Hollow beams for cold atom manipulation Fabienne DIRY Michaël Mestre, Bruno Viaris de Lesegno, Laurence Pruvost Laboratoire Aimé Cotton Orsay FRANCE
EGC 2008 Gif‐sur‐Yvette 2 July 2008 1
Goals To manipulate cold atoms with shaped laser beams • • •
Technique : shape laser by holography (device : Spatial Light Modulator) To apply them to cold atoms : non harmonic traps, original shaped traps… Application : guiding of atoms in a Laguerre Gaussian beam (hollow beam)
Why do we use hollow beams? |e>
|f>
δ>0
Dipolar Force :
δ
|f>
δ>0
r r ∇I F ∝−
Dipolar Force :
δ0 : Spontaneous emission rate
η∝
I (r )
I (r )
δ
δ2
Dark Regions : I= 0 η=0 No Spontaneous emission in these regions
Hollow beams are interesting if δ>0 : No dissipation and heating due to spontaneous emission
Holography The laser is diffracted by the hologram. We observe the diffraction pattern in the focal plane of a lens Diffraction pattern : Fourier Transform of the hologram Hologram Initial Light Field E
Modified Light Field
Lens
Focal Plane
Diffraction Pattern
E’
To see the desired intensity profile, we must choose the good hologram 7
The hologram : a SLM Spatial Light Modulator (SLM) : Programmable optical element which changes the intensity and/or the phase of a light field 1. 2.
Phase hologram : no losses of power Computer generated hologram : we can change the hologram (and so the intensity profile) dynamically. SLM Initial Light Field
Modified Light Field
Lens
Focal Plane
Field proportional to Fourier Transform of E’
E’
E
1)
2)
Iterative Computer addressing
Algorithms (FFT) Phase Hologram
Diffraction pattern 1) experimental 2) desired
8
Our SLM : Hamamatsu X8267
V
ITO electrode
ITO electrode ne
Addressing laser diode
no
Titanium Sapphire Laser
1. The photoconductor absorbs light from the adressing laser diode 2. An electric field is created 3. Molecules change their orientations 4. Birefringence is created
Photoconductor
Dielectric mirror
Technical informations : 768*768 1 pixel = 26µm
Liquid crystals
5. The phase of the laser is modified
9
A sort of hollow beams : k Laguerre Gauss (LG0 )
10
Properties of LGs phase and intensity • •
Analytical hologram : helical phase k : topological charge : number of sectors in the holograms
ϕ = kθ , k ∈ Ν * 0
2k
⎛r⎞ I (r ) = A(r ) ∝ ⎜ ⎟ e ⎝ω ⎠ 2
2π
⎛ r2 −⎜⎜ 2 ⎝ω
⎞ ⎟ ⎟ ⎠
LG01
TF
11
Differents orders of LG beams ϕ = kθ , k ∈ Ν * Holograms
Holograms with shifter
Images of LG0k near focal plane
LG02
LG04
LG06
LG08
12
Combination of holograms LG0k
Shifter
+
=
+ LG0k
=
Seperate the LG (1st order) from the 0th order :
Mode cleaning
De-focus by a lens :
Control of the diameter
Lens 13
LG01
I (r ) ∝ r
2
LG01 14
LG03
I (r ) ∝ r
6
LG03 15
LG08
I (r ) ∝ r
16
LG08 16
LG08
I (r ) ∝ r
16
17
Summary : intensity and diameter of LG beams Theory k
D(k ) ∝ k
D Imax
D(k ) ∝ k
I max Experiment
k ∝ exp(−k ) k!
I max ∝ − k
0.6
Max Intensities of LG beams
Diameter of LG beams (with f=500mm projecting lens) Position : +25 mm from F’
(with f=500 mm projecting lens) in arbitrary units
650
550
40000
500
35000
450 400 350 300
experimental data k^0,6 k^0,5
250
Maximal intensity
Diameter of LG (µm)
experiment theory corrected by diffraction efficiency
45000
600
30000 25000 20000 15000
200 0
2
4
6
k
8
10
10000 0
2
4
k
6
8
10
18
Guiding of cold atoms
19
The SLM in the Atom Optics Experiment Atom cloud Detection laser
87Rb
T = 20µK
1. Adress the SLM by a computer generated hologram
IMAGE 2. Consequence : Change the beam profile
P~ 0,5 W λ=780nm
3. Preloading atoms in Titanium-Sapphire laser
δ~+20_500 GHz
4. Free fall (laser on)
Titanium sapphire laser
Computer addressing
SLM
5. Consequence : The balistic expansion of the atoms is modified 6. Image at 1 cm below the initial atomic cloud 20
Guiding of cold atoms Atom cloud Detection laser
Atoms in free fall
Atoms are guided
Titanium sapphire laser SLM Computer adressing
Guiding efficiency : 22% 21
Experimental results Study of guiding efficiency versus k and δ
Size of atom cloud : 1 mm Size of LG beams : between 200 and 600 µm according to k
• When k increases, there are more caught atoms: the overlap between the guide and the atom cloud is better. However, guiding efficiency saturates for higher k. • When δ increases, the number of a caught atoms increases a little bit : potential barriers are higher 22
The diffraction efficiency of the SLM Efficiency : 75% without lens with a 5 meters lens 300*(1-0,3*(k-1)/11)
Light power in the LG beams (mW)
300 280
• When k increases, the power in the LG beams decreases PLG012 = 70% * PLG01 only
260 240
P(k) = P(1)*(1-0,3*(k-1)/11)
220 200
• When we add a lens, the power in the LG decreases too.
180 160 0
2
4
6
8
Order of LG
10
12
PLG + 5 meters lens ~70% * PLG without lens
The diffraction efficiency of the SLM depends on the hologram
Capture : Model Nomber of atoms caught in the guide at t=0 : Integral of the probability density in phase space
C=∫
rmax
0
2π r dr ∫
v max
0
W(r, v)2π vdv
W(r,v) : normalized gaussian functions of position and motion of the atom cloud
limited by the guide whose 2D potential is
1 ⎛ 2r 2 ⎜⎜ 2 U(r) ∝ k! ⎝ ω
k ⎛ − 2r ⎞ ⎟⎟ .Exp ⎜⎜ 2 ω ⎝ ⎠
2
⎞ ⎟⎟ ⎠
We study this integral versus 2 dimensionless parameters : a=w2/4σ02 (spatial overlap) and b= U0/kBT (energy overlap) Here ω : waist of the laser σ0 and T : size and temperature of the atoms U0 : Umax of the gaussian beam with the same waist
24
Results • Here « a » (spatial overlap) is constant and a= 0.0375 (LG with a 5 meters lens) • A curve = an experimental detuning (we change the value of « b », energy overlap) Capture efficiency (non-corrected power)
Capture efficiency (corrected power)
We find similar changes as experimental results if we consider the diffraction efficiency of the SLM
Prospects
26
To make different types of hollow beams Non symmetrical Hologram Box for atoms, To study dynamic of atoms inside a square of light
Square
Hologram with dislocation Applications : To trap atoms inside a LG and open it….
« open » LG
27
Conclusion • SLM tools to shape laser beams (advantages : phase modulation and computer generated holograms) • Laguerre Gaussian beams allow us to guid atoms and to understand the guiding efficiency versus the order of LG and the detuning of the laser • Today, other types of hollow beams are made in order to do other experiments (box…) Collaboration with E.Charron (LPPM Orsay)
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