Cavity-QED and Single Atom Maser and Laser

Cavity-QED and Single Atom Maser and Laser

Herbert WaltherHerbert Walther

85748 Garching bei München, Germany

85748 Garching bei München, Germany

Max-Planck-Institut für QuantenoptikMax-Planck-Institut für Quantenoptik

Herbert.Walther@mpq.mpg.deHerbert.Walther@mpq.mpg.dehttp://www.laser.physik.uni-muenchen.dehttp://www.laser.physik.uni-muenchen.de

Sino-GermanSymposiumSino-GermanSymposiumon Quantum Engineering, Beijing, on Quantum Engineering, Beijing, Nov. 23-27, 2005Nov. 23-27, 2005

Sino-GermanSymposiumSino-GermanSymposiumon Quantum Engineering, Beijing, on Quantum Engineering, Beijing, Nov. 23-27, 2005Nov. 23-27, 2005

SchottenhamelzeltSchottenhamelzeltSchottenhamelzeltSchottenhamelzelt

18961896

Einstein & Co.Einstein & Co.

„Quantum mechanics is certainly imposing.But an inner voice tells me that it is not yetthe real thing. The theory says a lot, but does not really bring us closer to the secretof the ‚Old One.‘ I, at any rate, am convincedthat He is not playing at dice.“

Outline of the Talk

Deterministic photon generation(by cavity- quantum electrodynamics) One-atom maser

Trapped single ions

Mode density distribution near resonance

cavity () = 1

2 VcQ

c

(c)2 + (c/2Q)2

Free atom versus atom in cavityFree Atom versus Atom in Cavity

Cavity Quantum Electrodynamics

Nc: Mode volume

Q: Quality factor Q = c

(33/4 Vc) . Q Q /ρ =free

Free Atom Atom in Cavity

~~cavity

c

Free Atom versus Atom in Cavity

Modification of spontaneous emission rate

Level shifts

Oscillatory energy exchange(determined by photon statistics)

(E.T. Jaynes, F.W. Cummings, Proc. IEEE 51, 89 (1963))

Consequences for the atom:

Single atomSingle atom -- Single mode of a cavity Single mode of a cavity

Atomcoupling constant g (Rabi-frequency)

Cavity field

coupling constant Cavity walls

Q

Strong coupling g

One-Atom Maser

Resonant superconducting cavity

Atom in excited state

Interaction-Hamiltonian

HI hg + a + a+ - + - Pauli operators for atomic system

(a, a+) annihilation and creation operators of radiation field

Atomic decay:

Steady state field is generated: In most of the parameter regions sub-Poissonian statistics is obtained i.e. nonclassical fields

LevelsLevels

n = 63Maser transition 21GHz

n = 61

Laser excitation

Ground state

Scheme Scheme

Cavity Field ionisation

Laser excitation

Atomic beam oven

One-Atom Maser

Temperature of the cavity 140 mK

. cav = 0.3 s

Velocity selected atoms = 1 - 4 %

10

Single photon Rabi frequency: g 40 000 s-1

Quality factor of cavity Q = 4 10g >

Q>

Maser Resonance

Q = 3 1010

T = 0.5 K-1 = 0.2 s

.

Rb85 63p3/2 – 61 d5/2

Resonanzfrequenz: 21.456 GHz

H. Walther, Phys. Rep. 219, 263 (1992)

Sup e r c o nd uc ting nio b ium c a vity

Sta te se le c tive fie ld io nisa tio n o f Ryd b e rg a to m s

Ve lo c ity se le c tivea ng le tune dUV la se r

Rub id ium o ve n

One-Atom Maser

, n cos ( n+1) , n i sin ( n+1) , n+1

Rubidium oven

Velocity selective angle tuned UV laser

Superconductingniobium cavity

State selective field ionisation ofRydberg atoms

Atoms leaving the cavity are entangled with the generated field

Puming Curve and Photon Statistics of the

One-Atom Maser

q =

n2 - n n

- 12

Nex = 40

q p

ara

me

ter

No

rma

lize

d p

hot

on

nu

mb

er

n /N

ex

Interaction time (µs)

Pump parameter (/)

n /Nex

q parameter

Theory: P. Meystre et al.

