Atom optics:

Coherent&Incoherent

Spin Manipulation, preparation and evolution

Ernst M. RaselInstitutfürQuantenoptik

Atom Quantum Sensors on ground and in space

Outline

Laser cooling

Bose-Einsteincondensation

Coherentcontrol of matter

Atom interferometry

AtomLaser

www.colorado.edu/physics/2000/index.pl

Lase

r C

oolin

g

Laser Cooling

Zeeman slower

Molasses cooling

Magneto-Optical Trap (MOT)La

ser

Coo

ling

Magneto-optical trap

S. Chu, C. Cohen-Tannoudji, W. PhillipsNobel Prize 1997

Magneto-Optical Trap (MOT)

Typical values

density n 109 - 1011 cm-3

temperature T 10 - 100mK

size∆x0.1…10 mm

Lase

r C

oolin

g

SourceConcept

Cold atom beam by 2D-MOT

X

Y

Z

Vakuum- pumpe

Kühllaser

Kamera/Fotodiode

Ablenk-Laser

pusher- Strahl

Detektions-strahl

2D-MOT x

Kühllaser

0 5 10 15 20

1,0x109

2,0x109

3,0x109

4,0x109

5,0x109

6,0x109

7,0x109

8,0x109

9,0x109

1,0x1010

1,1x1010

Ato

mflu

ss [N

/s]

Magnetfeldgradient [G/cm]

75mW 112mW 152mW 192mW 219mW

transversal

Divergence: 30 mrad

diameter: 0,9 mm

0 20 40 60 80 1000

100

200

300

400

500

600

700

N(v

) [b

el.E

inhe

iten]

longitudinale Geschwindigkeit [m/s]

211mW 189mW 128mW 75mW

Long. Velocity [m/s]

Num

ber

of a

tom

s [a

.u.]

3D-MOT loaded by cold atom beam

Loading: ~ 109 atoms/s

lifetime: ~ 90 ms

size: ~1.2 mm (diam.)

Temperature: ~ 100 µK

Laser parameter:

Beam size: 20 mm

axial magnetic

gradient: 12,8 G/cm

Total power 120 mW 2D-MOT

0 5 10 15 20-2

0

2

4

6

8

10

12

14

16

Fül

lrate

[108 A

tom

e/s]

Laserleistung pro MOT-Strahl [mW]

Load

ing

rate

[108

at/s

]

Laser power [mW/MOTbeam]

Lase

r S

ourc

e

Excerpt of the level diagram 87RbRelevant transitions for manipulation

with laser light

F=1F=2

F=1F=2

F=0

F=3

52S1/2

52P3/2

87Rb

F=1

F=2

mF=-1 mF=0 mF=1

mF=-2 mF=-1 mF=0 mF=1 mF=2

52S1/2

State preparation requires control of internal spin states

Bose-Einstein condensation

ClassicalQuantum ClassicalQuantum

Tow

ards

„Q

“-w

orld

Classical

properties

Quantum

features

Wave nature of matter

Louis Victor de Broglie Nobel prize 1929

v

d

High Temperaturesclassical particles

dBλ

Low Temperatureswave packets

T=TC

Bose-Einstein Condensation

T=0pure BEC

Ultra-cold Gas = extrem low kinetic energy

weak interatomic interaction dominant

Qua

ntum

Mat

ter

3dB

1

ρλ ≈

need ultra low temperatures

T=0.1 K ρ =1023 cm-3

T= 1 µKρ =1015 cm-3

condensedmatter

Gen

erat

ing

BE

C

11 3

dB3dB ≈⋅⇒≈ ρλρ

λ

Mag

netic

Tra

ppin

g

Magnetic field dependenceZeeman effect

Eva

pora

tiveC

oolin

g

n < 1

n >> 1

T > TC T < TC

Energy Energy

Par

ticle

Nu

mb

er

Bos

e-E

inst

ein

Con

dens

atio

n

n < 1

n >> 1

Energy Energy

Par

ticle

Nu

mb

er

Bos

e-E

inst

ein

Con

dens

atio

n

Fermions

Nobel Prize 2001• E. Cornell & C. Wieman• W. Ketterle

Lase

r-lik

e fe

atur

es

Pumping Gain medium

Mirror R=100%

Mirror R=9X %

… the atom laser… splitting a condensatewith lasers

MACROSCOPIC

QUANTUM COHERENCE

M.R. Andrews et al., Science 275, 637 (1997)

