The quantum trajectory theory of an open quantum system driven by a photoemissive source is formulated. The formalism is illustrated by applying it to photon scattering from an atom driven by strongly focused coherent light.
The theory of open systems is used in quantum optics in two distinct ways: to model sources of light such as lasers and parametric oscillators, and to describe the response of irradiated cavities and atoms. Sometimes the two applications are used in combination; first, statistical properties of the field radiated by a source are calculated, and these are then used in a separate calculation to determine the response of a system that is irradiated by the source. But the usefulness of this approach is quite hunted. It is essentially limited to coherent sources and certain broadband sources such as broadband squeezed or chaotic light. There exists no general theory for cascaded open systems - a theory that gives the response of system B to radiation emitted by system A when there exists an open-systems treatment for A and B separately. In this paper I develop such a theory using the quantum trajectory formulation of open systems. The source A and irradiated system B are described by a single stochastic wave-function. Generally the wavefunction describes an entangled state of the A and B subsystems. In the quantum trajectory formalism the wavefunction undergoes a coherent evolution governed by a nonunitary Schrödinger equation, interrupted at random times by wavefunction collapses. I derive the nonunitary Schrödinger equation and the form of the collapses. I illustrate the theory with some simple examples and discuss potential applications to problems involving the interaction of atoms with nonclassical light.
The study of open quantum systems – microscopic systems exhibiting quantum coherence that are coupled to their environment – has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the system onto known states via feedback in quantum measurements. Many mathematical frameworks have been developed to describe such systems, which for atomic, molecular, and optical (AMO) systems generally provide a very accurate description of the open quantum system on a microscopic level. In recent years, AMO systems including cold atomic and molecular gases and trapped ions have been applied heavily to the study of many-body physics, and it has become important to extend previous understanding of open system dynamics in single- and few-body systems to this many-body context. A key formalism that has already proven very useful in this context is the quantum trajectories technique. This method was developed in quantum optics as a numerical tool for studying dynamics in open quantum systems, and falls within a broader framework of continuous measurement theory as a way to understand the dynamics of large classes of open quantum systems. In this article, we review the progress that has been made in studying open many-body systems in the AMO context, focussing on the application of ideas from quantum optics, and on the implementation and applications of quantum trajectories methods in these systems. Control over dissipative processes promises many further tools to prepare interesting and important states in strongly interacting systems, including the realisation of parameter regimes in quantum simulators that are inaccessible via current techniques.
In this work, we discuss connections between different theoretical physics communities and their works, all related to systems that act as sources of particles such as photons, phonons, or electrons. Our interest is to understand how a low-dimensional quantum system driven by coherent fields, e.g., a two-level system, a Jaynes-Cummings system, or a photon pair source driven by a laser pulse, emits photons into a waveguide. Of particular relevance to solid-state sources is that we provide a way to include dissipation into the formalism for temporal-mode quantum optics. We will discuss the connections between temporal-mode quantum optics, scattering matrices, quantum stochastic calculus, continuous matrix product states and operators, and very traditional quantum optical concepts such as the Mandel photon counting formula and the Lindblad form of the quantum-optical master equation. We close with an example of how our formalism relates to single-photon sources with dephasing.
Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different “unravelings” of a mixed state master equation. I also comment briefly on the relationship of the theory to the consistent histories formalism and to spontaneous collapse models.
Quantum optics provides powerful means to probe quantum mechanics. In this \nthesis, we study various aspects of quantum phenomena arising in quantum optical \nsystems. Part I studies broadband quantum teleportation. After presenting three \ndifferent methods of analyzing the standard teleportation protocol, we study the \ninterplay between various bandwidths in determining the fidelity of a broadband \nquantum field teleportation. Explicit formulae for the degrees of first- and secondorder \ncoherence for the teleportation of resonance fluorescence are derived for this \npurpose. Part II studies entanglement arising in cascaded open quantum (optical) \nsystems. First, a detailed laser model is produced within quantum trajectory theory \nto study the total decoherence rate of a laser-driven qubit. Second, using this model, \nwe address the issue of laser quantum state, viewed in connection with separability \nof the laser-driven-qubit system. Third, a measure of entanglement within quantum \ntrajectory theory called ‘Contextual Entanglement’ is calculated for a few simple \nsystems and compared with the ‘Entanglement of Formation’. Lastly, we introduce \na method to quantify entanglement (based on the contextual entanglement) between \na source and the field it emits, which we call the ‘Entanglement Spectrum’. It is \napplied to study the entanglement between a laser-driven qubit and the field the \nqubit scatters.
Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. In this paper I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different ``unravelings'' of a mixed state master equation. I also comment briefly on the relationship of the theory to the Consistent Histories formalism and to spontaneous collapse models.