Transcript Slide 1

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 include:
The slow-light 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.
• Off-resonant laser locking with a dynamically tunable lock point over >10 GHz frequency range.
• Tunable pulse delay for optical information processing and quantum computing.
• Highly frequency dependent optical isolation and filtering.
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. [2]
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
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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 x-direction (red) is
delayed by 0.6-ns with respect to a noninteracting 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
o
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. [2]
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.
Top: 16.5oC
Middle: 25.0oC
Bottom: 36.6oC
The probe intensity was
32 nW/mm2
i.e. I / Isat = 0.002 [1]
D2
Transmission difference for the
o
16.5 C spectrum
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.
(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]
(b) The difference in transmission between
theoretical and measured data. The
experimental data were obtained with reddetuned light. The origin of the detuning axis
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is from the Rb Fg = 2 → Fe = 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.
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].
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.
References
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).
Acknowledgements
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).
This work is funded by EPSRC