This thesis covers open quantum systems and information transfer in the face of \ndissipation and disorder through numerical simulation. \nIn Chapter 3 we present work on an open quantum system comprising a two-level system, single bosonic mode and dissipative environment; we have included \nthe bosonic mode in the exact system treatment. This model allows us to gain an understanding of an environment’s role in small energy transfer systems. We observe \nhow the two-level system-mode coupling strength and the spectral density form characterising the environment interplay, affecting the system’s coherent behaviour. We \nfind strong coupling and a spectral density resonantly peaked on the two-level system oscillation frequency enhances the system’s coherent oscillatory dynamics. \nChapter 4 focusses on a physically motivated study of chain and ladder spin \ngeometries and their use for entanglement transfer between qubits. We consider a \nnitrogen vacancy centre qubit implementation with nitrogen impurity spin-channels \nand demonstrate how matrix product operator techniques can be used in simulations \nof this physical system. We investigate coupling parameters and environmental decay \nrates with respect to transfer efficiency effects. Then, in turn, we simulate the effects \nof missing channel spins and disorder in the spin-spin coupling. We conclude by \nhighlighting where our considered channel geometries outperform each other. \nThe work in Chapter 5 is an investigation into the feasibility of routing entanglement between distant qubits in 2D spin networks. We no longer consider a physical \nimplementation, but keep in mind the effects of dissipative environments on entanglement transfer systems. Starting with a single sending qubit-ancilla and multiple \naddressable receivers, we show it is possible to target a specific receiver and establish transferred entanglement between it and the sender’s ancilla through eigenstate tunnelling techniques. We proceed to show that eigenstate tunnelling-mediated entanglement transfer can be achieved simultaneously from two senders across one spin network.
This thesis covers open quantum systems and information transfer in the face of \ndissipation and disorder through numerical simulation. \nIn Chapter 3 we present work on an open quantum system comprising a two-level system, single bosonic mode and dissipative environment; we have included \nthe bosonic mode in the exact system treatment. This model allows us to gain an understanding of an environment’s role in small energy transfer systems. We observe \nhow the two-level system-mode coupling strength and the spectral density form characterising the environment interplay, affecting the system’s coherent behaviour. We \nfind strong coupling and a spectral density resonantly peaked on the two-level system oscillation frequency enhances the system’s coherent oscillatory dynamics. \nChapter 4 focusses on a physically motivated study of chain and ladder spin \ngeometries and their use for entanglement transfer between qubits. We consider a \nnitrogen vacancy centre qubit implementation with nitrogen impurity spin-channels \nand demonstrate how matrix product operator techniques can be used in simulations \nof this physical system. We investigate coupling parameters and environmental decay \nrates with respect to transfer efficiency effects. Then, in turn, we simulate the effects \nof missing channel spins and disorder in the spin-spin coupling. We conclude by \nhighlighting where our considered channel geometries outperform each other. \nThe work in Chapter 5 is an investigation into the feasibility of routing entanglement between distant qubits in 2D spin networks. We no longer consider a physical \nimplementation, but keep in mind the effects of dissipative environments on entanglement transfer systems. Starting with a single sending qubit-ancilla and multiple \naddressable receivers, we show it is possible to target a specific receiver and establish transferred entanglement between it and the sender’s ancilla through eigenstate tunnelling techniques. We proceed to show that eigenstate tunnelling-mediated entanglement transfer can be achieved simultaneously from two senders across one spin network.
This thesis is concerned with modelling the dynamics of open quantum systems in several different contexts. Of principal interest is the manner in which the environment can modify, or even dominate, a system’s quantum behaviour in order to facilitate the transport of energetic excitations. In the first research chapter, a time-local, non-Markovian quantum master equation is derived in a variationally defined reference frame, for networks of two-level systems coupled to bosonic environments. The predictions of this master equation are then compared with those derived using both weak-coupling and polaron approximations. The variational master equation is found to agree with these standard approaches in their regimes of validity, whilst interpolating between them in intermediate parameter regimes. The second research chapter focusses on the dynamics of a superconducting double quantum dot embedded in a resonant circuit. The device is considered in a regime where the ground state consists of a coherent spatial superposition of a single Cooper pair, which can be excited by a variety of interactions with the environment. The relevant transition rates are calculated and the processes responsible are identified. A numerical simulation of the system is then used to explain experimental data, and show that for certain parameters a significant fraction of excitations occur via absorption of photons from the environment. The final chapter considers a model for an olfactory receptor, in which odorant molecules are recognised by their vibrational modes. Electron transfer occurs in the receptor, dependent on the presence of a vibrational mode of the right frequency. A quantum master equation for the system is derived, and the resulting dynamics is compared to earlier semi-classical treatments. The behaviour of the receptor is found to be sensitive not only to the frequency of the vibrational mode, but also to the character of the surrounding environment. Increased dissipation on the odorant mode, as well as the presence of higher frequencies in the environment is found to improve the frequency resolution of the receptor.
