NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
BoseBose--Fermi mixtures of Fermi mixtures of metastablemetastable helium helium
AndreyAndrey Tychkov Tychkov
Tom Tom JeltesJeltes
John MJohn MccNamaraNamara
WimWim VassenVassen
WimWim HogervorstHogervorst
BEC of BEC of 44He*: He*: JanuaryJanuary 27, 200527, 2005DFG of DFG of 33He*: November 18, 2005He*: November 18, 2005
Modern Trends in Atomic Physics IIModern Trends in Atomic Physics IIJune 2June 2ndnd , Gothenburg, Sweden, Gothenburg, Sweden
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
Group leader : Prof. Group leader : Prof. WimWim UbachsUbachsResearch themes: molecular physics, XUV spectroscopyResearch themes: molecular physics, XUV spectroscopy
- search for possible variation of µµµµ=Mp/me over cosmological time
Staff member: Dr. Staff member: Dr. KjeldKjeld EikemaEikemaResearch: Research: ultrafastultrafast lasers, frequency comb spectroscopylasers, frequency comb spectroscopy
Staff member: Dr. Staff member: Dr. WimWim VassenVassenResearch: laser cooling & trappingResearch: laser cooling & trapping
Atomic, Molecular & Laser PhysicsAtomic, Molecular & Laser Physicsgroupgroup
Common theme: metrologyCommon theme: metrology
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
XUV-laser setup with PDA: ∆νννν ~ 250 MHz
HH22 spectroscopy in lab spectroscopy in lab vsvs Quasar dataQuasar data
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
ESO-VLT ChileNew set of more accurate quasar data:Uncertainty claimed: 2 x 10-7 - 1 x 10-6
Ivanchik, Petitjean et al, A&A 440, 45 (2005)
39 lines in Q 0347-383(z = 3.0248992)
37 lines in Q 0405-443(z = 2.5947328)
Q0347-383
and
Various tests performed
-blending with Lyman forest
-kinetics (J-effects)
-calibrations
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
Q0347
Q0405
weighted fit
510)59.044.2(
−×±=
∆
µ
µ
unweighted fit
510)57.001.2(
−×±=
∆
µ
µ
Total set
PRL 96, 151101 (21 april 2006):“Indication of a Cosmological Variation of the Proton-Electron Mass Ratio Based on Laboratory Measurement and Reanalysis of H2 spectra”
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
frequency comb laser
AOM
piezo
pump laser5 W green
Rb atomic clock 10 GHz
Waveformgenerator
BBOPBS
λ/2
λ/2
PBS
APD
holey fiber
PID
PID
temp.
control
10 fs,75 MHz Ti:Sa laser
filter
Oscilloscope
FrequencyCounters
SpectrumAnalyzer
GPS receiver
12 digit accuracydue to Rb-clock + GPS correction
f:2f interferometer
frequency
I
0
f0
fr
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
4p
5p
2 x 212 nm
84Kr: 4p6 � 4p55p[1/2]0:∆ν∆ν∆ν∆ν= 2 820 833 097.7 (3.5) MHz
Isotope shifts: 84Kr-80Kr: 302.02 (28) MHz84Kr-82Kr: 152.41 (15) MHzetc.
Science 307, 400 (2005)
evolution oflaser field:
ti LL ωφ =
evolution ofatom:
tiA 0ωφ =
Direct metrology or quantum interference scheme
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
2 2 33SS11 state: state: τ τ = = 8000 s, 8000 s, Laser cooling: Laser cooling: λλ==1083 nm1083 nm
20 20 eVeV internal energy: single internal energy: single He*He*
atom detectionatom detection
Penning ionization: Penning ionization: HeHe++
( He* + He* ( He* + He* →→ He + HeHe + He+ + + e+ e── ))
33He* He* fermionfermion and and 44He* He* bosonboson
Scattering lengths large and positive!Scattering lengths large and positive!
