rudolf grimm

ultracold.atoms

JOŽEF STEFAN days, Ljubljana, 19 March 2012

ULTRAHLADNI ATOMI: MODELSKI SISTEMI ZA KVANTNE SNOVI

Ultracold atoms: Model kits for quantum matter

Rudolf Grimm

“Center for Quantum Physics” in Innsbruck

Austrian Academy of Sciences

University of Innsbruck

ultracold.atoms

outline

ultracold quantum gases:

introduction into the general ideas

example #2: strongly interacting

Fermi gases

example #1: Efimov‘s mysterious

quantum states

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ultracold quantum gases: the general ideas

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decelerated atomic beam

few m/s (~1K)

laser cooling

Ofen

~500K

atom trap

accumulation and

further trapping a billion atoms

at a millionth degree Kelvin

important developments: mid 80‘s – early 90‘s

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conservative atom traps

K. Dieckmann, PhD thesis, U Amsterdam, 2001

“atom chip”

TU Vienna

magnetic traps

focused beam trap

crossed-beam

trap

standing-wave

trap (1D lattice)

optical dipole traps

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colder

and

denser

evaporative cooling

extremely efficient !!!

reduction of the potential barrier 1/1000

evaporative cooling: basic idea

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BEC at JILA and MIT

BEC at MIT, Nov. 1995 (sodium)

BEC in Boulder, June 1995

(rubidium)

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attainment of BEC <2000

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attainment of BEC

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degenerate Fermi gases

molecular BEC (2003)

Fermi superfluids (2004, 05)

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optical lattices

review: I. Bloch, Nature Phys. 01, 23 (2005)

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Mott insulator phase transition

Mott insulator: disappearance of diffraction pattern

superfluid: diffraction pattern shows coherence

review: I. Bloch,

Nature Phys. 01, 23 (2005)

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V = 0 Er

V = 19 Er freeze

melt

superfluid

superfluid

84Sr Mott insulator in Innsbruck

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our detectors: imaging of atom clouds

the high end: quantum gas microscopy

Greiner group @ Harvard

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interactions

single parameter characterizes everything

s-wave scattering length a

but can we control it?

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Feshbach resonance

review: Chin, Grimm, Julienne, Tiesinga, RMP 74, 1205 (2010)

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table-top set up

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magneto-optically trapped Sr atoms (461nm)

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Sr and Li: two-species MOT (461nm and 671nm)

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magneto-opically trapped erbium (583nm)

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ultracold group in Innsbruck (April 2011)

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ultracold PIs

Hanns-Christoph Nägerl

Cs - ground-state molecules

1D quantum gases

RbCs - heteronuc. molecules

Francesca

Ferlaino

Er - new, strongly

dipolar quantum gas

Florian Schreck

Sr - quantum simulations

RbSr - ground state molecules

Cs - few-body physics

LiK - Fermi-Fermi mixtures Li - fermionic spin mixtures RG

4 PIs

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mysterious Efimov quantum states

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43 years ago ...

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42 years ago ...

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three identical bosons 133Cs (Innsbruck) Kraemer et al., Nature 440, 315 (2006)

Knoop et al., Nature Phys. 5, 227 (2009) 39K (Florence) Zaccanti et al., Nature Phys. 5, 586 (2009)

7Li (Ramat Gan, Rice) Gross et al., PRL 103, 163202 (2009)

Pollack et al., Science 326, 1683 (2009)

three-component spin mixture of fermions

6Li (Heidelberg, Penn State Univ., U Tokyo) Ottenstein et al., PRL 101, 203202 (2008)

Huckans et al., PRL 102, 165302 (2009)

Williams et al., PRL 103, 130404 (2009)

Lompe et al., Science 330, 940 (2010)

Nakajima et al., PRL 106, 143201 (2011)

Bose-Bose mixture 41K – 87Rb (Florence) Barontini et al., PRL 043201 (2009)

Efimov observations in three-body systems

85Rb (Boulder) Wild et al., arXiv:1112.0362

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Vitaly Efimov visiting Innsbruck, 23 Oct 2009