Steps to BEC

• External MOT

• Chip-MOT

• Moving MOT

• Molasses

• State transfer

• Storage in magn. trap

• Evaporation

• Analysis of BEC

Sun (surface)boiling water

liquid nitrogen

supra conductivity

‘Bose-Einstein Condensation’

Temperature velocity

4000°C - 1 Mio. °C100 °C

-196 °C

-260 °C

5000 - 100.000 m/s700 m/s240 m/s

90 m/s

3 mm/s10 billionth Kelvin

Limits of Laser cooling 3 cm/s1 millionth Kelvin

Latest Temperature record “35 pK”!above

T = 0 Kelvin = - 273 °C

The

Kel

vin

Sca

le

Matter- Wave Interferometry

Atom-optics components forcoherent manipulation of matter waves

MIXER

The

ato

mic

rul

er Louis Victor de Broglie Nobel prize 1929

dBatat

atatatat

hvm

kpvm

λ=

⋅==⋅v

hrv

dBat

2k

λπ=

v

Atomic momentum

De-Broglie wavelength

Planck‘s constant

Classical World Quantum World

λλλλdBUnits in de Broglie wavelength

The

lase

r ru

ler…

λλλλ Units in light wavelength

c=⋅λνλπω 2

k,e)t,r(E )trk(i =∝ ⋅−⋅vv vv

Laser field

…based on

the mechanical effect of light

Laser

|g, pat⟩⟩⟩⟩

|e, pat+ħk⟩⟩⟩⟩

|g, pat⟩⟩⟩⟩

Lkr

Ato

mic

Bea

m S

plitt

er

Coherent Beamsplitterfor Atoms

g

e

Standing light waves as phase gratings

( )

∆πµ=

ω−ω=∆∆π

Ω=∆π

⋅µ=⋅=

h

rr

hh

rrrrrrr

2d

22

)r(E)r(Ed)r(V

2

AL

22

Dynamic Stark-shift

2/

2G

λπ=

v

Mechanical Effect of Light

recoilsphoton2

2

Gkk

2atomphoton

=

=⇒=λπ

vrr

Atomic Mach-Zehnder Phase-grating Interferometer

E.M. Rasel, M.K. Oberthaler, H. Batelaan, J. Schmiedmayer, A. Zeilinger

“Atom Wave Interferometry With Diffraction Gratings of Light“

Phys. Rev. Lett. 75, 2633 (1995)

Light Crystals

• Bloch States• Pendellösung• Anomalous Transmission• Bloch-Oscillations• Anderson Localisation • Mott-Transition

Bose-Einstein Condensate in an opttical lattice, I. Bloch, Nature 2002

Bragg Scattering

g

e

E

]k[pr

h-1 0 +1

Bragg Resonance

=

Resonant two-photon transiton

1Φ

Fringe position

Gϑ

ϑ=λ⋅ cosd2n

periodicityM

ergi

ng th

e tw

o ru

lers

Sir William Henry Bragg &William Lawrence BraggNobel Prize 1915

… in the case of Bragg diffraction

The mechanical effect of light

Laser 1 Laser 2

kgr

h0,1 kgr

h2,2 +

ker

h2,+Raman-process

Laser 1

Laser 2

kr

hr

atomm2

v =∆

Ram

an-L

aser

Atom-Optics components made out of Light

MIXER

pulse2/ −π

pulse2/ −π

pulse−π

Puls Duration [µs]

Exc

itatio

npr

obab

ility

Laser 1 Laser 2

kgr

h0,1 kgr

h2,2 +

ker

h2,+

kgkgr

hr

h 2,2, 22 ++

T. Müller et al., "Versatile compact sources for high resolution dual atom interferometry" subm. to Phys. Rev. A 2007

|e⟩⟩⟩⟩

|g⟩⟩⟩⟩

position

time

S ∼ cos[(φ3 - φ2)-(φ2 -φ1)]

