References

1. Acknowledgements This work is funded by EPSRC Slow light Faraday effect L. Weller, P. Siddons, C.S. Adams and I.G. Hughes Department of Physics, Durham University, Durham DH1 3LE, UK Motivation 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. • Some applications of slow light Faraday effect 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 Faraday effect also has applications which utilise continuous-wave light: • Interferometers used to measure electric and magnetic fields with high spectral sensitivity. • Highly frequency dependent optical isolation and filtering [1]. • Off-resonant laser locking with a dynamically tunable lock point over >10 GHz frequency range [2]. Experimental method 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. Optical pulse propagation in a slow-light medium. Pulse form at various temperatures for a pulse centred at zero detuning [4]. 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. 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). Probe differencing signal produced by scanning the probe versus red detuning, ∆, from the D187Rb F = 2 → F’ = 1 transition. The dashed black curve shows the experimentally measured signal. The measured data is compared to theory (red). Theoretical model for atom-light interactions 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 [3,5,7]. 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 oC 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 [4]. Total Lorentzian (FWHM) Number density / cm-3 Natural (FWHM) Self-broadening rate coefficient / Hz cm3 T = 171.8 ± 0.2 oC Γtot/2π = 23.7 ± 0.2 MHz 85Rb = 0.7217 Optically controlled Faraday rotation At number densities greater than 1013 cm−3 (~125oC) the resonant dipole–dipole interactions between two identical atoms, in superpositions of the ground and excited states, give rise to the phenomenon of self-broadening 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 [6]. 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. 87Rb 52P3/2 PUMP F’ = 2 52P1/2 1 FARADAY F = 2 52S1/2 1 See [7] for references References 1. R. P. Abel, U. Krohn, P. Siddons, I. G. Hughes & C. S. Adams, Opt Lett. 34 3071 (2009). 2. A. L. Marchant, S. Händel, T. P. Wiles, S. A. Hopkins, C. S. Adams & S. L. Cornish, Opt Lett. 36 64 (2011) 3. P. Siddons, C. Ge, C. S. Adams & I. G. Hughes, J. Phys. B: At. Mol. Opt. Phys.41 155004 (2008). 4. P. Siddons, N. C. Bell, Y. Cai, C. S. Adams & I. G. Hughes, Nature Photon. 3 225-229 (2009). 5. P. Siddons, C. S. Adams & I. G. Hughes, J. Phys. B: At. Mol. Opt. Phys. 4 175004 (2009). 6. P. Siddons, C. S. Adams & I. G. Hughes, Phys. Rev. A. 81 043838 (2010). 7. L. Weller, R. J. Bettles, P. Siddons, C. S. Adams & I. G. Hughes J. Phys. B: At. Mol. Opt. Phys. 44 195006 (2011).