This dissertation treats quantum open system dynamics, focusing on the coherent evolution of a two-level atom (as the system) interacting with an electromagnetic field (as the bath), for purposes relevant to quantum computing. In order to maintain the quantum correlations that develop between the system and bath throughout the evolution path integral formalisms such as the influence functional and closed time path formalisms are used. Predictions of effects due to the quantum correlations in the composite interacting system are computed. Conventional treatments using Schr\"odinger-master equation and Heisenberg-Langevin approaches usually ignore system+bath quantum correlations as a technical simplification. It is argued that although neglect of system+bath correlations is generally a good approximation when the bath has a large continuous set of degrees of freedom, a residual coherence effect remains due to the non-zero bath correlation time. Though small, these effects are becoming more relevant as, with the advent of ultra cold atom sources, atom optics experiments are reaching levels at which such residual effects are becoming measurable. Three specific problems are investigated in this thesis: First is a self-dressing rederivation of the Casimir-Polder retardation force. The well known stationary atom result is reproduced and a result for a slowly moving atom is obtained which is up to twice the stationary atom correction. Second is the entangled evolution of a qubit with an initially thermal low temperature bath. The diagonal matrix elements are found to thermalize and the off-diagonal elements to decohere as expected, however they do so non-exponentially due to the quantum correlations that develop between the qubit and bath. Third is a calculation of qubit dynamics in the presence of quantized atomic motion as well as zero point fluctuations of the electromagnetic field. The decoherence rate of the qubit is found to increase slightly in that case due to the additional degree of freedom.
This dissertation treats quantum open system dynamics, focusing on the coherent evolution of a two-level atom (as the system) interacting with an electromagnetic field (as the bath), for purposes relevant to quantum computing. In order to maintain the quantum correlations that develop between the system and bath throughout the evolution path integral formalisms such as the influence functional and closed time path formalisms are used. Predictions of effects due to the quantum correlations in the composite interacting system are computed. Conventional treatments using Schr"odinger-master equation and Heisenberg-Langevin approaches usually ignore system+bath quantum correlations as a technical simplification. It is argued that although neglect of system+bath correlations is generally a good approximation when the bath has a large continuous set of degrees of freedom, a residual coherence effect remains due to the non-zero bath correlation time. Though small, these effects are becoming more relevant as, with the advent of ultra cold atom sources, atom optics experiments are reaching levels at which such residual effects are becoming measurable. Three specific problems are investigated in this thesis: First is a self-dressing rederivation of the Casimir-Polder retardation force. The well known stationary atom result is reproduced and a result for a slowly moving atom is obtained which is up to twice the stationary atom correction. Second is the entangled evolution of a qubit with an initially thermal low temperature bath. The diagonal matrix elements are found to thermalize and the off-diagonal elements to decohere as expected, however they do so non-exponentially due to the quantum correlations that develop between the qubit and bath. Third is a calculation of qubit dynamics in the presence of quantized atomic motion as well as zero point fluctuations of the electromagnetic field. The decoherence rate of the qubit is found to increase slightly in that case due to the additional degree of freedom.
We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the complete evolution of the combined qubit-EMF system, thus allowing for the coherent backaction from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find nonexponential decay for both the diagonal and nondiagonal matrix elements of the qubit's reduced density matrix in the pointer basis. The former shows the qubit relaxing to thermal equilibrium with the bath, while the latter shows the decoherence rate beginning at the usually predicted thermal rate, but changing to the zero-temperature value as the qubit and bath become entangled. The decoherence and relaxation rates are comparable, as in the zero-temperature case. On the entanglement of a qubit with the EMF we calculated the fidelity and the von Neumann entropy, which is a measure of the purity of the density matrix. The present more accurate non-Markovian calculations predict lower loss of fidelity and purity as compared with the Markovian results. Generally speaking, with the inclusion of quantum correlations between the qubit and its environment, the non-Markovian processes tend to slow down the drive of the system to equilibrium, prolonging the decoherence and better preserving the fidelity and purity of the system.
The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In optically resonant alkali-metal atom systems, we find the effect to be negligibly small. The framework presented here can nevertheless be used for general considerations of the coherent evolution of qubits in moving atoms in an electromagnetic field.
We perform a first-principles derivation of the general master equation to study the non-Markovian dynamics of a two-level atom (2LA) interacting with an electromagnetic field (EMF). We use the influence functional method, which can incorporate the full back reaction of the field on the atom, while adopting Grassmannian variables for the 2LA and the coherent-state representation for the EMF. We find exact master equations for the cases of a free quantum field and a cavity field in the vacuum. In response to the search for mechanisms to preserve maximal coherence in quantum computations in ion trap prototypes, we apply these equations to analyze the decoherence of a 2LA in an EMF, and find that decoherence time is close to relaxation time. This is at variance with the claims by authors who studied the same system but used a different coupling model. We explain the source of difference and argue that, contrary to common belief, the EMF, when resonantly coupled to an atom, does not decohere it as efficiently as a bath does on a quantum Brownian particle. The master equations for non-Markovian dynamics derived here are expected to be useful for exploring new regimes of 2LAEMF interaction, which is becoming physically important experimentally.
