Claude Cohen-Tannoudji INMETRO Rio de Janeiro, 16 January 2006 · 2005-12-19 · - Atom-photon interactions 2. Using conservation laws for manipulating atoms - Laser cooling - Optical

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Quantum physics and its impact on daily life

Claude Cohen-Tannoudji

INMETRORio de Janeiro, 16 January 2006

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Quantum physicsQuantum mechanics is a fundamental theory which is essential for understanding the microscopic world.Quantum concepts are not easy to grasp because they arevery far from our classical intuition based on our experienceof the macroscopic world. The work of Max Planck andAlbert Einstein at the beginning of the last century has laidthe foundations for this conceptual revolution

Now, most of the technical objects that we are using in ourdaily life are based on quantum physics. So, quantumphysics is not an abstract theory for specialists. We mustinclude it in our scientific education and in our culture. It is abeautiful example of the generality and of the power ofphysics.

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Outline• Introduction of a few quantum ideas We will focus here on the quantum description of light and atoms.

Other important topics: solid state physics, particle physics, … - Wave particle duality for light and atoms - Atom-photon interactions

2. Using conservation laws for manipulating atoms - Laser cooling - Optical pumping3. A few examples of practical applications Lasers, atomic interferometry, MRI, atomic clocks, transistors,…4. New perspectives - Observation of single atomic particles - Macroscopic quantum gases. Bose-Einstein condensates

- Quantum information

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A FEW BASIC NOTIONS

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Light

Interferences Diffraction

Wave-particle duality

Frequency : ν Speed of propagation : c = 3 x 108 m/s

Light is an electromagnetic wave

h = Planck’s constant = 6.36 x 10-34 J.s

Energy : E = h ν Momentum : p = h ν / c

Light is a beam of particles called photons(Einstein 2005)

Both wave and particle aspects are essential

Interferencesin water

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Quantum mechanics

Only certain solutions of this equation are physically acceptable(analogy with the resonance frequencies of a music instrument)

More generally,The state of a matter particle is described by a wave function obeying the Schrödinger equation

With every matter particle of mass M and velocity vis associated a wave with a wavelength λdB given by :

Louis de Broglie 1924

Wave- particle duality extended to matter

Energy spectrumGround state

1st excited state

2nd excited state

The energy of an atom cannot take any value. It is quantized

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Elementary interaction processesbetween atoms and photons

Conservation of energye gE E hν− =

The atom goes from e to g by emitting a photon h νEmission

e

g

hν

The atom goes from g to e by absorbing a photon h νAbsorption

e

g

hν

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Light : a source of informationon the structure of atoms

Spectroscopy : an essential source of information on varioustypes of media, in particular in astrophysics

• Galaxies, expansion of the universe• Stellar and planetary atmospheres• Interstellar molecules• Plasmas, flames• Detection of pollution (LIDAR)…

Measuring with a spectrometer the frequencies (Eb-Ea)/h of the linesemitted by an atom allows one to reconstruct its energy diagramA spectrum of lines characterizes an atom. It’s a « finger print »

H

Hg

Ne

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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 twopossible values of Jz : Spin up ⇑ Spin down ⇓

Atoms have also a magnetic moment Mz proportional to Jz

In 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 νz

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MANIPULATING ATOMS WITH LIGHT

- Transfer of linear momentum from photons to atoms Laser cooling- Transfer of angular momentum from photons to atoms Optical pumping

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Recoil of an atom absorbing a photon

The atom, in the ground state g, absorbs a photon with momentum hν/c.It jumps to the excited state e and gains this linear momentum hν/c.It recoils with a velocity vrec= hν / Mc.

Spontaneous emission of a photon

After 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 directions

On the average, the loss of linearmomentum in the spontaneousemission process is equal to zero.

g erecv /ν=M h c

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Mean velocity change δv in a fluorescence cycleAbsorption followed by spontaneous emission.

Atom in a resonant laser beamMean number of cycles per second : W

W ≈ 1 / τR ≈ 108 s-1

Mean acceleration a (or deceleration) of the atom a = velocity change per second = velocity change δv per fluorescence cycle x number of cycles per second W = vrec x (1 / τR)

Huge radiation pressure force!

a = 10-2 x 108 m/s2 = 106 m/s2 = 105 g

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Slowing down and cooling atoms with lasers

The forces exerted by laser beams on atoms allow one - to reduce their mean velocity Slowing down atoms - to reduce the velocity spread around the mean value, i.e. to reduce the disordered motion of the atoms Cooling atomsSeveral cooling mechanisms have been demonstrated(Doppler cooling, « Sisyphus cooling », subrecoil cooling)

At room temperatures (T = 300 K), atomic velocities are on the order of 1 km/s

Obtention of temperatures on the order of a few 10-6 Kand of atomic velocities on the order of 1 cm/s

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MANIPULATING ATOMS WITH LIGHT

- Transfer of linear momentum from photons to atoms Laser cooling- Transfer of angular momentum from photons to atoms Optical pumping

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Optical pumping (A. Kastler, J. Brossel)

