1. William Guerin A random laser with cold atoms Institut Non Linéaire de Nice (INLN) CNRS and Université Nice Sophia-Antipolis

2. 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 What is a laser ? ?

3. William Guerin 3OCA, Nice, May 2014 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 ?

4. William Guerin 4OCA, Nice, May 2014 Photons make a random walk between scatterers  Diffusion process ℓ t = transport length = mean-free-path for isotropic scattering ℓ sc Interference effects are ignored !!! Model justified for L >> ℓ sc With gain ? Diffusion model with gain V. S. Letokhov, Sov. Phys. JETP 26, 835 (1968). “Photonic bomb” Threshold on the system size:

5. William Guerin 5OCA, Nice, May 2014 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

6. William Guerin 6OCA, Nice, May 2014 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:

7. William Guerin 7OCA, Nice, May 2014 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 (C0 2 ) - Amplification in the near IR in  Carinae (Fe II and O I ) Multiple scattering (radiation trapping) is also common (e.g. in stars). A random laser could happen naturally in space

8. William Guerin 8OCA, Nice, May 2014 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

9. William Guerin 9OCA, Nice, May 2014  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 

10. William Guerin 10OCA, Nice, May 2014 Typically, on resonance, b 0 = 10 – 100 With some efforts: up to b 0 ~ 200 Rubidium 85 = 780 nm  /2  = 6 MHz MOT parameters: N ~ 10 8 -10 10 atom T ~ 50-100 µK L ~ 1-5 mm n ~ 10 11 at/cm 3 Experimental setup

11. William Guerin 11OCA, Nice, May 2014 Phys. Rev. Lett. 91, 223904 (2003). Radiation trapping in cold atoms

12. William Guerin 12OCA, Nice, May 2014 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 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)

13. William Guerin 13OCA, Nice, May 2014 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)

14. William Guerin 14OCA, Nice, May 2014  Introduction  The two necessary ingredients  Both together ? The quest for the best gain mechanism  Experimental signature of random lasing  Criterion: random laser threshold  Comparison between different gain mechanisms Outline  

15. William Guerin 15OCA, Nice, May 2014 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 !!!   

16. William Guerin 16OCA, Nice, May 2014 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  :

17. William Guerin 17OCA, Nice, May 2014 b 0 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)

18. William Guerin 18OCA, Nice, May 2014 Let’s compare [1] Phys. Rev. Lett. 102, 173903 (2009). [2] Opt. Express 17, 11236 (2009). Gain mechanismEvaluation method b 0cr Validity of the diffusion approx. Other problemRef. Mollow gain Analytical  ~ 300 Pump penetration  [1] NDFWM Exp. & Num.∞ Inelastic scattering  Raman gain (Zeeman) Exp.~ 200 Detection  [2] Raman gain (Hyperfine) Num.~ 90

19. William Guerin 19OCA, Nice, May 2014 Let’s compare [1] Phys. Rev. Lett. 102, 173903 (2009). [2] Opt. Express 17, 11236 (2009). Gain mechanismEvaluation method b 0cr Validity of the diffusion approx. Other problemRef. Mollow gain Analytical  ~ 300 Pump penetration  [1] NDFWM Exp. & Num.∞ Inelastic scattering  Raman gain (Zeeman) Exp.~ 200 Detection  [2] Raman gain (Hyperfine) Num.~ 90 Raman gain (Hyperfine) + additional scattering Num.~ 30

20. William Guerin 20OCA, Nice, May 2014  Introduction  The two necessary ingredients  Both together ? The quest for the best gain mechanism  Experimental signature of random lasing Outline    Raman gain between hyperfine levels with additional scattering  Experimental observations 

21. William Guerin 21OCA, Nice, May 2014 Raman gain between hyperfine levels with additional scattering

22. William Guerin 22OCA, Nice, May 2014 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 b 0 with a constant atom number.  changes are only due to collective effects

23. William Guerin 23OCA, Nice, May 2014 Observations 1- Overall increase of fluorescence  Amplified spontaneous emission

24. William Guerin 24OCA, Nice, May 2014 Observations 2- Increase of fluorescence around  = 0 1- Overall increase of fluorescence  Amplified spontaneous emission  combined effect of gain and multiple scattering

25. William Guerin 25OCA, Nice, May 2014 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 b 0 Nature Phys. 9, 357 (2013).

26. William Guerin 26OCA, Nice, May 2014 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).

27. William Guerin 27OCA, Nice, May 2014 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 b 0, different pump parameters) - Study the dynamics - Other signature of the transition (e.g. excess noise at threshold) ?  Short term projects (work in progress):

28. William Guerin 28OCA, Nice, May 2014 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… - 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 ?

29. William Guerin 29OCA, Nice, May 2014 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. Bongs World 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 (?)

30. 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)

31. William Guerin 31OCA, Nice, May 2014 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

32. William Guerin 32OCA, Nice, May 2014 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).