In this Thesis the interaction of an electromagnetic field and matter is studied from various aspects in the general framework of cold atoms. Our subjects cover a wide spectrum of phenomena ranging from semiclassical few-level models to fully quantum mechanical interaction with structured reservoirs leading to non-Markovian open quantum system dynamics. Within closed quantum systems, we propose a selective method to manipulate the motional state of atoms in a time-dependent double-well potential and interpret the method in terms of adiabatic processes. Also, we derive a simple wave-packet model, based on distributions of generalized eigenstates, explaining the finite visibility of interference in overlapping continuous-wave atom lasers. In the context of open quantum systems, we develop an unraveling of non-Markovian dynamics in terms of piecewise deterministic quantum jump processes confined in the Hilbert space of the reduced system - the non-Markovian quantum jump method. As examples, we apply it for simple 2- and 3-level systems interacting with a structured reservoir. Also, in the context of ion-cavity QED we study the entanglement generation based on collective Dicke modes in experimentally realistic conditions including photonic losses and an atomic spontaneous decay.
In this Thesis the interaction of an electromagnetic field and matter is studied from various aspects in the general framework of cold atoms. Our subjects cover a wide spectrum of phenomena ranging from semiclassical few-level models to fully quantum mechanical interaction with structured reservoirs leading to non-Markovian open quantum system dynamics. Within closed quantum systems, we propose a selective method to manipulate the motional state of atoms in a time-dependent double-well potential and interpret the method in terms of adiabatic processes. Also, we derive a simple wave-packet model, based on distributions of generalized eigenstates, explaining the finite visibility of interference in overlapping continuous-wave atom lasers. In the context of open quantum systems, we develop an unraveling of non-Markovian dynamics in terms of piecewise deterministic quantum jump processes confined in the Hilbert space of the reduced system - the non-Markovian quantum jump method. As examples, we apply it for simple 2- and 3-level systems interacting with a structured reservoir. Also, in the context of ion-cavity QED we study the entanglement generation based on collective Dicke modes in experimentally realistic conditions including photonic losses and an atomic spontaneous decay.
Due to the improvement within cavity quantum electrodynamics experiments during the last decades, what was former seen as 'toy models' are today realized in laboratories. A controlled isolated coherent evolution of one or a few atoms coupled to a single mode inside a cavity is achievable. Such systems are well suited for studying purely quantum mechanical effects, and also for performing quantum gates, necessary for quantum computing. The Jaynes-Cummings model has served as a theoretical description of the interaction. However, as the experimental techniques are improved, for example, atom cooling, the use of multi-level atoms or multi-modes and driving of atoms or elds by external lasers, extensions of the original Jaynes-Cummings model are needed. In this thesis we study some of these extended models, and in particular multi-level models, time-dependent models and quantized motion models. Both analytical and numerical analysis are considered. The two-level structure of the Jaynes-Cummings model leads to applications of known solvable time-dependent two-level Schrödinger equations. In other cases, di erent forms of adiabatic approximate solutions are used, and with the analytically solvable models, the amplitudes of non-adiabatic contributions may be estimated. For higher dimensional systems, STIRAP and multi-STIRAP methods are applied. It is shown how the time-dependent models may be used for preparation of various kinds of non-classical states, and also to generate universal sets of quantum gates, both on atomic and eld qubits. When the atoms are cooled to very low temperatures, their velocities must be treated quantum mechanically, and we have studied the dynamics of such cases for di erent coupling shapes. Again numerical and analytical approaches have been used and compared, wave-packet propagations of the atom, approaching and traversing the cavity, have been performed. For periodic couplings, standing wave cavity modes, the dynamics has been described by e ective parameters; group velocity or atomic index of refraction and effective mass. Tunneling resonances for ultra cold atoms have been exhibited in the STIRAP models for certain initial conditions.
In this chapter, we discuss a purely quantum approach to the interaction between an atom and the electromagnetic field. In this treatment, the atom and electromagnetic field form a single quantum system, whose evolution is handled globally within a unified formalism. This will thus have the merit of being fully consistent from the theoretical standpoint. But the main advantage in an entirely quantum approach is that it can treat the full range of matter–radiation interaction phenomena. In particular, it provides a rigorous description of the spontaneous emission of light by an excited atom , something that falls outside the scope of the semi-classical framework applied in Chapters 2 and 3, where the lifetime of an excited atomic state had to be fed in phenomenologically. It can describe other phenomena of the same type, such as parametric fluorescence by a nonlinear crystal subjected to pumping radiation (see Chapter 7), which underlies many recent developments in quantum optics. The fully quantum approach also has the merit of allowing a simple interpretation in terms of photons for the various matter–radiation interaction processes, such as absorption, stimulated emission, scattering, and also the basic processes of nonlinear optics. Indeed, it provides a unified framework for both stimulated and spontaneous processes. Finally, it can be used to tackle completely new situations where matter and radiation interact, which lie outside the scope of any semi-classical description, such as cavity quantum electrodynamics or the production of single-photon or entangled-photons states .
