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