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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
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