A random laser with cold atoms
William Guerin
Institut Non Linéaire de Nice (INLN)
CNRS and Université Nice Sophia-Antipolis
What is a laser ?
random laser :
Two ingredients for a standard
1) An amplifying material
2) An optical cavity Multiple scattering
Role of the optical cavity: Multiple scattering
- To provide feedback
 Chain reaction: intensity grows until gain saturation
- Fabry-Perot interferometer
 Mode selection: spatial and temporal coherence properties
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What is a random laser ?
Two ingredients for a random laser :
1) An amplifying material
2) Multiple scattering
Role of the multiple scattering:
- To provide feedback
 Chain reaction: intensity grows until gain saturation
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Diffusion model with gain
Photons make a random walk between scatterers  Diffusion process
Interference effects
are ignored !!!
Model justified for L >> ℓsc
ℓt = transport length = mean-free-path for isotropic scattering ℓsc
With gain ?
Threshold on the system size:
“Photonic bomb”
V. S. Letokhov, Sov. Phys. JETP 26, 835 (1968).
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Mode and coherence properties
Random lasers are complex systems: open, highly multimode and nonlinear
 What are the mode and coherence properties of random lasers ?
New theoretical approaches have been developed
Türeci, Ge, Rotter & Stone, Science 2008
The nature of the ‘modes’ has been a long debate in the last years…
Review: J. Andreasen et
al., Adv. Opt. Photon.
3, 88 (2011).
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Link to this workshop (I)
Experiments on the coherence properties of random lasers
Poissonian photon statistics and
G(2)(0) = 1 above threshold
 temporal coherence
Cao et al., PRL 2001
But without spatial coherence:
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Link to this workshop (II)
Amplification of radiation by stimulated emission
(“laser” for astrophysicists) is known in space.
- “Space masers” are common
- Far IR amplification in MWC349A (H)
- Amplification at 10 µm in the atmospheres of Mars
and Venus (C02)
- Amplification in the near IR in h Carinae (FeII and OI)
Multiple scattering (radiation trapping) is also common
(e.g. in stars).
A random laser could happen naturally in space
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A random laser with cold atoms ?
• Cold atoms are clean and well-controlled systems:
- Simple system (“easy” to model)
- All the same (monodisperse sample)
- Almost no Doppler effect
- No absorption (but still inelastic scattering )
- Well isolated from environment (quantum effects ?)
 Possibility of
ab initio models
• Cold atoms are different: strong resonance / very dispersive
• Disorder-configuration averaging is easy (even unavoidable )
• Cold atom are versatile:
-The scattering cross-section is tunable
- Several gain mechanisms are possible
• Cold atoms are gas (≠ cond. mat.)  closer to astrophysical systems
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Outline
 Introduction

 The two necessary ingredients
 Multiple scattering in cold atoms
 Gain and lasing with cold atoms
 Both together ? The quest for the best gain mechanism
 Experimental signature of random lasing
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Experimental setup
Rubidium 85
l = 780 nm
G/2p = 6 MHz
MOT parameters:
N ~ 108-1010 atom
T ~ 50-100 µK
L ~ 1-5 mm
n ~ 1011 at/cm3
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Typically, on resonance, b0 = 10 – 100
With some efforts: up to b0 ~ 200
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Radiation trapping in cold atoms
Phys. Rev. Lett. 91, 223904 (2003).
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Gain with cold atoms
Several mechanisms are possible
Mollow gain:
Raman gain:
- Two level atoms + one pump
- Three-level atoms + one pump
- 3 photon transition (population
inversion in the dressed-state basis)
- 2 photon transition (population
inversion between the two ground
states)
- Hyperfine levels or Zeeman levels
wpump
wpump
wpump
Parametric gain:
R
- Two-level atoms + two pumps
 Degenerate four-wave mixing (DFWM)
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A laser with cold atoms (& cavity)
Laser radiation  300 µW
Cold atoms inside !
- Mollow laser for small pump detuning.
- (Zeeman) Raman laser for larger pump detuning, single pump.
- DFWM laser for larger pump detuning and two pumps.
Phys. Rev. Lett. 101, 093002 (2008).
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Outline
 Introduction


