Transcript Collective atomic recoil laser: an example of classical

Superradiance and Collective Atomic Recoil Laser:
what atoms and fire flies have in common
Claus Zimmermann
Physikalisches Institut der Universität Tübingen
Self-organization
A.-L. Barabási, Nature 403, 849 (2000)
pace maker cells, chirping crickets, fire flies,..
Bènard convection, laser arrays, Josephson junctions, CARL...
economy ...
see for instance S. H. Strogatz, Physica D 143, 1 (2000)
chirping crickets
applause synchronization
milleniums bridge
glow worms
Strogatz, et. al, Nature, 438, 43-44 (2005)
Kuramoto model
• universal coupling (each to all others)
• constant amplitude (implies reservoir)
• different resonances (within a small range)
Experiment: atoms in a resonator-dipole-trap
B. Nagorny et.al., Phys, Rev. A 67, 031401 (R) (2003);
D. Kruse et al., Phys. Rev. A 67, 051802 (R) (2003)
Elastic scattering from a single localized atom
Classical model
Cavity
Atom
Many atoms: instability and self organization
reverse field:
source term
loss
bunching parameter:
(see also: structure factor, Debey Waller factor)
b  e
m
instability:
b  
2ikxm
movie1
First proof of principle: CARL
1. pump cavity from both sides
2. load atoms into the dipole trap
3. atoms are prebunched
4. block the reverse pumping
5. look at the beat signal
6. observe new frequency
atoms
D.Kruse et al. PRL 91, 183601 (2003)
Compare experiment and simulation
time domain:
frequency
domain:
approximate analytic
experession
numerical simulation
experiment
• Interplay between bunching and scattering similar to free electron laser
• Collective atomic recoil laser "CARL" (R.Bonifacio)
Include damping: viscous CARL
1. pump cavity from a single side
2. load atoms into the dipole trap
3. activate optical molasses
4. look at the beat signal
reverse mode starts spontaneously from noise!
D.Kruse et al. PRL 91, 183601 (2003)
Simulation
add a friction term...
...and do the simulation
Threshold behavior observed !
P+(W)
threshold due to balance between friction and diffusion.
Theory: G.R.M. Robb, et al. Phys. Rev. A 69,041403 (R) (2004)
Experiment: Ch. von Cube et al. Phys. Rev. Lett. 93, 083601 (2004)
Focker-Planck Simulation
BEC in a Ringresonator
Ringresonator
L = 85 mm (round trip)
nfsr= 3.5 GHz
w0 = 107 μm
finesse: 87000 (p-polarisation), 6400 (s-polarisation)
Einblicke ins Labor
BEC in a ringcavity
Christoph v. Cube and Sebastian Slama
Rayleigh scattering in the quantum regime
only internal degrees
include center of mass motion
Scattering requires bunching
atom in a momentum eigenstate:
homogeneous distribution: destructive interference in backward direction
atom in a superposition state:
periodic distribution: constructive interference for light with k=Dk/2
Rayleigh scattering is a self organization process
momentum optical dipole
eigenstates
potential
momentum
eigenstates
scattering
more reverse light
deeper dipole
potential
stronger mixing
stronger bunching
enhanced scattering
threshold behavior:
decay due to decoherence
Superradiant Rayleigh scattering
exponential gain for matter waves and optical waves
Inouye et al. Science 285, 571 (1999)
see also Piovella at al. Opt. Comm. 194, 167 (2001)
Two regimes
Bad cavity:
coherence is stored
in the density distribution !
Good cavity:
coherence is stored in the light !
Simulation of good cavity regime
(classical equations)
Resonantly enhanced "end fire modes" of
thermal atoms
BEC atoms (time of flight)
light
experiment
theory
forward
power
• fully classical model
• superradiant peak with several revivals
• same qualitative behavior for BEC and thermal cloud
Varying the atom number
good cavity limit (high finesse)
- - -: N 4/3
..... : N 2
superradiant limit (low finesse)
- - -: N 4/3
..... : N 2
includes mirror
scattering
Future: collective Rabi-oscillations
Excursion: Bragg reflection
setup for Bragg reflection
observed Bragg reflection
Bragg beam resonant with 5p-6p transition (421.7nm)
waist: 0.25 mm, power: 3µW
3000 Bragg planes with 106 atoms total
Reflection angle and lattice constant
quadratic increase with atom number
as expected for coherent scattering
Bragg-interferometer
Observing the phase of Rayleigh scattering
crucial:
Lamb Dicke regime
Bragg enhancement
Sebastian Slama
Gordon Krenz
Simone Bux
Phillipe Courteille
CARL team
Dietmar Kruse
(now Trumpf)
Christoph von Cube
(now Zeiss)
Benjamin Deh
(now Rb-Li-mixture in Tübingen)
Antje Ludewig
(now Amsterdam)
Scattering requires bunching
1. Scattering depends on density distribution
scattered power depends on N2
for homogeneous r no scattering
2. This also holds for a single atom
no scattering if the atom is in a momentum eigenstate:
3. Scattering requires a superposition state
Self organization in the quantum picture
1. classical ensemble
threshold behavior:
diffusion due to heat
2. quantum ensemble
(BEC)
threshold behavior:
decay due to decoherence
Results
temperatur dependence
pump dependence
TOF-Aufnahmen
Parameter
Momentum distribution
experiment:
bimodal distribution
RIR-spectrum of
a thermal distribution
Christoph von Cube
(now Zeiss)
Benjamin Deh
(different projekt in Tübingen)
Antje Ludewig
(now Amsterdam)
Phillipe Courteille
Sebastian Slama
Gordon Krenz
(not on the picture)
Visit us in Tübingen !
Atoms trapped in the modes of a cavity
Running wave mode
atoms don‘t hit the mirror !