Decoherence in nonlinear quantum systems

Gehad Kandeel Sadiek, Purdue University

Abstract

Decoherence represents one of the most fundamental problems in quantum mechanics since its birth. Interest in decoherence has been primarily academic until recently when the advances in experimental techniques in different fields of physics such as superconducting quantum interferometers; quantum optics and neutron interferometry sparked the practical interest in this quantum mechanical phenomenon. One particular field where decoherence is of crucial role is quantum computing, where decoherence stands as one of the main obstacles toward realizing practical progress in the field. On the other hand, the ability to manipulate linear superpositions of quantum states is expected to lead to considerable advances in that field. The purpose of this dissertation is to present a study of decoherence in nonlinear quantum systems. We started by studying the coherent superposition of distinct basis states in a single-degree-of-freedom model of SQUID with a variable potential barrier between the basis flux states. We numerically integrated Schrödinger equation of the system. We found that linear superpositions of the basis states, with relatively little residual excitation, can be formed by pulsed modulation of the potential barrier, provided the pulse duration exceeds the period of small oscillations of the flux. Two pulses applied in sequence exhibit strong interference effects, which we propose to use for an experimental determination of the decoherence time in SQUIDS. In addition, we developed, using quantum field theory techniques, a general formalism to study decoherence in a quantum system due to coupling to a non-linear environment. This formalism can be used to investigate decoherence in many of the existing two state quantum systems proposed for quantum computing and reveals important information about them such as decoherence time. Moreover, we used this formalism to compare decoherence induced in a simple two-state quantum system (qubit) for two different initial states of the environment: canonical (fixed temperature) and microcanonical (fixed energy), for the general case of a fully interacting oscillator environment. We found that even a relatively compact oscillator bath (with effective number of degrees of freedom as low as 10), initially in a microcanonical state, will typically cause decoherence almost indistinguishable from that caused by a macroscopic, thermal environment, except possibly at singularities of the environment's specific heat (critical points). In the latter case the precise magnitude of the difference between the canonical and microcanonical results depends on the critical behavior of the dissipative coefficient, characterizing the interaction of the two-state quantum system with the environment.

Degree

Ph.D.

Advisors

Khlebnikov, Purdue University.

Subject Area

Condensation

COinS