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Optical Pumping on Rubidium Optical Pumping on Rubidium E. Lance (Dated: March 27, 2011) By means of optical pumping the values of gf and nuclear spin for Rubidium were determined. 85 87 85 For Rb gf was found to be .35. For Rb gf was found to be .50. The nuclear spin for Rb was found to be 2.35 with a theoretical value of 2.5, for Rb87 the nuclear spin was found to be 1.5 with a theoretical value of 1.5. Quadratic Zeeman effect resonances were observed around magnetic fields of 6.98 gauss and RF of 4.064 MHz. I. INTRODUCTION Rabi equation: Optical pumping refers to the redistribution of oc- cupied energy states, in thermal equilibrium, inside an ∆W µ ∆W 4M 1=2 W (F; M) = − − j BM± 1+ x+x2 : atom. The redistribution is achieved by polarizing inci- 2(2I + 1) I 2 2I + 1 dent light, therefor, pumping electrons to less absorbent (4) energy states. By confining electrons in less absorbent A plot of Breit-Rabi equation is shown in figure 2, this energy states we can then study the relationship between plot shows how when the magnetic field becomes large, magnetic fields and Zeeman splitting. the energy splittings stop behaving in a linear fashion and a quadratic Zeeman effect can be seen. II. THEORY We will be dealing with Rubidium atoms which can, essentially, be conceived as a hydrogen like single elec- tron atoms. The single valence electron in Rubidium can be described by a total angular momentum vector J which couples the orbital angular momentum L with the spin orbital angular momentum S. By simple coupling of momenta we can construct the Fine structure for the en- ergy levels inside the atom. If one takes into account the nuclear moment of the atom this produces yet another splitting of the energy levels, the Hyperfine Structure. The Hyperfine structure is conceived much like the Fine structure, by coupling the nuclear moment I with J re- sulting in a total angular momentum F . If we impose a magnetic field the energy levels inside the Hyperfine structure split yet again as shown in figure 1. The hamil- tonian expressing the nuclear moment and magnetic field relationship is µ µ H = haI · J − j · B − I I · B: (1) J I FIG. 1. Zeeman splitting for Rubidium 87 If the the nucleus of the atom is accounted for, the interaction of the atom with an external magnetic field can be expressed as: W = −gf µoBM (2) It is the structure shown in figure one that we are in- terested, it will allow us to confine electrons into less where W is the magnetic energy and gj is the Lande g- absorbent states. A circularly polarized source of light, factor given by: incident on our rubidium gas, provides one unit of angu- lar momentum. By selection rules ∆M= ±1 or ∆M=0, F (F + 1) + J(J + 1) (I − 1) transitions from 2S F=2 M=2 to 2P F=2 M=3 will g = g I : (3) 1=2 1=2 f j 2F (F + 1) not occur since there is no M=3. Since transitions with ∆M=0 are allowed, radiating electrons from the first ex- 2 If the interaction energy with the magnetic field is not ited state may fall into S1=2 F=2 M=2 state, confining small then the interaction can be expressed by the Breit- the electrons in such state. 2 IV. EXPERIMENT 1: LOW FIELD RESONANCES In order to carry out our first experiment the appa- ratus should be aligned such that beam output of the discharge lamp is aligned with the north-south axis of the earth's magnetic field. The set of vertical Helmholtz coils are used to cancel out vertical components of earth's magnetic field across our gas cell. The set of horizon- tal Helmholtz coils cancel out horizontal components of earth's magnetic field. When the magnetic field inside our gas cell is 0 the energy levels become degenerate and there is no splitting, we can see a big increase in absorp- tion as shown in figure 4. As the magnetic field increases inside the gas cell the energy levels split and we can ob- serve the Zeeman effect. If we radiate our sample with a set rf field we will see, at some point, a resonance ef- fect where our rf frequency matches the energy gap in the Zeeman energy splitting. In this experiment we want FIG. 2. Breit-Rabi plot. to determine the nuclear spin for our isotopes. Figure 5 shows the data obtained in this experiment. In order to obtain an experimental value for spin we must find a re- lationship between the magnetic field and the frequency, this allows us to obtain a value for gf we can easily then solve for I in the Lande g-factor equation (3). FIG. 4. Transmitted Intensity vs Magnetic Field FIG. 3. Experiment Design III. EXPERIMENTAL DESIGN V. EXPERIMENT 2: QUADRATIC ZEEMAN EFFECT The experiment consists of two isotopes of Rubidium Rb85 and Rb87, a discharge lamp emitting light at 795 nm in wave length, temperature controlled gas cell, silicon The goal of this part of the experiment is to study the photodiode detector, .25 wave plate, interference filter behavior of the energy level splitting as it stops behaving and other optics, 2 sets of Helmholtz coils whose axis linearly with respect to the magnetic field. A stronger are perpendicular to each other, oscilloscope and an RF magnetic field was applied, around 6.9 gauss, and mul- programmer. A schematic of such design is presented in tiple resonances were observed at a frequency of 4.064 figure 3. MHz. 3 VI. RESULTS The values of gf and nuclear spin for Rubidium were found to be .35 and 2.35 for Rb85, .50 and 1.5 for Rb87. Quadratic Zeeman effect resonances were observed around magnetic fields of 6.98 gauss and RF of 4.064 MHz. 4 FIG. 5. Obtained values for Rubidium isotopes.
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