Cold Metastable Neon Atoms Towards Degenerated Ne*- Ensembles

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 Metastable neon 3 P 2 -Lifetime 3 D 3 3 P 2 2p 6 τ 2 Elastic collisions and scattering length Inelastic collisions and their suppression Evaporative cooling Outlook Population RF-knife (η=e/kt) Energy

2p 6 J =0 J =1 J =2 J =3 Neon Naturally occurring Neon-Isotopes 3 D 3 Mass Abundance [%] Nuclear Spin 3p[5/2] 3 20 90.48 0 21 0.27 3/2 22 9.25 0 3 P 0 3s [1/2] 0 1 P 1 3s [1/2] 1 3 P 1 3 P 2 E1 640 nm 3s[3/2] 1 3s[3/2] 2 1 S 0 τ =? 2 M2 16.6 ev 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:? M. Zinner et al., PRA 67, 010501(R) (2003) 640 nm 16,6 ev Collision physics Rates of elastic and inelastic collisions Suppression of Penning-Ionization by spinpolarization: 10 4? 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 BEC thermal

From atomic physics to BEC Atomic physics Lifetime of the metastable state:? M. Zinner et al., PRA 67, 010501(R) (2003) 640 nm 16,6 ev Collision physics Rates of elastic and inelastic collisions Suppression of Penning-Ionization by spinpolarization: 10 4? 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 BEC thermal

Experimental Setup

Lifetime of the metastable state 3 D 3 3p[5/2] 3 After Loading the MOT 3 P 0 3s [1/2] 0 1 P 1 3s [1/2] 1 3 P 1 3 P 2 E1 640 nm observation of decay by fluorescence 3s[3/2] 1 τ 2 3s[3/2] 2 M2 16.6 ev 1 S 0 2p 6 J =0 J =1 J =2 J =3

Fluorescence of 20 Ne in a MOT MOT decay N& = α N β N 2 1000000 excitation 47% α -1 = 21.7 s 3 D 3 3 P 2 π 3 π 2 V eff τ 2 Origins of one-body losses α = π 2 τ τ 2 + + γ p π 3 τ 3 radiative decay Fluorescence [au] 100000 10000 2p 6 + α background collisions FT finite trap depth 1000 excitation 0.5% α -1 = 14.4 s population of 3 P 2 -state: π 2 population of 3 D 3 -state: π 3 100 0 20 40 60 80 100 120 time of MOT decay [s]

Background gas collisions: γ p Pressure dependency of MOT decay Offset of pressure gauge: 4(7) 10-12 mbar 0,14 background gas collisions γ = 5.2(1)*10 7 mbar -1 s -1 Ionization processes: Ne* + X = Ne + X + + e - 0,12 Ion signal on MCP: R ion (t) = c 1 (p) N(t) + c 2 N²(t) α [s -1 ] 0,10 1,0 0,9 0,8 0,08 0,06 background gas collision rate 1/640s @ p=3 10-11 mbar 0 25 50 75 100 125 p display [10-11 mbar] c 1 [arb. units] 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 0 1 2 3 4 5 6 7 8 9 10 11 12 p display [10-11 mbar]

Influence of finite trap depth For an infinitely large MOT: trap depth and escape velocity become infinite α [s -1 ] 0,35 0,30 0,08 0,07 π 3 = 0.016 therefore: let the gradient B approach zero! In practice: Trap depth remains finite due to finite size of laser beams 0,06 0,05 0 20 40 60 80 100 Gradient [G/cm] No significant dependency of α on B No correction needed for low excitation measurements

Lifetime τ 2 of the metastable 3 P 2 -state 0,07 14.3 α p=0 [s -1 ] 0,06 0,05 16.7 20.0 α p=0-1 [s] 0,04 25.0 0,0 0,1 0,2 0,3 0,4 0,5 Population in 3 D 3 -state (π 3 ) Error budget: measured α 0.06918(51) s -1 p=0 extrapolation - 0.00156(37) s -1 π=0 extrapolation + 0.00028(13) s -1 thus: α(p=0, π=0) 0.06790(64) s -1 τ 2 14.73(14) s

From atomic physics to BEC Atomic physics Lifetime of the metastable state: 14.73(14)s M. Zinner et al., PRA 67, 010501(R) (2003) 640 nm 16,6 ev Collision physics Rates of elastic and inelastic collisions Suppression of Penning-Ionization by spinpolarization: 10 4? 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 BEC thermal

