Download Laser beam Diffusor Correlation length

Matter-wave analogue of an optical
random laser
Marcin Płodzień
Jagiellonian University
Marian Smoluchowski
Institute of Physics
Cracow, Poland
Cargese, 2014.07.02
Atomic Optics Department. Quantum Gases Group (theory)
Jakub Zakrzewski
Omyotti Dutta
Małgorzata Mochol
Krzysztof Sacha
Mateusz Łącki
Arkadiusz Kosior
Jan Major
Marcin P
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
Motivation
1. Can we prepare disordered potential which is
„transparent” for narrow band of momenta ?
Random potential for cold atoms
„Speckle”
Potential experienced by atoms
Diffusor
Laser beam
Random potential for cold atoms
„Speckle”
Diffusor
Laser beam
Obtaining localization length (phase formalizm
Random potential for cold atoms
„Speckle”
Atom with momentum
k undergo multiple scattering
and finaly localize.
Localization length
(Born approximation)
Correlation length σ ~ R-1
Two-point correlation function
Power spectrum
Light intensity function
on a diffusor
Diffusor
Laser beam
Localization length depends
on the aperture.
Effective „mobility edge”
Shaping localization length in 1D
„Speckle”
How we can change
the power spectrum ?
Diffusor
Laser beam
Shaping localization length in 1D
„Speckle”
Let us put an obstacle
inside the diffusor.
Diffusor
Laser beam
Interference of „two”
diffusors.
How does power spectrum change ?
M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)
Shaping localization length in 1D
„Speckle”
Non-monotonic behaviour
of localization length
Diffusor
Laser beam
M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)
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
Laser beam
M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)
Disorder can work
as a band-pass filter
for momenta.
Shaping localization length in 1D
M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)
Shaping localization length in 1D
„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)
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
Diffusor
Laser beam
M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)
What does the momentum
distribution of atoms
inside/outside the disorder
look like?
Momentum distribution
Parameters for simulations
Disorder size atoms
Red-detuning
Born approximation
Transfer matrix
calculations
Evolution Times:
a) 2.9 s
b) 2 s
c) 5.7 s
d) 5.7 s
Fraction of atoms
that escaped the
disordered region:
a) 9% b) 9%
c) 20% d) 20%
M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)
Atoms which
leave the disorder
Atoms which remain
in the disorder
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)
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)
Two dimensions
We can shape localization
length by changing the aperture
M. Płodzień, K. Sacha, Phys. Rev. A, 023624 (2011)
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
Thank you for your attention !