Abstract We contribute further to recent theoretical studies of entanglement dynamics in open quantum systems to include a continuous variable N-harmonic oscillator ring system bathed in Ornstein–Uhlenbeck noise. Despite the fact that harmonic oscillator systems are one of the most studied systems in physics, we believe that our work here is unique and sheds a new perspective in terms of a potential application. We present two sets of differential equations that govern the dynamics of N harmonic oscillators derived from first principles, one for a Markovian environment and the other for non-Markovian one. With these two sets, we are able to compare their entanglement dynamics between environments given an initial state of our oscillators. Across several system and environmental parameters, we show that the entanglement dynamics between oscillator pairs in a non-Markovian environment may be significantly enhanced in both magnitude and duration when compared to its Markovian approximation. We showcase this by numerically simulating a specific solution, i.e., we choose N = 4 oscillators, where two harmonic oscillators are initialized as a two-mode squeezed state while the remaining oscillators are vacuum states. By leveraging our N = 4 results, we consider a slightly larger number of oscillators, i.e., N = 6, and show how we can generate a hidden quantum network, in the absence of direct coupling, that may allow multiple parties to secretly and passively entangle oscillators in their possession. This is accomplished by exploiting the environmental memory effect and maintaining resonance with other oscillators or the central frequency in a shared non-Markovian bath, which may allow for autonomous entanglement distribution over a network of oscillators and aid in future quantum technologies.
Abstract We contribute further to recent theoretical studies of entanglement dynamics in open quantum systems to include a continuous variable N-harmonic oscillator ring system bathed in Ornstein–Uhlenbeck noise. Despite the fact that harmonic oscillator systems are one of the most studied systems in physics, we believe that our work here is unique and sheds a new perspective in terms of a potential application. We present two sets of differential equations that govern the dynamics of N harmonic oscillators derived from first principles, one for a Markovian environment and the other for non-Markovian one. With these two sets, we are able to compare their entanglement dynamics between environments given an initial state of our oscillators. Across several system and environmental parameters, we show that the entanglement dynamics between oscillator pairs in a non-Markovian environment may be significantly enhanced in both magnitude and duration when compared to its Markovian approximation. We showcase this by numerically simulating a specific solution, i.e., we choose N = 4 oscillators, where two harmonic oscillators are initialized as a two-mode squeezed state while the remaining oscillators are vacuum states. By leveraging our N = 4 results, we consider a slightly larger number of oscillators, i.e., N = 6, and show how we can generate a hidden quantum network, in the absence of direct coupling, that may allow multiple parties to secretly and passively entangle oscillators in their possession. This is accomplished by exploiting the environmental memory effect and maintaining resonance with other oscillators or the central frequency in a shared non-Markovian bath, which may allow for autonomous entanglement distribution over a network of oscillators and aid in future quantum technologies.
We investigate qubit entanglement dynamics in a two-qubit cavity system with stochastically fluctuating coupling strength, comparing white noise (Markovian) and Ornstein-Uhlenbeck noise (non-Markovian) processes. We analytically solve the system dynamics for both Fock and coherent cavity states and systematically characterize how initial qubit configurations affect entanglement generation and preservation. Our results reveal distinct dynamical regimes: in the Fock-state cavity, initial states in the single-excitation subspace generate robust qubit entanglement in decoherence-free subspaces, while initially entangled states in the double-excitation subspace exhibit inevitable decay without protective symmetries. For coherent cavities, we identify a critical photon-number threshold in the intermediate coherent-state amplitude regime where dynamics transition from low-frequency to high-frequency entanglement oscillations, while universal entanglement loss occurs at large amplitudes. Remarkable resilience against entanglement sudden death emerges under strong non-Markovian noise with long correlation times, where repeated revivals occur. These findings establish cavity photon statistics and environmental memory time as key control parameters for engineering qubit entanglement dynamics in qubit-cavity systems, revealing how system-environment correlations govern quantum information preservation.
Environmental noise is a prevalent issue that hinders the widespread adoption of quantum technologies. Standard practice to mitigate noise involves minimizing the coupling between a quantum system and its environment, which is usually modeled in the Markovian regime. By moving slightly beyond this regime into the weak non-Markovian regime, we can achieve an effective coupling that is multiple orders of magnitude smaller by exploiting the environmental memory effect. To demonstrate this effect, we simulate state swapping in a Markovian and non-Markovian environment between two modes: a cavity mode initialized as a vacuum state and an atomic motional mode initialized as a displaced squeezed coherent state. To measure the quality of state swapping between environments, we calculate and compare their corresponding multi-mode fidelity for Gaussian states. We find that a non-Markovian environment has superior state swapping fidelity across the following parameters: mean phonon number, cavity decay rate, and vibrational frequency of the atomic motional mode. The fidelity is near-unit for a non-Markovian environment within the parameter ranges mentioned in the results. These results could enable enhanced quantum information exchange between a network and chain of cavity-atom nodes and contribute toward a more prevalent adoption of quantum technologies.
