Ultra-coldatomsJean DalibardLaboratoire Kastler Brossel, Departement dePhysique,Ecole NormaleSuperieure, Paris, France

Tuesday, 3 May- 2:30 p.m,

Laser light isoften associatedwith thenotionof heat. However, when properly adjusted,laserbeamscan coolatoms at extremely lowtemperatures, onebilliontimeslower than room temperature, openingthusthepathto awea lth ofnovel phenomena .

Mytalkwill first present the physica l principles of laser cooling,whicharebased ontheexchange ofmomentum andenergy between lightandmatter. Iwill then provide some illustrationsof thisvery activefieldof research , rangingfrom metrology to collective behaviours, likeinterference of matter wavesand superfluidity.Themetrological applicationshave been theinitial drivingforce ofthedomain, withthesimple idea thatslowatoms canbeprobed fora longtime in anatomic clock, hence leadingtoanincreased precisionofthe device.The research oncollective phenomena hasbeen boosted bythesuccess of evaporativecooling,whichhasprovided theultimate stepto bring a laser-cooled atomicassemblydown to thequantum regime.

The quantum gases thatare produced inthisway areeitherBose-Einsteincondensates ordegenerateFermi fluids(ormixtures ofboth), dependingonthestatisticalnature oftheatomicspecies. Inthelastpartofthe talk Iwilldescribehowthiscold quantummattercan provide answersto questions thatarestill open forotherphysicalsystems, such assuperconducting materia lsorneutron stars.

Ultra-cold atoms

Jean DalibardEcole normale supérieureCNRS and UPMC

How one can use light to generate novel states of matter, or simulate already existing states

photo NIST

Light = source of information on matter

Spectroscopy gives us insights on the composition of stars, chemical elements in flames, gases in an electric discharge...

Can we use light to “act” on matter?

The elementary process in light-matter interaction

g: ground state

e: excited statelifetime τ quasi-resonant

photon:

In a photon absorption or emission process, the velocity of the centre-of-mass of the atom changes by

recoil velocity: 3 cm/s for sodium atoms (m = 23 u.m.a.), 3 mm/s for cesium atoms (m = 133 u.m.a.)

Photon momentum:

Internal energy levels of an atom

m: mass of the atom

The radiation pressure force

With a laser, the repetition rate is limited only by the lifetime of the electronic excited state (typically 10-8 s)

acceleration in the range 104 to 105 gatomresonant photons

The repetition of these elementary “collisions” creates a force on the atoms

The velocity drops from 100 m/s to 0 m/s on a distance ≈

cm.

Kepler : orientation of comets tails with respect to the sun

Outline of the talk

1. Laser cooled atoms and metrology

2. From optical molasses to Bose-Einstein condensates

3. Quantum gases: superfluidity and quantum simulators

The optical molasses

atoms

~ 2 cm

106 sodium atoms

NIST

cooling

Doppler cooling (Hänsch-Schawlow): an atom travelling to the right (resp. left) interacts more with the wave travelling to the left (resp. right)

Characteristic energy scale:

Choose

laserbeams

atomone-dimension model:

How to measure the temperature of the atoms?

The temperature is a measurement of the disordered motion of atoms in a gas, a liquid or a solid.

Cesium Δv = 1 cm/s

T = 2 μK

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, and S. Guellati, Europhys. Lett. 12, 683 (1990) : Laser cooling of cesium atoms below 3 microKelvins

Sisyphus cooling

Y. Castin and J. Dalibard, Europhys. Lett. 14, 761 (1991) :Quantization of atomic motion in optical molasses.

The temperature scale for laser cooled gases

1 K 100 K 104K 106K1 mK1 μK T

You are here

sun (surface)

sun (centre)

liquidnitrogen

BoseEinsteincondensates

Nobel 2001E. Cornell, W. Ketterle, C. Wieman

opticalmolasses

Nobel 1997S. Chu, C. Cohen-Tannoudji, W. Phillips

superfluidhelium

Principle of an atomic clock

Definition of the unit of time (‘second’):

a

b a and b are the two lowest energy levels of the cesium atom (isotope 133)

By definition, the electromagnetic wave that is resonant with the a-b transitionperforms 9 192 631 770 oscillations in a time interval of one second.

