william guerin a random laser with cold atoms institut non linéaire de nice (inln) cnrs and...

William Guerin

A random laser with cold atoms

Institut Non Linéaire de Nice (INLN)CNRS and Université Nice Sophia-Antipolis

William Guerin 2OCA, Nice, May 2014

Two ingredients for a standard laser :

1) An amplifying material

2) An optical cavity

Role of the optical cavity:

- To provide feedback

Chain reaction: intensity grows until gain saturation

- Fabry-Perot interferometer

Mode selection: spatial and temporal coherence properties

random

Multiple scattering

Multiple scattering

What is a 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

What is a random laser ?


Photons make a random walk between scatterers Diffusion process

ℓt = transport length = mean-free-path for isotropic scattering ℓsc

Interference effects are ignored !!!

Model justified for L >> ℓsc

With gain ?

Diffusion model with gain

V. S. Letokhov, Sov. Phys. JETP 26, 835 (1968).

“Photonic bomb”

Threshold on the system size:


Review: J. Andreasen et al., Adv. Opt. Photon. 3, 88 (2011).

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

The nature of the ‘modes’ has been a long debate in the last years…

Türeci, Ge, Rotter & Stone, Science 2008


Experiments on the coherence properties of random lasers

Link to this workshop (I)

Cao et al., PRL 2001

Poissonian photon statistics and G(2)(0) = 1 above threshold

temporal coherence

But without spatial coherence:


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 Carinae (FeII and OI)

Multiple scattering (radiation trapping) is also common (e.g. in stars).

A random laser could happen naturally in space


• 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 ?)

• 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

A random laser with cold atoms ?

Possibility of ab initio models


Introduction

The two necessary ingredients

Both together ? The quest for the best gain mechanism

Experimental signature of random lasing

Multiple scattering in cold atoms

Gain and lasing with cold atoms

Outline


Typically, on resonance, b0 = 10 – 100

With some efforts: up to b0 ~ 200

Rubidium 85

= 780 nm

/2 = 6 MHz

MOT parameters:

N ~ 108-1010 atom

T ~ 50-100 µK

L ~ 1-5 mm

n ~ 1011 at/cm3

Experimental setup


Phys. Rev. Lett. 91, 223904 (2003).

Radiation trapping in cold atoms


Gain with cold atoms

Several mechanisms are possible

Mollow gain:

- Two level atoms + one pump

- 3 photon transition (population inversion in the dressed-state basis)

pump pump

Raman gain:

- Three-level atoms + one pump

- 2 photon transition (population inversion between the two ground states)

- Hyperfine levels or Zeeman levels

R

pump

Parametric gain:

- Two-level atoms + two pumps

Degenerate four-wave mixing (DFWM)


Laser radiation 300 µW

Cold atoms inside !

Phys. Rev. Lett. 101, 093002 (2008).

- Mollow laser for small pump detuning.

- (Zeeman) Raman laser for larger pump detuning, single pump.

- DFWM laser for larger pump detuning and two pumps.

A laser with cold atoms (& cavity)


Introduction




Criterion: random laser threshold

Comparison between different gain mechanisms

Outline


The scatterers and the amplifiers are the same atoms !

Is it possible to get enough scattering and gain simultaneously ?

Gain

Saturation elastic scattering

inelastic scattering

Pumping

Combining gain and scattering ?

Gain and scattering do not occur at the same frequency !!!


What is measured in transmission experiments:

with the extinction length

Letokhov’s diffusive model (interference effects are ignored)

= mean free path(sphere geometry)

= linear gain length

Letokhov’s threshold

Both lengths are related to the same atomic density n. We can use cross-sections :


b0 is an intrinsic parameter of the sample and is easily measured.

depends on the pumping parameters and of the frequency.

Criterion to compare the different gain mechanisms

Phys. Rev. Lett. 102, 173903 (2009).

Letokhov’s threshold with atoms

On-resonance optical depth :

= on-resonance atomic cross-section

= polarizability (~ : dimensionless)


Let’s compare

[1] Phys. Rev. Lett. 102, 173903 (2009).[2] Opt. Express 17, 11236 (2009).

Gain mechanism Evaluation method

b0cr Validity of the diffusion approx.

Other problem Ref.

