Cold Metastable Neon Atoms

Cold Metastable Neon Atoms Towards Degenerated Ne*- Ensembles Supported by the DFG Schwerpunktprogramm SPP 1116 and the European Research Training Network „Cold Quantum Gases“

Peter Spoden, Martin Zinner, Norbert Herschbach, Wouter van Drunen Gerhard Birkl and W.E.

Institut für Quantenoptik

Outline 3D 3

• Metastable neon

3P 2

• 3P2-Lifetime

2p6

τ2

• Elastic collisions and scattering length

• Evaporative cooling

Population

• Inelastic collisions and their suppression RF-knife (η=E/kT)

• Outlook E n e rg y

Neon Naturally occurring Neon-Isotopes Mass

3D

3p[5/2]3

Abundance [%] Nuclear Spin

20

90.48

0

21

0.27

3/2

22

9.25

0

3

1P 1

3s’[1/2]1

3P 0

3s’[1/2]0

E1 640 nm

3P 1

3P 2

3s[3/2]1

3s[3/2]2 τ2 = ? M2 16.6 eV

1S 0

2p6

J =0

J =1

J =2

J =3

• Laser-cooling parameters: Wavelength

640 nm

Doppler limit

200 µK

Recoil limit

2.3 µK

Penning-Ionization:

Ne*+Ne*

Ne+ + Ne + e-

From atomic physics to BEC Atomic physics • Lifetime of the metastable state: ?

640 nm

16,6 eV

M. Zinner et al., PRA 67, 010501(R) (2003)

Collision physics • Rates of elastic and inelastic collisions • Suppression of Penning-Ionization by spinpolarization: 104 ?

Electronic Detection • Direct, highly efficient detection of Ne* and Ne+ • Real-time detection of ions • Spatially resolved detection of atoms

Bose-Einstein-Condensation • Investigation of collective excitations • Measurement of higher order correlation functions

thermal BEC

From atomic physics to BEC Atomic physics • Lifetime of the metastable state: ?

640 nm

16,6 eV





thermal BEC

Experimental Setup

Lifetime of the metastable state 3D

After Loading the MOT

3

3p[5/2]3 1P 1

3s’[1/2]1

3P 0

3s’[1/2]0

E1 640 nm

3P 1

3P 2

3s[3/2]1

τ2

1S 0

3s[3/2]2 M2 16.6 eV

2p6

J =0

J =1

J =2

J =3

observation of decay by fluorescence

Fluorescence of 20Ne in a MOT 3D 3

• MOT decay

excitation 47% α-1 = 21.7 s

2 N N& = − α N − β Veff

π2 π3 α= + ττ2 τ 3 2

radiative decay

+γ⋅p background collisions

1000000

τ2 Fluorescence [au]

• Origins of one-body losses

3P 2

2p6

100000

10000

1000

+ α FT

excitation 0.5% α-1 = 14.4 s

finite trap depth

• population of 3P2-state: π2 • population of 3D3-state: π3

100 0

20

40

60

80

time of MOT decay [s]

100

120

π3 π2

Background gas collisions: γ⋅p • Pressure dependency of MOT decay background gas collisions 7 -1 -1 γ = 5.2(1)*10 mbar s

0,14

• Offset of pressure gauge: 4(7) 10-12 mbar • Ionization processes: Ne* + X = Ne + X+ + e-

0,12

• Ion signal on MCP: = c1(p) N(t) + c2 N²(t)

0,10 1,0 0,9 0,8

0,08

background gas collision rate -11 1/640s @ p=3 10 mbar

c1 [arb. units]

-1

α [s ]

Rion(t)

0,7 0,6 0,5 0,4 0,3 0,2 0,1

0,06 0

25

50

75

100

125

0,0 0

-11

pdisplay [10

mbar]

1

2

3

4

5

6

7

8

9

pdisplay [10-11mbar]

10

11

12

Influence of finite trap depth 0,35

• For an infinitely large MOT:

π3 = 0.016

0,30

escape velocity become infinite

• therefore: let the gradient B‘ approach zero!