Cesium atomic beam electromagnetic cavity detector

feedback loop

Cold atom fountain

The precision of the clock is better if the atoms interact for a long time with the electromagnetic wave

height : 1 meterInteraction time : 1 second

Clock precision : 10-16

Drift smaller that one minute for a clock that would operate since the Big-Bang!

Paris observatory (A. Clairon, C. Salomon,…)

Towards even better clocks

Universal time reference

Tests of fundamental physics

ACES mission

Planned launching date: 2013Duration : 1.5 to 3 years

Colombus

Outline of the talk

1. Laser cooled atoms and metrology

2. From optical molasses to Bose-Einstein condensates

3. Quantum gases: superfluidity and quantum simulators

Classical or quantum matter?

High temperature:Newtonian mechanics

Low temperature:wave mechanics

de Broglie, 1923 Sodium vapour at room temperature: λ

= 0.2 Angströms

To each material particle of mass m and velocity v, one can associate a “matter wave” of wavelength :

proportional to

The energy levels of the centre-of-mass of an atom

Because of the wave nature of themotion, a measurement of the centre-of-mass energy can only give quantized results

What is the repartition of the atoms on these levels at very low temperature?

.

.

.

Can two identical particles be in the same state?

The two classes of particles existing in Nature

Bosons, particles with a gregarious behaviour, whichcan accumulate with an arbitrary large number in the same quantum state

photons, hydrogen atoms, 23Na, 133Cs atoms,…

Fermions, particles with an individualistic behaviour:never two particles in the same quantum state

electrons, protons, neutrons, quarks,6Li, 40K atoms,…

Einstein Bose

Fermi Dirac

Bose-Einstein condensation1924-25

Gas at room temperature, d = 20 Angströms and λ

=0.2 Angströms

Threshold for Bose-Einstein condensation: where d is the average distance between neighbouring particles

T = 0high temperature low temperature

Very far from threshold …

ideal gas

condensate

How to reach the condensation threshold?

One switches a magnetic trap around the cold atoms

Energy of a magnetic dipole:

If the dipole and the field have opposite directions,this energy reads:

ENS

E Bμ= − ⋅rr

| | | |E Bμ= +rr

Potential well around a point where takes its minimal value( )B rr r

N N / 100

T T / 100Evaporative cooling

imaging using a resonantlaser pulse

Images of a Bose-Einstein condensate

MITAtoms that have already “condensed”: H, Li, Na, K, Rb, Cs, He, Yb, Cr, Ca, Sr

Outline of the talk

1. Laser cooled atoms and metrology

2. From optical molasses to Bose-Einstein condensates

3. Quantum gases: superfluidity and quantum simulators

Quantum physics at the macroscopic scale

SuperconductorsSuperfluid liquid helium

Classical and quantum rotation

Rotating classical gasrigid body rotation

The only way to generate a non-trivial rotation field

is to nucleate quantum vortices Feynman, Onsager

Rotating quantum gasmacroscopic wave function:

At a place where , the velocity field a zero curl:

Rotating condensates

We stir our condensatewith a moving laser beamand take an image after

ballistic expansion

0 ΩcRotation frequency Ω

K. Madison, F. Chevy, V. Bretin, P. Rosenbuch

ENS

z

Ω

Evidence for quantum vortices

Towards quantum Hall effect?Clear proof of superfluidity

200 μm

Optical lattices

Standing light waves in which the atoms accumulate at the intensity antinodes

laserlaserlaserlaser

lase

rla

ser

lase

rla

ser

Regular lattice of“optical tweezers”

“egg box” for atoms

Visualizing atoms in an optical lattice

Group of Immanuel Bloch & Steffan Kuhr (Munich) Nature 467, 68 (2010)

Each point is a single rubidium atom trapped at a site of a two-dimensional square lattice

Lattice period: 0.53 μm

Simulation of electrical conduction?

