The Slow-Light Effect

First year talkMark Zentile

Project Members

Lee Weller Charles Adams Ifan Hughes

19/04/23 1st year talk, Mark Zentile

Outline

• Slow-light:– What is slow-light? What conditions are needed to

see it? What are the applications?– Phase shift and absorption from the electric

susceptibility.– Transmission spectra to extract key parameters for

the model.– Using the our model for the electric susceptibility

with Fourier analysis to model pulse propagation.– Experimental method and examples of data with

theoretical predictions.

19/04/23 1st year talk Mark Zentile

Outline

• Future outlook:– Introduce the Faraday effect.– Use a Faraday signal to make a tuneable laser lock

over ± 20 GHz detuning.– Harness the slow-light Faraday effect to make an

optical switch.

19/04/23 1st year talk Mark Zentile

What is ‘Slow-Light’?

19/04/23 1st year talk Mark Zentile

What is ‘Slow-Light’?

19/04/23 1st year talk Mark Zentile

Slow-light with EIT

19/04/23 1st year talk Mark Zentile

Better interferometers

19/04/23 1st year talk Mark Zentile

Image rotation Image coding

19/04/23 1st year talk Mark Zentile

Optical Delay Line

19/04/23 1st year talk Mark Zentile

Optical Switch

19/04/23 1st year talk Mark Zentile

Outline

• Slow-light:– What is slow-light? What conditions are needed to

see it? What are the applications?– Phase shift and absorption from the electric

susceptibility.– Transmission spectra to extract key parameters for

the model.– Using the our model for the electric susceptibility

with Fourier analysis to model pulse propagation.– Experimental method and examples of data with

theoretical predictions.

19/04/23 1st year talk Mark Zentile

Complex refractive index

19/04/23 1st year talk Mark Zentile

ABSORPTION DISPERSION

Transmission Spectra

19/04/23 1st year talk Mark Zentile

The model for the electric susceptibility

• Our model has been developed over many years:

19/04/23 1st year talk Mark Zentile

Siddons et al. J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 155004

• Accurate up to ~ 120oC• Includes:

absolute linestrengths Doppler broadening Temperature

dependent number density.

Result of solving the optical Bloch equations for a two level atom.

The model for the electric susceptibility

• Inclusion of self-broadening:

19/04/23 1st year talk Mark Zentile

Weller et al. J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 195006

• Accurate up to ~ 360oC• Includes:

absolute linestrengths Doppler broadening Temperature

dependent number density.

Self-broadening for binary-collision approximation

The model for the electric susceptibility

• Inclusion of magnetic field:

19/04/23 1st year talk Mark Zentile

Weller et al. J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 055001

• Tested up to 0.6 T• Includes:

absolute linestrengths Doppler broadening Temperature

dependent number density.

Self-broadening for binary-collision approximation

Magnetic energy level shift.

Outline

• Slow-light:– What is slow-light? What conditions are needed to

see it? What are the applications?– Phase shift and absorption from the electric

susceptibility.– Transmission spectra to extract key parameters for

the model.– Using the our model for the electric susceptibility

with Fourier analysis to model pulse propagation.– Experimental method and examples of data with

theoretical predictions.

19/04/23 1st year talk Mark Zentile

Transmission: Extracting parameters

• We want to use transmission spectra to measure experimental parameters.– Transmission χ(ω) dispersion slow-light theory.

19/04/23 1st year talk Mark Zentile

• Why model transmission spectra? Can’t we just use Kramers-Kronig?– Yes, but...

Transmission: Extracting parameters

• Rubidium 75 mm long cell, room temperature.

19/04/23 1st year talk Mark Zentile

Excellent agreement.One fit parameter:

Temp = (20.70 ± 0.13) oC

Transmission: Extracting parameters

• 2 mm long 98.2% 87Rb cell:

19/04/23 1st year talk Mark Zentile

3 fit parameters:

Temp = (90.2 ± 0.1)oC

Lorentzian FWHM = 2π ∙ (165 ± 1) MHzVery large! => Buffer gas.

Ratio of 87Rb to 85Rb = 0.982 ± 0.009

Transmission: Extracting parameters

• 2 mm long 87Rb cell (high temp):

19/04/23 1st year talk Mark Zentile

2 fit parameters:

Temp = (182.1 ± 0.4)oC

Lorentzian FWHM = 2π ∙ (170 ± 4) MHzVery large! => Buffer gas.

Outline

• Slow-light:– What is slow-light? What conditions are needed to

see it? What are the applications?– Phase shift and absorption from the electric

susceptibility.– Transmission spectra to extract key parameters for

the model.– Using the our model for the electric susceptibility

with Fourier analysis to model pulse propagation.– Experimental method and examples of data with

theoretical predictions.

19/04/23 1st year talk Mark Zentile

Fourier Method for pulse propagation

• Electric susceptibility model is designed for monochromatic continuous wave light.

• Pulses are clearly not monochromatic continuous wave light!

• Solution: Use a Fourier transform to write the pulse in terms of continuous wave light.

19/04/23 1st year talk Mark Zentile

Fourier Method for pulse propagation

• Fourier decomposition:

19/04/23 1st year talk Mark Zentile

Good conditions for slow-light?