α [s-1]

trap depth and 0,08 0,07 0,06 0,05 0

20

40 60 Gradient [G/cm]

80

• In practice: Trap depth remains finite due to finite size of laser beams

• No significant dependency of α on B’ • No correction needed for low excitation measurements

100

τ2

of the metastable 3P2-state

0,07

14.3

0,06

16.7

0,05

20.0

0,04 0,0

αp=0-1 [s]

αp=0 [s-1]

Lifetime

25.0 0,1

0,2

0,3

0,4

0,5

Population in 3D3-state (π3)

Error budget:

thus:

measured α p=0 extrapolation π=0 extrapolation α(p=0, π=0)

τ2

0.06918(51) s-1 - 0.00156(37) s-1 + 0.00028(13) s-1 0.06790(64) s-1

14.73(14) s

From atomic physics to BEC Atomic physics • Lifetime of the metastable state: 14.73(14)s

640 nm

16,6 eV





thermal BEC

Preparation of spin-polarized atoms

Preparation of Magnetically Trapped Atoms Sequence

Beam collimation and slowing

MOT loading 400 ms

Compressed spin MOT polarization σr=1.3mm

N=6x108

78% in mJ=+2

+2 +1

0

-1 -2

0 µs

2 µs

4 µs

Doppler Cooling PSD = 4.5x10-7 axial: ~200 µK radial: ~450 µK

Transfer to MT and adiabatic compression B0= 25 G N = 3x108

8 µs

Stern-Gerlach Experiment

Doppler-cooling in the magnetic trap • σ+-σ+- irradiation in axial direction of magnetic trap

Taxial

2000

Tradial

T [µK]

1500

1000

500

Axial: Doppler cooling Radial: cooling by reabsorption

• Optimized parameters: ∆ = -0.5 Γ I = 5x10-3 Isat

• 50-fold gain in phase space density

TDoppler = 196 µK 0 0

500

1000

t [ms]

1500

2000

Elastic collisions

Cross-dimensional Relaxation 22 Ne

• Kinetic energy is not in equilibrium after Doppler-cooling T [µK]

700

• Aspect ratio of the cloud changes

600

T axial

500

T radial

σ ax A= σ rad

T 400 0

1

2

3

4

5

t* [s] 1,4

A

1,2

• Determination of the relaxation rate

A& = γ rel ( A(t) − Aeq )

1,0

Mean density: 9 -3 2.9 10 cm 9 -3 6.4 10 cm 10 -3 1.3 10 cm

0,8

0

1

2

3

t* [s]

4

5

Cross-dimensional Relaxation 2.5

22Ne

• Description of the relaxation rate

γrel = σ rel n v

γrel [s-1]

2.0

1.5

• Connection to elastic collisions

1.0

0.5

0.0 0.0

σ rel = 5.0x1015

1.0x1016

1.5x1016

2.0x1016

2.5x1016

n v [m-2 s-1]

• Relaxation rate is proportional to density: Kinetic energy is redistributed by elastic collisions!

σ el ⋅ v 5rel 4.24 v 4rel

T T

v

G. M. Kavoulakis, C. J. Pethick, and H. Smith Phys. Rev. A 61, 053603 (2000)

Cross Section of elastic collisions 10

V [meV]

5 0 -5

u( r ) ∝ sin(kr + δ 0 ( k ))

-10 -15 -20 0

100

200

300

400

500

600

700

800

900

1000

r [a0]

• Centrifugal barrier for d-waves: 5,8 mK

Regime of s-wave-scattering

• Interaction potential: Short range: Long range:

• Cross section:

S. Kotochigova et al., PRA 61, 042712 (2000) A. Derevianko und A. Dalgarno, PRA 62, 062501(2000)

8π σ el ( k ) = 2 sin 2 (δ 0 (k )) k

Effective-range approximation: 2

σ ER =

8π a

k a + ( k re a − 1) 2

2

1 2

2

2

Relaxation cross section -16

2,0x10

Unitarity limit

22

Ne: a= 100 a0 a=-6500 a0 20

Ne: , a= +20 a0

-16

1,5x10

2

σrel [m ]

a= -130 a0 -16

1,0x10

-17

5,0x10

0,0 200

400

600

800

1000

T [µK]

Effective range approximation

Numerical calculation (shown)

20Ne:

-105(18) a0

-120(10) a0 or +20(10) a0

22Ne:

+150 a0 < a < +1050 a0

(or +14.4 a0)

+70 a0 < a < +300 a0 (100 a0)

Inelastic collisions

Simple model of Penning-Ionization 0.0015

• Ionization with unit probability below a minimal distance

σ ion ,l =

k

2

(2l + 1) PT ( k , l )

0.0005

0.0000

Ionization

π

0.0010

V [meV]

• Model (Xe*, NIST)

l=0 l=1 l=2 l=3

PT(l=3)

-0.0005

-0.0010 50

PT.. transmission probability

100

150

200

r [a0] -9

10

-10

10

3

β ~ 2-3 10-10 cm3s-1

β [cm /s]

• Result:

-11

10

l=0: s-waves l=1: p-waves l=2: d-waves l=3: f-waves β unpol

0,1

1

T [mK]

10

Unpolarized atoms • Measurement in MOT 2 N N& = − α N − β Veff

• Consideration of excited atoms S+S collisions: Kss S+P collisions: Ksp

Fluorescence [arb. units]

7

10

6

10

5

10

4

10

0

5

t [s]