Filipowicz, Javanainen, Meystre, Optics Comm. 58, 327 (1986)

Poissonian photon statistics

Photon Statistics in the One-Atom Maser

gtint. Nexthreshold for maser

NN

==

==corresponds to quantum non-demolition situation

q p

ara

me

terq parameter

Low TemperatureBehaviour of the

Micromaser

Low TemperatureBehaviour of the

Micromaser

Low Temperature Behaviour of the One-Atom-Maser

Fa

no

Ma

nd

el q

Pa

ram

ete

r

No

rma

lise

d

Ph

oto

n N

um

be

r <

n>

/Nex

Thermal photon number = 0.1 Nex = 50 g= 39 kHz

Thermal photon number = 10-4

Nex = 50 g= 39 kHz

P.Meystre, G.Rempe, H.Walther, Opt. Lett. 13, 1078 (1988)

Low Temperature Behaviour of the One-Atom-Maser

Low Temperature Behaviour of the One-Atom-Maser

Trapping states are characterised by the pair of numbers (nq, k) that satisfies the relation:

nq+1 gtint = k

Interaction time (µs)

Nor

mal

ised

pho

ton

num

ber

PHOTON NUMBER STATES are directly diplayed

The Micromaser Pump Curveat Low Temperatures

Trapping states are characterised by the pair of numbers (nq, k) that satisfies the rela-tion: nq+1 gtint = k

M. Weidinger, B.T.H. Varcoe, R. Heerlein, H. Walther, Phys. Rev. Lett. 82, 3795-3798 (1999)

Trapping states appear as valleys in the Nex direction

they correspond to PHOTON NUMBER STATES

= 45 µs

deviates from trapping con-dition

tint tint = 58

interaction time for the (1, 1) trapping state

Photon-Fock-states on demandPhoton-Fock-States on Demand

S. Brattke, B.T.H. Varcoe, H. Walther, Phys. Rev. Lett. 86,3534-3537 (2001)

TT

Other Cavity QEDSystems

Other Cavity QEDSystems

Summary Cavity QED Experiments

Cavity

Field ionisation

Laser excitation

Atomic beam oven

Walther et al. Haroche et al.

Lange et al., Nature 414, 49 (2001) andNature 431, 1075, (2004)

Kimble et al. Nature 425, 268 (2003)Rempe et al.

Microwave

single single photon photon pulsepulse

pump-pump-pulsepulse

4040CaCa++

2D3/2

2P1/2

2S1/2

Visible

Optical Experiments – Atoms in Cavities

Coupling constant is increased by reducingmode volume of cavity mode

g = (2 0 / 2h 0 V)=1/2

Strong Coupling Experiments with atoms

Trapped atom experiment; trapping time 17 sTrapped ion experiment; trapping time many hours

Walther et al. 1985,1990 7 kHz 0.4 Hz 500 Hz 1.5Haroche et al.1994 48 kHz 400 Hz 5 Hz 3 . 104

Kimble et al. 1994 7.2 MHz 0.6 MHz 5 MHz 5 . 106

Rempe et al.* 2005 5 MHz 5.0 MHz 3 MHzKimble et al. 2003 16 MHz 4.2 MHz 2.6 MHzLange et al.** 2004 1 MHz 0.9 MHz 1.7 MHzFeld et al. 1994 340 kHz 190 kHz 50 kHz 8 . 106

g/2 /2 /2 Rth

(atoms/s)g > (,)>

g: atom-field coupling constant: decay rate of cavity field: spontaneous decay of atomic polarizationRth: pumping rate at threshold

)*** )

