Resonant dipole-dipole energy transfer

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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
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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
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A Gedanken Experiment- Resonant Energy Transfer
Collisions
Energy?
Cross section?
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Resonant Dipole-dipole Collisions of two Na atoms

t
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
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Faster atoms in the beam collide with slower
atoms
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Observed collisional resonances
What is the cross Section? What is the
width? Width 1GHz Collision
rateNsv 106s-1108cm-3s105cm/s s10-7cm2109Å2
Compare to Gas kinetic cross section 100Å2
collision time 1ps
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Dipole-dipole collision in terms of rf
spectroscopy
Atom 1 has many oscillating Dipoles.
18p
17p
17s-16p dipole produces a field at Atom 2
of E1µ1/r3 cos?t
17s
µ1
16p
15p
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Collision of atom 1 with atom 2
If E1 drives the 17s-17p transition in Atom 2
the energy transfer occurs. We require µ2E1t1
For n20 Cross section 109 a02
10-7cm2 Width 0.2x10-8
1GHz
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Measurement of the cross section
Measure the fractional population Transfer as a
function of the time and the density of Rydberg
atoms.
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Observed values of the cross sections and widths
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A molecular approach
Consider two molecular states ss and pp
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
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At the resonance field the dipole dipole
interaction lifts the degeneracy, Creating the
superposition states

Energy
-
R
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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 p.

Energy
-
t
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Setting the Area equal to p yields
The same result we obtained before. Since µn2,
we see that
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The velocity, or temperature, dependence of the
collisions is at least as interesting as the n
dependence
Cross section
Width
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The velocity dependence of collisions of K atoms
Stoneman et al PRL
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Experimental Approach
L N2 trap
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cell beam velocity Selected Beam T1K
240 MHz 57 MHz 6 MHz
When the earths field is cancelled the 1K
resonance is 1.4 MHz wide.
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What happens if you shorten the time the atoms
are allowed to collide? Reduce t
t
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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
Thomson et al PRL
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A timing sequence which leads to 1 MHz wide
collisional resonances
Individual collisions
We do not know when each collision started and
ended. If we move the detection pulse earlier
detection pulse
0
3 time (µs)
we can transform the resonance and know when the
collision started And stopped.
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Extrapolation to lower temperatures
107
10-3
Width (Hz)
10-5
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Cross section (cm2)
103
10-7
300 K 300 mK
300 µK
Temperature (K)
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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?
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Rb 25s33s?24p34p energy transfer
Excite 25s 33s with lasers Tune energies with
field Detect 34p by field ionization
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Excitation and Timing
34p
energy transfer
33s
25s
field ramp
laser
24p
T
480 nm
5p
0 1 2
t (µs)
34p 33s
780 nm
5s
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Observed resonances
Rb 25s33s?24p34p energy transfer at 109 cm-3
How does this observation compare to the
collision picture?
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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
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In a MOT, where T300 µK N109cm-3 Rav
10-3cm v20 cm/s
10-3cm
n30 diameter 10-5cm 1 of Rav On
experimental time scale,1µs, motion 2x10-5
cm The atoms are effectively frozen. Its not a
collision! Many body interactions can be more
important than binary interactions, especially if
the atoms are in a lattice.
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Observed resonances
Rb 25s33s?24p34p energy transfer
There are no collisions, How exactly is the
energy transferred?
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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.
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At the resonance field the dipole dipole
interaction lifts the degeneracy, Creating the
superposition states
R

25s33s/24p34p
s 25s s 33s p 24p p 34p
-
Energy
R
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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 p.

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.
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With the pulsed lasers we excite ss, the
coherent superposition of and at some
internuclear separation R.

2Vdd
25s33s/24p34p
s 25s s 33s p 24p p 34p
-
Energy
R
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The coherent superposition beats at twice the
dipole-dipole frequency, oscillating between ss
and ppa classic quantum beat experiment.
ss pp
1
probability
Probability
0
time
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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
0
time
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The widths are density dependent , but they do
not match the expectation based on the average
spacing.
5 MHz
Observed widths gt 5 MHz
Essentially the same results were observed by
Mourachko et al.
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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
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Introduction of the always resonant
processes(23) s s p p 1.
25s33s?24p34p s,s 2. 25s24p?24p25s p,p 3.
33s34p?34p33s
Interactions 2 and 3 broaden the final state in
a multi atom system. Akulin, Celli
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Showing the importance of the always resonant
processes(23) by adding another one (4) 1.
25s33s?24p34p 2. 25s24p?24p25s 3.
33s34p?34p33s 4. 34s34p?34p34s
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Showing that other interactions are important
Mourachko , Li ..
925
126
495
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Explicit observation of many body resonant
transfer Gurian et al LAC
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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