aa4444=+7.512 nm ; a=+7.512 nm ; a3434=+28.8 nm=+28.8 nm
MetastableMetastable heliumhelium
He ground state:1s2 1S0
He* metastable state:1s2s 3S1
I=1/2I=1/2 I=0I=0
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
MagnetoMagneto--optical trap (MOT) setupoptical trap (MOT) setup
Loading and cooling of ~2 × 109 4He*
atoms in ~1 second at T ~ 1 mK
(phase-space density ~10-7)
impression by J. Mimpression by J. MccNamaraNamara
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
Detection methodsDetection methodsHe*, HeHe*, He++, absorption imaging, absorption imaging
HeHe** MCPMCP
on translation stageon translation stage
HeHe++ MCP MCP (not visible)(not visible)
to CCD to CCD
cameracamera
trap axistrap axis
TurboTurboPump 1Pump 1
TurboTurbo
Pump 2Pump 2
UHV UHV
chamberchamberP ~ 10P ~ 10
--1111mbarmbar
TOFTOF
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
11--D Doppler cooling in magnetic trapD Doppler cooling in magnetic trap
Circularly polarized laser beam along the z-axis at high (24 G) B0
Laser cooling in axial (z) direction: σ+- cycling transition
Cooling in radial direction:reabsorption of spontaneously emitted red-detuned photons (collisions, anharmonic mixing)
“cloverleaf” magnetic trap“cloverleaf” magnetic trap
Successfully used to cool spin-polarized 3He* fermions (>1××××109)
s-wave collisions are forbidden – Pauli principle Cooling in radial direction – reabsorption of scattered photons
222222
222)( z
my
mx
mrV zyxext ωωω ++=
(ωx= ωy>> ωz)
••T=0.15 T=0.15 mKmK (3(3××TTDopplerDoppler ))•• PhasePhase--space density increase ~ 600space density increase ~ 600
•• No atoms lost during Doppler coolingNo atoms lost during Doppler cooling
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
BEC reached after 15 s BEC reached after 15 s rf rf (50 (50 –– 8 MHz) evaporative cooling ramp8 MHz) evaporative cooling ramp
BEC also observed after 2 s BEC also observed after 2 s rfrf rampramp(with less atoms)(with less atoms)
M=+1M=+1
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
Observation of BECObservation of BEC
�� TimeTime--ofof--flight:flight:
–– Number of atoms, NNumber of atoms, N00(BEC), N(BEC), Nthth
–– Temperature, TTemperature, T
–– Expansion in xExpansion in x--direction (vertical)direction (vertical)
�� Absorption imaging:Absorption imaging:
–– MCP calibration (MOT)MCP calibration (MOT)
–– Expansion in y,z planeExpansion in y,z plane
�� HeHe++ ions: nonions: non--destructivedestructive
–– Loss processesLoss processes
–– BEC formation and decayBEC formation and decay
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
NN0 0 via via µµµµµµµµ or integralor integral
µµNN00
TT
Method 1:Method 1:
NN0 0 = integral of green = integral of green curve times MCP curve times MCP calibration (20% accuracy)calibration (20% accuracy)
from fit from fit noncondensednoncondensed part:part: TTcc~2 ~2 µK µK and and NNTT
maximum number maximum number deduced: deduced: NN00=1 x 10=1 x 107
7
However: saturation of However: saturation of MCP for NMCP for N00 > 1 x 10> 1 x 1066
NN00 too smalltoo small
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
µµ extracted from width of extracted from width of TOF signal (radial expansion TOF signal (radial expansion only!) gives only!) gives NN00 = = 5 x 105 x 107
7( )
52
015
2
=
ho
hoTF
m
aN
ω
ωµ
h
h
Method 2Method 2 : N: N0 0 via chemical potentialvia chemical potential
µµNN00
TT
However: Absorption imaging However: Absorption imaging reveals anomalous expansion reveals anomalous expansion of the BEC as a result of too of the BEC as a result of too slow trap switchslow trap switch--off: off: stretching in radial direction.stretching in radial direction.
