1. References Acknowledgements This work is funded by EPSRC 1.Paul Siddons, Charles S. Adams, Chang Ge & Ifan G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment”, J. Phys. B. 41, 155004 (2008). 2. Paul Siddons, Nia C. Bell, Yifei Cai, Charles S. Adams & Ifan G. Hughes, “A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect”, Nature Photon. 3, 225-229 (2009). Having a theoretical model which predicts the absorption and refractive index of a medium is useful, for example, in predicting the magnitude of pulse propagation effects. We have performed a comprehensive study of the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. Theoretical model for atom-light interactions Beginning from the exact lineshape calculated for a two-level atom, a series of approximations to the electric susceptibility are made. These simplified functions facilitate direct comparison between absorption and dispersion and show that dispersion dominates the atom–light interaction far from resonance. Top: 16.5 o C Middle: 25.0 o C Bottom: 36.6 o C The probe intensity was 32 nW/mm 2 i.e. I / I sat = 0.002 [1] Slow light Faraday effect Department of Physics, Durham University, Durham DH1 3LE, UK Department of Physics, Durham University, Durham DH1 3LE, UK L. Weller, P. Siddons, C.S. Adams and I.G. Hughes L. Weller, P. Siddons, C.S. Adams and I.G. Hughes (a) The thick solid red curve shows experimental data, whilst the dashed black curve shows the transmission calculated using the Voigt function. The Gaussian and Lorentzian approximations to the Voigt function are shown as solid black and dashed blue curves, respectively. [3] Transmission difference for the 16.5 o C spectrum (b) The difference in transmission between theoretical and measured data. The experimental data were obtained with red- detuned light. The origin of the detuning axis is from the 87 Rb F g = 2 → F e = 1 transition. [3] Optically controlled Faraday rotation Optical control of the Faraday effect could be used for all-optical single qubit rotations for photons and consequently opens new perspectives for all-optical quantum information processing. A pulsed field will be used to drive population into the excited state in a time less than the excited state lifetime. The nanosecond switching time, combined with the Gigahertz bandwidth off-resonant. Faraday effect could permit rapid high-fidelity switching at low light levels. Future experiments will be carried out in a 2 mm Rubidium vapour cell. Initial results show that the theoretical code described in [1], fails to fit to temperatures above 140 ºC. The measured rotation angles, for no optical control (squares), a red-detuned control field (circles), and a blue-detuned control field (triangles). The curves are from theory [4]. Optical pulses are generated using a Pockels Cell (PoC). A 50:50 beam splitter is then used to produce a time delayed second pulse. The c.w. light is attenuated with a neutral density (ND) filter and a small fraction of the beam is used to perform sub-Doppler spectroscopy in a reference cell. Wave plates (λ/2 and λ/4) control the polarization of both beams before they pass through the experiment cell. The two orthogonal linear components of the pulse are collected on separate fast photodiodes (FPD), and the two components of the c.w. beam are collected on a differencing photodiode (DPD). In a slow-light medium we can dynamically control the propagation speed and polarisation state of light. Consequently slow light is a useful tool for quantum information processing and interferometry. Here in Durham we are mainly interested in the propagation of light through atomic media with a linear response to electric field. Such systems have a large frequency range (tens of GHz) over which slow-light effects occur, compared to nonlinear media which have sub-MHz bandwidth. The GHz bandwidth available to us means that nano or even picosecond optical pulses can be transmitted with low attenuation/distortion. Motivation Experimental method 3.Paul Siddons, Charles S. Adams & Ifan G. Hughes, “Off-resonance absorption and dispersion in vapours of hot alkali-metal atoms”, J. Phys. B: At. Mol. Opt. Phys. 42, 175004 (2009). 4. Paul Siddons, Charles S. Adams & Ifan G. Hughes, “Optical control of Faraday rotation in hot Rb vapor”, Phys. Rev. A. 81, 043838 (2010). The Faraday effect in a slow-light medium The Faraday effect is a magneto-optical phenomenon, where the rotation of the plane of polarization is proportional to the applied magnetic field in the direction of the beam of light. In slow-light the Faraday effect results in large dispersion and high transmission over tens of gigahertz. This large frequency range opens up the possibility of probing dynamics on a nanosecond timescale. In addition, we show large rotations of up to 15π rad for continuous-wave light. Broadband Faraday rotation in a slow- light medium. An input 1.5-ns pulse initially linearly polarized in the x-direction (red) is delayed by 0.6-ns with respect to a non- interacting reference pulse (black), in the absence of an applied magnetic field. The pulse is red-detuned from the weighted D1 transition centre by 10 GHz. For a temperature of 135 o C and a field of 80 G (green) or 230 G (blue) the pulse is rotated into the y-direction while retaining its linear polarization and intensity. [2] Optical pulse propagation in a slow-light medium. Pulse form at various temperatures for a pulse centred at zero detuning. [2] Probe differencing signal produced by scanning the probe versus red detuning, ∆, from the D 1 87 Rb F = 2 → F’ = 1 transition. The dashed black curve shows the experimentally measured signal. The measured data is compared to theory (red). D2D2 Some applications of slow light include: Coherent state preparation and entanglement in atomic ensembles. Polarisation switching of narrow and broadband pulses. Tunable pulse delay for optical information processing and quantum computing. The slow-light effect also has applications which utilise continuous-wave light: Interferometers used to measure electric and magnetic fields with high spectral sensitivity. Off-resonant laser locking with a dynamically tunable lock point over >10 GHz frequency range. Highly frequency dependent optical isolation and filtering. Schematic of the experimental apparatus. The output of an external cavity diode laser (ECDL) is split by a polarization beam splitter (PBS), for the c.w. (red) and pulsed (blue) experiments.