10

15

for small excitation πp:

β = Kss + 2 (KSP-KSS) πp

-9

1,0x10

-10

cm /s

-8

3

Kss= 2.5(8) 10

3

Ksp= 1.0(4) 10 cm /s

20Ne

22Ne

Kss [cm³ s-1] 2.5(8) 10-10

8(5) 10-11

Ksp [cm³ s-1] 1.0(4) 10-8

5.9(25) 10-9

β [cm³/s]

-10

7,5x10

-10

5,0x10

-10

2,5x10

0,0 0,000

0,005

0,010

0,015

πp

0,020

0,025

Suppression of Penning-Ionization Exchange process

• Dominant loss process in MOT τ < 1s @ n=109 cm-3 (MOT)

-

3s

+

• Suppression for spin polarized ensembles

Limitation of suppression by anisotropic contributions to the interaction during collisions He*: 105 ⇒ BEC Xe*: 1 ⇒ BEC Ne* ?

-

core 2p5

Ne* + Ne* S=1

3s

⇒

S=1 ⇒

S tot = 2

Ne

+

core 2p5

+ Ne+

S=0 S=1/2

+ eS=1/2

S tot ≤ 1

Spin polarized atoms 750

108

N

Tmean [µK]

700

107

650

600

550

106 0

10

t [s]

20

0

30

2

4

t' [s]

2 N N& = − α N − β Veff

Heating!

6

Trap loss t

Analysis:

2 N N& = − α N − β Veff

N(t)-N( 0 )

= −α − β

t

∫ N(t')dt'

N 2(t') ∫0 Veff (t') dt' t

∫ N(t')dt'

0

0

20Ne -0,1

-1

Suppression: 50(20) N ( t ) − N ( 0) t

22Ne

β = 9.4(24) 10-12 cm3 s-1 Suppression: 9(6)

20Ne

(N(t)-N0) / N(t)dt [s ]

β = 5.3(15) 10-12 cm3 s-1

∫ N (t ' )dt ' 0

[s ] -0,2 −1

-0,3 10 1x10

10 2x10 N 2 (t' ) dt ' -3 0 V / ( n(t)N(t)dt N(t)dt [cm ] eff t ' ) −3 [ ] cm t N ( t ' )dt '

∫

t

∫

0

Heating • Inherent heating due to 2-body-losses 750 22

Ne: β = 10,2(27) 10

N& inelast ( r , t ) ∝ − β n 2 ( r , t )

T& 1 = βn T 4

3

cm s

-1

700

Tmean [µK]

• other mechanisms • collisions with background gas • secondary collisions

-12

650

600 20Ne:

βheat = βloss =

5.6(15) 5.3(15)

22Ne:

βheat = βloss =

10.2(27) 10-12 cm3s-1 9.4 (24) 10-12 cm3 s-1

10-12 cm3s-1 10-12 cm3 s-1 550 0

1

2

3

4

t' [s]

5

6

7

Population

Evaporative cooling

Inelastic collisions

RF-knife (η=E/kT)

Elastic collisions

Energy

Conditions for evaporative cooling • „Good-to-bad“ ratio

R=

Efficiency parameter

γ el γ loss

χ =−

20Ne:

R~5-15 22Ne: R~30-50

1,0

R=10 R=30 R=50

0,5

22Ne

is better suited for evaporative cooling than 20Ne ! χ

•

d (ln ρ Φ ) d (ln N)

0,0

-0,5

-1,0 4

6

8

η

Cut-off parameter η=ETrap/kBT

10

Experimental realization 1500

Tax

• Ramp: from 80 MHz to 44 MHz

Trad

Trap depth: from 5.5 mK to 1.2 mK Initial cut-off parameter: η=4,5

T [µK]

1250

T

1000

• variable duration of RF-irradiation

750

• Observation:

500 0

1000

1500

2000

tRampe [ms] 1.50x1010

n0

1.25x1010

n0 [cm-3]

T

Phase space density ?

500

1.00x1010

7.50x109

5.00x109 0

500

1000

tRampe [ms]

1500

2000

Increase in phase space density Evaporation protocol RF [MHz] 80 Ramp #1 44 Ramp #2 34 Ramp #3 29

• Initial conditions

ETrap [mK] 5.5 1.2 1.0 0.6

η 4.5 2.7 3.9 4.5

N n0 T ρ

= = = =

5 x 107 1,3 x 1010 cm-3 1.2 mK 1.6 x 10-8

• Final conditions -6

Phase space density

10

N n0 T ρ

Start Ramp #1 Ramp #2 Ramp #3

= = = =

5 x 105 5 x 109 cm-3 130 µK 1.9 x 10-7

-7

10

• Efficiency of evaporative cooling

χ ≈ 0.6 -8

10

5

10

6

7

10

10

N

8

10

Prospects for BEC • Ne* as compared to Bose-condensed species: very high loss rates high rates of elastic collisions • Numerical simulation of optimized evaporative cooling

