j. mauricio lópez r. centro nacional de metrología, cenam
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J. Mauricio López R.
Centro Nacional de Metrología, CENAM
62s1/2
F = 3
F = 4
9.2 GHz
62p3/2
F’ = 5
F’ = 4
F’ = 3
F’ = 2
251 MHz
201 MHz
151 MHzD2
852 nm
62s1/2
F = 3
F = 4
9.2 GHz
62p3/2
F’ = 5
F’ = 4
F’ = 3
F’ = 2
251 MHz
201 MHz
151 MHzD2
852 nm
Cs 133
The use of the atomic transitions as references to built atomic clocks was first proposed by I. Isaac Rabi from the Universidad of Columbia during
the 1930s decaade.
The Nobel Prize in Physics 1944
Isidore Isaac Rabi
Nuclear magnetic resonance
Magnetic moment
JμJ
Classic approximation
kH0 0HStatic magnetic field
Larmour frequency
J
H
0
02 0
0
z
Interaction between H and
0HμE
Angular momentum evolution
dtdL
Hμ 0
z z
kH0 0HStatic magnetic field
Larmour frequency
J
H
0
02 0
0
)cos(sin11 jiH ttH
Rotating magnetic field perpendicular to H0
Classic approximation
The Nobel Prize in Physics 1989
Norman F. Ramsey
An improvement of the Rabi method was proposed by Norman Ramsey. His method is now used to built atomic
clocks
Nuclear magnetic resonance
z
kH0 0HStatic magnetic field
Larmour frequency
J
H
0
02 0
0
)cos(sin11 jiH ttH
Rotating magnetic field perpendicular to H0
Applied in pulses!
Classic approximation
Ramsey method
Ramsey method
Rabi method
Definition of the unit of time
Electric
85
0nm
Electron-nucleus
9192631770 Hz
F’=5
F’=4
F’=3
F’=2
F’=4
F’=3
F’=4
F’=3
251MHz
200MHz
150MHz
1167MHz
+ Zeeman effect
11 subniveles
9 subniveles
7 subniveles
5 subniveles
9 subniveles
7 subniveles
9 subniveles
7 subniveles
+
INTERACTION
EN
ER
GY
Spin-orbit
62P3/2
62P1/2
62S1/2
10
0GH
z
894n
m
+
Not
a s
cale
CampoMagnético Constante (Campo C)
Contenedor con Cesio 133
Cavidad de Ramsey
Campo Magnético Inhomogéneo
(Campo B)
Campo Magnético Inhomogéneo
(Campo A)
FilamentoIncandescente
(Ionizador)
Detector
Generador deMicroondas
Lazo deamarre
Vacío
Ramsey Method
Alfred Kastler France
École Normale Supérieure, Université de Paris Paris, France b.1902d.1984
The Nobel Prize in Physics 1966
The descovery of the optical methods for the study of radio resonance in atoms was made by Alfred
Kastler.
Optical pumping
a
b
aE
bE
c cE
Optical pumping
baa EEE
h
EE ac
ac
Cerca del visible
h
EE ab
ab
Radiofrecuencia
Optical pumping in Cesio-133
Eléctrica
85
0nm
Electrón Núcleo
9192631770 Hz
F’=5
F’=4
F’=3
F’=2
F’=4
F’=3
F’=4
F’=3
251MHz
200MHz
150MHz
1167MHz
+ Efecto Zeeman
11 subniveles
9 subniveles
7 subniveles
5 subniveles
9 subniveles
7 subniveles
9 subniveles
7 subniveles
+
INTERACCION
EN
ER
GIA
Espín-órbita
62P3/2
62P1/2
62S1/2
10
0GH
z
894n
m
+
No
a es
cala
CampoMagnético Constante (Campo C)
Contenedor con Cesio 133
Cavidad de Ramsey
Generador deMicroondas
Lazo deamarre
Láser de bombeo
Láser de detección
FotodetectorVacío
Ramsey method + optical pumping
Steven Chu Claude Cohen-
Tannoudji William D. Phillips
USA France USA
Stanford University Stanford, CA, USA
Collège de France; École Normale Supérieure Paris, France
National Institute of Standards and Technology
Gaithersburg, MD, USA b.1948 b.1933 b.1948
The Nobel Prize in Physics 1997
During the 90´s decade Stephen Chu, Claude Cohen-Tannoudji y William Phyllips, among others, developed the techniques for the manipulation of atoms with ligth.
