Probing the quantum speed limit of atomic matter waves in optical lattices

Abstract

The development of quantum technologies requires a deep knowledge of quantum systems and a high level of control of quantum states. In this thesis I report on my contribution to three areas that are important to quantum technologies: (i) Imaging of quantum states (ii) Fast transport of matter wave packets (iii) Estimation of the speed limit of quantum evolution. The platform here used consists of single neutral caesium-133 atoms trapped in a state dependent optical lattice potential. The control over the internal state of the atoms and the potential landscape is used as a tool to study the atomic wave packet dynamics. <br /> In the first part of the thesis I present the experimental setup as well as various experimental techniques that are required for the measurements presented in the following chapters. Two new implementations have been done in order to realize the desired measurements. One of them is a technique to measure the motional ground state population fraction, with an accuracy that is robust over a wide range of temperatures of the thermal ensemble. The second one is a pair of Raman beams to couple two hyperfine states with Rabi frequencies of around 6.5MHz. Much faster than the observed wave packet dynamics. <br /> In chapter 3, I present a new technique to obtain time-resolved single-pixel images of quantum wave packets using Ramsey interferometry. The technique shares a clear analogy to classical optical imaging and can be potentially extended to obtain multi-pixel images that contain the same information as the full wave function. Even though the measurements presented in this thesis are restricted to single-pixel images, important information is extracted from them, including the Hamiltonian moments, the energy spectrum of the Hamiltonian and the population probabilities in the basis of motional eigenstates. <br /> In the last part of the thesis, the quantum speed limit of two different processes are studied. In chapter 4, the Mandelstam-Tamm and the Margolus-Levitin bounds are verified for atomic wave packets in a static optical lattice potential. The bounds impose a limit to the maximum rate of change of a quantum state. Two different regimes are covered: one where the Mandelstam-Tamm bound is more restrictive and one where the Margolus-Levitin bound is more restrictive. Moreover, it has been observed that the atomic wave packets evolve at a rate very close to the limit imposed by the Mandelstam-Tamm bound. In chapter 5, the speed limit of a different quantum process is studied, namely, fast atom transport without motional excitations over distances much longer than the width of the atomic wave packet. The transport trajectories are obtained with optimal quantum control, making possible to realize transport operations down to the shortest fundamental duration - the quantum speed limit. The Mandelstam-Tamm bound is found to predict an absurdly small estimate of the minimum transport duration, but a meaningful bound consistent with the measured speed limit is obtained based on geometric arguments.