Emergence of Classicality from Quantum Physics: Continuous Spontaneous Measurement xxx (extension of the accepted Thesis)

Shohini Ghose, Barry C. Sanders

You Yang Xu

Abstract Identifying which quantum states qualify as macroscopic superpositions remains a fundamental challenge in quantum physics, as no universally accepted operational criterion currently exists. In this work we introduce a dynamical criterion for macroscopic quantum superposition based on the continuous-measurement-based measure of quantum superposition together with the principle of macrorealism. The key idea is to characterize macroscopicity through the rate of purity decay of the quantum state under continuous monitoring, which quantifies the susceptibility of quantum coherence to classicalizing mechanisms. Two classes of macrorealistic dynamics are considered: environmental decoherence described by a Lindblad master equation (class A) and objective collapse dynamics in the continuous spontaneous localization model (class B). Applying this framework to an optomechanical oscillator, we show that the emergence of macroscopic superposition depends on the competition between measurement-induced decoherence and the macrorealistic mechanism. In class A the relevant contributions increase with excitation number, whereas in class B large excitation numbers can suppress macroscopicity. Unlike many existing macroscopicity measures based solely on phase-space structure or decoherence times, the present criterion directly relates macroscopicity to experimentally accessible parameters in continuous quantum measurement.

Maurice A. de Gosson

Shuichi Matsumoto, 修一 松本

An extension of the concept of physical state is introduced. It is shown that if we accept all the "generalized states" as initial states of an apparatus, then we can circumvent the Ozawa's theorem which rules out the existence of repeatable measuring processes for continuous observables. A generalization of the Wigner-Araki- Yanase theorem is argued.

M. D. Srinivas

Jessica K. Eastman

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.