Claude Cohen-Tannoudji BRIDGES Dialogue Towards A Culture .
Manipulating atoms with lightClaude Cohen-TannoudjiBRIDGESDialogue towards a culture of peaceThailand, December 20041
Outline1. What is light?- From light waves to photons2. How does it interact with atoms?- Quantum mechanics- Emission and absorption of photons by an atom3. Can one use and master these interactions?- Light : a source of information on atoms- Light : a tool for acting on atomsOptical pumping ; Laser cooling4. What are the new perspetives opened by these methods?- New research fields- New applications2
Light wavesFrequency : νPeriod : 1 / νSpeed of propagation : c 3 x 108 m/sWavelength : λ c / νAt a given time, sinusoidal wave with aperiod λλInterferencesDiffraction3
Light interferencesSE1BAE2MS : point light sourceE1: screen with 2 slitsA and BE2:observation screen To go from S to M, light canfollow 2 pathsSAM and SBM Depending on the position of Mon E2, the 2 waves arriving in Mcan be- in phase(constructive interferences)- out of phase(destructive interferences) The light intensity observed onthe observation screen isspatially modulated4
PhotonsLight is also a beam of particles called « photons »,with an energy E and a linear momentum p.Planck-Einstein relationsThe photons associated with a light wave withfrequency ν have an energy E and a linearmomentum p given by :E hνp hν /ch : Planck’s constant 6.36 10-34 J.sWave-particle duality5
AtomsPlanetary modelElectrons, light particles with a negative charge,orbiting around a nucleus, particle with a muchheavier mass and with a positive chargeFailure of these modelsThey predict that electrons should radiate energy becauseof their accelerated motion around the nucleus. Theythus should fall into the nucleus Atoms should thus be instable The emitted spectrum should be continuous2 predictions in contradiction with experiment Atoms are stable The emitted spectrum consists of discrete lines6
Quantum mechanicsWave- particle duality extended to matterWith every matter particle of mass M and velocity vis associated a wave with a wavelength λdB given by :Louis de Broglie 1924More generally,The state of a matter particle is described by awave function obeying the Schrödinger equationOnly certain solutions of this equation are physicallyacceptable (analogy with the resonance frequenciesof a music instrument)Quantization of physical quantities7
Quantization of the energy of an atomThe various possible oscillation frequencies of the wavefunction correspond to well defined energies of the atomThe internal energyof an atom can onlytake discrete valuesE32nd excited stateE21st excited stateE1Ground stateSpectrum of energy levels8
Elementary interaction processesbetween atoms and photonsbbhνhνEmissionAbsorptionaaEb - Ea hνConservation of energyPrinciple of spectroscopyMeasuring ν with a spectrometer gives Eb - EaLight is a source of informationon the structure of atoms and a probefor detecting their presence in a medium9
Spontaneous emission of a photonAn atom does not remain indefinitely in the excited state e.After a finite time τR, it falls back to the ground state g byspontaneously emitting a photon in all possible directions.τR : Radiative lifetime of e, on the order of 10-8 segInduced emission of a photon (Einstein 1917)hνegA photon with energy h ν Ee-Ef , impinging on an atom inthe excited state e induces (or stimulates) this atom to emit aphoton exactly identical to the impinging photon (same energy,same direction of propagation, same polarization)10
Amplification of lightThermodynamic equilibriumIn an ensemble of atoms inequilibrium, a lower lever E1is always more populated thanan upper level E2.Population inversionNon equilibrium situation wherean upper level E2 is more populatedthan a lower level E1.E2E1E2E1If a light beam with frequency ν passes through a mediumwhere populations are inverted, the new photons whichappear by induced emission are in a greater number thanthe photons which disappear by absorption.The incident light beam is thus amplified11
New light sources : lasersC. Townes, A. SchawlowAmplifying atomicmedium put betweentwo mirrorsLight can make several round trips between the 2 mirrorsand be amplified several times.If the cavity is « tuned », and if the gain is larger than thelosses, one gets an « oscillator » for light.« Laser » source with completely new characteristicsas compared to usual thermal light sources(intensity, directivity, coherence, monochromaticity ) Emergence of new research fields A huge number of applications12
