Efimov physicsin ultracold gases

Efimov physicsin ultracold gases

Rudolf GrimmRudolf Grimm

“Center for Quantum Optics” in Innsbruck“Center for Quantum Optics” in Innsbruck

Austrian Academy of SciencesAustrian Academy of Sciences

University of Innsbruck University of Innsbruck

FB18, Santos, 26 Aug 06FB18, Santos, 26 Aug 06

FB18, Santos, 26 Aug 06FB18, Santos, 26 Aug 06

Efimov physicsin ultracold gases

Efimov physicsin ultracold gases

Rudolf GrimmRudolf Grimm

“Center for Quantum Optics” in Innsbruck“Center for Quantum Optics” in Innsbruck

Austrian Academy of SciencesAustrian Academy of Sciences

University of Innsbruck University of Innsbruck

1995: Bose-Einstein condensation

2003: molecular condensates

1999: degenerate Fermi gas

2004/05: fermionic condensates and superfluids

milestones in the field

2002/03: ultracold dimers

cold atoms in a nutshell

atom trap: electromagnetic field(our case: focus of powerful infrared laser)

cooling to nanokelvin:laser cooling & subsequent evaporative cooling

atomic species:bosons and fermions

nKnK

2006: Efimov states !!!

BEC

interaction tuning through Feshbach resonances !interaction tuning through Feshbach resonances !

molecular structure: scattering length

r

U(r)

incident channel

B

a

s wave scattering length a determined by last bound level

abg

last boundlevel many

vib.levels

molecular structure: scattering length

B

a

abg

r

U(r)

incident channel

bound state

coupling

Feshbach resonance

r

U(r)

incident channel

bound state

magnetic moment of bound statediffers from the magnetic moment of the incident channel

B

a

s wave scattering length a as a function of magnetic field B

abg

B0

0

1BB

aa bg

coupling

very large scattering lenghts

rr0

U(r)

r

„quantum halo states“:deuteron, He2, Feshbach molecules !!!

weakly bound last level:

scattering length a>>r0

binding energy Eb = - h2/(ma2)

a system with universal properties !!!

weakly bound last level:

scattering length a>>r0

binding energy Eb = - h2/(ma2)

a system with universal properties !!!

open-channel dominated resonance: single-channel model

energy1/a

quantum states near two-body resonance

a < 0 a > 0

Edimer = h2/(ma2)

weaklybounddimer

energy1/a

quantum states near two-body resonance

weakly bound trimer

a < 0 a > 0

even more weaklybound trimer

×22.7

×(22.7)2

infinite series of weakly bound trimer statesfor resonant two-body interaction

„Efimov states“

infinite series of weakly bound trimer statesfor resonant two-body interaction

„Efimov states“

36 years ago ...

35 years ago ...

energy1/a

Efimov resonancesEfimov resonances

a < 0 a > 0

three atoms couple to anthree atoms couple to anEfimov trimer:Efimov trimer:

„„triatomictriatomic Efimov resonance“Efimov resonance“

three atoms couple to anthree atoms couple to anEfimov trimer:Efimov trimer:

„„triatomictriatomic Efimov resonance“Efimov resonance“one atom and a dimer couple to anone atom and a dimer couple to anEfimov trimer:Efimov trimer:

„„atom-dimer Efimov resonance“atom-dimer Efimov resonance“

one atom and a dimer couple to anone atom and a dimer couple to anEfimov trimer:Efimov trimer:

„„atom-dimer Efimov resonance“atom-dimer Efimov resonance“

resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979)

resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979)

energy1/a

universalityuniversality

a < 0 a > 0

universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

energy1/a

universalityuniversality

a < 0 a > 0

universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

energy1/a

universalityuniversality

a < 0 a > 0

universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

universality discussed in Sov. J. Nucl. Phys. 29, 546 (1979)

locations of Efimov states / resonance positionsnot universal !!!

additional parameter needed

locations of Efimov states / resonance positionsnot universal !!!

additional parameter needed

experimental observations

nuclear physicsnuclear physics(Halo nuclei)(Halo nuclei)

molecular physicsmolecular physics(He beams)(He beams)

ultracoldultracoldatom physicsatom physics

none !

none !

many new opportunitiesmany new opportunitiesfor Efimov-relatedfor Efimov-related

few-body physics ! few-body physics !

the probe

three-body recombination

atomic systems have deeply bound dimers states

three-body recombination

three-body recombination

three-body recomb. theory basics

L3: three-body loss coefficient [cm6/s]

Fedichev et al., PRL 77, 2921 (1996)

prediction of a4 scaling, C = 3.9

Nielsen & Macek, PRL 83, 1566 (1999)Esry et al., PRL 83, 1751 (1999)Bedaque et al., PRL 85, 908 (2000)Braaten & Hammer, PRL 87, 160407 (2001)

CC((aa) = ) = CC(22.7(22.7aa)) with upper limit with upper limit ~~70 for 70 for aa>0>0

oscillatory behavioroscillatory behavior

× × ee ~~ 22.7 22.7

Esry-Greene-Burke theory

PRL 83, 1751 (1999) calculations for a sech2(rij/r0) model potential

definition ofa recombination length

L3~a4

L3~a4

destructiveinterference effect

destructiveinterference effect

Efimov resonance !Efimov resonance !

