accurate density measurement of a cold rydberg gas via non-collisional two-body process anne...
TRANSCRIPT
Accurate density measurement of a cold Rydberg gas via non-collisional
two-body process
Anne Cournol, Jacques Robert, Pierre Pillet, and Nicolas Vanhaecke
EDOM 2011
- Dipole-dipole interaction
- Landau-Zener transition in frozen pairs of Rydberg atoms : principle
- Accurate density measurement of a cold Rydberg gas
- Conclusions and prospects
OutlineAccurate density measurement of a cold Rydberg gas
via non-collisional two-body process
Dipole-dipole interaction
Long range Anisotropic
dipole blockadeT. Vogt et al, PRL 99, 083003 (2006) quantum information : two atoms
entanglementA.Gaëtan et al, Nat. Phys. 5, 115 (2009)
resonant inelastic collisionsT.F. Gallagher et al, PRA 25, 1905 (1982) In ultracold gas : energy transferW.R. Anderson et al, PRL80, 249 (1998)
Pairs energy levels exhibit avoided crossing
Rydberg atoms pair in electric field and dipole-dipole interaction :
1+2
3+4
13 243
04dip dipVr
Rydberg atoms are initially prepared in ns state
Detection of np states and characterisation of the production.
Electric
Field
Interatomic distance
Ato
ms
pa
ir le
vel
en
erg
y
final pair statenp – (n-1)p
initial pair statens - ns
Relative distance the atoms moved during a transition << typical distance to the nearest neighbour .
Landau-Zener transitionsns ns – np (n-1)p
Nd:YAG@532nm 1.0 mJ/pulse
-2 2 4 6 8
20
40
60
80
100
120
F(t) (V/cm)
P2 P3 P4Laser excitation
x50 x1ionisation 48p
ionisation 48s,47p
Temps (μs)
EXPERIMENTAL CONTROL OF THE EFFICIENCY OF NON COLLISIONAL TWO BODY PROCESS
Red and green curves : transitions induced for different slew rates.Experimental points are corrected with the black body radiation absorption.
Landau-Zener transitions48s 48s – 47p 48p
small slew rate
big slew rate
Rydberg atoms density measurementTheoretical model
Landau-Zener model :
F
6
0
( , , ) 1 exp( , )LZ t
t
rP D F r
r D F
12 63
0 20
2 48 48 48 47 ( )( , )
(4 )tt
s p s p fr D F
D F
Inter-atomic distance (mm)
Nearest neighbour distance distribution :
Expected value of Landau-Zener transition for one crossing :2
2
,0 0 0
' ( , ) ( , , ) sin( )t
LZ tD Fss pp r P r D F d d r dr
34
( , ) exp3
r r
48p atoms number produced in the experimental volume V is :
The measured 48p state signal is fitted by :
Introducing a detection efficiency parameter g :
Rydberg atoms density measurementExperimental parameters
148 48 48 47
2V s s p p
48 48 47 1T p s pS S S S g
48 148 48 48 47
2T
p T
gSS S s s p p
Total Rydberg signal (nV.s)
sig
nal (
nV.
s)
75000 experimental points48p+48s+47p
48p
1/ (V/cm/ms) -1
Total Rydberg signal (nV.s)48p+48s+47p
s
igna
l (n
V.s)
48p
1 / / (V/cm/ms)-1
Rydberg atoms density measurementResults
TgS 48 148 48 48 47
2T
p T
gSS S s s p p
g = 4.150×1015 cm-3/(Vs)
σ = 4×1012 cm-3/(Vs) s2 =(0.15)2 (nVs)2
Model limitations
denser regime : 3 body contribution
less dense regime : small dF/dt forces
Erlang distribution uniforme 1 body distribution
Rydberg atoms density measurementDISCUSSION
Rydberg standard signal: ~15nV.s, i.e. 4.4 107 cm-3
Agreement with fluorescence measurements (3S-3P)
The model doesn’t need either the Rydberg gas volume, or the detection efficiency
Nearest neighbour distribution probe
Accurate and direct Rydberg atoms density measurement without the knowledge either of the volume or the detector efficiency
Conclusions and Prospects
Detection process calibration (ionisation, collection, conversion)
Applications : cold Rydberg gas, cold plasmas
Test on three body effects
In dipole blockade regime : - two-body distribution - anisotropy