# 2003 Projects

2003 should be my last semester as an undergraduate in Stony Brook. My focus during this year is to understand population transfer proceses of two level and later three level atoms. During my Laser's course under Prof. Thomas Weinacht we learned about population transfer while covering the rate equations and the density matrix. These topics cover the effects of light fields on two level atoms assembles. Howevere, these situations were usually idealized because interactions between the atoms and the medium were neglected in the modeling. For my work of this semester Im going to use the Bloch equations which are a modification of the density matrix. These equations were originally used in magnetic resonance to study the spin of particles (two possible levels, spin up and spin down). However, it was noticed that these equations could be also used to describe the case of two level atoms.

By numerically solving this system of equations we can find the population probability in our two level atom. We represent this probability by a vector moving in a three- dimensional space formed by 3 pseudo-axis each one representing the probability of our atom to be in a particular state (ground, excited or mix of both states). The trace of the tip of our vector is confined in the surface of a unity sphere or Bloch Sphere. The radious of this vector would be equal to the probability of finding the atom anywhere if our two level system which is equal to 1. These are the Bloch vectory (which tell us the state probability) and the Torque vector (which tell us about the light field bathing the system). There is a relation between these two vector that causes the Bloch vector to orbitate around the Torque vector. Since my model deals with light fields slowly varying in frequency. I expect and I observed the Bloch vector slowly orbiting the Torque vector as it moves from the south pole (ground state) to the north pole (excited state).

The idea of our computer model is to simulate the population transfer from the ground to the excited state using adiabatic rapid passage. In practice this means that we ramp very slowly the frequency of the light field bathing the atom from a large negative detuning towards resonance and then towards a very large positive detuning. Negative and positve just mean that we are going from one side to the other in frequency space of the particular resonant frequency of the atom. However, the beauty of the process is that that slowly ramping the frequency of the light field we can transfer most of the atoms into the excited state. Once there we can do all sorts of things to the atoms as long we do it faster than the time it for the excited level to spontaneously decay.

We hace created a simple computer simululation in MatLab to numerically solve the Optical Bloch Equations and plot the result in a three dimensional axis. After giving initial values for the properties of the light field we then run the program by slowly changing the frequency of the light field as a fucntion of time.

Useful Definitions:
• Dressed State: ?
• Dark State: Atomic States that cannot be excited by the light field.
• VSCPT(Velocity selective coherent population trapping)

Useful references:

Stimulated Raman adiabatic passage with amplitude modulated fields. L.P. Yatsenko, B.W. Shore, K. Bergmann, V.I. Romanenko. The European Physics Journal D

On the topology of adiabatic passage. L.P. Yatsenko, S. Guerin and H.R.Jauslin. Laboratoire de Physique de l'Universite de Bourgogne.

Population transfer between molecular vibrational levels by stimulated Raman scattering with partially overlapping laserfields. A new concept and experimental results. U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann. J. Chem. Phys. 92 (9), 1 May 1990

Population switching between vibrational levels in molecular beams U. Gaubatz, P. Rudecki, M. Becker, S. Schiemann, M. Kulz and K Bergmann. Chemical Physics letters Volume 149, number 5,6.

General theory of population trasfer by adiabatic rapid passage with intense, chirped laser pulses. V.S. Malinovsky and J.L. Krause. Eur. Phys. J. D 14, 147-155 (2001)

Coherent population transfer among quantum states of atoms and molecules. K. Bergmann, H. Theuer, and B.W. Shore Reviews of Modern Physics, Vol. 70, No. 3, July 1998. This is one of the most important papers written about population transfer using adiabatic rapid passage.

Latonus@hotmail.com, Jose.Mawyin@osa.org
Stony Brook Laser Teaching Center
Last updated: 4 May 2003