X-Ray Absorption and Diffraction on Crystal Structures
Guillem Cucurull, Matthew Kim
(Dated: February 25, 2024)
We use optical pumping to measure the Landé g-factors of 85 Rb and 87
Rb. We find the g-factors
85
of Rb and 87 Rb to be g85 = 0.510 ± 0.020 and g87 = 0.333 ± 0.013.
I. INTRODUCTION Therefore the Hamiltonian for a small magnetic field B
along the z-direction is:
q
Optical pumping is used in which light excites elec- the magnetic moment is given as µ = 2mL
trons at an atom from one energy level to a higher one.
In the case of this experiment, the metal used is Rubid-
HB = gF µB mF Bz (2)
ium, which has an external DC and RF magnetic fields
used to alter the excited state. In these atoms, there where µB is the Bohr magneton, L is the orbital angu-
is interaction between the electrons and the nucleus and lar momentum, and µF the total magnetic moment of
the magnetic field, also known as the Hamiltonian of the the atom due to the total atomic angular momentum F ,
system in the Coulomb interaction: represented by the following:
p2 Ze2 e
HC = − (1) µF = −gF F (3)
2m r 2m
where is the total magnetic moment due to F . The
material used for this experiment, Rubidium (Rb), has
two isotopes Rb and Rb. The g-factor of each is found by
measuring the resonant frequency of each, if the magnetic
field is known. The temperature of the absorption cell is
set at 323 K to reach thermal equilibrium. The sweep
rate is set at 10 seconds, considered a slow sweep rate
for the magnetic field current, and the parameters of the
sweep field coils used are a mean radius of 0.164m, B =
8.99x10−3 IN/R, and 11 turns on each side
where N is the number of turns, I is the current in A,
FIG. 1. Random walk simulation example for 1 Dimension and R is the mean radius of the Helmholtz coils. The
sweep coil current passes through a resistor of 1Ω where
an equal amount of voltage at the sweep monitors. To
measure the g-factors, we use (2) to get:
µB
υ = gF B (4)
h
II. SETUP
The Rb lamp emits light of wavelengths 780 nm and
795 nm through an interference filter. This light goes
through a linear polarizer and a quarter wave plate
to form a circularly polarized light, which is then sent
through the cell with Rb vapor. A photodiode detector
is used to measure the intensity of this light, as shown in
FIG2.
A magnetic field is applied and induces transitions.
The sweep coils are to tune this magnetic field which.
It is applied transversely on the horizontal optical axis
FIG. 2. Random walk simulation example for 2 Dimension ramping the current and the magnetic field. An oscillo-
scope is used to measure the signal proportional to the
There is also splitting due to spin-orbit coupling and an TF current at the connector on the cell holder. In order
external magnetic field, presented as the Zeeman effect. for the signal to be proportional to the amplitude of the
Guillem Cucurull, Matthew Kim
(Dated: February 25, 2024)
We use optical pumping to measure the Landé g-factors of 85 Rb and 87
Rb. We find the g-factors
85
of Rb and 87 Rb to be g85 = 0.510 ± 0.020 and g87 = 0.333 ± 0.013.
I. INTRODUCTION Therefore the Hamiltonian for a small magnetic field B
along the z-direction is:
q
Optical pumping is used in which light excites elec- the magnetic moment is given as µ = 2mL
trons at an atom from one energy level to a higher one.
In the case of this experiment, the metal used is Rubid-
HB = gF µB mF Bz (2)
ium, which has an external DC and RF magnetic fields
used to alter the excited state. In these atoms, there where µB is the Bohr magneton, L is the orbital angu-
is interaction between the electrons and the nucleus and lar momentum, and µF the total magnetic moment of
the magnetic field, also known as the Hamiltonian of the the atom due to the total atomic angular momentum F ,
system in the Coulomb interaction: represented by the following:
p2 Ze2 e
HC = − (1) µF = −gF F (3)
2m r 2m
where is the total magnetic moment due to F . The
material used for this experiment, Rubidium (Rb), has
two isotopes Rb and Rb. The g-factor of each is found by
measuring the resonant frequency of each, if the magnetic
field is known. The temperature of the absorption cell is
set at 323 K to reach thermal equilibrium. The sweep
rate is set at 10 seconds, considered a slow sweep rate
for the magnetic field current, and the parameters of the
sweep field coils used are a mean radius of 0.164m, B =
8.99x10−3 IN/R, and 11 turns on each side
where N is the number of turns, I is the current in A,
FIG. 1. Random walk simulation example for 1 Dimension and R is the mean radius of the Helmholtz coils. The
sweep coil current passes through a resistor of 1Ω where
an equal amount of voltage at the sweep monitors. To
measure the g-factors, we use (2) to get:
µB
υ = gF B (4)
h
II. SETUP
The Rb lamp emits light of wavelengths 780 nm and
795 nm through an interference filter. This light goes
through a linear polarizer and a quarter wave plate
to form a circularly polarized light, which is then sent
through the cell with Rb vapor. A photodiode detector
is used to measure the intensity of this light, as shown in
FIG2.
A magnetic field is applied and induces transitions.
The sweep coils are to tune this magnetic field which.
It is applied transversely on the horizontal optical axis
FIG. 2. Random walk simulation example for 2 Dimension ramping the current and the magnetic field. An oscillo-
scope is used to measure the signal proportional to the
There is also splitting due to spin-orbit coupling and an TF current at the connector on the cell holder. In order
external magnetic field, presented as the Zeeman effect. for the signal to be proportional to the amplitude of the