Almost all quantum systems are open; interactions with the surrounding \nenvironment generally lead to complex dissipative behaviour with a sensitive \ndependence on the details of the system-environment coupling. This \nthesis presents results from theoretical investigations into such behaviour \nin single and two-site quantum systems with a particular emphasis on \nstrong system-environment coupling regimes, and also the effects of spatial \ncorrelations in the environment fluctuations. \nWithin a weak system-environment coupling framework, it is found \nthat an increased level of correlation is able to protect coherence shared \nbetween two spatially separated two-level quantum systems. Moreover, \nit is found that these correlations are in fact able to generate coherence \nbetween the two systems, and in certain regimes, cause the systems to \nbecome entangled. \nUsing a polaron transform strong coupling master equation technique, \nthe discussion is extended to the strong system-environment coupling or \nhigh temperature regime. To assess the validity of this approach in an experimentally \nrelevant system, it is applied to the description of excitonic \nRabi oscillations in a resonantly driven quantum dot. For most of the \nparameters of interest, the strong coupling theory is found to be valid over \na far greater range of temperatures and coupling strengths than the standard \nweak-coupling theory. The coherent or incoherent nature of energy \ntransfer dynamics is then studied by applying the strong coupling theory \nto a donor-acceptor pair model. Increased spatial correlations are found \nto extend the range of temperatures which allow coherent energy transfer \nto take place. \nFinally, a variational theory is introduced which allows for exploration \nof certain parameter regimes where both the weak-coupling and strong coupling \ntheories become invalid. The variational theory is then used \nto investigate the ground state properties of a double two-level impurity \nmodel. High levels of spatial correlation are found to suppress the tunnelling \namplitude within each impurity.
The title of the present dissertation Decoherence in Quantum Network sounds very general and all-inclusive. Indeed it embraces two topics (decoherence and quantum network) from the area of Quantum Mechanics each of which is described in all respects by a huge literature developed in the last three decades [...]. Quantum decoherence, as the name lets it mean, is the mechanism that makes a quantum system loose its coherence properties, and with them the capability of giving rise to interference phenomena or to other interesting quantum effects [...]. The key idea promoted by decoherence is the insight that realistic quantum systems are never isolated, but are immersed in the surrounding environment and interact continuously with it [...]. As an example one may consider a two-level quantum system (i.e. a quantum bit, usually shortened with a terminology from information science to \\qubit" ) in contact with a wide environment. Hence, quantum systems are open systems, and continuously interact or exchange information with an external environment whose degrees of freedom are too numerous to be monitored. The resulting correlation between the system and the environment spoils quantum coherence and brings about the transition from a pure quantum state to a mixture of quantum state resulting a classical state. To describe decoherence different kind of approaches can be used (for example Master equation, random matrix, etc). A quantum network typically consists of a number of quantum objects (e.g., atoms, ions, quantum dots, cavities, etc.), to be referred to hereafter as the sites or the nodes of the network. They can interact and the interactions (or their correlations) will be usually described by the edges of a graph. Quantum networks can address different information processing tasks. For instance a quantum state can be transferred from qubit to qubit down a chain solely due to the interactions, that is according to the laws of quantum physics [...]. Quantum networks offer us new opportunities and phenomena as compared to classical networks. An extension to large scale of the idea of a quantum network could lead to a futurible quantum internet [...]. The study of networks has traditionally been the territory of graph theory [...], also with the advent of their quantum versions. Within simple quantum network model information processing is usually described by assuming perfect control of the underlying graph. However, this is not much realistic since randomness is often present and it leads to decoherence effects [...]. In contrast, the conservation of coherence is essential for any quantum information process [...], hence there is a persistent interest in decoherence effects in quantum networks, which motivate us to study models for describing such noisy effects. We consider a simple model of quantum network, employing qubits (spin-1/2 particles) attached to the nodes of an underlying graph and we study the simplest task, namely information storage (on a single and two qubits), when the graph randomly changes in time. Actually we randomly add edges to an initially disconnected graph according to the Gilbert model characterized by a weighting parameter ex [...] and in an identically and independent way at each time step. We find that by increasing ex the dynamics of relevant quantities like fidelity, entropy or concurrence, gradually transforms from damped to damped oscillatory and finally to purely oscillatory. That leads to the paper [see, Information dissipation in random quantum networks, by U. Farooq and S. Mancini, OSID 21(3), 1450004, 2014]. We also study a system composed by pairs of qubits attached to each node of a linear chain, a model that stems from quantum dot arrays. Here we use the approach of evolution with a stochastic Hamiltonian to describe the noisy effects. We then evaluate the effect of two most common disorders, namely exchange coupling and hyperfine interaction fluctuations, in adiabatic preparation of ground state in such model. We show that the adiabatic ground state preparation is highly robust against these disorders making the chain a good analog simulator. Moreover, we also study the adiabatic information transfer, using singlet-triplet states, across the chain. In contrast to ground state preparation the transfer mechanism is highly affected by disorders. This suggested that for communication tasks across such chains adiabatic evolution is not as effective and quantum quenches would be preferable. That leads to the paper [see, Adiabatic many-body state preparation and information transfer in quantum dot arrays, by U. Farooq, A. Bayat, S. Mancini and S. Bose Phys. Rev. B 91, 134303, 2015]. The present work is organized as follows. In chapter 1, we shall give a survey of the various types of approach which can be employed to analyse the dynamics of open quantum systems that leads to decoherence effects. In chapter 2, we shall give a general description about quantum network and its possible applications. In chapter 3, we shall discuss the problem of quantum state transfer in qubit network and shall give a brief overview of some scheme that enable nearly prefect state transfer. In chapter 4, we shall discuss singlet-triplet networks, that is networks having on each site a pair of (generally entangled) qubit. Then within this framework we propose a model stemming from quantum dot array. There we shall address the problem of ground state preparation and state transfer. Finally we shall describe the inherent entanglement of the ground state of strongly correlated systems can be exploited for both classical and quantum communications. In chapter 5, we shall propose a decoherence model for qubit networks based on edges representing XY interactions randomly added to a disconnected graph accordingly to a suitable probability distribution. In this way we shall describe dissipation of information initially localize in single or two qubits all over the network. In chapter 6 we shall model the noisy effects in the quantum dot array introduced in chapter 4 and investigate their consequences on the preparation of ground state and quantum state transfer mechanism. Finally we shall draw conclusions.