Cold atoms
Doppler cooling
Ene
rgy E2
E1
012 hEEE
Laboratory reference frame
F=0- F=0-0
v
R = F + k·v + … 0
L= F - k·v + …<< 0
Atom´s reference frame
0
Doppler cooling
...22
12
20
2
00
Mch
cv
abs
vk
kpF2
dtd Fuerza sobre el átomo como resultado del proceso
de absorción/emisión de un fotón
Doppler cooling
Fue
rza
2kv/-1 1
Total force on the atom
20
2
12
kv
II
kF
v
III
IkF 2
0
0
2
2´1
2
4
20
2/1
2
kv
II
kF
Friction type force
vF )(I
Lowest temperature achieved by eDoppler cooling
Doppler cooling
2
BDopplerkT
Cesium-133K124
Sodium K240h 6,610-34
Js kB 1,310-23 J/K
Phys. Rev. Lett. 61, 169–172 (1988)[Issue 2 – 11 July 1988 ]
Observation of atoms laser cooled below the Doppler limit
Paul D. Lett, Richard N. Watts, Christoph I. Westbrook, and William D. Phillips Electricity Division, National Bureau of Standards, Gaithersburg, Maryland 20899
Phillip L. Gould Department of Physics, University of Connecticut, Storrs, Connecticut 06268
Harold J. Metcalf Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794
Received 18 April 1988 We have measured the temperature of a gas of sodium atoms released from ``optical molasses'' to be as low as 43±20 µK. Surprisingly, this strongly violates the generally accepted theory of Doppler cooling which predicts a limit of 240 µK. To determine the temperature we used several complementary measurements of the ballistic motion of atoms released from the molasses.
©1988 The American Physical Society
Doppler cooling assumes quantum systems of two energy levels. However, atoms have are multi energetic systems
The model of two energy levels for alkaline atoms (like Cesium) are not valid if a magnetic field is not zero. The Zeeman effect brakes the degeneration of
states rising up the multi energetic behavior of atoms.
Firts energy levels of the Cs-133 atom
Eléctrica
85
0nm
Electrón Núcleo
9192631770 Hz
F’=5
F’=4
F’=3
F’=2
F’=4
F’=3
F’=4
F’=3
251MHz
200MHz
150MHz
1167MHz
+ Efecto Zeeman
11 subniveles
9 subniveles
7 subniveles
5 subniveles
9 subniveles
7 subniveles
9 subniveles
7 subniveles
+
INTERACCION
EN
ER
GIA
Espín-órbita
62P3/2
62P1/2
62S1/2
10
0GH
z
894n
m
+
No
a es
cala
0122Bmg
I
hE FBI
HFS
2022
22
012
41
2
1B
h
ggB
h
gg
I
mh
HFS
JIB
HFS
JIBFHFS
Magnetic field/
Teslas
En
ergy
/ J
oule
s
10h H
FS
Region of interest
F=4
F´=5
m = +4
m = -4
m = 0
m = -5
m = +5
m = 0
852
nm
0 1B / Gauss
No
a es
cala
GaussHzB
hE/10
/ 7
GaussHzB
hE/10
/ 6
E
nerg
í a
Temperatures below the Doppler limit
x
0 4 2
lineal - + -lineal lineal
z
ym = -3/2 m = -1/2 m = +1/2 m = +3/2
m = -1/2 m = +1/2J = 1/2
J = 3/2
Stark effect
g-½
g+½
0
lineal - + -lineal lineal
Ene
rgy
Position
8
z0 4 38 2 58
z
Ene
rgía
8 4 38 2 58
g-½ g+½
Sisyphus effect
However, atom´s velocity interval for capture is proportional to the light intensity
“Fricción” type force is independent of the laser intensity
Force
2kv / 0.1 0.2-0.1-0.2
I1>I2>I3>I4
I1
I2
I3 I4
m1
0
-1
m1
0
-1
mF = -1
mF = 1
h0
hL
hL
z0
Ene
rgía
B(z) = Az
z2 z1z3z4
J=0
J=1
Posición
~1 mmF = -v - kzF = -v - kz
Frecuencia
E • t h/4
• t 1/4
1Hz
01010Hz
/ 10-15
Prob
abil
idad
de
tran
sici
ón
0
Ramsey Method + ultracold Cs atoms
Thermal beam clocks Cold atoms clocks
Ramsey pattern for Cs-133
Ramsey Method + Optical Pumping
Ramsey fringe
Frequency that defines the duration of the unit of time
1 kHz
Tra
nsit
ion
prob
abil
ity
(central line of the Ramsey spectrum)
Optical set up for a magneto-optical trap
E
E
/4
/4 E
DHP
L
AOM
L
DHPL
/4
LAOM
E
80 MHz
85 MHz
Láser maestro
Electrónica lazo de amarre
Filtro pasa-bajas
Amplificador
Multiplicador
AO Cesio
EDH
L
DH
100 Hz
E
Láser Esclavo
L/2
DH/2
E
/2
DHP
/2
DHP
/4
/4
/4/4
E
E
/4 M
O
T
E
FDFD
Mechanical part of a magneto-optical trap (MOT)
Optical set up for a MOT
Mauricio López R.
mauricio.lopez@cenam.mx
+ 52 (442) 211 0543
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