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
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
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
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
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