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