Cold atoMS in optical potentials: Quantum Levy kicked rotor

Abstract

The invention of laser cooling and trapping techniques for neutral atoms provides a platform to visualize quantum effects associated with matter. In addition, this technique lends control and manipulation of the factors that re flect changes in the dynamics of a system in quantum regime. One of such examples is a kicked rotor system. Particles in a delta kicked spatially periodic potential, mimics this system. The dynamical evolution of this system in the quantum regime is very different from that in a classical regime. Average energy of a classical system increases linearly as the number of kicks increases whereas, for a quantum system, the average energy saturates to a certain limit. This key feature of saturation in a quantum system is caused by suppression of momentum diffusion. At this point, the system is analogous to a crystal with defects that shows localization of electrons near lattice sites, popularly known as Anderson localization. The energy-time relation of a kicked rotor system can be mapped to the position-momentum relation of such a defective crystal. This deviation in energy evolution can be considered as a 'meter-scale' to understand the transition from quantum to classical regime. Small amount of noise coupling to a quantum system leads to decoherence in the evolution of the system. For a classical system the energy gained by the system does not saturate, instead, it increases linearly with increase in number of kicks. By increasing the amount of noise, the system can undergo a complete transition to the classical regime. The noise could be generated by various means such as noise in amplitude of each kicks, fluctuation in the periodicity of the kicks or any other mechanism which causes loss in coherence. It has been predicted that noise in the periodicity of kicks, where the periodicity follows Lèvy's statistics the decoherence is suppressed. In fact, in certain parameter space, the decoherence-time increases to in finity. This is very important to prepare decoherence free system for experiments such as quantum information processing and quantum emulation. The use of ultra-cold atoms is very important because as the temperature goes down, the momentum distribution confi nes to very small range. The corresponding wavelength of the particles becomes large enough to observe the interference effect and therefore the atoms' energy reaches a state where quantum behaviour dominates. Red detuned counter propagating laser beams can be used to create periodic optical potentials. Fast ashes of such field, given on ultra-cold atoms exactly mimics a kicked rotor system. This system is very simple to study the dynamical evolution with the additional noise. We trap Rb atoms in Magneto-optic Trap and further cool them down by Sysiphus cooling to prepare particles for the experiment. At temperature below 10 microK, ashes of standing wave are applied to the atoms which leads to redistribution of momenta of the atoms. After certain time of free evolution, atoms are imaged to observe the momentum distribution and consequently the measurement of the energy. In this thesis, we report the progress towards experiments to study the evolution of system in which periodicity of the kicks follows Lèvy's statistics.