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

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

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

Faster atoms in the beam collide with slower atoms

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

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

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 a02 10-7cm2 Width 0.2x10-8 1GHz

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

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

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

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

Setting the Area equal to π yields The same result we obtained before. Since μ=n2, we see that

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

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

Experimental Approach L N2 trap

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.

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

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

A timing sequence which leads to 1 MHz wide collisional resonances 0 3 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 0 3 time (μs) we can transform the resonance and know when the collision started And stopped.

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

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 34p energy transfer 33s 25s field ramp laser 24p 480 nm 5p 0 1 2 t (μs) 34p 33s 780 nm 5s

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 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

In a MOT, where T=300 μK N=109cm-3 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.

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

+ - 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

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

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

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.

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

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+25s 3. 33s+34p→34p+33s 4. 34s+34p→34p+34s

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

Explicit observation of many body resonant transfer Gurian et al LAC

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