Introduction

The objective of this lab was to study the hyperfine structure of Rubidium using saturation spectroscopy. This was done using a tunable diode laser, an evacuated Rubidium cell, gold mirrors and photodiodes. The purpose of each of these will be discussed later in the procedure, what follows here is an introduction to hyperfine structure, Doppler broadening, and saturation spectroscopy.

In my discussion of hyperfine structure I will assume that you know the basic system of classification to describe the structure of an atom including: the principle quantum number = n, the letter S,P,D, or F which describes the orbital angular momentum = l, and the fraction which is a multiple of 1/2 (e.g. 1/2, 3/2, 5/2) that is related to the sum of the orbital and spin angular momenta = J. Another level of classification is for the sum of the orbital, electron-spin and nuclear-spin momenta, this level is represented by F and is an integer; this relates to the hyperfine structure and is the property of the atom we are most concerned with in this lab. Using the first three labels the ground state of Rubidium is represented as 5S_1/2. This means at the ground state Rubidium: n = 5, l = 0, and J = 1/2. J is always a fraction and I( represents the sum of the nuclear and electron spin vectors) is also a fraction(both are multiples of 1/2). The sum of the vectors J and I equals F, and F is always an integer.

For an atomic spectrum the basic lines represent transitions between states of the principle quantum number(e.g. n = 2 to n = 3). These lines split due to properties of the atom. The first splitting of the lines in the spectrum is called the fine structure. This splitting is caused by magnetic properties of the electrons that surround the nucleus. The electron spins and moves around the nucleus, this causes it to have a magnetic field. This magnetic field causes the splitting of the basic line based on the quantum number state into multiple lines based on the magnetic properties of the electrons. Other magnetic interactions can cause splitting on an even smaller scale. This time the splitting is because the nucleus also has spin and interacts with the electron because of the charge of the moving electron and the closeness of the electron's magnetic field. This splitting of the spectral lines is called the hyperfine structure. 1

In this lab we wanted to find the hyperfine structure of rubidium. In our sample of rubidium there were two isotopes: Rb87 and Rb85. Each isotope has a different hyperfine splitting. By looking at the absorption spectrum and the emission spectrum of the rubidium we could determine the hyperfine structure for rubidium. This is a rough graph of what we expect the hyperfine structure to look like.

The absorption spectrum of the rubidium is due to the absorption of the photons of the laser beam by the atoms in the cell of rubidium. For a certain wavelength of the laser the excitation of the rubidium atoms absorbs photons from the laser beam so that the beam that enters the photodiode is reduced in intensity. If no absorption of photons occurs then the intensity of the laser will not change. The absorption of the photon causes an electron to jump to an excited state in an atom. Ideally, this only occurs for atoms at zero velocity in relation to the laser beam. What happens in reality will be discussed later. Emission occurs when the electrons in an excited state of an atom fall back down to the ground state emitting a photon. This is aided by the laser beam, because when it is at a certain wavelength the excited electrons, with zero velocity with respect to the laser beam, will fall back down to the ground state and a photon will be emitted. We used photodiodes to detect both emission and absorption. The setup of the detectors with the laser and the rubidium cell is below.

The absorption spectrum is the laser or part of the laser that makes it through the rubidium cell. The emission spectrum is the photons that are released when the electrons of a rubidium atom make the transition from an excited state to the ground state. Here is what we expect each to look like:

Notice that the absorption spectrum is a dip and the emission is a hump. The absorption takes away from the intensity of the laser beam, and the emission is nothing. The arrows address the non-ideal situation, and what is actually observed when the spectra are seen. What the arrows show is the Doppler broadening of the signal. The Doppler shift is due to the thermal excitation of the atoms. So the atoms are moving in all directions, and this causes some atoms to absorb photons at larger or smaller wavelengths. Ideally, as I said before the atoms would only be excited for one wavelength and when they are at zero velocity with respect to the laser beam, but because of the thermal excitation of the atoms some of the atoms moving toward the laser beam will be excited because they think that the laser beam is moving at a lower frequency than it actually is because of the Doppler effect. The same would be true for atoms moving in the same direction as the laser beam. When the laser beam is at a higher frequency, the atoms moving in the same direction react as if the wavelength is actually the lower expected wavelength for excitation, again because of the Doppler effect. The Doppler broadening shows there will be a range of wavelengths over which the certain state of the atom is detected.

Doppler broadening is reduced by using saturated spectroscopy. In terms of our laboratory set-up, saturation spectroscopy is having one beam go through the cell one way and another more intense beam with the same wavelength go through the other way saturating the atoms in the sample. So the more intense beam(pump beam) goes through the sample and its photons are absorbed faster, so that when another weaker beam(probe beam) passes through it would find the absorption less for some wavelengths. This method is called the Lamb dip after the scientist who first realized its advantages.

The Doppler width does not disappear, but the atoms that absorb photons from the pump beam do not absorb photons from the probe beam, so the intensity of the probe beam is less for certain wavelengths(frequencies). In fact the Doppler effect is at work again because the smaller peaks that are produced come from reactions by the pump beam and these reactions are picked up by the probe beam. The two beams are always the same frequency because they come from the same source. What is expected in this case is three peaks of less absorption inside a larger peak of absorption.

The left peak represents a point where the frequency is equal to the first hyperfine splitting in the excited state of the atom, and the right peak is where the frequency is equal to the second hyperfine splitting of the excited state. The middle peak is an average between the right and left peak.

The absorption spectrum that we expected was to see two large peaks for each of the isotopes of Rubidium. The two peaks for the Rb87 isotope are outside the two peaks of the Rb85 isotope. Then we expected to see three peaks of smaller absorption within each larger peak. The two large peaks for each isotope represent two different F values for the ground state of the atom. The three smaller peaks also represent two different F values for the excited state of the atom, because the middle peak of three is considered an average of the outer two. For Rb85 the F = 3 & 2, and for Rb87 F = 1 & 2. The energy levels we wanted to see from our experiment were:

The arrows represent the possible transitions from the ground state to the excited state.