1

-1

10

phase space density

phase space density

1

-2

10

-3

10

-4

10

-5

-11

10

β = 10

3 -1

cm s -12 3 -1 β = 10 cm s -13 3 -1 β = 10 cm s

-6

10

-7

a = 100 a0 a = 310 a0 a = 1000 a0

-1

10

-2

10

-3

10

-4

10

-5

10

-6

10

-7

10

4

10

5

10

6

10

N

7

10

8

10

10

2

10

3

10

4

10

5

10

N

6

10

7

10

8

10

Results

Summary

• Penning ionization (unpolarized, 20Ne) Kss = 2.5(8) 10-10 cm³ s-1 Ksp = 1.0(4) 10-8 cm³ s -1

• Elastic collisions 20Ne: 22Ne:

a = +20(10) a0 or -110(20) a0 +70 a0 < a < +1050 a0

• Penning ionization (unpolarized, 22Ne) Kss = 8(5) 10-11 cm³ s-1 Ksp = 5.9(25) 10-9 cm³ s -1

• Evaporative cooling Phase space density x 10 Efficiency χ~0,6

• Two-body losses (spin-polarized) 20Ne: β = 5.3(15) 10-12 cm3 s-1 22Ne: β = 9.4(24) 10-12 cm3 s-1

• Lifetime of the 3P2-state (20Ne): 14.73(14) s M. Zinner et al., PRA 67, 010501(R) (2003)

• Suppression of Penning ionization 20Ne: ~ 50 22Ne: ~9

Outlook

• Continue experiments on evaporative cooling of 22Ne to highest possible phase space density • Ion rate measurements with the MCP • Investigation of collision properties, especially influence of external (magnetic) fields • Manipulation of Interactions? • Transfer into an optical dipole trap

• Photo-association spectroscopy

Collisions in cold gases Elastic Collisions

Interaction potential

• Scattering length a: σ el ,T →0 = 8π

0.0015 0.0010

V [meV]

0.0005

a2

• „motor“ of evaporative cooling • Stability of a BEC • Scattering resonances

0.0000 -2 -4 -6 -8 -10

Inelastic Collisions

l=0 l=1 l=2 l=3

-12 -14 -16 -18

• Loss parameter β:

-20 5

10

15

20 50

100

150

200

N& inel = − 2 σ inel v rel N

r [a0]

• Potential depth: ~20 meV • Long-range potential:

C 6 h 2 l (l + 1) VLR (r ) = − 6 + r 2m r 2

σ inel ,T →0 ∝

• • • •

T

1 k

n =− βn

„brake“ of evaporative cooling Heating Penning-Ionization Influence of spin-polarization

Numerical calculation of scattering phases 0,5 π -340 a0

• Interaction potential

-144 a0

0,0 π

+ 59 a0 +151 a0

-0,5 π δ0

• S. Kotochigova et al., PRA 61, 042712 (2000) • A. Derevianko und A. Dalgarno, PRA 62, 062501(2000)

- 58 a0

• Numerical determination of the s-wave radial wavefunction gives δ0

+301 a0

-1,0 π -1,5 π -2,0 π 0,00

ul ( r ) ∝ sin(kr + δ 0 ( k ))

0,02

0,04

0,06

0,08

0,10

-1

k [a0 ] 0.5 π

• Cross section

8π 2 (δ 0 (k )) sin 2 k

δ0

σ el ( k ) =

0.0 π

-0.5 π

a= -342,1 a0 a= -104,3 a0 a= - 58,0 a0 a= + 44,3 a0

-1.0 π

a= +101,1 a0 a= +301,1 a0

10-4

10-3

10-2

k [a0-1]

10-1

Relaxation cross sections 10-15

σ [m²]

10-16

10-17 a= -100 a0: 10-18

σel σrel

a= +100 a0: σel

10-19

σrel

10-20 10

100

1000

T [µK]

10000

Inelastic collisions of metastable neon

MOT MT

discharge (310K) Sheverev et al. J. Appl. Ph. 92, 3454 (2002)

Suppression 20Ne:

50(20)

22Ne:

9(6)

Decay rate vs. Gradient II 5 4 3

Parameters: ∆= -0.17Γ, s=5

π 3 = 0.41

-1

α [s ]

0,07 0,06 0,05 0,04 0,03

0 < LM < 0.005

0,02 0

5

10

15

20

25

30

35

G rad ien t [G /cm ] Problems: • Theories hold for small saturation • Models discussed fail to explain the data quantitatively • Ionizing background collisions