Bose-Fermi mixtures of metastable helium

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


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


XUV-laser setup with PDA: ∆νννν ~ 250 MHz

HH22 spectroscopy in lab spectroscopy in lab vsvs Quasar dataQuasar data


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


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”


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


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


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


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


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


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


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


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


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


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


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


�� 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::


+−= TCC NNN

4

11

τ&



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)


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


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


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


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!


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:


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


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

Bose-Fermi mixtures of metastable helium

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