Floquet Engineering in an Atom-Optics Kicked Rotor

Abstract

Implementing the Floquet operator in a cold atoms system is a fascinating field of research. This implication opens the path for the study of dynamical localization in the quantum kicked rotor system. The quantum kicked rotor system provides a platform to simulate analogue Anderson localization in both lower and higher dimensions, including the observation of the Anderson insulator-metal transition in three dimensions. It is also a unique tool to study quantum chaos. Since dynamical localization phenomena are based on the destructive quantum interference of the atomic wave-function, this system provides a platform for studying the exponential and non-exponential loss of coherence by coupling the quantum system with an external bath in an arbitrary way. The present aim of this thesis is to coherently control quantum interference by engineering different dynamical phase evolution without introducing decoherence into the system. As we know, the classical counterpart of the system is fully chaotic in nature. Therefore, coherent control must be systematically engineered; otherwise, quantum interference may be disrupted in the system, causing it to behave classically. This thesis focuses on controlling dynamical localization in periodically kicked ultra-cold atoms with a 1D optical lattice. Two methods are explored: periodic modulation of a control parameter to induce competition between quantum diffusion and localization, leading to enhanced in localization length of localized system. In second method, we demonstrate a simple and intuitive method for controlling dynamical localization using a single parameter with Bose-Einstein condensate. This coherent control approach, operates through a single knob, enables systematic control over dynamical localization across a wide range without introducing any decoherence into the system. Further in this thesis, our study also investigates the asymmetric dynamical localization and it’s stability, by launching the initial wave-function with varying recoil velocities within periodically kicked optical lattices. Noteworthy velocity-dependent features are observed in different time-evolution. Utilizing the velocity dependent feature in early time dynamics, we created a method for direct measurement of micromotion (100’s µm/s) of the Bose-Einstein condensate (BEC). This micromotion velocity is order of magnitude less than the one recoil photon momentum, as well as mean velocity associated with BEC temperature. By utilizing a feature coming from broken parity symmetry due to the micromotion, measurement of such a small velocity is possible, which is not significantly affected by velocity distribution of the BEC, that is a common challenge in spectroscopy techniques. This approach offers a precise measurement of micromotion without relying heavily on the time-of-flight method, which often requires a substantial time for measurable movement, making it unfeasible in many systems. The precise measurement of such low velocities of the BEC contributes significantly to precision measurements, such as in atom interferometers for measuring rotation and acceleration, helping nullify unknown shifts in measurements comes from the micromotion.