Ultra-coldatoms Jean Dalibard - Institute of...
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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.
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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
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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?
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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
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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
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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
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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:
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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.
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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
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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
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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,…)
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Towards even better clocks
Universal time reference
Tests of fundamental physics
ACES mission
Planned launching date: 2013Duration : 1.5 to 3 years
Colombus
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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
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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
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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?
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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
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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
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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
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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
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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
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Quantum physics at the macroscopic scale
SuperconductorsSuperfluid liquid helium
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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:
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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
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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
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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
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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
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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
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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
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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
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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, …
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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
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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
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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
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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
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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
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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