Set-up for Levy Flight of Photons in Resonant Atomic Vapor

1. Set-up for Levy Flight of Photons in Resonant Atomic Vapor Danielle Citro (SUNY Oswego), Adailton Feliciano (UFPB), Martine Chevrollier (UFPB), Marcos Oria (UFPB) Introduction Objective Light propagation in resonant atomic vapors have been shown to not follow Gaussian (normal) statistics. Instead, during the multiple scattering process, it is better described by superdiffusion. The small probability that a photon will be scattered far from resonance leads to the occurrence of rare but very long flights, called Lévy flights, which change the whole dynamic of the system. Send a laser through a heated Rubidium cell at the resonance frequency and collect the fluorescence light with a fiber. The light collected should have a Doppler shape. Theory and Methods • Theory: • Gaussian statistics is able to accurately describe many systems in nature, yet light propagation in resonant atomic vapors in not one of them. During normal diffusion, steps occur in random directions with slightly varying lengths around the average value. However, due to Lévy flights, Superdiffusion is a better statistical description of resonant atomic vapor systems. Lévy flights are “abnormally long steps interrupting a sequence of apparently regular jumps1.” These Lévy flights are rare, but have a huge impact on the whole system. Lévy flights come from the small but finite probability that a photon will be scattered with a frequency far from resonance during frequency redistribution. • . Pictures: Set-up: Figure 6: Shows the set-up of the current supply used to heat the cell. We kept track of the current used to heat the bottom of the cell. The current used was around 1.65 amperes. • Figure 6 Figure 7: Shows the side angle of the exit side of the cell. The cell is heated to between 105oC and 115oC so that the atomic density is increased and the resonant laser beam is totally absorbed. Figure 5 Figure 1a: Shows the graph of a Doppler (Gaussian) spectral distribution. Figure1b: Shows the graph of a Lorentzian distribution. Note how the wings are larger for the Lorentzian distribution, leading to long steps (Lévy flights) in a resonant vapor. Figure 5: Shows the top view of the set up. The red line follows the path of the laser. • Figure 1b Figure 1a Radiation Trapping: Radiation trapping is “the phenomenon of resonant multi-scattering of light in atomic vapours1.” Particles get repeatedly deflected by other particles during multiple scattering. When an incident photon enters a medium, it can be absorbed and re-emitted many times throughout its travel through the medium. During radiation trapping, the incident photons are first absorbed by the atoms in the gas medium at a frequency (v) that is close to the atomic transition of (vo). Next, when the excited atoms return to ground state, they emit a photon that can then be absorbed by another atom. This absorption occurs when the incident photon frequency is at resonance, with the resonance of Rubidium being 780.241 nm. Depending on the absorption spectral shape, the absorption of the photon is greater at the center of resonance. • Figure 7 Figure 8: Shows the side view of the cell and the two lens system The first lens that the light enters has a focal length of 5cm and the second lens has a focal length of 1cm. The light then proceeds to the fiber. • Figure 8 Figure 9: Shows the fiber used to collect the fluorescent light and send it to the photo- detector. After confirming that the light entering the photo-detector is all fluorescent light, the fiber will be used to send that light through another cell. Doppler (Gaussian) and Lorentzian Lineshapes: “Doppler broadening is due to the distribution of atomic velocities, which each have a Doppler shift with respect to an observer2.” Cold, resonant atomic vapors have more of a Lorentzian shape than a Doppler. In a thermal vapor, the Doppler effect changes the shape to a Doppler one. To increase the probability of a large amount of scatterings, the density may be increased. One way to increase the density is to increase the temperature of the cell reservoir. The desired shape of the fluorescence light is the Gaussian (Doppler) shape, similar to the adsorption spectral shape of atoms in the vapor. • Figure 3 • Figure 9 Figure 3: Shows the layout of the experiment. The laser was sent through an optical isolator so there would be no reflection of light back to the laser. After a lens and a few mirrors, the laser was sent through the heated Rubidium cell at an angle. A two-lens system at the exit of the cell collected the fluorescent light where it would be sent through the fiber and finally into the photo- detector. B Figure 10: Shows the controls for the laser and the photo-detector. The laser controls are (A), where the top controls the temperature and the bottom controls the current. By changing both of these, the frequency of the laser can be set. The Oscilloscope is (B). A Methods: Send the laser through the Rubidium cell at a slight angle as to not collect the resonant laser with the lens as it exits the cell. By slightly increasing the temperature of the cell, you increase the atomic density, increasing the fluorescence and the absorption of the resonant beam. After sending the laser through, collect only the fluorescent light using a two lens system and a fiber that is sent to a photo-detector. • Figure 10 • This controls the screen for the input from the photo-detector. Here the fluorescence intensity can be seen when the laser frequency is scanned around the resonance. Future Steps: After collecting the Fluorescence of Rubidium, the next step is to use the light from the fiber which already has a Doppler shape to measure the distribution of the steps length for a thermal vapor excited by a Gaussian spectrum excitation. • Figure 4 Results: Figure 4: Shows the fluorescence in a long cell with the incident photons having a Doppler-broadened distribution1. The brighter the spot, the higher the fluorescence intensity. For this project a shorter cell was used. Figure 2: Shows the results printed from the oscilloscope. The green line on the graph shows the intensity of the fluorescent light. When the laser is off resonance, the oscilloscope should not read anything (right). Figure 2 References Conclusion Acknowledgements Now that the fluorescent light has been collected, the line shape of the light can be tested to see if it has a Doppler line shape. Once tested and confirmed, part two of this project can be started. The fluorescent light will be sent through another cell where that light will be scattered and measured to observe the distribution of the steps length for a thermal vapor excited by a Gaussian spectrum excitation. 1 Martine Chevrollier (2012): Radiation trapping and Lévy flights in atomic vapours: an introductory review, Contemporary Physics, DOI:10.1080/00107514.2012.684481 2 "Spectroscopic Lineshapes." Stage 2 Chemistry Social Relevance Projects.. N.p., n.d. Web. 24 Jul 2012. <http://www.chemistry.adelaide.edu.au/external/soc- rel/content/lineshap.htm