In the first part of this thesis, we investigate the dynamics of open quantum systems coupled in a purely dephasing way to their environment, which is a paradigmatic example of decoherent dynamics. We focus more specifically on the emergence of non-Markovian effects in the dynamics of such open systems. After reviewing different measures of non-Markovianity, we obtain an analytical expression for the reduced density operator of a finite-dimensional open system coupled with its environment through time-dependent purely dephasing interactions. When the system is initially uncorrelated with its environment, we obtain the time-local master equation that describes its dynamics. In this case, we also derive an exact expression for the witness of non-Markovianity based on the volume of accessible states of the open system. These results are then applied to spin systems coupled to either a spin or a bosonic environment. For spin environments, we study non-Markovianity for different ranges of interaction and in different thermodynamical limits. Moreover, the generation of entanglement between the open system and its environment as well as between spins within the open system is investigated. For bosonic environments, we study the effect of the initial state of the environment on non-Markovianity. We also show that time-dependent modulations of the system-environment coupling can dramatically alter the non-Markovian behavior of the open system. Finally, we consider the case of an open quantum system simultaneously coupled to spin and bosonic baths. In that case, we study how the coupling between the different baths and of the presence of initial correlations in the environment affect the non-Markovianity displayed by the open quantum system. The second part of this thesis is a contribution to the investigation of how quantum systems can be used to process information. More precisely, we focus on the implementation of gate-based quantum computing using neutral atoms trapped in optical or magnetic lattices and interacting through dipole-dipole interactions when excited to Rydberg states. In this context, we present protocols implementing two-qubit quantum gates between atoms far apart in the lattice. To this end, we propose to use a chain of non-coding ancilla atoms to transfer the state of the control qubit to an atom near the target qubit. Before discussing entangling gates between distant qubits, we present two protocols that implement state transfer along a chain of two-level atoms relying respectively on single- and two-atom laser pulses combined with dipole blockade. After reviewing protocols implementing CZ and CNOT gates between nearby qubits using dipole-dipole interactions, we show how the state-transfer protocols previously presented can be used to perform entangling gates between distant qubits. The performance of the state-transfer and gate protocols are assessed using the process fidelity. Moreover, we provide a theoretical explanation for the behavior of the process fidelity with respect to dissipation and imperfect blockade.
An understanding of strongly coupled open quantum systems is crucial for the realisation of many of today’s emerging quantum technologies. However, actually simulating a quantum system that strongly interacts, or couples, with its environment is no easy task. This thesis tackles a number of topics in the field of strongly coupled open quantum systems. Given the computational challenges of solving the full open system dynamics, we first discuss how and why a quasiclassical stochastic approach can be used to simulate the dynamics of a quantum harmonic oscillator that is strongly coupled to its environment. We build upon the established analytical agreement by implementing the quasiclassical stochastic case numerically in the SpiDy.jl Julia package. Motivated by the applications to magnetic modelling, we then solve the full open quantum systems model for a single spin coupled arbitrarily strongly to multiple heat baths. In doing so, we find that the presence of multiple baths can actually increase the system-environment entanglement in the steady state. We also compare this to a fully classical approach and find that, for isotropic environmental coupling, the environment-induced effects in the equilibrium state only appear quantum mechanically. Finally, we couple these two topics together by considering the quasiclassical stochastic simulation of a single quantum spin, helping to understand the regimes of validity beyond the linear harmonic oscillator. This is with the larger aim to eventually be able to encode quantum effects into more realistic systems, such as those that describe magnetic materials.
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.