No Arabic abstract
Controlling the translational motion of cold atoms using optical lattice potentials is of both theoretical and experimental interest. By designing two on-resonance time sequences of kicking optical lattice potentials, a novel connection between two paradigms of nonlinear mapping systems, i.e., the kicked rotor model and the kicked Harper model, is established. In particular, it is shown that Hofstadters butterfly quasi-energy spectrum in periodically driven quantum systems may soon be realized experimentally, with the effective Planck constant tunable by varying the time delay between two sequences of control fields. Extensions of this study are also discussed. The results are intended to open up a new generation of cold-atom experiments of quantum nonlinear dynamics
We give an overview of different paradigms for control of quantum systems and their applications, illustrated with specific examples. We further discuss the implications of fault-tolerance requirements for quantum process engineering using optimal control, and explore the possibilities for architecture simplification and effective control using a minimum number of simple switch actuators.
A time crystal is a macroscopic quantum system in periodic motion in its ground state, stable only if isolated from energy exchange with the environment. For this reason, coupling separate time crystals is challenging, and time crystals in a dynamic environment have yet not been studied. In our experiments, two coupled time crystals made of spin-wave quasiparticles (magnons) form a macroscopic two-level system. The two levels evolve in time as determined intrinsically by a nonlinear feedback. Magnons move from the ground level to the excited level driven by the Landau-Zener effect, combined with Rabi population oscillations. We thus demonstrate how to arrange spontaneous dynamics between interacting time crystals. Our experiments allow access to every aspect and detail of the interaction in a single run of the experiment, inviting technological exploitation-- potentially even at room temperature.
This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from the Pontryagin Maximum Principle. In a three-level quantum system, we show that the Stimulated Raman Adiabatic Passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.
We place two atoms in quantum superposition states and observe coherent phase evolution for 3.4x10^15 cycles. Correlation signals from the two atoms yield information about their relative phase even after the probe radiation has decohered. This technique was applied to a frequency comparison of two Al+ ions, where a fractional uncertainty of 3.7+1.0-0.8x10^-16/sqrt{tau/s} was observed. Two measures of the Q-factor are reported: The Q-factor derived from quantum coherence is 3.4+2.4-1.1x10^16, and the spectroscopic Q-factor for a Ramsey time of 3 s is 6.7x10^15. As part of this experiment, we demonstrate a method to detect the individual quantum states of two Al+ ions in a Mg+-Al+-Al+ linear ion chain without spatially resolving the ions.
We propose a system for observing the correlated phase dynamics of two mesoscopic ensembles of atoms through their collective coupling to an optical cavity. We find a dynamical quantum phase transition induced by pump noise and cavity output-coupling. The spectral properties of the superradiant light emitted from the cavity show that at a critical pump rate the system undergoes a transition from the independent behavior of two disparate oscillators to the phase-locking that is the signature of quantum synchronization.