The precise characterization of dynamics in open quantum systems often presents significant challenges, leading to the introduction of various approximations to simplify a model. One commonly used strategy involves Markovian approximations, assuming a memoryless environment. In this study, such approximations are not used and an analytical dynamical depiction of an open quantum system is provided. The system under consideration is an oscillator that is surrounded by a bath of oscillators. The resulting dynamics are characterized by a second-order complex coefficient linear differential equation, which may be either homogeneous or inhomogeneous. Moreover, distinct dynamical regions emerge, depending on certain parameter values. Notably, the steady-state average excitation number (AEN) of the system shows rapid escalation with increasing non-Markovianity, reflecting the intricacies of real-world dynamics. In cases where there is detuning between the system frequency and the environmental central frequency within a non-Markovian regime, the AEN maintains its initial value for an extended period. Furthermore, the application of pulse control can effectively protect the quantum system from decoherence effects without using approximations. The pulse control can not only prolong the relaxation time of the oscillator, but can also be used to speed up the relaxation process, depending on the specifications of the pulse. By employing a kick pulse, the Mpemba effect can be observed in the non-Markovian regime in a surprisingly super-cooling-like effect.
This work strives to better understand how the entanglement in an open quantum system, here represented by two coupled Brownian oscillators, is affected by a nonMarkovian environment (with memories), here represented by two independent baths each oscillator separately interacts with. We consider two settings, a 'symmetric' configuration wherein the parameters of both oscillators and their baths are identical, and an 'asymmetric' configuration wherein they are different, in particular, a 'hybrid' configuration, where one of the two coupled oscillators interacts with a nonMarkovian bath and the other with a Markovian bath. Upon finding the solutions to the Langevin equations governing the system dynamics and the evolution of the covariance matrix elements entering into its entanglement dynamics, we ask two groups of questions: (Q1) Which time regime does the bath's nonMarkovianity benefit the system's entanglement most? The answers we get from detailed numerical studies suggest that (A1) For an initially entangled pair of oscillators, we see that in the intermediate time range, the duration of entanglement is proportional to the memory time, and it lasts a fraction of the relaxation time, but at late times when the dynamics reaches a steady state, the value of the symplectic eigenvalue of the partially transposed covariance matrix barely benefit from the bath nonMarkovianity. For the second group of questions: (Q2) Can the memory of one nonMarkovian bath be passed on to another Markovian bath? And if so, does this memory transfer help to sustain the system's entanglement dynamics? Our results from numerical studies of the asymmetric hybrid configuration indicate that (A2) A system with a short memory time can acquire improvement when it is coupled to another system with a long memory time, but, at a cost of the latter. The sustainability of the bipartite entanglement is determined by the party which breaks off entanglement most easily.
When a quantum system interacts with many other quantum mechanical objects, the behaviour of the system is strongly affected; this is referred to as an open quantum system (OQS). Since the inception of quantum theory the development of OQSs has been synonymous with realistic descriptions of quantum mechanical models. With recent activity in the advancement of quantum technologies, there has been vested interest in manipulating OQSs. Therefore understanding and controlling environmental effects, by structuring environments, has become an important field. The method of choice for tackling OQSs is the master equation approach, which requires approximations and doesn’t allow direct assessment of the environment. This thesis tackles the issues of OQSs with an unorthodox method; we employ a series of coupled quantum harmonic oscillators to simulate an OQS. This permits the use of the covariance matrix technique which allows us to avoid approximations and analyse the environment modes. We investigate the Markov approximation and Rotating-Wave approximation (RWA), which are commonly used in the field. By considering four OQS models, we study an entanglement-based non-Markovian behaviour (NMB) quantifier (ENMBQ). The relevance of detuning, coupling strength and bath structures in determining the amount of NMB is noted. A brief study of the factors that affect a fidelity-based NMB quantifier is also conducted. We also analyse the effect on the ENMBQ if the terms excluded by the RWA are included in the models. Finally, an examination of the applicability of the RWA in the presence of strong coupling is undertaken in a three oscillator model. The fidelity-based analysis utilised could allow one to ascertain when and if the RWA can be applied to a model of interest, including OQSs. The knowledge within, and the methodology used throughout this thesis, could arm researchers with insights to control the flow of quantum information in their systems.
This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.