Light is also a tool for acting on atomsBy using resonant or quasi-resonant interactions betweenatoms and photons, one can control the various degreesof freedom of an atom (spin, energy, velocity, position)Resonant exchanges of energy, angular momentum,linear momentum between atoms and photonsUsing the basic conservation lawsfor manipulating atoms13
TRANSFER OF ANGULAR MOMENTUMFROM PHOTONS TO ATOMSOptical pumping14
Atomic angular momentumAtoms are « spinning tops »They have an internal angular momentum JThe projection Jz of J along the z-axis is quantizedFor example, for a « spin 1/2 » atom, there are twoSpin down possible values of Jz : Spin up Atoms have also a magnetic moment Mz proportional to JzIn a static magnetic field B, the 2 spin states have oppositemagnetic energies proportional to B Energy splitting E proportional to B E h νz Magnetic resonance : transitions between the 2 spin statesinduced by a radiofrequency wave with frequency νz15
Optical pumping (A. Kastler, J. Brossel)At room temperatures and in low magnetic fields both spinstates are nearly equally populated.Very weak spin polarizationMagnetic resonance signals are proportional to thedifference of populations between the 2 spin states.Easy to observe only in dense systems (solids or liquids)Polarized photons have also an angular momentum andit is easier to polarize light than atomsBy absorbing polarized photons, atoms can gain the angularmomentum of these photons and become polarized.Gaseous samples with large spin polarizationOne can easily obtain in this way large signals of magneticresonance with dilute gaseous samples16
Images de résonance magnétiquedu poumon humain (IRM)IRM-ProtonProton3He 3HeIRM-Duke Univ., CAMRDhttp://camrd4.mc.duke.edu/ (1997)Centres IRMpour le poumon Princeton Boston B&W H., St Louis Mainz U., Paris-Orsay, Nottingham U Duke U., U. of Virginia, U. of Pennsylvania.Plusieurs autres centres en cours de création 17
LIGHT SHIFTS18
Light shifts (or ac-Stark shifts)A non resonant light excitation displaces the ground state geeωL ωAωAgωL ωAωAδEggδEgδEg is proportional to the light intensity δEg has the same sign as ωL - ωA Two Zeeman sublevels g1 and g2 have in general differentlight shifts depending on the light polarization. Light shift of the magnetic resonance curve in gC. Cohen-Tannoudji, C.R.Acad.Sci. 252, 394 (1961)19
TRANSFER OF LINEAR MOMENTUMFROM PHOTONS TO ATOMSRadiation pressure force20
Recoil of an atom absorbing a photongeM v rec hν / cThe atom, in the ground state g, absorbs a photon with momentum hν/c.It jumps to the excited state e and gains this momentum hν/c.It recoils with a velocity vrec hν / Mc.Spontaneous emission of a photonAfter a mean time τR (radiative lifetime of e, of the order of 10-8 sec),the atom falls down in g by spontaneous emission of a photon, withequal probabilities in 2 opposite directionsOn the average, the loss ofmomentum in the spontaneousemission process is equal to zero.21
Mean velocity change δv in a fluorescence cycleAbsorption followed by spontaneous emission.Atom in a resonant laser beamMean number of cycles per second : WW 1 / τR 108 s-1Mean acceleration a (or deceleration) of the atoma velocity change per second velocity change δv per fluorescence cyclex number of cycles per second W vrec x (1 / τR)a 10-2 x 108 m/s2 106 m/s2 105 gHuge radiation pressure force!22
SLOWING DOWNAND COOLING ATOMS23
Slowing down and cooling atoms with lasersThe forces exerted by laser beams on atoms allow one- to reduce their mean velocitySlowing down atoms- to reduce the velocity spread around the mean value,i.e. to reduce the disordered motion of the atomsCooling atomsSeveral cooling mechanisms have been demonstrated(Doppler cooling, « Sisyphus cooling », subrecoil cooling)Obtention of temperatures on the order of a few 10-6 Kand of atomic velocities on the order of 1 cm/sAt room temperatures (T 300 K), atomic velocities areon the order of 1 km/s24
