J. Mauricio López R. Centro Nacional de Metrología, CENAM

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 Classic approximation Static magnetic field Larmour frequency 00 z  Interaction between H and  Angular momentum evolution

zz Static magnetic field Larmour frequency 00   Rotating magnetic field perpendicular to H 0 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 Static magnetic field Larmour frequency 00  Rotating magnetic field perpendicular to H 0  Applied in pulses! Classic approximation

Ramsey method Rabi method

Definition of the unit of time Electric  850nm Electron-nucleus 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 ENERGY Spin-orbit 6 2 P 3/2 6 2 P 1/2 6 2 S 1/2  100GHz  894nm + Not a scale

CampoMagnético Constante (Campo C) Contenedor con Cesio 133 Cavidad de Ramsey Campo Magnético Inhomogéneo (Campo B) Campo Magnético Inhomogéneo (Campo A) Filamento Incandescente (Ionizador) Detector Generador de Microondas Lazo de amarre Vacío Ramsey Method

Alfred Kastler France École Normale Supérieure, Université de Paris Paris, France b.1902 d.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

Cerca del visible Radiofrecuencia

Optical pumping in Cesio-133 Eléctrica  850nm Electrón Núcleo 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 ENERGIA Espín-órbita 6 2 P 3/2 6 2 P 1/2 6 2 S 1/2  100GHz  894nm + No a escala

Campo Magnético Constante (Campo C) Contenedor con Cesio 133 Cavidad de Ramsey Generador de Microondas Lazo de amarre Láser de bombeo Láser de detección Fotodetector Vacío Ramsey method + optical pumping

Steven ChuClaude Cohen- Tannoudji William D. Phillips USAFranceUSA Stanford University Stanford, CA, USA Collège de France; École Normale Supérieure Paris, France National Institute of Standards and Technology Gaithersburg, MD, USA b.1948b.1933b.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 Energy E2E2 E1E1 Laboratory reference frame F = 0 -  0 v

R = F + k·v + …  0 L = F - k·v + …<< 0 Atom´s reference frame 0 Doppler cooling Fuerza sobre el átomo como resultado del proceso de absorción/emisión de un fotón

Doppler cooling Fuerza 2kv/  1 Total force on the atom Friction type force

Lowest temperature achieved by eDoppler cooling Doppler cooling Cesium-133 Sodium h  6,6  J  s k B  1,3  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 Phillip L. Gould Department of Physics, University of Connecticut, Storrs, Connecticut Harold J. Metcalf Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 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  850nm Electrón Núcleo 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 ENERGIA Espín-órbita 6 2 P 3/2 6 2 P 1/2 6 2 S 1/2  100GHz  894nm + No a escala

Magnetic field/ Teslas Energy / Joules 1 0 h HFS Region of interest

F=4 F´=5 m = +4 m = -4 m = 0 m = -5 m = +5 m = 0  852 nm 0 1 B / Gauss No a escala Energía

Temperatures below the Doppler limit x 0 44 22 lineal -- ++ -- z y m = -3/2 m = -1/2m = +1/2 m = +3/2 m = -1/2 m = +1/2 J = 1/2 J = 3/2

Stark effect g-½g-½ g+½g+½ 0 lineal -- ++ -- Energy Position 88 z 0 443838 225858

z Energía 88 443838 22 5858 g-½g-½ g+½g+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 /  I 1 >I 2 >I 3 >I 4 I1I1 I2I2 I3I3 I4I4

m 1 0 m 1 0   m F = -1   m F = 1 h  0 h  L h  L z 0 Energía B(z) = Az z2z2 z1z1 z3z3 z4z4 J=0 J=1 Posición ~1 mm F = -  v - kz

Frecuencia  E  t  h/4    t  1/4   1Hz 0  Hz  /  Probabilidad de transición 0  Ramsey Method + ultracold Cs atoms

Thermal beam clocksCold 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 Transition probability (central line of the Ramsey spectrum)

Optical set up for a magneto-optical trap

Mechanical part of a magneto-optical trap (MOT)

Optical set up for a MOT

Mauricio López R (442)