NN00 too largetoo large
lengthscatteringa
potentialchemical
zyxho
−
−
=
µ
ωωωω 3
1.5 x 101.5 x 1077<N<N00< 4 x 10< 4 x 107
7
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
Decay of the condensate:Decay of the condensate:the effect of atomic transferthe effect of atomic transfer
Model :Model :P. Zin, A. Dragan, S. Charzynski, N. Herschbach, P. Tol,W. Hogervorst, W. Vassen, J. Phys. B 36, L149 (2003)
Assumption: Assumption:
BEC + thermal cloud remain in BEC + thermal cloud remain in thermodynamic equilibrium during thermodynamic equilibrium during decaydecay
�� Output: NOutput: N00(t), N(t), Nthth(t), T(t)(t), T(t)
�� Input: NInput: N00(0), N(0), Nthth(0), (0), ττ -- lifetime,lifetime,
ββ (two(two--), ), LL (three(three--body loss rate body loss rate
constant)constant)
BEC is detected up to t=75 sBEC is detected up to t=75 s
(Cloud lifetime (Cloud lifetime ττττττττ ~ 3 min)~ 3 min)
•• -- quasiquasi--pure BECpure BEC
-- NN00=N=Nth th (t=0)(t=0)
BEC lifetime BEC lifetime
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
�� Atoms lost from the condensate Atoms lost from the condensate are lost from the trap, or are lost from the trap, or transferred to the thermal cloud. transferred to the thermal cloud.
�� The presence of a thermal cloud The presence of a thermal cloud reduces the lifetime of a BECreduces the lifetime of a BEC
�� In thermal equilibrium transfer In thermal equilibrium transfer has to occur: a condensate atom has to occur: a condensate atom has less energy than a thermal has less energy than a thermal atomatom
�� More complicated equations More complicated equations when also twowhen also two--body (body (ββ) and ) and threethree--body (L) losses are body (L) losses are incorporatedincorporated
When only background gas When only background gas collisions are taken into collisions are taken into acountacount::
Decay of the condensate:Decay of the condensate:the effect of atomic transferthe effect of atomic transfer
+−= TCC NNN
4
11
τ&
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
Decay of the condensate:Decay of the condensate:the effect of atomic transferthe effect of atomic transfer
BEC is detected up to t=75 sBEC is detected up to t=75 s
(Cloud lifetime (Cloud lifetime ττττττττ ~ 3 min)~ 3 min)
Estimated loss rate constants:Estimated loss rate constants:ββ=2(1) =2(1) ××1010
--1414cmcm
33/s/s
L=9(3) L=9(3) ××1010--2727
cmcm66/s/s
•• -- quasiquasi--pure BECpure BEC
-- NN00=N=Nth th (t=0)(t=0)
BEC lifetime BEC lifetime
For quasiFor quasi--pure BEC the model gives pure BEC the model gives decay without atomic transferdecay without atomic transfer(upper curve)(upper curve)
Theoretical predictions:Theoretical predictions:ββ=1=1××1010--1414 cmcm33/s/sLL=2=2××1010--2727 cmcm66/s/s
P.O. P.O. FedichevFedichev et alet al., Phys. Rev. ., Phys. Rev. LettLett. . 7777, 2921 (1996), 2921 (1996)
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
44He* He* vsvs 33HeHe**BosonsBosons FermionsFermions
T=0T=0
AnisotropicAnisotropic momentum distributionmomentum distribution Isotropic momentum distributionIsotropic momentum distribution
kkBBTTCC = 0.94 (N= 0.94 (Nbb))1/31/3
ħħῶῶbb
Phase transitionPhase transition
EEF F == kkBBTTFF = (6 N= (6 Nff))1/31/3
ħħῶῶff
Gradual changeGradual change3/1
23.2
=
C
F
C
F
N
N
T
T
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
Sympathetic coolingSympathetic cooling
Start with 10Start with 10--100 times more 100 times more 44HeHe
TOF measurements: TOF measurements: blow away blow away 44He* using resonant lightHe* using resonant light
Scattering lengths large and positive!Scattering lengths large and positive!aa4444=+7.512 nm ; a=+7.512 nm ; a3434=+28.8 nm=+28.8 nm
0 1 2 3 4 5Ramp length HsL
0
100
200
300
400
500
Tem
pera
tureHΜ
KL
H L
4He
TT 3He
open: in mixtureopen: in mixtureclosedclosed: pure: pure
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
Individual components at TIndividual components at T << 10 10 µµKK ::rfrf output couplingoutput coupling
m = +1m = +1
m = 0m = 0
m = m = --11
m = +1/2m = +1/2
m = +3/2m = +3/2
m = m = --1/21/2
m = m = --3/23/2
33He*He*44He*He*
8 MHz8 MHz 5.3 MHz5.3 MHz
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
33HeHe**
33He*He*
44He* He* BECBEC
T=0.8 T=0.8 µµµµµµµµKK, N=2.1, N=2.1××101066
T/TT/TF F = 0.45= 0.45 kkBBTTFF = (6N)= (6N)1/3 1/3
ħħῶῶ
Degenerate Degenerate metastablemetastable Fermi gas!Fermi gas!