Stopping an atomic beamLaserbeamAtomicbeamTapered solenoidAtoms coming from an oven with a velocity v0 103 m/s are decelerated bythe radiation pressure force exerted by the laser and stop after a timet v0/a 103/106 10-3s . They travel over a distance L v02 / 2a 0.5 mZeeman slowerJ. Prodan, W. Phillips, H. Metcalf, P.R.L. 49, 1149 (1982)The Doppler detuning due to the deceleration of the atoms iscompensated by a spatially dependent Zeeman shiftAnother solution : chirpof the laser frequency25
Laser Doppler coolingT. Hansch, A. Schawlow, D. Wineland, H. DehmeltTheory : V. Letokhov, V. Minogin, D. Wineland, W. Itano2 counterpropagating laser beamsSame intensitySame frequency νL (νL νA)νL νAνL νAvAtom at rest (v 0)The two radiation pressure forces cancel each other outAtom moving with a velocity vBecause of the Doppler effect, the counterpropagatingwave gets closer to resonance and exerts a strongerforce than the copropagating wave which gets fartherNet force opposite to v andproportional to v for v smallFriction force “Optical molasses”26
Measurement of the temperatureTime of flight methodThe time of flight signal depends on:MolassesProbelaser7cmPhotodiode the acceleration due to gravity the initial position distribution(which can be deduced froma photo of the molasses) the initial velocity distribution(which is determined by thetemperature)Experimental resultsThey don’t agree with the predictions deduced from the theory ofDoppler cooling and they are about 100 times lower than the lowestpossible temperatures predicted by such a theory!P. Lett, R. Watt, C. Westbrook, W. Phillips, P. Gould, H. MetcalfPhys. Rev. Lett. 61, 169 (1988)27
Sisyphus cooling(J. Dalibard, C. Cohen-Tannoudji)Several ground state sublevelsSpin upSpin downIn a laser standing wave, spatial modulation of the laser intensity andof the laser polarization Spatially modulated light shifts of g and g due to the laser light Correlated spatial modulations of optical pumping rates g g The moving atom is always running up potential hills (like Sisyphus)!Very efficient cooling scheme leading to temperatures in the µK range28
Sisyphus coolingJ. Dalibard, C. Cohen-TannoudjiOptical pumpingLight shiftedatomic sublevels29
TRAPS FOR NEUTRAL ATOMSLaser traps30
Laser trapsSpatial gradients of light shiftsFocused laser beam with a red detuning (ωL ωA)The light shift δEg of the ground state g is negativeand its absolute value is maximum at the focusAttractive potential well in which neutral atomscan be trappedOther types of traps using radiation pressure forces ofpolarized waves and magnetic field gradientsMagneto-optical traps (MOT) J. Dalibard31
Evaporative coolingE4E2E1U0E3Atoms trapped in apotential well witha finite depth U02 atoms with energiesE1 et E2 undergo anelastic collisionAfter the collision, the2 atoms have energiesE3 et E4, withE1 E2 E3 E4If E4 U0, the atom withenergy E4 leaves the wellThe remaining atom has amuch lower energy E3.After rethermalization of theatoms remaining trapped,the temperature of thesample decreases32
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Applications of ultracold atoms1- Long observation timesBetter atomic clocks2- Long de Broglie wavelengthsAtomic interferometry3- High phase space densitiesBose-Einstein CondensationAtom lasers and matter waves35
ATOMIC CLOCKS36
The width ν of theatomic resonance isinversely proportionalto the observation time TUltracold atoms moveslowly and providelong observation timesInterrogationThe narrower theatomic resonance,the better the accuracyof the clockCorrectionPrinciple of an atomic clockQuartz oscillatorwhose frequency ismaintained at the centerνo of an atomic resonanceQuartz oscillatorAtomic resonance ννν037
Atomic fountains- Sodium fountains :- Cesium fountains :Stanford S. ChuBNM/SYRTEC. Salomon, A. ClaironStability : 1.6 x 10-16 for an integration time 5 x 104 sAccuracy : 7 x 10-16Transportable fountains38
Parabolic flights39
Tests of PHARAO with parabolic flights40
Atomic clocks with cold atomsA.Clairon, C.Salomon (B.N.M./L.P.T.F.) Thermal beam :v 100 m/s, T 5 ms ν 100 Hz Fountain :v 4 m/s, T 0.5 s ν 1 Hz PHARAO :v 0.05 m/s, T 5 s ν 0.1 Hz41
ACES (Atomic Clock Ensemble in Space)cnesesa Time reference Validation of space clocks Tests of fundamental theoriesC. Salomon et al , C. R. Acad. Sci. Paris, t.2, Série IV, p. 1313-1330 (2001)42
INTERFERENCES BETWEENDE BROGLIE WAVES43