)( with 34

3 aCCm

aCL

0a

* || a

*22

*

sinh)72.1)*

|ln(|0

(sin

)2sinh( 4590)(

asaC

)(aC

Three-body loss coefficient

)(aC

* a

0a

)1( 8.16

)sinh)76.1)*

ln(0

((cose 1.67)(

*4

*2

*22

e

asaC

loss into deeply bound molecules

loss into shallow dimer

effective field theory (Braaten & Hammer)

Efimov resonancesEfimov resonances

Phys. Rep. 428, 259 (2006)

ultracold.atoms Innsbruck

two teams working on Efimov physics with ultracold cesium atoms

T. Kraemer, M. Mark, J. Danzl, S. Knoop, F. FerlainoB. Engeser, K. Pilch, A. Lange

two teams working on Efimov physics with ultracold cesium atoms

T. Kraemer, M. Mark, J. Danzl, S. Knoop, F. FerlainoB. Engeser, K. Pilch, A. Lange H.-C. Nägerl, R. Grimm

magnetic tunability of Cs

150 G50 G 100 G

-1000

1000

2000

-2000

3000

0

magnetic field (G)

scat

terin

g le

ngth

(a

0)

F=3, mF=3F=3, mF=3

0

there should be an Efimov resonance !there should be an Efimov resonance !there should be an Efimov resonance !there should be an Efimov resonance !

CsBEC

exp. results !

T = 10nK

200nK

triatomictriatomic

Efimov resonanceEfimov resonance

Braaten-Hammertheory*=1/210a0, *=0.06

exp. results !

Braaten-Hammertheory

Esry, Greene, Burketheory 1999

!!

!!

triatomictriatomic

Efimov resonanceEfimov resonance

T = 10nK

200nK

exp. results (again)

T = 10nK

200nK

higher temperature (200nK)recombination rate is unitarity limited& shift of loss maximum

higher temperature (200nK)recombination rate is unitarity limited& shift of loss maximum

triatomic continuum resonance

1/a

Efimov-trimer

200 nK

100 nK 50 nK

Efimov-resonance

(a<0)

E=0

Bringas, Yamashita, Frederico, PRA 69, 040702(R) (2004)

resonance shift

B. Engeser et al., to be published

linear fit

theoretical calculations of T-dependent shift by three groups:Yamashita et al., Esry et al., S. Jonsell

(work in progress)

energy1/a

Efimov resonancesEfimov resonances

a < 0 a > 0

resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979)

resonance scenarios predicted in Sov. J. Nucl. Phys. 29, 546 (1979)

triatomictriatomic

atom-atom-dimerdimer

energy structure of cesium

atoms

dimers

energy structure of cesium

dimers

atoms

we can measure inelastic we can measure inelastic atom-dimer collisionsatom-dimer collisions

at various magnetic fields !at various magnetic fields !

we can measure inelastic we can measure inelastic atom-dimer collisionsatom-dimer collisions

at various magnetic fields !at various magnetic fields !

inelastic atom-dimer collisions

atom-dimer resonanceatom-dimer resonance

new !new !Aug. 06Aug. 06

inelastic atom-dimer collisions

a a 400a 400a00

atom-dimer resonanceatom-dimer resonance

+r0-r0

universal ???

outlookoutlook

outlook I

taking full advantage of Cs tunabilitytaking full advantage of Cs tunability

our exptsso far

the idealFeshbach resonancefor Efimov physics ?!

can we see the fullcan we see the fullEfimov period (x22.7) ?Efimov period (x22.7) ?

outlook II

spectroscopy on Efimov states spectroscopy on Efimov states (rf-spectroscopy or modulation method)(rf-spectroscopy or modulation method)

energy1/a

a < 0 a > 0

hh

outlook III

Few-body physics & Efimov states in an optical latticeFew-body physics & Efimov states in an optical lattice

optical lattice:optical lattice:a 3D array of nanotrapsa 3D array of nanotraps

Stoll & Köhler, PRA 71, 022714 (2005)

making Efimov trimers inan optical lattice

85Rb

outlook IV

other three-body systemsother three-body systems

1 2

3

a12

a23a13

three non-identical particles

equal masses

6Lilowest threespin states

mixed-species systems

different masses

Mm

M

many combinations availableBose-Bose, Bose-Fermi, Fermi-Fermi

e.g., mass ratio 6Li-174Yb 1:29

outlook V

four-body physicsfour-body physics

energy1/a

a < 0 a > 0

D+AD+A

A+A+AA+A+A

TriTri

TriTri

outlook V

four-body physicsfour-body physics

energy1/a

a < 0 a > 0

D+A+AD+A+A

D+DD+D

A+A+A+AA+A+A+A

Tri+ATri+A

Tri+ATri+A

TetramerTetramerstates ?states ?

dimer-dimerdimer-dimerscattering resonances?scattering resonances?

ConclusionConclusion

ultracoldatoms

nanokelvin

Feshbachresonances

FBFB

ultracold atoms with tunable interactionsa new era of few-body physics is just beginning!

ultracold atoms with tunable interactionsa new era of few-body physics is just beginning!

loss minimum

three-body loss after 200ms storage in recompressed trap

minimum at 210minimum at 210aa00

half Efimov period (22.71/2): min.-max. loss !

expt. optimization of evaporative cooling towards BEC

!!

→ → 210210aa00 ! !Kraemer et al.,Appl. Phys. B 79, 1013 (2004)

but r0 100a0 (vdW range):applicability of universaltheory questionable !

but r0 100a0 (vdW range):applicability of universaltheory questionable !