Fit to FermiFit to Fermi--DiracDirac distribution:distribution:
degeneratedegenerate mixture (BEC+mixture (BEC+DFGDFG))
NN33=4.2=4.2××101055
NN44=1.0=1.0××101055
T/TT/TF F = 0.5= 0.5
RfRf cut to end frequency below 8.4 MHzcut to end frequency below 8.4 MHzremoves all removes all 44He* atoms from the trapHe* atoms from the trap
Maximum number of degenerate fermions observed:Maximum number of degenerate fermions observed: 44××101066
in ramp of 2.5 s!in ramp of 2.5 s!
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
T=0.8 T=0.8 µµµµµµµµKK, N=2.1, N=2.1××101066
T/TT/TF F = 0.45= 0.45 kkBBTTFF = (6N)= (6N)1/3 1/3
ħħῶῶ
33HeHe**
33He*He*
44He* He* BECBEC
Degenerate Degenerate metastablemetastable Fermi gas!Fermi gas!
Fit to FermiFit to Fermi--DiracDirac distribution:distribution:
degeneratedegenerate mixture (BEC+mixture (BEC+DFGDFG))
NN33=4.2=4.2××101055
NN44=1.0=1.0××101055
T/TT/TF F = 0.5= 0.5
RfRf cut to end frequency cut to end frequency just above 8.4 MHz:just above 8.4 MHz:
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
AA: degenerate Fermi gas: degenerate Fermi gas(T/T(T/TFF=0.5)=0.5)
BB: Fermi or Bose gas in : Fermi or Bose gas in classical limit classical limit (T>>T(T>>TFF,T,TCC))
CC: Bose gas just above T: Bose gas just above TCC
Check: MaxwellCheck: Maxwell--BoltzmannBoltzmann fits to the wingsfits to the wings
NNVNNV--AMO meeting, AMO meeting, LunterenLunteren 11.11.200511.11.2005Laser Centre Vrije Universiteit, Amsterdam
SummarySummary
�� Large Large 44He* BECHe* BEC�� SofarSofar 2 degenerate 2 degenerate fermionicfermionic species (species (66Li, Li, 4040K); K);
now a third one: now a third one: 33HeHe�� New physics with New physics with 33He* fermions:He* fermions:
–– HanburyHanbury Brown and Brown and TwissTwiss experiment (collaboration LCFIO experiment (collaboration LCFIO OrsayOrsay))–– Phase separationPhase separation–– Search for Search for FeshbachFeshbach resonances: vary scattering lengths?resonances: vary scattering lengths?–– PP--wave Cooper pairingwave Cooper pairing–– Optical latticeOptical lattice–– Suppression of spontaneous emissionSuppression of spontaneous emission–– Metrology: QED, nuclear charge radius Metrology: QED, nuclear charge radius
(2 (2 33SS11 –– 2 2
11SS00 magnetic dipole @1.56 magnetic dipole @1.56 µµm)m)
�� MetastabilityMetastability–– Enhanced detection efficiencyEnhanced detection efficiency–– Access to major density dependent lossesAccess to major density dependent losses