In this dissertation, I explore interactions between matter and propagating light. The electromagnetic field is modeled as a reservoir of quantum harmonic oscillators successively streaming past a quantum system. Each weak and fleeting interaction entangles the light and the system, and the light continues its course. Within the framework of open quantum systems, the light is eventually traced out, leaving the reduced quantum state of the system as the primary mathematical subject. Two major results are presented. The first is a master equation approach for a quantum system interacting with a traveling wave packet prepared with a definite number of photons. In contrast to quasi-classical states, such as coherent or thermal fields, these N-photon states possess temporal mode entanglement, and local interactions in time have nonlocal consequences. The second is a model for a three-dimensional light-matter interface for an atomic ensemble interacting with a paraxial laser beam and its application to the generation of QND spin squeezing. Both coherent and incoherent dynamics due to spatially inhomogeneous atom-light coupling across the ensemble are accounted for. Measurement of paraxially scattered light can generate squeezing of an atomic spin wave, while diffusely scattered photons lead to spatially local decoherence.
Rapid advances in quantum technology have made possible the control of quantum states of elementary material quantum systems, such as atoms or molecules, and of the electromagnetic radiation field resulting from spontaneous photon emission of their unstable excited states to such a level of precision that subtle quantum electrodynamical phenomena have become observable experimentally. Recent developments in the area of quantum information processing demonstrate that characteristic quantum electrodynamical effects can even be exploited for practical purposes provided the relevant electromagnetic field modes are controlled by appropriate cavities. A central problem in this context is the realization of an ideal transfer of quantum information between a state of a material quantum system and a quantum state of the electromagnetic radiation field which contains a small number or even a single photon only. Despite much recent work in cavity quantum electrodynamics, which has explored this problem successfully in cases in which the number of accessible electromagnetic field modes is strongly restricted by a cavity, currently still much less is known about ideal quantum state transfer between matter and few-photon quantum states of the electromagnetic field in the extreme opposite case of free space. In this contribution we review recent work which explores characteristic quantum electrodynamical phenomena governing the interaction of a material quantum system with the electromagnetic field in extreme many-mode cases which are close to cavity-free situations. For this purpose the simplest possible quantum electrodynamical situation, namely the interaction of a single material two-level system with the wave packet of a single optical photon, is investigated in free space and in situations in which a large cavity modifies the mode structure of the electromagnetic field modes. It is demonstrated that perfect excitation of an atom by a properly shaped single-photon wave packet is possible even in free space. In particular, it is demonstrated that perfect excitation of an atom can be achieved by a single optical photon which is prepared initially in an appropriate superposition of plane-wave modes, provided this photon is focused subsequently onto the absorbing atom by a parabolic cavity.
The study of light-matter interaction in superconducting quantum circuits has seen remarkable progress over the last 20 years. By engineering artificial atoms, novel quantum phenomena have been demonstrated, and old ideas have come into a new light. Beyond their application to basic science, the prospect of implementing large-scale quantum information processing with superconducting circuits has fueled a rapid development of surrounding technologies, with ever-increasing control over their behavior as a result. The field's success stems primarily from the flexible design and strong non-linearity of the artificial atom, whose coherent interaction with both electrical and mechanical degrees of freedom has opened many doors for science. This thesis deals with the interaction between artificial atoms and quantum fields in one-dimensional waveguides. The waveguide represents a one-dimensional environment for the atom, which we use to study the properties of open quantum systems. All quantum systems are, in fact, open, and interactions between the system and its environment lead inevitably to a loss of energy and quantum coherence. A continuous loss of information into the environment is called a Markovian process. The work contained in this thesis indicates that deviations from a Markovian process can be detected in the steady state of driven systems. This could simplify the detection of non-Markovianity in open quantum systems, as no information about the system's transient dynamics would be necessary.Specifically, this thesis considers both electromagnetic fields in microwave transmission lines and acoustic fields in the form of surface acoustic waves (SAWs) traveling on the surface of solids. The recent realization of artificial atoms interacting with acoustic waves has opened up a new research field called quantum acoustics. We have built a model of the interaction between atoms and SAWs that predicts the existence of a new regime where the atom forms its own cavity. Additionally, we have considered synthesizing electromagnetically induced transparency, a quantum optics phenomena in opaque media where the absorption of photons is canceled, in waveguides using multiple closely spaced two-level systems. Some of the work in this thesis represents experimental work done in collaboration. In the first experiment, we studied the routing of acoustic waves at the quantum level. In the other experiment, we demonstrated electromagnetically induced transparency by creating an effective Lambda system using a giant artificial atom. This thesis reviews the numerical techniques used to model these experiments.
An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..