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Matter-wave analogue of an optical random laser

This paper discusses the preparation of disordered potentials for cold atoms and the shaping of localization length in one dimension. It explores the possibility of using correlated disorder as a band-pass filter and presents the concept of a matter-wave analogue of an optical random laser.

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Matter-wave analogue of an optical random laser

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  1. Matter-wave analogue of an optical random laser Marcin Płodzień Jagiellonian University Marian Smoluchowski Institute of Physics Cracow, Poland Cargese, 2014.07.02

  2. Atomic Optics Department. Quantum Gases Group (theory) Jakub Zakrzewski Krzysztof Sacha Omyotti Dutta Mateusz Łącki Jan Major Arkadiusz Kosior Małgorzata Mochol Marcin Płodzień

  3. Outline 0. Motivation 1. Random potential for cold atoms 2. Shaping localization length in 1D 3. Matter-waves analogue of an optical random laser 4. Conclusions

  4. Motivation 1. Can we prepare disordered potential which is „transparent” for narrow band of momenta ?

  5. Random potential for cold atoms „Speckle” Potential experienced by atoms Diffusor Laser beam

  6. Random potential for cold atoms „Speckle” Obtaining localization length (phase formalizm) Diffusor Laser beam

  7. Random potential for cold atoms Localization length (Born approximation) „Speckle” Atom with momentum k undergo multiple scattering and finaly localize. Correlation length σ ~ R-1 Power spectrum Two-point correlation function Light intensity function on a diffusor Diffusor Localization length depends on the aperture. Laser beam Effective „mobility edge”

  8. Shaping localization length in 1D „Speckle” How we can change the power spectrum ? Diffusor Laser beam

  9. Shaping localization length in 1D „Speckle” Let us put an obstacle inside the diffusor. Interference of „two” diffusors. Diffusor How does power spectrum change ? Laser beam M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  10. Shaping localization length in 1D „Speckle” Non-monotonic behaviour of localization length Diffusor Laser beam M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011) M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  11. Shaping localization length in 1D Non-monotonic behaviour of localization length. Below „mobility edge” localization length can exceed the system size. Particles do not localize efficiently. Diffusor Disorder can work as a band-pass filter for momenta. Laser beam M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011) M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  12. Shaping localization length in 1D M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011) M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  13. Shaping localization length in 1D „Speckle” „Speckle” Diffusor Question: Can we prepare disorder in a such way that some atoms remain in the system while other escape ? Laser beam M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  14. BEC evolution in disorder „Speckle” 1. Atoms in ground state of the harmonic trap (Thomas-Fermi density profile with upper cut-off in momenta at mobility edge) 2. Harmonic trap – off/disorder - on 3. First stage - evolution dominated by atom-atom interactions 4. Second stage – density drops, atoms feel only disorder What does the momentum distribution of atoms inside/outside the disorder look like? Diffusor Laser beam M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  15. Momentum distribution Red-detuning Parameters for simulations Disorder size - Disorder size - atoms atoms Born approximation Transfer matrix calculations Evolution Times: a) 2.9 s b) 2 s c) 5.7 s d) 5.7 s Atoms which leave the disorder Fraction of atoms that escaped the disordered region: a) 9% b) 9% c) 20% d) 20% Atoms which remain in the disorder M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  16. Atom laser Standard laser for matter - waves: 1. Accumulation of atoms in the ground state of the trap. (Macroscopic occupation at the begining) 2. Trap determins emitted mode of atoms – counter part of a cavity in optical lasers. 3. Passive medium (no gain) 4. Gradual release of atoms from trapped BEC. M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  17. Atom laser + disorder Standard laser for matter - waves: 1. Accumulation of atoms in the ground state of the trap. (Macroscopic occupation at the begining) 2. Trap determins emitted mode of atoms – counter part of a cavity in optical lasers. 3. Passive medium (no gain) 4. Gradual release of atoms from trapped BEC. 5. Multiple coherent scattering processes determine emited mode Similar mechanism of emitted mode as in an optical random laser „Matter-wave analogue of an optical random laser” BEC + Coherent scattering in disordered medium M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  18. Two dimensions We can shape localization length by changing the aperture M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)

  19. Conclusions 1. Simple modification of an aperture leads to non-monotonic localization length. 2. Properly prepared correlated disorder can work as a band-pass filter. 3. Expanding BEC in such a disorder is a realization of a matter-wave analogue of an optical random laser

  20. Thank you for your attention !

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