The object of this PhD Thesis is light and matter quantum interaction including studies on cavity and circuit quantum electrodynamics (CQED and cQED), quantum information theory and entanglement dynamics in open systems. In recent years both theoretical and experimental efforts have been devoted to study problems regarding the transfer of quantum correlations, quantum memories, entanglement protection against decoherence and new regimes accessible in cQED. One of the fundamental model underlying these topics is the well known Jaynes-Cummings (JC) one for light-matter interaction, introduced in quantum optics already in 1963. This paradigmatic model describes the coherent exchange of a single excitation between a qubit (a two-level system) and a mode of a quantized harmonic oscillator. The JC model describes a lot of purely quantum effects such as Rabi oscillations and generation of entangled quantum states, which were confirmed by several sophisticated experiments in CQED. This model has been then applied in many other frameworks. Analytical results can be derived only under the so-called rotating wave approximation (RWA), which allows to neglect the energy contributions coming from the counter-rotating terms, which describe the simultaneous excitation (or de-excitation) of the qubit and the field mode. In this Thesis a first interesting investigation, based on the JC model, is related to the realization of quantum memories. The main aspect is the transfer of generic quantum entangled states of a propagating radiation to some qubits, such as two-level atoms placed in separated optical cavities. Generalizing previous results for bipartite entangled systems, I investigated the more complex case of tripartite systems, where the very quantification of entanglement is still an open problem. This issue is broadened to open systems in contact with a common environment which induces decoherence effects unavoidable in realistic implementations. The main result of this analysis is that it is possible to map in an optimal way a quantum state from radiation to qubits in the unitary dynamics, and even in the presence of a dissipative environment a significative amount of entanglement can be transferred. This study has been carried on with either theoretical calculations or numerical simulations performed adopting the powerful Monte Carlo wave function method. A second important problem for quantum memories faced in this PhD Thesis, regards the protection of qubits entanglement for long enough times in order to implement quantum information tasks. A possible way to obtain this goal is to add an external coherent field driving two or more two-level atoms interacting with a common mode of a cavity electromagnetic field. In fact it is possible to demonstrate that, under certain conditions, an effective Hamiltonian of the whole system involves, together with the familiar JC terms, also the counter-rotating ones. The main feature that comes out from this analysis is the possibility to freeze, during system dynamics, peculiar quantum entangled states of the atomic qubits in so called decoherence-free subspaces. This important property allows to store the entanglement in matter qubits, isolating the quantum state from environment induced decoherence. Though the system includes dissipation, analytical results have been obtained for multipartite entanglement and decoherence by solving the master equation through a projection on a suitable basis and using the method of characteristics. In particular it is possible to monitor the rate of decoherence via measurements of joint atomic probabilities, shading light on the fascinating border between the quantum and the classical world. A last topic investigated in this Thesis concerns the recently developed and quite promising implementation of the JC model well outside CQED, that is cQED. Here superconductive circuits, which play the role of artificial atoms, interact on-chip with transmission line resonators, instead of the usual electromagnetic cavities. These systems have the advantage of being quite easily engineered exploiting the most advanced available technologies. Moreover they allow a great flexibility in handling the relevant parameters, since the inter-system coupling is here of capacitive or inductive nature, instead of the usual electric dipole interaction in CQED. In this way a strong and ultrastrong coupling regime have become available, giving a direct access to the physics beyond the JC model and its possible applications. I first performed a detailed characterization of system dynamics in order to test the main approximations usually introduced to describe superconductive circuits as qubits. Then I described, both analytically and numerically, the dissipative dynamics of a superconductive qubit coupled to a resonator mode in the deep strong regime.
Abstract The emerging quantum technologies heavily rely on the understanding of dynamics in open quantum systems. In the Born approximation, the initial system-bath correlations are often neglected which can be violated in the strong coupling regimes and quantum state preparation. In order to understand the influence of initial system-bath correlations, we study the extent to which these initial correlations and the distance of separation between the qubits influence the dynamics of quantum entanglement and coherence. It is shown that at low temperatures, the initial correlations have no role to play while at high temperatures, these correlations strongly influence the dynamics. Furthermore, we have shown that the distance of separation between the qubits in presence of a collective bath helps to maintain entanglement and coherence at long times.
A new mechanism of development of quantum correlations due to the combined effects of a common heat bath and a resonant classical electromagnetic field is analyzed for a system of two two-level atoms coupled by dipole-dipole interaction. Conditions are found under which arbitrary steady-state entanglement can be created in the absence of measurement in an entangled basis. The analysis of dynamics of entanglement is focused on the effects of dipole-dipole interaction, mean number of thermal photons, degree of squeezing of thermal radiation, classical field strength, and presence of additional decay channels.