Accurate density measurement of a cold Rydberg gas via non- collisional two-body process

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. OutlineAccuratedensitymeasurement of a cold Rydberg gas via non-collisionaltwo-body process - Dipole-dipole interaction - Landau-Zener transition in frozen pairs of Rydberg atoms : principle - Accuratedensitymeasurement of a cold Rydberg gas - Conclusions and prospects

3. Dipole-dipole interaction Pairs energylevelsexhibitavoidedcrossing Long range Anisotropic • 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) • dipole blockade T. Vogt et al, PRL 99, 083003 (2006) • quantum information : two atoms entanglement A.Gaëtan et al, Nat. Phys. 5, 115 (2009) Rydberg atoms pair in electricfield and dipole-dipole interaction : 1+2 3+4

4. Landau-Zener transitionsns ns – np (n-1)p initial pair state ns - ns Relative distance the atomsmovedduring a transition << typical distance to the nearestneighbour . Atoms pair levelenergy Electric Field Nd:YAG@532nm 1.0 mJ/pulse Interatomic distance Rydberg atoms are initiallyprepared in ns state final pair state np – (n-1)p Detection of npstates and characterisation of the production.

5. ionisation48s,47p ionisation48p Landau-Zener transitions48s 48s – 47p 48p smallslew rate F(t) (V/cm) Red and green curves : transitions induced for differentslew rates. Experimental points are correctedwith the black body radiation absorption. bigslew rate x50 x1 Temps (μs) P3 P4 P2 Laser excitation EXPERIMENTAL CONTROL OF THE EFFICIENCY OF NON COLLISIONAL TWO BODY PROCESS

6. Rydberg atomsdensitymeasurementTheoretical model Nearest neighbour distance distribution : Landau-Zener model : Expected value of Landau-Zener transition for one crossing : Inter-atomic distance (mm)

7. Rydberg atomsdensitymeasurementExperimentalparameters 48p atoms number produced in the experimental volume V is : Introducing a detection efficiency parameter g : The measured 48p state signal is fitted by :

8. Total Rydberg signal (nV.s) Total Rydberg signal (nV.s) 48p+48s+47p 48p signal (nV.s) signal (nV.s) 1 / / (V/cm/ms)-1 1/ (V/cm/ms)-1 Rydberg atomsdensitymeasurementResults 48p+48s+47p 75000 experimental points 48p g= 4.150×1015 cm-3/(Vs) σ = 4×1012 cm-3/(Vs) s2 =(0.15)2 (nVs)2

9. Rydberg atomsdensitymeasurementDISCUSSION • 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 • Model limitations • denser regime : 3 body contribution • less dense regime : small dF/dt forces • Erlang distribution uniforme 1 body distribution

10. Conclusions and Prospects • Nearest neighbour distribution probe • Accurate and directRydberg atoms density measurement without • the knowledge either of the volume or the detector efficiency • 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