William Guerin

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

2. What is a laser ? Two ingredients for a standard laser : random • An amplifying material • An optical cavity Multiple scattering • 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 Multiple scattering ?

3. What is a random laser ? Two ingredients for a random laser : • An amplifying material • Multiple scattering • Role of the multiple scattering: • To provide feedback •  Chain reaction: intensity grows until gain saturation

4. Threshold on the system size: “Photonic bomb” V. S. Letokhov, Sov. Phys. JETP 26, 835 (1968). with gain Diffusion model 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 ?

5. Mode and coherence properties Random lasers are complex systems: open, highly multimode and nonlinear  What are the mode andcoherence 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).

6. 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:

7. 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

8. 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 ?) • 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  Possibility of ab initio models

9. Outline • 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

10. 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 Typically, on resonance, b0 = 10 – 100 With some efforts: up to b0 ~ 200

11. Radiation trapping in cold atoms Phys. Rev. Lett. 91, 223904 (2003).

12. R wpump wpump wpump Gain with cold atoms Several mechanisms are possible • Raman gain: • Three-level atoms + one pump • 2 photon transition (population inversion between the two ground states) • Hyperfine levels or Zeeman levels • Mollow gain: • Two level atoms + one pump • 3 photon transition (population inversion in the dressed-state basis) Parametric gain: - Two-level atoms + two pumps  Degenerate four-wave mixing (DFWM)

13. 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).

14. Outline • 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

15. Gain   elastic scattering  Saturation   inelastic scattering  Combining gain and scattering ? The scatterers and the amplifiers are the same atoms ! Pumping Gain and scattering do not occur at the same frequency !!!    Is it possible to get enough scattering and gain simultaneously ?

16. = linear gain length = mean free path 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 : Letokhov’s threshold Letokhov’s diffusive model (interference effects are ignored) (sphere geometry)

17. 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).

18. Let’s compare [1] Phys. Rev. Lett. 102, 173903 (2009). [2] Opt. Express 17, 11236 (2009).

19. Let’s compare [1] Phys. Rev. Lett. 102, 173903 (2009). [2] Opt. Express 17, 11236 (2009).

20. 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

21. Raman gain between hyperfine levels with additional scattering

22. 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.

23. Observations 1- Overall increase of fluorescence  Amplified spontaneous emission

24. Observations 1- Overall increase of fluorescence  Amplified spontaneous emission 2- Increase of fluorescence around d = 0  combined effect of gain and multiple scattering

25. 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).

26. 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. 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) ?

28. 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. • Make a beat note with the Raman laser to access the spectrum. • Comparison with theory ? • Random laser in hot vapors ? Closer to astrophysical systems…

29. 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)

30. People currently involved in this project at INLN: Collaborators: • 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) Dmitriy Kupriyanov et al. (St-Petersburg) Stefan Rotter (Vienna) Chong Yidong (Singapour) Past collaborators: R. Carminati (Paris) L. Froufe-Pérez (Madrid) S. Skipetrov et al. (Grenoble) € : ANR, DGA, PACA, CG06, INTERCAN

31. Publications related to this project Mechanisms 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

32. 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).