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quantum states near two-body resonance

energy

1/a

a < 0 a > 0

Edimer =

h2/(ma2)

weakly

bound

dimer

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quantum states near two-body resonance

energy

1/a

weakly bound trimer

a < 0 a > 0

even more weakly

bound trimer

×22.7

×(22.7)2

infinite series of weakly bound trimer states

for resonant two-body interaction

„Efimov states“

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Efimov states: Borromean region

Borromean region

trimers without

pairwise binding

energy

1/a

a < 0 a > 0

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Borromean states in nuclear physics

9Li

n n

review on halo states in nuclear physics: Jensen, Riisager, Fedorov, Rev. Mod. Phys. 76, 215 (2004)

11Li

ultracold.atoms search for Efimov states in He (1994-2005)

2005:

inconclusive end...(?)

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three-body recombination

Eb/3

2Eb/3

dimer + free atom

three atoms

elementary

process

causes trap loss → our observable

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three-body recomb. theory basics

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

a4 - scaling !

very strong

dependence on

scattering length

dimensional analysis

dimensionless

valid if a exceeds all other length scales (vdW length of molecular potential, typ. 30 – 100a0)

good near a Feshbach resonance

early theory paper:

Fedichev et al., PRL 77, 2921 (1996), a4 scaling with C = 3.9

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discrete scale invariance in 3-body decay

C(a) = C(22.7a)

analytic expression available, based on effective-field theory

need two parameters:

three-body parameter (universal)

decay parameter (non-universal)

review: Braaten and Hammer, Phys. Rep. (2006)

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Efimov resonances

energy

1/a

a < 0 a > 0

resonance scenarios predicted in

Sov. J. Nucl. Phys. 29, 546 (1979)

three atoms couple to an Efimov trimer:

„triatomic Efimov resonance“

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exp. results (2005) !

Braaten-Hammer

theory

L*=1/230a0, h*=0.08

T = 10nK

200nK

Efimov resonance

Kraemer et al., Nature 440, 315 (2006)

Kraemer et al.,

Nature (2006)

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magnetic tunability of Cs

three broad s-wave FRs

plus many d- and g-wave FRs (not shown)

Innsbruck

2006 - 2009

Innsbruck

since 2010

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very recent results

observation of three new Efimov resonances

how universal is the three-body parameter? M. Berninger et al., PRL 107, 120401 (2011)

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variations of the three-body parameter?

one tenth of

Efimov period

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variations of the three-body parameter?

one tenth of

Efimov period

very small, if any!

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Vitaly with Cs team

Martin Berninger Alessandro

Zenesini

Cheng Chin

U Chicago Francesca

Ferlaino

Hanns-

Christoph-

Nägerl

RG

& Walter

Harm

Vitaly Efimov & the Innsbruck Cs team

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2, 3, 4,…. many

J. Phys. B 43, 101002 (2010) PRL 103, 240401 (2010)

few-body interactions important

to understand and control many-body physics

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Strongly interacting Fermi gases

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two-component Fermi gas

scattering length > interparticle distance:

strongly interacting regime

in contrast to Bose gases:

stable !!! (Pauli blocking of three-body decay)

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neutron star

http://www.astro.umd.edu/

~miller/nstar.html

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interesting question

what happens if a → ? (so-called Bertsch problem)

answer is simple:

renormalized chem. potential →

with 0.37

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spin mixture of

two lowest states

stable against

two-body decay

6Li spin mixture

0 250 500 750 1000 1250 1500

-4

-2

0

2

4

magnetic Field [G]

a (1

000 a

0)

prediction: Houbiers et al., PRA 57, R1497 (1998)

precise characterization:

Bartenstein et al., PRL 94, 103201 (2005)

Feshbach resonance

interaction

control knob

weakly bound

molecules

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table-top trapping apparatus

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optical trap for evaporative cooling

ultracold.atoms BEC of molecules

final trap power 28mW 3.8mW

number of molecules 400.000 200.000

temperature 430nK few 10nK

condensate fraction ~20% >90%

partially

condensed

almost

pure

mBEC:

excellent starting point

for studies on

BEC-BCS crossover

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two classes

Bosons integer spin

Fermions half-integer spin

all in ground state:

Bose-Einstein condensate

trapped atoms

at T=0

only one particle per state:

degenerate Fermi gas

these two

worlds

are connected !