19/04/23 1st year talk Mark Zentile

Rubidium at natural abundance 98.2% 87Rb

Fast-Light

19/04/23 1st year talk Mark Zentile

Outline

• Slow-light:– What is slow-light? What conditions are needed to

see it? What are the applications?– Phase shift and absorption from the electric

susceptibility.– Transmission spectra to extract key parameters for

the model.– Using the our model for the electric susceptibility

with Fourier analysis to model pulse propagation.– Experimental method and examples of data with

theoretical predictions.

19/04/23 1st year talk Mark Zentile

Experimental Setup

19/04/23 1st year talk Mark Zentile

Advantages/disadvantages of FPD

• Works over one shot

• Slow rise time => poor resolution

• Need relatively intense pulses

=> may not be weak probe.

19/04/23 1st year talk Mark Zentile

Picture from http://www.eotech.com/product/14/2GHz_Amplified/

Advantages/disadvantages of SPCM

• Slightly better timing resolution.

• Works for much less

Intense pulses.

• Must build a pulse profile

over many repetitions.

19/04/23 1st year talk Mark Zentile

Picture from http://excelitas.com/downloads/DTS_SPCM_AQRH.pdf

Preliminary experimental data (FPD)

19/04/23 1st year talk Mark Zentile

Group refractive index of ~1000

Experimental data with theory (FPD)

19/04/23 1st year talk Mark Zentile

• 87Rb cell.•Laser locked by polarization spectroscopy.• Carrier frequency on resonant with 85Rb D1 Fg=2 Fe=2,3 transition frequency.

Pink = Measured output

Red Dashed = Theory

Reference

Experimental data with theory (SPCM)

19/04/23 1st year talk Mark Zentile

• Rb natural abundance cell.•Counted over a relatively short time

Reference

Red = Measured output

Black Dashed = Theory

Outline

• Future outlook:– Introduce the Faraday effect.– Use a Faraday signal to make a tuneable laser lock

over ± 20 GHz detuning.– Harness the slow-light Faraday effect to make an

optical switch.

19/04/23 1st year talk Mark Zentile

The Faraday Effect

• Linearly polarized light can be constructed from a circularly polarized basis.

19/04/23 1st year talk Mark Zentile

The Faraday Effect

• A magnetic field breaks the degeneracy for right and left circular components

19/04/23 1st year talk Mark Zentile

The Faraday Effect

• Have already seen that the model can accurately predict Faraday rotation:

19/04/23 1st year talk Mark Zentile

Weller et al. J. Phys. B: At. Mol. Opt. Phys. 45 (2012) 055001

A Faraday signal as a laser lock

• Take inspiration from this paper. Locking off-resonance

19/04/23 1st year talk Mark Zentile

Marchant, A. L., Händel, S., Wiles, T. P., Hopkins, S. A., Adams, C. S., & Cornish, S. L. (2011). Optics letters, 36, 64-6.

A Faraday signal as a laser lock

• Can use our 1 mm long cell placed in a permanent magnet to achieve high magnetic fields

• We will be able to lock on-resonance as well as off.

19/04/23 1st year talk Mark Zentile

Outline

• Future outlook:– Introduce the Faraday effect.– Use a Faraday signal to make a tuneable laser lock

over ± 20 GHz detuning.– Harness the slow-light Faraday effect to make an

optical switch.

19/04/23 1st year talk Mark Zentile

The Slow-light Faraday effect

19/04/23 1st year talk Mark Zentile

Large rotation with little absorption

Siddons, P., Bell, N., Cai, Y., Adams, C. S., & Hughes, I. G. (2009). Nature Photonics, 3, 225

Use optical pumping to control rotation

19/04/23 1st year talk Mark Zentile

• Can also cause a rotation by having an unbalanced distribution in the populations of the Zeeman sub-levels.

Use optical pumping to control rotation

19/04/23 1st year talk Mark Zentile

Summary

– Seen what slow-light is and what its applications are.

– Phase shift and absorption from the electric susceptibility.

– How we use transmission spectra to measure parameters for the model.

– Seen how to model pulse propagation with the Fourier analysis, once χ in known.

– Experimental method and examples of data with theoretical predictions.

19/04/23 1st year talk Mark Zentile

Summary

– Explained the Faraday effect.– Want to use a Faraday signal to make a tuneable

laser lock.– Harness the slow-light Faraday effect to make an

optical switch.

19/04/23 1st year talk Mark Zentile

End

Thanks for listening.

19/04/23 1st year talk Mark Zentile

Fit with magnetic field

19/04/23 1st year talk Mark Zentile

Controlled Faraday rotation

19/04/23 1st year talk Mark Zentile

Siddons, P., Adams, C. S., & Hughes, I. G. (2010). Physical Review A, 81, 043838

Pump-Probe energy level diagram

19/04/23 1st year talk Mark Zentile

Jitter in arrival time

• FPD shows a ‘jitter’ in the arrival time and peak height.

19/04/23 1st year talk Mark Zentile

• This will broaden a photon counted pulse!

Simulating photon counting pulses

19/04/23 1st year talk Mark Zentile