This is a summary of the topics in linear optics we have covered in module 10.
We have studied optical tweezers. Optical tweezers consists of a single laser beam, which is focused by a high-numerical-aperture objective lens to a diffraction-limited spot. A transparent particle located near the focal point refracts the light. Photons change direction and therefore transfer momentum to the particle. The total momentum transfer due to all refracted photons in the beam always points toward the focus of the laser beam. The light-atom interaction mechanism is stimulated emission.
We have studied the spectra of single electron atoms. The spectra of atoms with one electro outside closed shells resemble the spectra of single electron atoms.
The Coulomb interaction between the electron and the core is the dominant interaction. The Hamiltonian H0 for the electron is p2/(2m) + V(r). Common eigenfunctions of H0, L2, and Lz are of the form ynlm(r) = Rnl(r)Ylm(q,f). The eigenenergies are degenerate and depend only on the quantum numbers n and l.
Correction terms due to the spin-orbit interaction break the degeneracy. Energy levels characterized by n and l split according to the value of j (J = L + S). This is called the fine-structure splitting.
The hyperfine interaction breaks the degeneracy of levels characterized by n, l, j. These levels split according to the value of f (F = J + I). This produces the hyperfine structure.
In a weak external magnetic field levels characterized by n, l, j, f split according to the value of the magnetic quantum number mf. This is called the Zeeman effect.
An electromagnetic wave can induce transitions between energy levels E1 and E2 as long as |E1 - E2| = hw. The dipole transition selection rules are Dl = ± 1, Dm = 0, ± 1, neglecting the fine structure and hyperfine structure splitting. An electromagnetic field is most likely to induce a transition between an initial and a final state if these selection rules are satisfied. If these selection rules are not satisfied a transition is less likely and is said to be forbidden. If the fine structure and hyperfine structure splitting are not neglected, then the dipole selection rules then become Df = 0, ±1, Dj = 0, ±1, Dl = ±1, Dmf = 0, ±1.
Spontaneous transition rates are related to the induced transition rates via the Einstein coefficients.
We have studied saturation spectroscopy. If the frequency of a laser beam propagating through an atomic vapor is scanned across the absorption profile for a particular transition, then the intensity of the absorbed radiation as a function of frequency will reproduce the full Doppler-broadened line shape. If the light from the laser is split into two beams, a saturating beam and a probe beam, arranged so that they cross in a region of a gas cell containing the atomic vapor, then both beams will interact with the same atoms, if the velocity components of the atoms along the direction of propagation of the light is approximately zero. But the strong, saturating beam will quickly deplete the number of atoms in the initial state, leaving very few for the probe beam to interact with. The probe beam therefore travels through the vapor cell without being depleted even though it is at resonance. We observe spikes in the Doppler broadened absorption spectrum, at the Doppler-free transition frequency, with a width approximately equal to the natural linewidth of the transition.
We have discussed various ways to stabilize the frequency of a diode laser by locking it to a feature in the saturated absorption spectrum. Side locking, peak locking, and the Dichroic-Atomic-Vapor Laser Lock (DAVLL) technique are most often employed.
We have studied laser cooling. Laser cooling involves converting the atom’s translational kinetic energy into optical energy carried away by spontaneously emitted photons. The laser has to be in resonance with an atomic transition. One way to maintain resonance between the laser frequency and the atomic transition frequency as the atom slows down is Zeeman tuned cooling. The atomic transition frequency is swept with an inhomogeneous magnetic field.
To create optical molasses in one-dimension two lasers tuned slightly below the resonant frequency of an atomic transition in the absence of a magnetic field counter-propagate along the z-axis.
We have investigated a magneto-optic trap. In order to confine the atoms in coordinate space, a position dependent restoring force is needed. A magneto-optic trap (MOT) can provide such a restoring force. A MOT combines optical molasses with an inhomogeneous magnetic field.
A pair of anti-Helmholtz coils can produce the inhomogeneous magnetic field. In a typical three-dimensional MOT three cooling lasers are arranged to propagate along the x, y, and z, axis and to reflect back onto themselves. Six laser beams therefore intersect in the region near the origin. The z-axis is the symmetry axis of the pair of anti-Helmholtz coils. The laser beams are circularly polarized, so that the projections onto the propagation axes of the angular momentum vectors of photons moving towards the origin point opposite to the direction of the magnetic field. Atoms are trapped near the origin where the magnetic field is near zero.