The
two necessary ingredients
 Both together ? The quest for the best gain mechanism
 Criterion: random laser threshold
 Comparison between different gain mechanisms
 Experimental signature of random lasing
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Combining gain and scattering ?
The scatterers and the amplifiers are the same atoms !
Pumping
Gain 
Saturation 
 elastic scattering 
 inelastic scattering 
Gain and scattering do not occur at the same frequency !!!   
Is it possible to get enough scattering and gain simultaneously ?
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Letokhov’s threshold
Letokhov’s diffusive model (interference effects are ignored)
= linear gain length
= mean free path
(sphere geometry)
What is measured in transmission experiments:
with the extinction length
Both lengths are related to the same atomic density n. We can use cross-sections s :
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Letokhov’s threshold with atoms
= on-resonance atomic cross-section
= polarizability (~ : dimensionless)
On-resonance optical depth :
b0 is an intrinsic parameter of the sample and is easily measured.
a depends on the pumping parameters and of the frequency.
 Criterion to compare the different gain mechanisms
Phys. Rev. Lett. 102, 173903 (2009).
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Let’s compare
Gain mechanism
Evaluation
method
b0cr
Analytical a
~ 300
Exp. & Num.
Raman gain
(Zeeman)
Raman gain
(Hyperfine)
Mollow gain
NDFWM
Validity of the
diffusion approx.
Other problem Ref.

Pump
[1]
penetration 
∞

Inelastic
scattering 
Exp.
~ 200

Detection 
Num.
~ 90

[2]
[1] Phys. Rev. Lett. 102, 173903 (2009).
[2] Opt. Express 17, 11236 (2009).
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Let’s compare
Gain mechanism
Evaluation
method
b0cr
Analytical a
~ 300
Exp. & Num.
Raman gain
(Zeeman)
Raman gain
(Hyperfine)
Mollow gain
Validity of the
diffusion approx.
Other problem Ref.

Pump
[1]
penetration 
∞

Inelastic
scattering 
Exp.
~ 200

Detection 
Num.
~ 90

Raman gain
(Hyperfine) +
Num.
additional scattering
~ 30

NDFWM
[2]
[1] Phys. Rev. Lett. 102, 173903 (2009).
[2] Opt. Express 17, 11236 (2009).
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Outline
 Introduction


The
two necessary ingredients
 Both together ? The quest for the best gain mechanism

