Rydberg atoms in an oscillating field : extracting classical motion from quantum spectra

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1998.Includes bibliographical references (p. 191-199).by Neal W. Spellmeyer.Ph.D

Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles

This review is devoted to the problem of thermalization in a small isolated conglomerate of interacting constituents. A variety of physically important systems of intensive current interest belong to this category: complex atoms, molecules (including biological molecules), nuclei, small devices of condensed matter and quantum optics on nano- and micro-scale, cold atoms in optical lattices, ion traps. Physical implementations of quantum computers, where there are many interacting qubits, also fall into this group. Statistical regularities come into play through inter-particle interactions, which have two fundamental components: mean field, that along with external conditions, forms the regular component of the dynamics, and residual interactions responsible for the complex structure of the actual stationary states. At sufficiently high level density, the stationary states become exceedingly complicated superpositions of simple quasiparticle excitations. At this stage, regularities typical of quantum chaos emerge and bring in signatures of thermalization. We describe all the stages and the results of the processes leading to thermalization, using analytical and massive numerical examples for realistic atomic, nuclear, and spin systems, as well as for models with random parameters. The structure of stationary states, strength functions of simple configurations, and concepts of entropy and temperature in application to isolated mesoscopic systems are discussed in detail. We conclude with a schematic discussion of the time evolution of such systems to equilibrium.Comment: 69 pages, 31 figure

The emergence of chaos in continuously monitored open quantum systems

This thesis makes a unique contribution to the field of quantum chaos by theoretically demonstrating the effect that measurement has on the emergence of chaos from the quantum world and demonstrating a means to control the onset of chaos in the quantum system using adaptive measurements. Here we investigate how the choice of the continuous measurement strategy for an open quantum system affects the emergence of chaos in the transition from the quantum limit to the classical limit when the system is dissipative. We consider two models in our research. The Duffing oscillator is classically chaotic and also dissipative( ie. an open quantum system), whereas the driven top is classically a closed system; adding dissipation via continuous measurement therefore changes the behaviour in from the classical limit. The first half of this thesis presents the investigation of a dissipative system whose classical limit is chaotic. We explore the emergence of chaos from the open quantum system that is continuously monitored and investigate the dependence on the choice of monitoring by changing a single parameter in a homodyne measurement scheme, effectively changing the information gained by the measurement. We show that the emergence of chaos in the regime where quantum effects are still present can be determined solely by changing the measurement parameter. This is a result of the interplay between the quantum interference effects induced by the nonlinear dynamics and the localisation and decoherence that occurs due to the measurement. We also investigate the case where the classical limit is regular for the Duffing oscillator, and demonstrate the semiclassical effect of chaos induced by the measurement back-action. A certain choice of measurement leads to a noise which drives the system to large spread in the dimensionless position enabling a non-classical transition mechanism that is classically forbidden, inducing chaos in the system. These results are verified by the numerical calculation of the maximal Lyapunov exponent in the quantum regime. The second part of this thesis investigates the possibility of controlling the degree of chaos with quantum control. We design an effective control scheme to control the degree of chaos using the measurement dependency of the state. We propose an adaptive measurement scheme which changes the homodyne measurement angle in real time depending on the direction of the state's interference fringes in phase space. This is done using the knowledge gained by the measurement signal. We show that this control scheme can enhance or suppress chaos. By enhancing the degree of chaos we are also able to push the onset of chaos further into the quantum regime than was possible before. By suppressing chaos we generate highly non-classical states and regular motion. The feasibility of experimentally realising this control technique is discussed in detail. The final section of this thesis considers a chaotic system that is not dissipative in the classical limit: the driven top. We investigate the effect that opening the quantum system to decoherence has on the degree of chaos when we continuously measure the system. We demonstrate that the presence of decoherence suppresses the chaos and alters the dynamics of the quantum system. This is seen to worsen as the strength of the measurement is increased unless a particular measurement is chosen that perfectly cancels out the decoherence resulting in the Hamiltonian evolution in addition to noise from the measurement. These results are verified by the separation time between classical and quantum dynamics

Termolecular Association of Ions in Gases

Issued as Technical reports [nos. 1-4], and Final report, Project no. G-41-61

Water Dynamics and the Effect of Static and Alternating Electric Fields

Having a net dipole moment, water molecules tend to align with an external electric field. The re-orientation of water molecules to align with the field direction can result in structural and dynamic changes in liquid water. Studying these changes can help us to understand the role of an E-field in many biological systems, chemical reactions, and many technological advancements. In short, the application of static electric fields causes molecules to stay aligned with the field, so, fewer hydrogen bonds break, and molecules have slower dynamics. This type of field can be used when the mobility of water molecules needs to be reduced, like in electroporation. Alternating electric fields, on the other hand, cause continuous re-orientation of dipole moments, which results in more H bond breaking, water is less structured, and molecules have faster motion. Water under static and alternating electric fields have several applications in science and technology. Although many of the interesting usages of the application of electric fields to water happen at surfaces, the response of hydrogen bonding of water molecules to an E-field is still not fully understood even in bulk. For instance, the rate of hydrogen bond breaking, the re-orientation of water molecules, and the random walk of water molecules under the restrictions of the static electric field have not been thoroughly assessed. The static electric field limits the re-orientation of water molecules, but the translation reduces at the same time, this is clear evidence of roto-translational coupling, and the static electric field is a great groundwork for studying this coupling which is generated by the hydrogen bonds. For studying the effects of an E-field on H-bonding dynamics in depth, we need a model of hydrogen bonding. There are a few models for dynamics of H-bonding and reorientation of water molecules, including Luzar and Chandler model, published in 1996, and the Laage and Hynes jump model, published in 2006, which are described in the introduction chapter. The two models are related but have different perspectives, so it would be very interesting to look for a more general framework of hydrogen bonding by combining these two models, with the help of the influence of external electric fields. We also explain the relation of the random walk diffusion of water molecules and the hydrogen bonding. Since the external electric field can change the dipole moment of water molecules, for a more realistic picture, we need do the simulations with sophisticated polarizable water models to obtain a better estimate of the behavior of experimental water in an electric field. In this thesis, we introduce our generalized hydrogen bond framework; then we assess this framework, as well as other static and dynamic properties of water under static and alternating electric fields