Signal at the output ports

MIRROR

Full quantum mechanical description by C. Antoine, C. Bordé

|e⟩⟩⟩⟩

|g⟩⟩⟩⟩

position

time

|e⟩⟩⟩⟩

|g⟩⟩⟩⟩

position

time

MIRROR

0,000 0,002 0,004 0,006 0,008 0,010-1,73

-1,72

-1,71

-1,70

-1,69

-1,68

-1,67

-1,66

-1,65

-1,64

phot

odio

de s

igna

l [V

]

time [s]

interferometer 1 interferometer 2

back ground

Exc

itatio

npr

obab

ility

Exc

itatio

npr

obab

ility

F=1F=2

F=1F=2

F=0

F=3

52S1/2

52P3/2

87Rb

1. • |F=2> to |F‘=2> (p-pol.light)• simultaneously:

repumper |F=1> to |F‘=2>• atoms in |F=2, mF=0>

F=2

F‘=2

mF=-2mF=-1mF=0mF=1 mF=2

mF=-2 mF=-1mF=0 mF=1mF=2

2. • Raman transition

|F=2,mF=0> to |F=1,mF=0>

F=1

F=2

mF=-1mF=0mF=1

mF=-2 mF=-1mF=0 mF=1mF=2

52S1/2

52P3/2

3. • „Blow-away“ |F=2> to |F‘=3>

removes atoms in |F=2>

Preparation of atoms in: |F=1,mF=0>

• repumperlater off thanpumper• all atoms in groundstate |F=2>,

most of them in |F=2,mF=0>

∆

Experimental sequence: Atomic source - Preparation

Dual Atom Interferometer for Earth rotation sensing

ΩE ≈ 7,2·10-5rad/smolassestheatomicensemblesarelaunched in oppositedirectiontowardstheinterferometerregion, wherebotharesilmultaneouslysplitt,redirected and re-combinedby a Ramanprocess to form an interferencepattern. State peperation has to beperformedbefore and thedetectionaftertheinterferometerregion.

Interferometer

MOT 1

π/2

ππ/2

15 cm

3 mm

A

PreparationDetection

MOT 2

C. Jentsch, T. Müller, E. Rasel, and W. Ertmer, Gen. Rel. Grav, 36, 2197 (2004)& Adv. At. Mol. Physics

Discriminates between both types of inertial forces, rotations and accelerations

transportable

Technical Implementation

3D-MOTmoving molasses

2D-MOTatomic source 2 detection

interferometer

preparation

Source 1Source 2

Detuning of the Raman lasers [Hz]

Exc

itatio

n pr

obab

ility

2 synchronously operated

Ramsey Interferometer

→ Light shift cancelation

→ magnetic field measurement time

Exc

itatio

n pr

obab

ility

2 synchronously operated Echo Interferometer

→ detection noise

→ phase noise of the RF source

→ magnetic field gradients

Mirror

λ/4

Beam block

fibre

diaphrg

Exc

itatio

n pr

obab

ility

C1 = 24% C2 = 22%T = 1ms, τ = 7,5µs

π/2π

π/2

Mirror

λ/4

Angle ϑ

fibre

Diaphrg.

Achromat

λ/4

T. Müller, T. Wendrich, M. Gilowski, C. Jentsch, E.M.Rasel and W. Ertmer, ""Dual atom interferometry with cold atoms" in prep.

temporal dual atom interferometer

→contrast reduced because of Doppler sensitive excitation

→ vibrations

PreparationPreparation

Coherent Superposition

Coherent Superposition

Coherent Evolution

Projection Projection

Increasingsensitivity

- Long interactiontimes

- Ultra coldatoms

-Coherence

Minimisingphasenoise

- Increasingnumber of atoms

- Beating theshotnoise

- Environmentalcontrol

- Ultrastablelasers (frequency, intensity)

Matter- Wave Interferometry

SUPERPOSITION PRINCIPLE WAVE-PARTICLE DUALITY

(DE-) COHERENCEWAVE-PARTICLE BEHAVIOR

TOOL FOR CORRELATIONS

Matter- Wave Interferometry

QUANTUM COMPUTING

QUANTUM METROLOGY

COHERENT STATE ENGINEERINGCOHERENT MATTER WAVE OPTICS

QUANTUM STANDARDS

PRECISION MEASURMENTS

TESTS IN FUNDAMENTAL PHYSICS

EARTH OBSERVATION

Bose-Einstein condensation

Laser cooling

Matter- Wave Interferometry