 Experimental signature of random lasing
 Raman gain between hyperfine levels with additional scattering
 Experimental observations
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Raman gain between hyperfine levels
with additional scattering
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Experiment
• The random laser emission:
- is not spatially separated from elastic scattering from the external lasers
- is very hard to spectrally separate
 We look at the total fluorescence (= pump depletion)
• We change b0 with a constant atom number.
 changes are only due to collective effects
• We sweep slowly (steady-state) the Raman laser (no probe) around the frequency
where Raman gain is on resonance with the |2>  |1’> transition.
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Observations
1- Overall increase of fluorescence  Amplified spontaneous emission
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Observations
1- Overall increase of fluorescence  Amplified spontaneous emission
2- Increase of fluorescence around d = 0  combined effect of gain and multiple scattering
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Signature of random lasing
Fit of the wings  we can subtract the “ASE” background
 More visible bump (Gaussian shape)
 The amplitude has a threshold with b0
Nature Phys. 9, 357 (2013).
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Qualitative ab initio modeling
For ASE, OBE + ballistic amplification (scattering neglected, saturation effects included):
For the RL-bump, OBE + Letokhov’s threshold (ASE neglected, saturation effects included)
Nature Phys. 9, 357 (2013).
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Conclusion and outlook
 First evidence of random lasing in atomic vapors
 The observations agree qualitatively with ab initio modeling based
on Letokhov’s threshold.
 Short term projects (work in progress):
- Acquire more data (larger b0, different pump parameters)
- Study the dynamics
- Other signature of the transition (e.g. excess noise at threshold) ?
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Outlook (longer term)
 Quantitative agreement with more evolved models (ASE + RL) ?
 Coherence / spectrum of the random laser ?
- Use a Fabry-Perot to filter the random laser
light and look at the photocount statistics or the
correlation function.
b0=14
b0=7
- Make a beat note with the Raman laser to
access the spectrum.
- Comparison with theory ?
 Random laser in hot vapors ? Closer to astrophysical systems…
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From cold atoms to astrophysics
• Light diffusion / radiation trapping / radiative transfer
• Polarization of the scattered light: work in progress with M. Faurobert
• Frequency redistribution due to the Doppler effect in hot vapors
 Superdiffusion (Lévy flights)
• Light-induced long range forces  plasma physics, gravity
• Gain and lasing in atomic vapors, random lasers (?)
Cold and hot atomic vapors: a testbed for astrophysics?
Q. Baudouin, W. Guerin and R. Kaiser,
in Annual Review of Cold Atoms and Molecules, vol. 2, edited by K. Madison, Y. Wang, A. M. Rey, and K. Bongs
World Scientific, Singapour, 2014 (in press, preprint hal-00968233)
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People currently involved in
this project at INLN:
Collaborators:
• Robin Kaiser
Dmitriy Kupriyanov et al. (St-Petersburg)
• William Guerin
Stefan Rotter (Vienna)
• Samir Vartabi Kashani (PhD)
Chong Yidong (Singapour)
• Alexander Gardner (joint PhD)
Past contributions:
Past collaborators:
• Quentin Baudouin (PhD, 2013)
• Djeylan Aktas (Master, 2013)
R. Carminati (Paris)
• Nicolas Mercadier (PhD, 2011)
L. Froufe-Pérez (Madrid)
• Verra Guarrera (Post-doc, 2011)
S. Skipetrov et al. (Grenoble)
• Davide Brivio (Master, 2008)
• Frank
OCA,
Nice, Michaud
May 2014
(PhD, 2008)
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€ : ANR, DGA, PACA, CG06, INTERCAN
Publications related to this project
Mechanisms for Lasing with Cold Atoms as the Gain Medium
W. Guerin, F. Michaud, R. Kaiser,
Phys. Rev. Lett. 101, 093002 (2008).
Threshold of a Random Laser with Cold Atoms
L. Froufe-Pérez, W. Guerin, R. Carminati, R. Kaiser,
Phys. Rev. Lett. 102, 173903 (2009).
Threshold of a random laser based on Raman gain in cold atoms
W. Guerin, N. Mercadier, D. Brivio, R. Kaiser,
Opt. Express 17, 11236 (2009).
Towards a random laser with cold atoms
W. Guerin et al.,
J. Opt. 12, 024002 (2010).
Steady-state signatures of radiation trapping by cold multilevel atoms
Q. Baudouin, N. Mercadier, R. Kaiser,
Phys. Rev. A 87, 013412 (2013).
A cold-atom random laser
Q. Baudouin, N. Mercadier, V. Guarrera, W. Guerin, R. Kaiser,
Nature Physics 9, 357 (2013).
http://www.inln.cnrs.fr/content/atomes_froids/publications
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Optical pumping due to radiation trapping
Multiple scattering  radiation trapping
 The intensity changes inside the sample.
 Could it change the equilibrium population such that it increases the fluorescence ?
YES, this is the dominant effect very close to
the |3>  |2> transition.
But it is negligible around d = 0 (-5 G from the
|3>  |2> transition).
Phys. Rev. A 87, 013412 (2013).
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