1. Resonant dipole-dipole energy transfer from 300 K to 300μK, from gas phase collisions to the frozen Rydberg gas K. A. Safinya D. S. Thomson R. C. Stoneman M. J. Renn W. R. Anderson J. A. Veale W. Li I. Mourachko

4. In the gas phase resonant collisional energy transfer is important in Both the HeNe laser and the CO 2 laser. However, it is difficult to study it In a systematic way. Of course, there are not ArNe, KrNe, or XeNe, lasers. There is evidently something special about the combination of He and Ne, the resonant energy transfer from the metastable states of He to Ne. In solid state lasers resonant energy transfer is important, and it is the basis for light harvesting systems. Photon absorption Charge separation Energy transfer

5. A Gedanken Experiment- Resonant Energy Transfer Collisions Energy→ A B Cross section→

6. Resonant Dipole-dipole Collisions of two Na atoms Safinya et al PRL 1980 t Populate 17s in an atomic beam Collisions (fast atoms hit slow ones) Field ramp to ionize 17p Sweep field over many laser shots

7. Faster atoms in the beam collide with slower atoms

8. Observed collisional resonances What is the cross Section? What is the width? Width: 1GHz Collision rate=Nσv 10 6 s -1 =10 8 cm -3 σ10 5 cm/s σ=10 -7 cm 2 =10 9 Å 2 Compare to Gas kinetic cross section 100Å 2 collision time 1ps

9. Atom 1 has many oscillating Dipoles. 17s 15p 18p 16p 17p μ1μ1 17s-16p dipole produces a field at Atom 2 of E 1 =μ 1 /r 3 cosωt Dipole-dipole collision in terms of rf spectroscopy

10. If E 1 drives the 17s-17p transition in Atom 2 the energy transfer occurs. We require μ 2 E 1 t=1 For n=20 Cross section 10 9 a 0 2 10 -7 cm 2 Width 0.2x10 -8 1GHz Collision of atom 1 with atom 2

11. Measurement of the cross section Measure the fractional population Transfer as a function of the time and the density of Rydberg atoms.

12. Observed values of the cross sections and widths

13. Consider two molecular states ss and pp’ W pp’ W ss E W However, the ss and pp’ states are coupled by the dipole-dipole interaction A molecular approach When the atoms are infinitely far apart the energies cross at the resonance field.

14. At the resonance field the dipole dipole interaction lifts the degeneracy, Creating the superposition states R Energy + -

15. What are the energies during this collision? + - The system starts in the ss state, a superposition of + and - Energy t It ends as pp’ if the area is π.

16. Setting the Area equal to π yields The same result we obtained before. Since μ=n 2, we see that

17. The velocity, or temperature, dependence of the collisions is at least as interesting as the n dependence Cross section Width

18. The velocity dependence of collisions of K atoms Stoneman et al PRL

19. Experimental Approach L N 2 trap

20. cell beam velocity Selected Beam T=1K 240 MHz 57 MHz 6 MHz When the earth’s field is cancelled the 1K resonance is 1.4 MHz wide.

21. t What happens if you shorten the time the atoms are allowed to collide? Reduce t

22. Thomson et al PRL Shorter exposure times lead to transform broadening. 0.2 μs 0.5 μs 1.0 μs 2.0 μs 3.0 μs 5.0 MHz 3.8 MHz 2.4 MHz 2.0 MHz 1.4 MHz

23. A timing sequence which leads to 1 MHz wide collisional resonances Individual collisions 0 3 time (μs) detection pulse We do not know when each collision started and ended. If we move the detection pulse earlier 0 3 time (μs) detection pulse we can transform the resonance and know when the collision started And stopped.

24. Extrapolation to lower temperatures Cross section (cm 2 ) Temperature (K) Width (Hz) 300 K 300 mK 300 μK 10 -7 10 -5 10 -3 10 5 10 3 10 7

25. At 300 μK the width should be 1 kHz, and the cross section 10 -3 cm 2. The impact parameter is thus about 0.3 mm. What actually happens in a MOT?