Mollow gainAnalytical ~ 300 Pump

penetration [1]

NDFWMExp. & Num. ∞ Inelastic

scattering

Raman gain (Zeeman) Exp. ~ 200 Detection [2]

Raman gain (Hyperfine) Num. ~ 90


Let’s compare

[1] Phys. Rev. Lett. 102, 173903 (2009).[2] Opt. Express 17, 11236 (2009).

Gain mechanism Evaluation method

b0cr Validity of the diffusion approx.

Other problem Ref.

Mollow gainAnalytical ~ 300 Pump

penetration [1]

NDFWMExp. & Num. ∞ Inelastic

scattering

Raman gain (Zeeman) Exp. ~ 200 Detection [2]

Raman gain (Hyperfine) Num. ~ 90 Raman gain (Hyperfine) + additional scattering

Num. ~ 30


Introduction




Outline

Raman gain between hyperfine levels with additional scattering

Experimental observations


Raman gain between hyperfine levels

with additional scattering


Experiment

• We sweep slowly (steady-state) the Raman laser (no probe) around the frequency where Raman gain is on resonance with the |2> |1’> transition.

• 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


Observations

1- Overall increase of fluorescence Amplified spontaneous emission


Observations

2- Increase of fluorescence around = 0

1- Overall increase of fluorescence Amplified spontaneous emission

combined effect of gain and multiple scattering


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).


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).


Conclusion and outlook

First evidence of random lasing in atomic vapors

The observations agree qualitatively with ab initio modeling based on Letokhov’s threshold.

- Acquire more data (larger b0, different pump parameters)

- Study the dynamics

- Other signature of the transition (e.g. excess noise at threshold) ?

Short term projects (work in progress):


Outlook (longer term)

Quantitative agreement with more evolved models (ASE + RL) ?

Coherence / spectrum of the random laser ?

Random laser in hot vapors ? Closer to astrophysical systems…

b0=7b0=14

- Use a Fabry-Perot to filter the random laser light and look at the photocount statistics or the correlation function.

- Make a beat note with the Raman laser to access the spectrum.

- Comparison with theory ?


From cold atoms to astrophysics

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. BongsWorld Scientific, Singapour, 2014 (in press, preprint hal-00968233)

• 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 (?)

William Guerin 30OCA, Nice, May 2014 € : ANR, DGA, PACA, CG06, INTERCAN

People currently involved in this project at INLN:

• Robin Kaiser

• William Guerin

• Samir Vartabi Kashani (PhD)

• Alexander Gardner (joint PhD)

Past contributions:

• Quentin Baudouin (PhD, 2013)

• Djeylan Aktas (Master, 2013)

• Nicolas Mercadier (PhD, 2011)

• Verra Guarrera (Post-doc, 2011)

• Davide Brivio (Master, 2008)

• Frank Michaud (PhD, 2008)

Past collaborators:

R. Carminati (Paris)

L. Froufe-Pérez (Madrid)

S. Skipetrov et al. (Grenoble)

Collaborators:

Dmitriy Kupriyanov et al. (St-Petersburg)

Stefan Rotter (Vienna)

Chong Yidong (Singapour)


Publications related to this projectMechanisms for Lasing with Cold Atoms as the Gain MediumW. Guerin, F. Michaud, R. Kaiser,Phys. Rev. Lett. 101, 093002 (2008).

Threshold of a Random Laser with Cold AtomsL. 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 atomsW. Guerin, N. Mercadier, D. Brivio, R. Kaiser,Opt. Express 17, 11236 (2009).

Towards a random laser with cold atomsW. Guerin et al.,J. Opt. 12, 024002 (2010).

Steady-state signatures of radiation trapping by cold multilevel atomsQ. Baudouin, N. Mercadier, R. Kaiser,Phys. Rev. A 87, 013412 (2013).

A cold-atom random laserQ. Baudouin, N. Mercadier, V. Guarrera, W. Guerin, R. Kaiser,Nature Physics 9, 357 (2013).

http://www.inln.cnrs.fr/content/atomes_froids/publications


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 = 0 (-5 from the |3> |2> transition).

Phys. Rev. A 87, 013412 (2013).

william guerin a random laser with cold atoms institut non linéaire de nice (inln) cnrs and...

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