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two classes

Bosons integer spin




trapped atoms

at T=0



„pairing“

is the key

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two classes

Bosons integer spin






interaction

control !!!

Feshbach

resonance

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two classes

Bosons integer spin






interaction

control !!!

universal !!!

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two classes

Bosons integer spin






crossover gas

as a high-Tc

superfluid

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establishing superfluidity

hydrodynamic

expansion

Duke, 2002

collective modes

Duke, Innsbruck, 2004

pair condensation JILA, MIT

2004

Duke

2005

heat

capacity

Innsbruck, 2004

pairing gap

vortices MIT, 2005

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crossover in Fermi gases

BEC-BCS crossover well understood,

remarkable benchmark for many-body theories

some open issues:

low-D Fermi gases, second sound...

new frontier:

strongly interacting Fermi-Fermi mixtures

“high-Tc” superfluidity established

experiments:

Innsbruck, Munich/Singapore, Amsterdam,

MIT, ENS Paris

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two-component Fermi system (spin mixture)

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two-species: Fermi-Fermi mixture

mass

imbalance species

selectivity

6Li

40K

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how about tunability?

Feshbach resonance

review: Chin, Grimm, Julienne, Tiesinga, RMP 74, 1205 (2009)

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elastic scattering

Li – K

spin

channels

1 – 3

1 – 2

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spin channels

FR @ 155G

lowest

spin state

third-to-lowest

spin state

6Li 40K

powerful tool-box of radio-frequency transitions

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experimental parameters

6Li: N = 1.9 x 105

EF = 1.6 µK

40K: N = 1.2 x 104

EF = 400 nK T = 330 nK

Li Fermi energy

our leading energy scale!

1/kFLi 3000 a0

polaronic regime

heavy 40K in

Fermi sea

of 6Li

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Impurity in a Fermi sea

weak (kF|a|<<1): simple mean-field description

stronger: quasi-particle (polaron)

à la Landau Fermi liquid theory

strong (kF|a| > 1): polaron or molecule?

? ?

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Innsbruck Fermi-Fermi team

Michael Jag

Matteo Zaccanti

Andreas Trenkwalder Christoph

Kohstall Florian

Schreck

Rudi Grimm

Pietro Massignan ICFO, Spain

Georg Bruun U Aarhus, Denmark

theory collaboration

Marco Cetina

Metastability and coherende of repulsive polarons

in a strongly interacting Fermi mixture

C. Kohstall et al., Nature, in press; arXiv:1112.0020

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energy diagram (T=0)

theory: P. Massignan and G. Bruun

repulsive polaron

E+

attractive

polaron

E-

Em

Em - F

molecule-hole

continuum

(MHC)

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“reverse” rf spectroscopy

K

in non-interacting

spin state

K

in (strongly) interacting

spin state

radio-

frequency

NB: different from standard rf probing !

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spectral response

1 ms p-pulse (w/o interaction)

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spectral response

polaron-molecule

transition

-1/Fa = 0.6

repulsive polaron

observed up to

-1/Fa = -0.3

1 ms p-pulse (w/o interaction)

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spectral response

let‘s crank up the rf power (100 x)

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spectral response

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energy diagram (T=0)

theory: P. Massignan and G. Bruun

repulsive polaron

E+

attractive

polaron

E-

Em

Em - F

molecule-hole

continuum

(MHC)

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measured decay rates

theory (two decay mechanisms)

repulsive to attractive polaron,

followed by decay into MHC

three-body process leading

directly into MHC

long

lifetime !

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the big question

phase separation

(ferromagnetism)

molecules

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general conclusion

ultracold atoms: unique, well-controllable model systems

for a wide range of phenomena • strongly interacting quantum matter

• condensed-matter physics

• few-body and many-body physics

• ....

exquisite benchmarks for quantum many-body theories

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thank you for your attention !

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how long?

60 min (incl. disc.) seminar talk

talk way too long!!

could have stopped after the Efimov part (50min)

general intro took 20min.

could only rush through fermion part

rudolf grimm

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