1. 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

2. - Dipole-dipole interaction - Landau-Zener transition in frozen pairs of Rydberg atoms : principle - Accurate density measurement of a cold Rydberg gas - Conclusions and prospects Outline Accurate density measurement of a cold Rydberg gas via non-collisional two-body process

3. Dipole-dipole interaction Long range Anisotropic  dipole blockade T. Vogt et al, PRL 99, 083003 (2006)  quantum information : two atoms entanglement A.Gaëtan et al, Nat. Phys. 5, 115 (2009)  resonant inelastic collisions T.F. Gallagher et al, PRA 25, 1905 (1982)  In ultracold gas : energy transfer W.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

4. Rydberg atoms are initially prepared in ns state Detection of np states and characterisation of the production. Electric Field Interatomic distance Atoms pair level energy final pair state np – (n-1)p initial pair state ns - ns Relative distance the atoms moved during a transition << typical distance to the nearest neighbour. Landau-Zener transitions ns ns – np (n-1)p Nd:YAG@532nm 1.0 mJ/pulse

5. F(t) (V/cm) P2 P3P4 Laser excitation x50 x1 ionisation 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 transitions 48s 48s – 47p 48p small slew rate big slew rate

6. Rydberg atoms density measurement Theoretical model Landau-Zener model : Inter-atomic distance (  m) Nearest neighbour distance distribution : Expected value of Landau-Zener transition for one crossing :

7. 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 measurement Experimental parameters

8. Total Rydberg signal (nV.s) signal (nV.s) 75000 experimental points 48p+48s+47p 48p 1/ (V/cm/  s) -1 Total Rydberg signal (nV.s) 48p+48s+47p signal (nV.s) 48p 1 / / (V/cm/ms) -1 Rydberg atoms density measurement Results g = 4.150×10 15 cm -3 /(Vs) σ = 4×10 12 cm -3 /(Vs) s 2 =(0.15) 2 (nVs) 2

9.  Model limitations  denser regime : 3 body contribution  less dense regime : small dF/dt forces  Erlang distribution uniforme 1 body distribution Rydberg atoms density measurement DISCUSSION  Rydberg standard signal: ~15nV.s, i.e. 4.4 10 7 cm -3  Agreement with fluorescence measurements (3S-3P)  The model doesn’t need either the Rydberg gas volume, or the detection efficiency

10.  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