Mass melectron atom

x 105

Distance d between sites3 10−10

m 3 10−7

mx 103

P. Aebi, Neuchâtel

Temperature300 K x 10-11

3 nK

Same characteristic parameter λ

/ d for the two situations

Study of the transition between a conductor and an insulator with cold atoms(I. Bloch, T. Esslinger,…): towards a model for high Tc superconductors?

de Broglie wavelength3 10−9

m 3 10−6

mx 103

From a conductor to an insulator with cold atoms

Group of Immanuel Bloch & Steffan Kuhr (Munich) Nature 467, 68 (2010)

Increasing the role of interactions with respect to motion from site to site

What about atoms with Fermi-Dirac statistics?

Ideal gas at zero temperature

Salomon et al.,ENS

Bose-Einstein Fermi-Dirac

Bose-Einstein : integer spinFermi-Dirac : half integer spin

Nelectrons = Nprotons

Statistical properties are governed by Nneutrons :

Boson if Nneutrons is even Fermion if Nneutrons is odd

A (very simplified) simulator of neutron stars

X ray image of RCW 103NASA

1 to 2 solar massesR=12 km T= 106 Kelvins

One knows how to prepare gases of fermionic atoms(6Li, 40K) in the same parameter range in terms of:

and

May provide answers to open questions concerning the superfluid character of this strongly interacting quantum matter

Conclusion and outlook

Clocks, gravimeters, gyrometers with cold atoms: industrial production

Quantum gases of cold atoms and collective aspects

Toward a universal simulator of other quantum systems?

• Ultracold chemistry: formation of dimers, trimers, … in the μK range

• Low dimension systems (1D, 2D)

• Addition of a controlled disorder using laser speckle

superfluidity, superconductivity, …

Cold atom gravimeter (LNE-SYRTE)

Excellent agreement between measurements and tide models

Long term stability ~ 5 10-10g

Comparison over 12 hours with a state-of-the-artconventional gravimeter (black dote)

atoms: red dots

F. Pereira Dos SantosA. Landragin

Why does indiscernability favours a gregarious behaviour?

Counting of the W possible configurations of a given system, with the same probability for each.

How many ways to put 3 particles in 2 boxes?

Discernables :

31 2

3

1 2 312

31

2

31 23

1 2 31

2 312

Gregarious in 2 cases out of 8: proba =1/4

Non-discernables :

Gregarious in 2 cases out of 4: proba =1/2

W=8 W=4

An atom laser

Once the BEC is produced at the centre of the trap,one produces a continuous “leak” of atoms

2 mm

The “tap” is a radio-frequency wave, which flips the magnetic moment of the atoms at a given location in the trap

The atoms in this beam are all in the same quantum state, as the photons ofa laser which all have the same wavelength and the same direction.

rubidium

Munich

Interference between two atom lasers

Young slit experiment

E

Radiofrequency 2Radiofrequency 1

z

T > Tc T < Tc

High contrast, which revealsthe macroscopic occupation

of a single quantum state

Munich

Interaction strengtha > 0a < 0

« Bardeen,Cooper,

Schrieffer »side

molecular BEC side

|a|=∞

V0

nbound states

n+1bound states

a

The BEC-BCS crossover

Feschbach resonance

Munich 2002

VV 00 = 10 = 10 ErEr VV 00 = 13 = 13 ErEr VV 00 = 16 = 16 ErEr

For large lattice depths, repulsive interactions dominate over tunnelling between sites

spatial coherence is lost!

Superfluid to Mott insulator transition

Bose-Hubbard

Fisher et al. 1989,Jaksch et al. 1998

The system evolves towards a state with a fixed number of atoms/site