At room temperatures and in low magnetic fields the variousspin states of an atom are nearly equally populated. Very weak spin polarization

By absorbing polarized photons, atoms can gain the angularmomentum of these photons and become polarized.Gaseous samples with large spin polarization

Polarized photons have also an angular momentum andit is easier to polarize light than atoms

One can easily obtain in this way large signals of magnetic resonance with dilute gaseous samples

Magnetic resonance signals are proportional to the difference of populations between 2 spin states.Easy to observe only in dense systems (solids or liquids)

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A FEW EXAMPLES OF APPLICATIONSOF QUANTUM PHYSICS

- The laser “Light Amplification by Stimulated Emission Radiation”- MRI Magnetic resonance in a magnetic field gradient- Atomic clocks Space clocks. GPS- Interferometers with atomic de Broglie waves- Solid state electronics The spectacular progress of computers

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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 by spontaneously emitting a photon in all possible directions.

e g

τR : Radiative lifetime of e, on the order of 10-8 s

Induced emission of a photon (Einstein 1917)

A photon with energy h ν = Ee-Ef , impinging on an atom in the excited state e induces (or stimulates) this atom to emit a photon exactly identical to the impinging photon (same energy, same direction of propagation, same polarization)

h νe g

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Amplification of light

Population inversion

If a light beam with frequency ν passes through a mediumwhere populations are inverted, the new photons which appear by induced emission are in a greater number thanthe photons which disappear by absorption. The incident light beam is thus amplified

Thermodynamic equilibriumIn an ensemble of atoms inequilibrium, a lower lever E1is always more populated than an upper level E2.

Non equilibrium situation wherean upper level E2 is more populatedthan a lower level E1.

E2

E1

E2

E1

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New light sources : lasers

« 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 applications

C. Townes, A. SchawlowAmplifying atomicmedium put betweentwo mirrors

Light can make several round trips between the 2 mirrors and be amplified several times.

If the cavity is « tuned », and if the gain is larger than the losses, one gets an « oscillator » for light.

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A few examples of applications of lasers

• Medical applications (retina)• Compact disks players• Bar codes in supermarkets• Optical telecommunications with optical fibers• Cutting of metals• Laser gyrometers for navigation• Telemetry• LIDAR• Guiding of missiles• …

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Proton 3HeProton-MRI 3He-MRI

• Princeton• Mainz U., Paris-Orsay, Nottingham U• Duke U., U. of Virginia, U. of Pennsylvania• Boston B&W H., St Louis About 10 more centers getting started

MRI Images of the Human Chest

Human lung MRI centres :

G.A.Johnson, L. Hedlund, J. MacFallPhysics World, November 1998

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Principle of an atomic clock

Quartz oscillator

Inte

rrog

atio

n Correction

The width ∆ν of the atomic resonance isinversely proportionalto the observation time TUltracold atoms move slowly and providelong observation times

The narrower theatomic resonance,the better the accuracyof the clock

Quartz oscillator whose frequency is maintained at the center νo of an atomic resonance. ν0 is universal

Atomic resonance

∆νν

ν0

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Stability : 1.6 x 10-16 for an integration time 5 x 104 sAccuracy : 7 x 10-16

Transportable fountains

Atomic fountains- Sodium fountains : Stanford S. Chu- Cesium fountains : BNM/SYRTE C. Salomon, A. Clairon

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Parabolic flights

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Tests of PHARAO with parabolic flights

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ACES (Atomic Clock Ensemble in Space)ACES (Atomic Clock Ensemble in Space)

• Time reference• Validation of space clocks (GPS)• Tests of fundamental theories

C. Salomon et al , C. R. Acad. Sci. Paris, t.2, Série IV, p. 1313-1330 (2001)

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Current accuracy: 7x 10-16

Target: 1x 10-16

1950 1960 1970 1980 1990 2000 201010-17

1x10-16

10-15

1x10-14

1x10-13

1x10-12

1x10-11

1x10-10

1x10-9

NPL

?

PTB

Optical clocks

NIST

Ca PTB

H MPQ

Cold atoms

Microwave clocksSlope: gain of 10 every 10 years

ACCURACY OF THE ATOMIC TIME

SYRTE

PTBNIST

PTBNRCNBSVNIIFTRI

NPLNBSLSRH

REL

ATIV

E AC

CU

RAC

Y

YEAR

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Interference fringes obtainedwith the de Broglie waves associated

with metastable laser cooled Neon atoms

F.Shimizu, K.Shimizu, H.Takuma Phys.Rev. A46, R17 (1992)

Cloud of cold atoms

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Experimental results

Each atom gives rise to a localized impact on the detectorThe spatial repartition of the impacts is spatially modulated

Wave-particle duality for atoms

The wave associated with the atom allows one tocalculate the probability to find the atom at a given point

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Atomic interferometers

Ω

Example of gyrometers (using, for atomic de Broglie waves, the equivalent of the “Sagnac effect” for light waves.