Preparation of spin-polarized atoms Preparation of Magnetically Trapped Atoms Sequence Beam collimation and slowing MOT loading 400 ms N=6x10 8 Compressed MOT σ r =1.3mm spin polarization 78% in m J =+2 +2 +1 0-1 -2 0 µs 2 µs Doppler Cooling PSD = 4.5x10-7 axial: ~200 µk radial: ~450 µk Transfer to MT and adiabatic compression B 0 = 25 G N = 3x10 8 4 µs 8 µs Stern-Gerlach Experiment

Doppler-cooling in the magnetic trap σ + -σ + - irradiation in axial direction of magnetic trap 2000 T axial T radial 1500 T [µk] 1000 Axial: Doppler cooling Radial: cooling by reabsorption Optimized parameters: = -0.5 Γ 500 0 T Doppler = 196 µk 0 500 1000 1500 2000 t [ms] I = 5x10-3 I sat 50-fold gain in phase space density

Elastic collisions

Cross-dimensional Relaxation Kinetic energy is not in equilibrium after Doppler-cooling 700 22 Ne Aspect ratio of the cloud changes σ A= ax σ rad T [µk] 600 500 T axial T radial 400 0 1 2 3 4 5 t* [s] 1,4 T 1,2 Determination of the relaxation rate A& = γ ( A(t) ) rel A eq A 1,0 0,8 6.4 10 9 cm -3 1.3 10 10 cm -3 0 1 2 3 4 5 t* [s] Mean density: 2.9 10 9 cm -3

Cross-dimensional Relaxation γ rel [s -1 ] 2.5 2.0 1.5 1.0 0.5 22 Ne 0.0 0.0 5.0x10 15 1.0x10 16 1.5x10 16 2.0x10 16 2.5x10 16 n v [m -2 s -1 ] Relaxation rate is proportional to density: Description of the relaxation rate γ rel = σ rel n v Connection to elastic collisions σ = σ el v 5 rel rel 4 4. 24 vrel G. M. Kavoulakis, C. J. Pethick, and H. Smith Phys. Rev. A 61, 053603 (2000) T T v Kinetic energy is redistributed by elastic collisions!

Cross Section of elastic collisions 10 5 V [mev] 0-5 -10-15 -20 0 100 200 300 400 500 600 700 800 900 1000 r [a 0 ] ( kr + δ ( )) u ( r ) sin k 0 Centrifugal barrier for d-waves: 5,8 mk Regime of s-wave-scattering Interaction potential: Short range: S. Kotochigova et al., PRA 61, 042712 (2000) Long range: A. Derevianko und A. Dalgarno, PRA 62, 062501(2000) Cross section: 8π 2 σ el ( k) = 2 0 k sin δ ( ( )) k Effective-range approximation: 2 σ ER = k 2 a 2 + 8π a ( ) 1 2 k r a 1 2 2 e

Relaxation cross section 2,0x10-16 Unitarity limit 22 Ne: a= 100 a 0 1,5x10-16 a=-6500 a 0 20 Ne:, a= +20 a 0 a= -130 a 0 σ rel [m 2 ] 1,0x10-16 5,0x10-17 0,0 200 400 600 800 1000 T [µk] Effective range approximation Numerical calculation (shown) 20 Ne: -105(18) a 0 (or +14.4 a 0 ) -120(10) a 0 or +20(10) a 0 22 Ne: +150 a 0 < a < +1050 a 0 +70 a 0 < a < +300 a 0 (100 a 0 )

Inelastic collisions

Simple model of Penning-Ionization Ionization with unit probability below a minimal distance Model (Xe*, NIST) σ = π k ( 2l 1) P ( k, ) ion, l + l 2 T P T.. transmission probability V [mev] 0.0015 0.0010 0.0005 0.0000-0.0005-0.0010 Ionization P T (l=3) 50 100 150 200 r [a 0 ] l=0 l=1 l=2 l=3 Result: 10-9 β ~ 2-3 10-10 cm 3 s -1 β [cm 3 /s] 10-10 10-11 l=0: s-waves l=1: p-waves l=2: d-waves l=3: f-waves β unpol 0,1 1 10 T [mk]

