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

3. copy

4. In the gas phase resonant collisional energy transfer is important in
Both the HeNe laser and the CO2 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.
Energy transfer
Photon absorption
Charge separation

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

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

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
106s-1=108cm-3σ105cm/s
σ=10-7cm2=109Å2
Compare to
Gas kinetic cross section 100Å2 collision time 1ps

9. Dipole-dipole collision in terms of rf spectroscopy
Atom 1 has many oscillating
Dipoles.
18p
17p
17s
17s-16p dipole produces a field
at Atom 2 of
E1=μ1/r3 cosωt μ1
16p
15p

10. Collision of atom 1 with atom 2
If E1 drives the 17s-17p
transition in Atom 2 the
energy transfer occurs.
We require μ2E1t=1
For n=20
Cross section 109 a cm2
Width x GHz

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

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

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

16. Setting the Area equal to π yields
The same result we obtained before.
Since μ=n2, 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 N2
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. What happens if you shorten the time the atoms are allowed to collide?
Reduce t t

22. Shorter exposure times lead to transform broadening.
5.0 MHz
3.8 MHz
2.4 MHz
2.0 MHz
1.4 MHz
Thomson et al PRL

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

24. Extrapolation to lower temperatures
10-3
107
Width (Hz)
Cross section (cm2)
10-5
105
10-7
103
300 K mK μK
Temperature (K)

25. At 300 μK the width should be 1 kHz, and the cross section 10-3 cm2.
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 34p energy transfer 33s 25s field ramp laser 24p
480 nm 5p
t (μs)
34p 33s
780 nm 5s

29. Observed resonances
Rb 25s+33s→24p+34p energy transfer at 109 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
In a MOT at density 109 cm-3
there are 104 closer atoms.
(typical interatom spacing
10-3 cm)
Other processes occur on
microsecond time scales.
0.3 mm

31. In a MOT, where T=300 μK
N=109cm Rav= 10-3cm v=20 cm/s
10-3cm
n=30 diameter 10-5cm 1% of Rav
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 +
s 25s
s’ 33s
p 24p
p’ 34p
25s33s/24p34p
Energy - 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. +
Excite ss’ -
Everything happens here,
for example. t
In the frozen gas we excite the atoms when
they are close together, and they do not move.

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

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

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.
0.3
probability
time

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

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+25s p,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 ..
925
126
495

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