The phase shift between the 2 waves propagating in the 2 armsof the interferometer depends on the angular rotation Ω of theplatform with respect to a Galilean frame.Atomic gyros are expected to have a sensitivity much higherthan laser gyros used in planes for navigationThey have already a sensitivity allowing one to detect rotation speedsabout 104 times slower that the rotation speed of the earth

Another example : gradiometers

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Solid state electronicsSpectacular improvement with respect to vacuum tubesQuantum physics is essential for understanding these devices.Combination of 2 basic quantum effects• Energy bands separated by band gaps for a de Broglie

wave propagating in a periodic potential• Fermi statistics for electrons preventing a given quantum

state to be occupied by more than one electronOne can understand in this way the existence of insulators, conductors, semiconductors. New devices (diodes, junctions, transistors, quantum wells…) have been developed. New techniques (beam epitaxy, lithography,…) allow now millions of transistors to be incorporated in small chips.Our ability to compute (labtop), to communicate (internet) has been dramatically improved by quantum physics

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A FEW NEW PERSPECTIVESIN QUANTUM PHYSICS

- Manipulation of single atomic particles

- Macroscopic quantum phenomena Gaseous Bose-Einstein condensates Atom lasers


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The possibility to cool atomic particles to very low temperatures and to trap them allows now measurements to be made on a single atom, a single ion, a single electron,a single molecule

Example : photo of 4 ions trapped in a linear trap anddetected by the observation of their fluorescent light

Innsbruck

Other rapidly developing techniques in nanophysics(scanning tunnel microscopes, atomic force microscopes)

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A few electrons in a Penning trap

Detection of a single electron

Seattle

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Bose-Einstein condensation (BEC)

At low enough temperatures and high enough densities, the de Broglie wavelength of the atoms becomes larger than themean distance between atoms. The atomic wave packets overlap and interfere. Pure quantum effect

Identical bosons in a trap are then predicted to condense inthe ground state of the trapMacroscopic number of atoms in the same quantum stateMacroscopic matter waves

Combination of laser cooling and trapping with previously developed methods for studying spin-polarized Hydrogen(magnetic trapping, evaporative cooling) have led to the observation of BEC in alkali gases Boulder, MIT, Houston (1995)

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Sketch of the waves associated with the trapped atoms

Evolution of thesewaves when T decreases from avalue much higherthan TC to a value much lower

T >> TC

T > TC

T ~ TC

T < TC

W. Ketterle

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Contribution of the condensed atoms

Narrow peak with a widthcorresponding to the ground state wave function of the well

Bimodal structure of the spatial distribution of bosons

Contribution of the non condensed atoms

Broad piedestal coming from atoms occupying excitedstates ot the well described by wave functions with alarger width

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Visualization of the atomic cloud

Spatial dependence of the absorptionof a laser beam by the cloud

44Phys. Rev. Lett. 75, 3969 (1995)

Science, 269, 198 (1995)

JILA

MIT

87Rb Boulder23Na MIT7Li Rice1H MIT4He* Orsay, LKB41K Florence

133Cs Innsbruck174Yb Kyoto

Molecular condensatesBoulder, Innsbruck,MIT, LKB

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Importance of gaseous Bose Eintein condensates

Matter waves have very original properties ( superfluidity,coherence,…) which make them very similar to other systems 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 dilute than air. Atom-atom interactions have then a much smaller effect which can be calculated more precisely Furthermore, these interactions can be modified at will, in magnitude and in sign (attraction or repulsion), using« Feshbach resonances » obtained by sweeping astatic magnetic field A great stimulation for basic research!

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Example of application

Atom laser : coherent beam of atomic de Broglie waves extracted from a Bose Einstein condensate

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Quantum informationClassical bits

Two-state system 0 and 1The system can be in 0 or in 1

Quantum bits (“qubits”)Two-state system φ0 and φ1The system can be now in φ0 , in φ1 , or in any linear superposition c0 φ0 + c1 φ1

Much richer variety of states for a qubit due to the factthat quantum states can be linearly superposed

Entanglement2 qubits can be in an “entangled state” where they cannotbe considered as 2 separate entities. Subtle quantum correlations opening the way to interesting applications :Quantum cryptography, quantum logic gates,…

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ConclusionOur ability to control and to manipulate quantum systems(atoms, ions, electrons) has considerably increased during the last few decadesThis is opening completely new research fields and allows us 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, in particular in physics - for improving our vision of the world - for solving the various problems (energy, environment, health) that mankind has to faceIt is highly probable that the advanced technologies which willbe used in 10 or 20 years from now will be the result of basicresearch performed today in the labs.

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THANKS TO

All our Brazilian Colleagues of

• Jean-Louis Courtiat (Attaché Scientifique in Brasilia)• René Quirin (Consulate in Recife)• Jean-Paul Lefèvre, Philippe Julliard (Consulate in Rio)

French Embassy and French Consulates in Brazil

• Universidade Federale de Pernambuco• Universidade Federale de Rio de Janeiro• INMETRO (Rio de Janeiro)

For their contributions to the organization of this event

Documents

Claude Cohen-Tannoudji INMETRO Rio de Janeiro, 16 January 2006 · 2005-12-19 · - Atom-photon interactions 2. Using conservation laws for manipulating atoms - Laser cooling - Optical