Effect of Drive-induced Dissipation on Quantum Dynamics: Applications in Quantum Control and Measurement

Chanda, Nilanjana (2024) Effect of Drive-induced Dissipation on Quantum Dynamics: Applications in Quantum Control and Measurement. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Nilanjana Chanda (16IP020)) 16IP020.pdf - Submitted Version Restricted to Repository staff only Download (6MB)

Abstract

The influence of the surrounding environment on any physical system is inevitable; no system can be entirely isolated. The interaction between them induces significant changes to the state of the system. Hence, analyzing the evolution of quantum systems by considering environmental couplings provides the most accurate and realistic portrayal of physical systems. Quantum systems of this kind are commonly classified as open quantum systems. In contrast to closed quantum systems, which are a mere idealization of real systems, the dynamics of open quantum systems cannot be described by a unitary time-evolution operator. Therefore, it seems necessary to formulate the dynamics of open quantum systems by means of an appropriate equation of motion for its density matrix, known as the quantum master equation. Quantum master equation has been derived in a variety of forms. The memoryless behavior of the system leads to Markovian master equation in the well-known Gorini-Kossakowski-Sudarshan-Lindblad form, which provides the most general generator for Markovian dynamics of the system. In general, open quantum systems are considered to be in contact with a thermal bath (as the environment). As they are allowed to exchange energy, the system eventually attains a state which is in thermal equilibrium with the bath. The dynamics becomes even more intriguing as the open system is subjected to an external drive (control), which inherently disrupts the equilibrium by transferring energy to the system while the system dissipates energy through system-environment coupling. The constant interplay between driving and dissipation leads to damped-driven dynamics, taking the system to a non-equilibrium steady state. The journey undertaken by such drivendissipative systems towards the steady state appears worthwhile to study. This thesis aims to explore the underlying dynamics of driven-dissipative systems using a fluctuation-regulated quantum master equation, a framework considering environmental fluctuations originating from thermal collisional processes. This master equation introduces dissipators with a natural regulator, emerging from ensemble-averaged fluctuations. Such regularized dissipators originate from the second-order contributions of the external drive as well as the system-environment coupling. The second-order system-environment coupling term results in the relaxation of the system, which is well-established and also supported by the pioneering works ofWangsness, Bloch, and Redfield. The distinctive feature of this master equation lies in the dissipator involving the drive term; it predicts that the drive employed to control the system, also induces dissipative dynamics in the system. This phenomenon is referred to as drive-induced dissipation. The primary objective of the thesis is to study the implications of drive-induced dissipation on various quantum control operations. In particular, we show that the competition between drive-induced dissipation and relaxation leads to an optimality condition on the drive amplitude in order to achieve the maximum fidelity of quantum gates and quantum search algorithm. We also demonstrate the optimal population transfer in a two-level system using adiabatic rapid passage. Furthermore, the thesis explores the interconnection between the long-standing quantum measurement problem and open system dynamics. We propose a dynamical model that elucidates the stochastic emergence of definite outcomes in quantum measurement and demonstrates the existence of a quasi-steady state during measurement in the presence of system-environment coupling, where the Born rule emerges as a dynamical feature. We expect that the findings of the thesis will have wide-ranging applications in the control of quantum operations as well as in the measurement theory.

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