Resonant dipole-dipole energy transfer from 300 K to 300μK, from gas phase collisions to the frozen...
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Resonant dipole-dipole energy transferfrom 300 K to 300μK, from gas phase collisions to the frozen Rydberg gas
K. A. SafinyaD. S. ThomsonR. C. StonemanM. J. RennW. R. AndersonJ. A. VealeW. LiI. Mourachko
In the gas phase resonant collisional energy transfer is important inBoth 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.
Photon absorptionCharge separation
Energy transfer
A Gedanken Experiment-Resonant Energy Transfer Collisions
Ene
rgy→
A BC
ross
sec
tion→
Resonant Dipole-dipole Collisions of two Na atoms
Safinya et al PRL 1980
t
Populate 17s in an atomic beam
Collisions (fast atoms hit slowones)
Field ramp to ionize 17p
Sweep field over many laser shots
Faster atoms in the beam collide with slower atoms
Observed collisional resonances
What is the crossSection?
What is the width?
Width: 1GHz
Collision rate=Nσv
106s-1=108cm-3σ105cm/s
σ=10-7cm2=109Å2
Compare toGas kinetic cross section 100Å2 collision time 1ps
Atom 1 has many oscillatingDipoles.
17s
15p
18p
16p
17p
μ1
17s-16p dipole produces a fieldat Atom 2 of
E1=μ1/r3 cosωt
Dipole-dipole collision in terms of rf spectroscopy
If E1 drives the 17s-17ptransition in Atom 2 theenergy transfer occurs.
We require μ2E1t=1
131
2 v
bb
v
n
vb
4212 ~
2
2/31
n
v
b
v
t
For n=20Cross section 109 a0
2 10-7cm2
Width 0.2x10-8 1GHz
Collision of atom 1 with atom 2
Measurement of the cross section
Measure the fractional population Transfer as a function of the time and the density of Rydberg atoms.
Observed values of the cross sections and widths
Consider two molecular states ss and pp’
2/2'1'21'
21
pppppp
ssss
Wpp’
Wss
E
W
However, the ss and pp’ states are coupled by the dipole-dipole interaction
1 2, ' 3ss ppV
R
mm=
A molecular approach
When the atoms are infinitely far apartthe energies cross at the resonance field.
At the resonance field the dipole dipole interaction lifts the degeneracy,Creating the superposition states
'
2ss ppy y
y±
±=
R
Ene
rgy
+
-
What are the energies during this collision?
+
-
The system starts in the ss state, a superposition of + and -
Ene
rgy
t
1 23
22 ddV b
mm=
collision
bt
v=
1 22
Areab v
mm@
It ends as pp’ ifthe area is π.
Setting the Area equal to π yields
21 2 bv
mmp s= =
The same result we obtained before.Since μ=n2, we see that
4n
vs =
The velocity, or temperature, dependence of the collisions is at least as interesting as the n dependence
1/2
1
v T
mms
¢= µ
3 3/4
1 1
t v T
mm¢= µ
Cross section
Width
The velocity dependence of collisions of K atoms
Stoneman et al PRL
Experimental Approach
L N2 trap
cell
beam
velocitySelectedBeam T=1K
240 MHz
57 MHz
6 MHz
When the earth’s field is cancelled the 1K resonance is 1.4 MHz wide.
t
What happens if you shorten the time the atoms are allowed to collide?Reduce t
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
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.
Extrapolation to lower temperatures
Cro
ss s
ectio
n (c
m2 )
Temperature (K)
Wid
th (
Hz)
300 K 300 mK 300 μK
10-7
10-5
10-3
105
103
107
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?
Rb 25s+33s→24p+34p energy transfer
Excite 25s 33s with lasers
Tune energies with field
Detect 34p by field ionization
Excitation and Timing
5s
5p
34p
780 nm
480 nm
laser field ramp
t (μs)
0 1 2
34p 33s
33s25s
24p
energy transfer
T
Observed resonances
Rb 25s+33s→24p+34p energy transfer at 109 cm-3
How does this observation compare to the collision picture?
Extrapolation to 300 μK gives
width 5 kHz impact parameter 0.3 mm
0.3 mm
In a MOT at density 109 cm-3
there are 104 closer atoms.(typical interatom spacing10-3 cm)
Other processes occur on microsecond time scales.
10-3cm
In a MOT, where T=300 μKN=109cm-3 Rav= 10-3cm v=20 cm/s
n=30 diameter 10-5cm 1% of Rav
On experimental time scale,1μs, motion 2x10-5 cmThe atoms are effectively frozen. It’s not a collision!
Many body interactions can be more important thanbinary interactions, especially if the atoms are in a lattice.
Observed resonances
Rb 25s+33s→24p+34p energy transfer
There are no collisions,How exactly is the energy transferred?
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.
At the resonance field the dipole dipole interaction lifts the degeneracy,Creating the superposition states
' '
2ss ppy y
y±
±=
R
Ene
rgy 25s33s/24p34ps 25s
s’ 33sp 24pp’ 34p
+
-
R
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.
' '
2ss ppy y
y±
±=
R
Ene
rgy 25s33s/24p34ps 25s
s’ 33sp 24pp’ 34p
+
-
With the pulsed lasers we excite ss’,the coherent superposition of + and – at some internuclear separation R.
2Vdd
Pro
babi
lity
The coherent superposition beats at twice the dipole-dipole frequency,oscillating between ss’ and pp’—a classic quantum beat experiment.
1
0
prob
abili
ty
time
ss’ pp’
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.
prob
abili
ty
time
0.3
0
The widths are density dependent , but they do not match the expectation based on the average spacing.
MhzRav
5.0~3
5 MHz
Essentially the same results were observed by Mourachko et al.
Observed widths > 5 MHz
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% populationtransfer- Anderson, Mourachko
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
Showing the importance of the always resonant processes(2&3) by adding another one (4) 1. 25s+33s→24p+34p 2. 25s+24p→24p+25s3. 33s+34p→34p+33s4. 34s+34p→34p+34s
Showing that other interactions are important Mourachko , Li ..
126
495
925
Explicit observation of many body resonant transfer Gurian et al LAC
In many cases there are clear parallels between the binaryresonant 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