26. Rb 25s+33s→24p+34p energy transfer Excite 25s 33s with lasers Tune energies with field Detect 34p by field ionization

28. Excitation and Timing 5s 5p 34p 780 nm 480 nm laser field ramp t (μs) 0 1 2 34p 33s 33s 25s 24p energy transfer T

29. Observed resonances Rb 25s+33s→24p+34p energy transfer at 10 9 cm -3 How does this observation compare to the collision picture?

30. Extrapolation to 300 μK gives width 5 kHz impact parameter 0.3 mm 0.3 mm In a MOT at density 10 9 cm -3 there are 10 4 closer atoms. (typical interatom spacing 10 -3 cm) Other processes occur on microsecond time scales.

31. 10 -3 cm In a MOT, where T=300 μK N=10 9 cm -3 R av = 10 -3 cm v=20 cm/s n=30 diameter 10 -5 cm 1% of R av On experimental time scale,1μs, motion 2x10 -5 cm The atoms are effectively frozen. It’s not a collision! Many body interactions can be more important than binary interactions, especially if the atoms are in a lattice.

32. Observed resonances Rb 25s+33s→24p+34p energy transfer There are no collisions, How exactly is the energy transferred?

33. In a random gas most of the observed effect is due to the nearest neighbor atom. It is similar to the binary collision problem except that we excite the atoms when They are close together and they do not move.

34. At the resonance field the dipole dipole interaction lifts the degeneracy, Creating the superposition states R Energy 25s33s/24p34p s 25s s’ 33s p 24p p’ 34p + - R

35. In the collision problem we excited the ss’ state, the superposition of + and – and observed the evolution over the collision. Maximum population transfer occurs when the area is π. t Everything happens here, for example. + - Excite ss’ In the frozen gas we excite the atoms when they are close together, and they do not move.

36. R Energy 25s33s/24p34p s 25s s’ 33s p 24p p’ 34p + - With the pulsed lasers we excite ss’, the coherent superposition of + and – at some internuclear separation R. 2V dd

37. Probability The coherent superposition beats at twice the dipole-dipole frequency, oscillating between ss’ and pp’—a classic quantum beat experiment. 1 0 probability time ss’ pp’

38. All pairs are not at the same internuclear spacing, so the beats wash out, with a result which looks like a saturation curve for the pp’ population. probability time 0.3 0

39. The widths are density dependent, but they do not match the expectation based on the average spacing. 5 MHz Essentially the same results were observed by Mourachko et al. Observed widths > 5 MHz

40. The discrepancy between the calculated and observed widths is due to two factors. There is a distribution of spacings, and pairs of atoms which are close together are responsible for most of the population transfer--Robicheaux and Sun More than two atoms interact at once. There are not enough close pairs to account for the observed for 20% population transfer- Anderson, Mourachko

41. Introduction of the always resonant processes(2&3) s s’ p p’ 1. 25s+33s→24p+34p s,s’ 2. 25s+24p→24p+25sp,p’ 3. 33s+34p→34p+33s Interactions 2 and 3 broaden the final state in a multi atom system. Akulin, Celli

42. Showing the importance of the always resonant processes(2&3) by adding another one (4) 1. 25s+33s→24p+34p 2. 25s+24p→24p+25s 3. 33s+34p→34p+33s 4. 34s+34p→34p+34s

43. Showing that other interactions are important Mourachko, Li.. 126 495 925

46. Explicit observation of many body resonant transfer Gurian et al LAC

49. In many cases there are clear parallels between the binary resonant collisions observed at high temperatures and energy transfer in the frozen Rydberg gas. Many body effects are likely to be enhanced in ordered samples. The dipole-dipole interactions imply forces, leading to motion, and often ionization, of the atoms