Unpolarized atoms Measurement in MOT N& = α N Consideration of excited atoms S+S collisions: K ss S+P collisions: K sp for small excitation π p : β = K ss + 2 (K SP -K SS ) π p 20 Ne 22 Ne K ss [cm³ s -1 ] 2.5(8) 10-10 8(5) 10-11 β N 2 V eff Fluorescence [arb. units] β [cm³/s] 10 7 10 6 10 5 10 4 1,0x10 K = 2.5(8) -9 ss 10-10 cm 3 /s K sp = 1.0(4) 10-8 cm 3 /s 7,5x10-10 5,0x10-10 2,5x10-10 0 5 10 15 t [s] K sp [cm³ s -1 ] 1.0(4) 10-8 5.9(25) 10-9 0,0 0,000 0,005 0,010 0,015 0,020 0,025 π p

Suppression of Penning-Ionization Dominant loss process in MOT Exchange process τ < 1s @ n=10 9 cm -3 (MOT) - 3s Suppression for spin polarized ensembles + core 2p5 3s - + core 2p5 Limitation of suppression by anisotropic contributions to the interaction during collisions He*: 10 5 BEC Xe*: 1 BEC Ne*? Ne* + Ne* Ne + Ne + + e - S=1 S=1 S=0 S=1/2 S=1/2 S tot = 2 S tot 1

Spin polarized atoms 750 10 8 700 N 10 7 T mean [µk] 650 600 10 6 0 10 20 30 t [s] 550 0 2 4 6 t' [s] N& = α N β N 2 V eff Heating!

Trap loss Analysis: N& = α N β N 2 V eff N(t)-N( 0 ) t 0 N(t')dt' 2 N (t') dt' Veff (t') 0 = α β t N(t')dt' t 0 20 Ne β = 5.3(15) 10-12 cm 3 s -1 Suppression: 50(20) 22 Ne β = 9.4(24) 10-12 cm 3 s -1 Suppression: 9(6) 0 N( t') dt' (N(t)-N 0 ) / N(t)dt [s -1 ] 1 [ s ] N( t) N(0) t -0,1-0,2-0,3 1x10 10 t 2 2x10 10 N V ( t') dt' ( t') n(t)n(t)dt / N(t)dt [cm -3 0 ] t 0 eff N( t') dt' 3 [ cm ] 20 Ne

Heating Inherent heating due to 2-body-losses 750 & N inelast ( r, t) β n 2 ( r, t) 22 Ne: β = 10,2(27) 10-12 cm 3 s -1 T& T = 1 4 β n 700 other mechanisms collisions with background gas secondary collisions T mean [µk] 650 600 20 Ne: β heat = 5.6(15) 10-12 cm 3 s -1 β loss = 5.3(15) 10-12 cm 3 s -1 22 Ne: β heat = 10.2(27) 10-12 cm 3 s -1 0 1 2 3 4 5 6 7 β loss = 9.4 (24) 10-12 cm 3 s -1 550 t' [s]

Evaporative cooling Population RF-knife (η=e/kt) Inelastic collisions Elastic collisions Energy

Conditions for evaporative cooling Good-to-bad ratio γ R = el γ loss Efficiency parameter ( ln ρ ) ( lnn) = d Φ χ d 20 Ne: R~5-15 22 Ne: R~30-50 22 Ne is better suited for evaporative cooling than 20 Ne! χ 1,0 0,5 0,0 R=10 R=30 R=50-0,5-1,0 4 6 8 10 η Cut-off parameter η=e Trap /k B T

Experimental realization 1500 Ramp: from 80 MHz to 44 MHz Trap depth: from 5.5 mk to 1.2 mk Initial cut-off parameter: η=4,5 T [µk] 1250 1000 T ax T rad T variable duration of RF-irradiation 750 Observation: T 500 0 500 1000 1500 2000 1.50x10 10 t Rampe [ms] n 0 1.25x10 10 Phase space density? n 0 [cm -3 ] 1.00x10 10 7.50x10 9 5.00x10 9 0 500 1000 1500 2000 t Rampe [ms]

Increase in phase space density Phase space density Evaporation protocol RF [MHz] E Trap [mk] η 80 5.5 4.5 Ramp #1 44 1.2 2.7 Ramp #2 34 1.0 3.9 Ramp #3 29 0.6 4.5 10-6 10-7 10-8 10 5 10 6 10 7 10 8 N Start Ramp #1 Ramp #2 Ramp #3 Initial conditions Final conditions N = 5 x 10 7 n 0 = 1,3 x 10 10 cm -3 T = 1.2 mk ρ = 1.6 x 10-8 N = 5 x 10 5 n 0 = 5 x 10 9 cm -3 T = 130 µk ρ = 1.9 x 10-7 Efficiency of evaporative cooling χ 0.6