Interference fringes obtainedwith the de Broglie waves associatedwith metastable laser cooled Neon atomsCloud of cold atomsF.Shimizu, K.Shimizu, H.Takuma Phys.Rev. A46, R17 (1992)44
Experimental resultsEach atom gives rise to a localized impact on the detectorThe spatial repartition of the impacts is spatially modulatedWave-particle duality for atomsThe wave associated with the atom allows one tocalculate the probability to find the atom at a given point45
Bose-Einstein condensation46
Bose-Einstein condensation (BEC)At low enough temperatures and high enough densities, thede Broglie wavelength of the atoms becomes larger than themean distance between atomsIdentical bosons in a trap are then predicted to condense inthe ground state of the trapMacroscopic number of atoms in the same quantum stateMacroscopic matter wavesCombination of laser cooling and trapping with previouslydeveloped methods for studying spin-polarized Hydrogen(magnetic trapping, evaporative cooling) have led to theobservation of BEC in alkali gasesBoulder, MIT, Houston (1995)BEC has been also observed in Hydrogen (MIT, 1998) andin metastable Helium (Orsay, ENS, 2001).Very recent observation of molecular condensates.47
T TCSketch of the wavesassociated with thetrapped atomsT TCEvolution of thesewaves when Tdecreases from avalue much higherthan TC to a valuemuch lowerT TCT TCW. Ketterle48
Bimodal structureof the spatial distribution of bosonsContribution of thecondensed atomsNarrow peak with a widthcorresponding to the groundstate wave function of the wellContribution of the non condensed atomsBroad piedestal coming from atoms occupying excitedstates ot the well described by wave functions with alarger width49
Visualization of the atomic cloudSpatial dependence of the absorptionof a laser beam by the cloud50
JILAScience, 269, 198 (1995)MITPhys. Rev. Lett. 75, 3969 (1995)87RbBoulder23NaMIT7LiRice1HMIT4He*Orsay, LKB41KFlorence133CsInnsbruck174YbKyotoMolecular condensatesBoulder, Innsbruck,MIT, LKB51
Importance of gaseous Bose Eintein condensatesMatter waves have very original properties ( superfluidity,coherence, ) which make them very similar to othersystems only found, up to now,in condensed matter(superfluid He, superconductors)The new feature is that these properties appear hereon very dilute systems, about 100000 times more dilutethan air. Atom-atom interactions have then a muchsmaller effect which can be calculated more preciselyFurthermore, these interactions can be modified at will,in magnitude and in sign (attraction or repulsion), using« Feshbach resonances » obtained by sweeping astatic magnetic fieldA great stimulation for basic research!52
Examples of applications- Magnetometers and masers with optically pumped atoms- MRI of the lung with optically pumped He3 atoms- Atomic clocks with ultracold atoms reaching a relativefrequency stability and an accuracy of a few 10-16- Atom lithography- Atomic gradiometers and gyrometers withde Broglie waves- Atom lasers : coherent beams of atomis de Brogliewaves extracted from a Bose Einstein condensate- Quantum information using a Bose Einsteincondensate trapped in an optical latticeMost of these applications were not planned in advanceand introduce discontinuous changes in the technology53
ConclusionOur ability to control and to manipulate quantum systems(atoms, ions, electrons) has considerably increasedduring the last few decadesThis is opening completely new research fields and allowsus to ask new questions and to investigate new systems,new states of matter.One can reasonably expect that this will lead us to a betterunderstanding of the world and to interesting new applicationsImportance of basic research- for improving our vision of the world- for solving the various problems (energy, environment,health) that mankind has to face- for improving, by scientific education, our ability to fightagainst intolerance, fundamentalism, and for promoting inthis way the establishment of peace between nations54
(J. Dalibard, C. Cohen-Tannoudji) Several ground state sublevels Spin up Spin down In a laser standing wave, spatial modulation of the laser intensity and of the laser polarization Spatially modulated light shifts of g and g due to the laser light Correlated spatial modulations of optical pumping rates g g
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