Fighting the Doppler Broadening
Using Nanotraps in Raman Gas
- Fig. 1. The output spectrum of the fiber in forward (a) and backward (b) direction.
- Fig. 2. The scheme of the nanotraps formation (a) and the distribution of population difference D (red), Raman gain GR (blue) and the potential (black) on the subwavelength scale.
- Fig. 3. The distribution of the potential along the fiber length (a) and two consecutive frames at 0 s and 2.3 s, showing motion of a scatterer.
The central idea of spectroscopy is to shine a light with variable wavelength on matter and to observe the output spectra. If the light is in resonance with a transition from one quantum state to another, strong absorption will occur. By analyzing the position of absorption peaks, one can determine the structure of an atom or molecule and how it moves.
A Key Issue of Spectroscopy
Unfortunately, the Doppler Effect, which is caused by thermal motion, leads to the broadening of the observed spectral lines, reducing the resolution. There are two ways to reduce the Doppler broadening: by either laser cooling the matter or by localizing it at a scale below the light wavelength. Laser cooling works well for atoms, but is hard to implement for molecules, for which subwavelength localization offers more viable perspectives. Here we propose a method to reduce the Doppler linewidth of molecules by 4 orders of magnitude for Raman-active gas in a light-pumped fiber.
Extreme Line Narrowing
The setup of the experiment is extremely simple: the radiation of a continuously-operating laser is directed at a hollow-core photonic bandgap fiber, and the spectral width of the output radiation (from both ends of the fiber) is measured. The fiber is designed to operate only at the wavelengths of the laser pump and the generated Stokes radiation respectively. The fiber is filled with hydrogen gas. The molecules of the hydrogen gas are either in ground rotational state or in an excited rotational state. Light can transfer a molecule from the ground state to the excited state. In this process, called Raman scattering, a part of the incoming photon energy is used to excite a molecule, and a new scattered photon is emitted with correspondingly reduced energy. The spectra of the scattered radiation (called Stokes radiation) in both forward and backward directions are illustrated in Fig. 1. One can see the spectral width of roughly 15 kHz, which is 4 orders of magnitude lower than the Doppler width of 140 MHz!
Formation of Nanotraps
The forward-propagating and backward-propagating Stokes radiation form an interference pattern called a standing wave.
A standing wave consists of a periodic spatial array of high electric field regions and low electric field regions, as presented in Fig. 2(a). The molecules in high-field regions are to a significant extend in the excited state (population difference D = 0), which is a high-energy state. The molecules in the low-field regions are predominantly in the ground state (population difference D = -1). The distribution of the molecular population and the energy of the molecules is shown in Fig. 2(b). One can see that narrow areas of low potential are formed, shown by the black curve in Fig. 2(b). The energy necessary to leave the low-potential zone is 0.08 eV, which is higher than the energy of the thermal motion (0.025 eV). Therefore hydrogen molecules remain trapped for a significant amount of time.
Nanotraps and Line Narrowing
The molecules which are trapped in the low-potential areas retain their thermal-motion energy. However, this motion does not lead to Doppler broadening, since the motion is strongly localized on the subwavelength scale of roughly 100 nm. This effect was known before as Lamb-Dicke narrowing and observed in dense gases. Here we show that Lamb-Dicke narrowing can reach extreme values. The theory of Lamb-Dicke narrowing predicts the narrowing with a factor of roughly 10100, in excellent agreement with the value of 104 observed in the experiment. Note that the molecules which are in the excited state do not contribute significantly to the Raman process [gR = 0 in fig. 2(b)], since they are saturated, while molecules in the ground state can actively participate in the generation of the Stokes radiation. This effect additionally contributes to the observed line narrowing.
The Motion of the Gas
Up to now we have discussed only the microscopic picture of the molecular dynamics and potential. However there is also a non-trivial macroscopic distribution of the fields – and therefore of the potential felt by the molecules – along the fiber. This distribution is illustrated in Fig. 3(a). One can see the significant drop in the potential towards the output end of the fiber. This should result in the forward flow of the hydrogen gas, with velocity determined by the viscosity of the gas, as well as by the potential difference at the fiber ends which can be interpreted as pressure difference. The calculations predict the flow velocity of roughly 1 m/s. Quite surprisingly, this flow is indeed visible with the naked eye. The scattering of light off the dust particles, which move together with the gas flow, is shown in Fig. 3(b). One can see the flow with velocities in the range of 1 to 4 m/s.
Conclusion and Outlook
The observed and explained mechanism can be used to engineer highly narrow-linewidth and powerful CW Raman lasers, optical micro-mirrors and micro-cavities made with gas-phase materials. One can generate high power and a scalable CW Raman generator with ultra-narrowed gain by simply adjusting the fiber length and a Raman active gas pressure.
The possibilities for investigations in the immediate future include finding out whether this scheme could lead to molecular cooling via the motional sidebands. This would enable the engineering of molecular non-classical state and entangled photons to mention only a couple. Finally, the high acceleration in this laser-gas interaction could be explored as a new tool for micro- and nanoparticle accelerators.
Anton Husakou1,2, Fetah Benabid1
1 GPPMM Group, XLIM Research Institute, University of Limoges, Limoges, France
2 Max Born Institute of Nonlinear Optics and Short Pulse Spectroscopy, Berlin, Germany
M. Alharbi, A. Husakou, M. Chafer, B. Debord, F. Gerome, and F. Benabid: Raman gas self-organizing into deep nano-trap lattice, Nature Communications 7, 12779 (2016).