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 phase space density 1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 β = 10-11 cm 3 s -1 β = 10-12 cm 3 s -1 β = 10-13 cm 3 s -1 10 4 10 5 10 6 10 7 10 8 N phase space density 1 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10 2 10 3 10 4 10 5 10 6 10 7 10 8 N a = 100 a0 a = 310 a0 a = 1000 a0

Summary Results Penning ionization (unpolarized, 20 Ne) K ss = 2.5(8) 10-10 cm³ s -1 K sp = 1.0(4) 10-8 cm³ s -1 Penning ionization (unpolarized, 22 Ne) K ss = 8(5) 10-11 cm³ s -1 K sp = 5.9(25) 10-9 cm³ s -1 Two-body losses (spin-polarized) 20 Ne: β = 5.3(15) 10-12 cm 3 s -1 22 Ne: β = 9.4(24) 10-12 cm 3 s -1 Suppression of Penning ionization 20 Ne: ~ 50 22 Ne: ~ 9 Elastic collisions 20 Ne: a = +20(10) a 0 or -110(20) a 0 22 Ne: +70 a 0 < a < +1050 a 0 Evaporative cooling Phase space density x 10 Efficiency χ~0,6 Lifetime of the 3 P 2 -state ( 20 Ne): 14.73(14) s M. Zinner et al., PRA 67, 010501(R) (2003)

Outlook Continue experiments on evaporative cooling of 22 Ne 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 0.0015 0.0010 Interaction potential Elastic Collisions Scattering length a: σ = 2 el, T 0 8π a V [mev] 0.0005 0.0000-2 -4-6 -8-10 -12 l=0-14 l=1-16 l=2-18 l=3-20 5 10 15 20 50 100 150 200 r [a 0 ] Potential depth: ~20 mev Long-range potential: C + V LR ( r) = r 2m r 2 6 h l( l 1) + 6 2 motor of evaporative cooling Stability of a BEC Scattering resonances Inelastic Collisions Loss parameter β: N& N inel = 2 σ inel σ inel, T 0 n brake of evaporative cooling Heating Penning-Ionization Influence of spin-polarization v rel T = 1 k β n

Numerical calculation of scattering phases Interaction potential S. Kotochigova et al., PRA 61, 042712 (2000) A. Derevianko und A. Dalgarno, PRA 62, 062501(2000) Numerical determination of the s-wave radial wavefunction gives δ 0 δ 0 0,5 π 0,0 π -0,5 π -1,0 π -1,5 π -340 a 0-144 a 0-58 a 0 + 59 a 0 +151 a 0 +301 a 0 u l ( kr + δ ( )) ( r ) sin k 0-2,0 π 0,00 0,02 0,04 0,06 0,08 0,10 0.5 π k [a 0-1 ] Cross section 8π 2 σ el ( k) = 2 0 k sin δ ( ( k) ) δ 0 0.0 π -0.5 π a= -342,1 a 0 a= -104,3 a 0 a= - 58,0 a 0 a= + 44,3 a 0-1.0 π a= +101,1 a 0 a= +301,1 a 0 10-4 10-3 10-2 10-1 k [a 0-1 ]

Relaxation cross sections 10-15 10-16 σ [m²] 10-17 10-18 10-19 a= -100 a 0 : σ el σ rel a= +100 a 0 : σ el σ rel 10-20 10 100 1000 10000 T [µk]

Inelastic collisions of metastable neon MT MOT discharge (310K) Sheverev et al. J. Appl. Ph. 92, 3454 (2002) Suppression 20 Ne: 50(20) 22 Ne: 9(6)

Decay rate vs. Gradient II 5 4 3 Parameters: = -0.17Γ, s=5 π 3 = 0.41 0,07 α [s -1 ] 0,06 0,05 0,04 0,03 0,02 0 < L M < 0.005 0 5 10 15 20 25 30 35 Gradient [G/cm] Problems: Theories hold for small saturation Models discussed fail to explain the data quantitatively Ionizing background collisions