Single-IonCavity Quantum Electrodynamics

Single-IonCavity Quantum Electrodynamics

August 2001 24

• deterministic ion-field interaction

• single-photon gun• single-ion laser

Single mode cavity QEDSingle mode cavity QED

strong atom-field couplingstrong atom-field coupling

Single ion trappingSingle ion trapping

• sub-wavelengthsub-wavelengthposition controlposition control

• unlimited unlimited observation timeobservation time

Combine thetechnologies:

Single-Ion Cavity QED

• Linear RF trap with open Linear RF trap with open electrode configurationelectrode configuration

• separate loading regionseparate loading region

• Ion transfer by DC fieldsIon transfer by DC fields

Trap design:Trap design:

How to place the ion between the mirrors?

no coating or charging of the dielectric mirrors even

at small cavity length

Setup: ion trap and optical cavity

Nature 414,49 (2001)

• transfer distance: 25 mm• transfer time: 4 ms

Loading

Shuttling

Region 2 (Cavity)Region 1

trap-axis

Ion Transfer from Loading Region to Cavity

Trap axis position (mm)

Po

ten

tial

(a.

u.)

A Single Ion in a Cavity

scan position of ion or cavity and ob-serve fluorescence

• resolution down to 10 nm

• first step towards single-ion cavity QED

single 40Ca+ ion as a nanometric probe of the electromagnetic field:

Test of the deterministic interaction of ion and cavity field

Single-Ion Mode Mapping (SIMM)

PMT

397 nm

longitudinal scan

transversalscan

Two-Dimensional Images of the Cavity Field

Horizontal ion position (µm)

Ver

tica

l p

osi

tio

n (

µm

)

TEM00

TEM01

image of the standing wave structure

zTranslation of the cavity along its axis:

Longitudinal Cavity-Mode Mapping

Visibility40 %

Cou

nt r

ate

(kH

z)

Longitudinal cavity position (in units of ) 0 1 2 3 4

0,5

1,0

1,5

= 397 nm

Resolution determined by wavefunction or residual motion of ion

2a

Related work by R. Blatt et al., Innsbruck

pulse with one single photon1 photon

single single photon photon pulsepulse

pump-pump-pulsepulse

4040CaCa++

• Single ion at a node of the cavity

• external pump pulse

• cavity with one leaky output mirror

g

C. K. Law, H. J. Kimble, J. Mod. Opt. 44, 2067 (97)

Single-photon pulseat pre-determined time

Deterministic Single Photon Gun

2D3/2

2P1/2

2S1/2

0 1 2 3 4 5 6

(d)

0 1 2 3 4

(a)

data model pump

0 1 2 3

Time t (s)

(c)

Eve

nts

(arb

. un

its)

0 1 2 3 4 5

(b)

Single Photon Pulse Shapes

a) Strong Gaussian pumpb) Weak Gaussian pump

c) Square-wave pumpd) Double peaked pump

Dotted lines indicate pump profiles (not to scale)

Nature,431,1075 ( 2004 )

-100 -50 0 50 100

0

2

4

6 (a)

Cor

rela

tions

Delay time (s)

-90 -60 -30 0 30 60 90

(b)

Delay time (minutes)

Photon Correlation

Nature 431, 1075, (2004)

Summary

Deterministic photon generation:

One-atom maser- controlled by internal feedback mechanism

Trapped ions- single photon wavepacket controlled by pumping pulse

Summary

Deterministic photon generation: Applications: Quantum phenomena in radiation- atom interaction ( one- atom maser ) Quantum communication; quantum repeaters and single photon sources (ion )

One-Atom MaserOne-Atom Maser

Cavity QED with IonsCavity QED with Ions

Theory: M.O. Scully W. Schleich P. Meystre B.G. Englert

Many thanks to…..

Pierre Thoumany Pierre Thoumany

ThomasBecker

ThomasBecker

Linas Urbonas Linas Urbonas

GabrieleMarchiGabrieleMarchi

MichaelGorodetsky MichaelGorodetsky

MichaelKlembovsky MichaelKlembovsky

Wolfgang LangeWolfgang Lange

BirgitLangeBirgitLange

Matthias KellerMatthias Keller