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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:
The slow light Faraday effect also has applications which utilise continuous-wave light:
• Coherent state preparation and entanglement in atomic ensembles.
• Interferometers used to measure electric and magnetic fields with high spectral sensitivity.
• Polarisation switching of narrow and broadband pulses.
• Highly frequency dependent optical isolation and filtering [1].
• Tunable pulse delay for optical information processing and quantum computing.
• Off-resonant laser locking with a dynamically tunable lock point over >10 GHz frequency range [2].
The Faraday effect in a slow-light medium
Experimental method
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, ∆,
87
from the D1 Rb 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.
Broadband Faraday rotation in a slowlight medium. An input 1.5-ns pulse
initially linearly polarized in the xdirection (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
o
10 GHz. For a temperature of 135 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 [4].
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].
Total Lorentzian (FWHM)
Number density / cm-3
Natural (FWHM)
Self-broadening rate
coefficient / Hz cm3
2  5 . 746 MHz
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 selfbroadening
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].
87Rb
52P3/2
52P1/2
PUMP
F’ = 2
1
FARADAY
52S1/2
F=2
1
See [7] for references
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.
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).
Acknowledgements
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).
This work is funded by EPSRC