Current Research Abstract

In my current research during my Masters degree, I am trying to study the three-level atom Microlaser using the Quantum Trajectory Method (QTM). The Microlaser is an important tool used to explore the fundamental interaction between a few number of atoms and photons. It consists mainly of a high quality optical cavity through which a beam of excited atoms passes. The Microlaser has been used since 1994 successfully for studies both theoretical and experimental of the quantum interaction between two level atoms and one privileged mode of the radiation field and helped to investigate the fundamental questions in cavity QED in addition to testing new ideas in quantum information.

As any quantum system interacting with a reservoir consisting of many degrees of freedom, the time evolution of the Microlaser is described by a master equation which in general has no simple analytical solution for realistic systems or requires intensive computational power for solving it.

The quantum trajectory method is a Monte Carlo Method applied to a quantum system. A single trajectory of the Microlaser is the one corresponding to a certain evolution of the atom-field state as the atoms pass through the Microlaser cavity subjected to a series of quantum jumps corresponding to all possible events that can occur during and after the interaction between the atom and the field inside the cavity. All photons emitted from the atom or the cavity are supposed to be detected immediately by perfect detectors. The physical properties of the system are obtained by averaging over a large number of trajectories. I am trying to study the photon statistics of the Microlaser at steady state and study the effect of the velocity distribution width of the atoms passing through the microlaser cavity on the field at steady state. I have been using two kinds of trajectories in my simulations; one simulating the field state as a single number state that evolve between quantum jumps by changing the number of photons by a maximum of one photon in each jump and the other method simulates the field wavefunction as a superposition of many number states. It would be interesting to compare the field statistical properties (i.e the intensity correlation function) resulting from each unravelling and see which scheme is closer to reality by comparing both of them with the solution obtained by solving the master equation by other numerical methods (e.g fourth order Runge Kutta method). Another interesting point to investigate in this research would be to use quantum trajectories to examine the behavior of the Microlaser in situations where the photon distribution at steady state is double-peaked and study the occurrence of spontaneous quantum jumps in the rate of atoms exiting the cavity in the ground state or the excited state corresponding to jumps between the two peaks (for the case of two level atoms.) The dynamical evolution of the field inside the cavity from the vacuum state until it reaches the steady state can also be investigated using the quantum trajectory method.

References:

1. Microlaser: A laser with One Atom in an Optical Resonator, Phys. Rev. Lett. 73, 1785-1788 (1994)

2. Laser spectroscopy and quantum optics Rev. Mod. Phys, Vol. 71, Issue 2, March 1999

Home