stokes S00(1) at 1131.4 nm. The range of pressure of H2 with which we filled the PBG fiber is from 5 to 50 bars. The pump laser is a narrow linewidth (400 kHz) CW laser with a maximum pump power Pin of 100 W. Figure 1(a) shows the typical linewidth trace of the forward emitted Stokes for a fiber length of 30 m, a gas pressure of 20 bar and a pump power of 12 W. Figure 1(b) shows a resolved spectrum of the Stokes central line, which demonstrates a linewidth of 2.7 kHz. This line is nearly 30 times narrower than the hydrogen molecule recoil frequency Vrecο1 = πh(mλs2) of ~78 kHz, 5 orders of magnitude narrower than the Doppler width and almost 6 orders of magnitude narrower than the H2 pressure broadened line. Linewidth(kHz)

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Physical Review A•Jun 9, 2008•9 citations
Recently we demonstrated a system for light-trapping molecules and stimulated Raman \nscattering based on a lattice of ultra-deep traps created by spatially modulated Raman \nsaturation, where Raman-active molecules are strongly localized in a one-dimensional array \nof nanometre-wide sections, resulting in a central line with a sub-recoil linewidth as low as 14 \nkHz. Here the theoretical modelling of such a process is presented in detail. The numerical \nformalism is presented on both microscopic and macroscopic scale. The field distribution \nin the fiber is discussed, and the predictions regarding the line narrowing, sidebands, and \nlattice motion are provided
Trapping or cooling molecules has rallied a long-standing effort for its impact in exploring new frontiers in physics and in finding new phase of matter for quantum technologies. Here we demonstrate a system for light-trapping molecules and stimulated Raman scattering based on optically self-nanostructured molecular hydrogen in hollow-core photonic crystal fibre. A lattice is formed by a periodic and ultra-deep potential caused by a spatially modulated Raman saturation, where Raman-active molecules are strongly localized in a one-dimensional array of nanometre-wide sections. Only these trapped molecules participate in stimulated Raman scattering, generating high-power forward and backward Stokes continuous-wave laser radiation in the Lamb-Dicke regime with sub-Doppler emission spectrum. The spectrum exhibits a central line with a sub-recoil linewidth as low as ∼14 kHz, more than five orders of magnitude narrower than conventional-Raman pressure-broadened linewidth, and sidebands comprising Mollow triplet, motional sidebands and four-wave mixing.
The recent findings of line narrowing in Raman-active continuous-wave-pumped gas [1] showed that the Stokes scattering occurs in a Lamb-Dicke regime and is associated to formation of array of deep subwavelength nanotraps, which resulted in a sub-recoil linewidth Stokes radiation [1]. The results also showed that this nanotrap lattice exhibits a macroscopic motion. Here we present theoretical and numerical analysis of this phenomenon, addressing the peculiarities of field distribution and fascinating effect of nanotrap lattice in motion.
Since the advent of atom laser-cooling, trapping or cooling natural molecules has been a long standing and challenging goal. Here, we demonstrate a method for laser-trapping molecules that is radically novel in its configuration, in its underlined physical dynamics and in its outcomes. It is based on self-optically spatially-nanostructured high pressure molecular hydrogen confined in hollow-core photonic-crystal-fibre. An accelerating molecular-lattice is formed by a periodic potential associated with Raman saturation except for a 1-dimentional array of nanometer wide and strongly-localizing sections. In these sections, molecules with a speed of as large as 1800 m/s are trapped, and stimulated Raman scattering in the Lamb-Dicke regime occurs to generate high power forward and backward-Stokes continuous-wave laser with sideband-resolved sub-Doppler emission spectrum. The spectrum exhibits a central line with a sub-recoil linewidth of as low as 14 kHz, more than 5 orders-of-magnitude narrower than in conventional Raman scattering, and sidebands comprising Mollow triplet, molecular motional-sidebands and four-wave-mixing.
Summary form only given. A new way to reach the Lamb-Dicke regime in molecular gases has been reported in [1]. This is achieved by trapping H2molecule during Stimulated Raman Scattering (SRS) in a photonic band gap hollow-core fiber (PBG HC-PCF) pumped with a high power CW laser [1]. The molecular trapping process occurs in a self-assembled manner, whereby the Raman active molecules are confined in nanometer-wide sections by a periodic and ultra-deep potential thanks to a spatially modulated Raman saturation. It has permitted to obtain sub-recoil linewidths as low as 14 kHz which is 5 orders of magnitude lower than the expected H2Doppler-broadened linewidth for a product of the input power and the pressure below 1000 W.bar. Above this threshold the linewidth broadens due to the generation of the second-order Stokes.Here, we report a further linewidth narrowing down to 2.7 kHz by increasing the length and decreasing the gas pressure. Longer fiber lowers the pump power required for the SRS generation and enables formation of the trapping potential for lower gas pressure, which in turn reduces the molecular collision rate. The Stokes generation was obtained using a set-up similar to the one used in [1]. The PBG fiber has been tailored in order to have a spectral window between 1000 and 1200 nm in order to filter out any other Raman generation except the first rotational Stokes S00(1) at 1131.4 nm. The range of pressure of H2 with which we filled the PBG fiber is from 5 to 50 bars. The pump laser is a narrow linewidth (400 kHz) CW laser with a maximum pump power Pin of 100 W. Figure 1(a) shows the typical linewidth trace of the forward emitted Stokes for a fiber length of 30 m, a gas pressure of 20 bar and a pump power of 12 W. Figure 1(b) shows a resolved spectrum of the Stokes central line, which demonstrates a linewidth of 2.7 kHz. This line is nearly 30 times narrower than the hydrogen molecule recoil frequency Vrecο1 = πh(mλs2) of ~78 kHz, 5 orders of magnitude narrower than the Doppler width and almost 6 orders of magnitude narrower than the H2 pressure broadened line. Linewidth(kHz)
We study the spectral profile of Rayleigh scattered light from molecular species trapped in optical lattices created by strong fields in the ${10}^{16}\text{ }\text{W}\text{ }{\text{m}}^{\ensuremath{-}2}$ range. We show that, for lattices with well depths on the order of 100 K, the motional sidebands imparted on spectra are shifted from the central Dicke-narrowed Rayleigh peak by hundreds of MHz. Our calculations for these short duration (30 ns) lattices show that these spectral features appear even in room temperature gases suggesting a new technique for measuring gas composition based on the frequency offset of the sidebands. Finally, we study the role of field-induced molecular alignment within the lattice and calculate its effect on the shape and position of the sidebands.