We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalized in the diagonal basis of the controller variable that is coupled to the controlled system. This causes decoherence in the controlled system that can be made small if the rate of diagonalization is fast. We give a detailed example based on the quantum optomechanical control of a mechanical resonator. The resulting equations are structurally similar to recently proposed models for consistently combining quantum and classical stochastic dynamics.
We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalized in the diagonal basis of the controller variable that is coupled to the controlled system. This causes decoherence in the controlled system that can be made small if the rate of diagonalization is fast. We give a detailed example based on the quantum optomechanical control of a mechanical resonator. The resulting equations are structurally similar to recently proposed models for consistently combining quantum and classical stochastic dynamics.
Controlling the dynamics of open quantum systems; i.e. quantum systems that decohere because of interactions with the environment, is an active area of research with many applications in quantum optics and quantum computation. My thesis expands the scope of this inquiry by seeking to control open systems in proximity to an additional system. The latter could be a classical system such as metal nanoparticles, or a quantum system such as a cluster of similar atoms. By modelling the interactions between the systems, we are able to expand the accessible state space of the quantum system in question.For a single, three-level quantum system, I examine isolated systems that have only normal spontaneous emission. I then show that intensity-intensity correlation spectra, which depend directly on the density matrix of the system, can be used detect whether transitions share a common energy level. This detection is possible due to the presence of quantum interference effects between two transitions if they are connected. This effect allows one to asses energy level structure diagrams in complex atoms/molecules. By placing an open quantum system near a nanoparticle dimer, I show that the spontaneous emission rate of the system can be changed ``on demand" by changing the polarization of an incident, driving field. In a three-level, Λ system, this allows a qubit to both retain high qubit fidelity when it is operating, and to be rapidly initialized to a pure state once it is rendered unusable by decoherence. This type of behaviour is not possible in a single open quantum system; therefore adding a classical system nearby extends the overall control space of the quantum system. An open quantum system near identical neighbours in a dense ensemble is another example of how the accessible state space can be expanded. I show that a dense ensemble of atoms rapidly becomes disordered with states that are not directly excited by an incident field becoming significantly populated. This effect motivates the need for using multi-directional basis sets in theoretical analysis of dense quantum systems. My results demonstrate the shortcomings of short-pulse techniques used in many recent studies. Based on my numerical studies, I hypothesize that the dense ensemble can be modelled by an effective single quantum system that has a decoherence rate that changes over time. My effective single particle model provides a way in which computational time can be reduced, and also a model in which the underlying physical processes involved in the system's evolution are much easier to understand. I then use this model to provide an elegant theoretical explanation for an unusual experimental result called ``transverse optical magnetism''. My effective single particle model's predictions match very well with experimental data.
Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature.
Optomechanics is the study of the interaction between nano-objects and light fields through radiation pressure. Recent sophisticated optomechanical systems consist of strongly coupled mechanical and optical resonators and are made using semiconductor nanofabrication techniques. Although the optomechanical systems have exhibited their powerful capability of controlling photons, they are scarcely used to control the solid-state artificial atoms that emit photons. The main reason is that an efficient coupling mechanism remains unexplored. Here, we hybridize a silicon-integrated optomechanical resonator with two-level atom-like emitters to demonstrate an optomechanical cavity quantum electrodynamic (cQED) effect. With this system and the effect, we realize the dynamic modulation of the spontaneous emission rate. We choose copper dopants in silicon as the emitters for its narrow linewidth (0.3 nm) and long lifetime ( ∼ 30 n s ). Our judiciously designed coupled-nanobeam optomechanical resonator achieves a strong Purcell effect and high cavity-modulation performances. The optical cavity of the optomechanical resonator is dynamically coupled to the emission line and, as a result, on-demand sharp pulses (up to 9.5-fold intensity enhancement and 3.5 ns in duration, which is one ninth of the emission lifetime) appear along the photoluminescence decay. These experimental results are exactly explained with an analytical model that combines optomechanical and cQED theories. Considering that dopants in silicon are highly competitive qubits, we believe that our optomechanical cQED technology will find important applications in the quantum era.
The interaction of a quantum system with a many degree of freedom environment entails damping and the loss of quantum coherence. In these two lectures we focus on two aspects of open quantum system dynamics. First, we present decoherence as a dynamical phenomenon and determine the corresponding time scales, discuss an experiment and the nature of robust states, and mention universal properties of short-time decoherence of macroscopic superpositions. Secondly, in analogy to the classical description of open systems in terms of Langevin equations, we present a stochastic approach to open quantum system dynamics in terms of a stochastic Schrödinger equation. We give a microscopic derivation that allows us to generalize the stochastic approach to non-Markovian situations. We discuss a convolutionless formulation of our theory and finally, we focus on the quantised version of Brownian motion as an often-employed example.
We describe quantum controllability under the influences of the quantum decoherence induced by the quantum control itself. It is shown that, when the controller is considered as a quantum system, it will entangle with its controlled system and then cause quantum decoherence in the controlled system. In competition with this induced decoherence, the controllability will be limited by some uncertainty relation in a well-armed quantum control process. In association with the phase uncertainty and the standard quantum limit, a general model is studied to demonstrate the possibility of realizing a decoherence-free quantum control with a finite energy within a finite time. It is also shown that if the operations of quantum control are to be determined by the initial state of the controller, then due to the decoherence which results from the quantum control itself, there exists a low bound for quantum controllability.
This paper derives conditions under which co-diagonalization of the controllability and observability Gramians can be performed in a physically consistent manner for the class of linear quantum stochastic systems that are common in the fields of quantum optics and related areas like quantum nano- and optomechanical systems. Such a class is essentially a quantum analogue of classical (non-quantum) linear stochastic systems. However, unlike their classical counterparts, the laws of quantum mechanics impose nonlinear equality constraints on the system matrices of linear quantum stochastic systems, the so-called physical realizability constraints. Therefore, a meaningful model reduction procedure must yield a physically realizable reduced model satisfying these constraints. Previous work has shown that model reduction by subsystem truncation preserves physical realizability, but did not propose a method for truncating a subsystem. One candidate approach for this truncation is a quantum adaptation of the well-known balanced truncation method for classical linear time-invariant systems. It is shown in this paper that balanced realization for linear quantum stochastic systems is only possible under a strongly restrictive necessary and sufficient condition. However, the paper also derives less restrictive necessary and sufficient conditions for other realizations with simultaneously diagonal controllability and observability Gramians, and introduces the notion of a quasi-balanced realization. An example of the application of the results is provided to demonstrate quasi-balanced truncation in the linear quantum stochastic setting.