Theory Of Open Quantum Systems Research Articles

Mutual friction and diffusion of two-dimensional quantum vortices

We present a microscopic open quantum systems theory of thermally-damped vortex motion in oblate atomic superfluids that includes previously neglected energy-damping interactions between superfluid and thermal atoms. This mechanism couples strongly to vortex core motion and causes dissipation of vortex energy due to mutual friction, as well as Brownian motion of vortices due to thermal fluctuations. We derive an analytic expression for the dimensionless mutual friction coefficient that gives excellent quantitative agreement with experimentally measured values, without any fitted parameters. Our work closes an existing two orders of magnitude gap between dissipation theory and experiments, previously bridged by fitted parameters, and provides a microscopic origin for the mutual friction and diffusion of quantized vortices in two-dimensional atomic superfluids.

Entanglement dynamics: Generalized master equation for uniformly accelerated two-level systems

We propose an alternative form for the quantum master equation in the theory of open quantum systems. This alternative formalism allows one to describe the dynamics of two-level systems moving along different hyperbolic trajectories with distinct proper times. In the Born-Markov approximation, we consider a quantum massless scalar field coupled with two-level systems. Starting from a separable state, we show the emergence of entanglement harvesting. For different proper accelerations we also verify the entanglement sudden death.

“What Is Life?”: Open Quantum Systems Approach

Recently, the quantum formalism and methodology have been used in application to the modelling of information processing in biosystems, mainly to the process of decision making and psychological behaviour (but some applications in microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modelling. In this paper, we turn to the famous Schrödinger’s book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed to order preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrödinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preserve the order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment [Formula: see text]: 1) entropy (disorder) increasing in the process of adaptation to the specific features of [Formula: see text]; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.

Density Matrix Formalism for Interacting Quantum Fields

We provide a description of interacting quantum fields in terms of density matrices for any occupation numbers in Fock space in a momentum basis. As a simple example, we focus on a real scalar field interacting with another real scalar field, and present a practicable formalism for directly computing the density matrix elements of the combined scalar–scalar system. For deriving the main formula, we use techniques from non-equilibrium quantum field theory like thermo-field dynamics and the Schwinger–Keldysh formalism. Our results allow for studies of particle creation/annihilation processes at finite times and other non-equilibrium processes, including those found in the theory of open quantum systems.

Canonically Consistent Quantum Master Equation

We put forth a new class of quantum master equations that correctly reproduce the asymptotic state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics. The correction not only steers the reduced system toward a correct steady state but also improves the accuracy of the dynamics, thereby refining the archetypal Born-Markov weak-coupling second-order master equations. In case of equilibrium, we use the exact mean-force Gibbs state to correct the Redfield quantum master equation. By benchmarking it with the exact solution of the damped harmonic oscillator, we show that our method also helps correct the long-standing issue of positivity violation, albeit without complete positivity. Our method of a canonically consistent quantum master equation opens a new perspective in the theory of open quantum systems leading to a reduced density matrix accurate beyond the commonly used Redfield and Lindblad equations, while retaining the same conceptual and numerical complexity.

Quantum master equations and steady states for the ultrastrong-coupling limit and the strong-decoherence limit

In the framework of the theory of open quantum systems, we derive quantum master equations for the ultrastrong system-bath coupling regime and, more generally, the strong-decoherence regime. In this regime, the strong decoherence is complemented by slow relaxation processes. We use a generalization of the F\"orster and modified Redfield perturbation theories known in the theory of excitation-energy transfer. Also, we show that the mean-force Gibbs state in the corresponding limits is stationary for the derived master equations.

Probing non-Markovian quantum dynamics with data-driven analysis: Beyond “black-box” machine-learning models

A precise understanding of the influence of a quantum system's environment on its dynamics, which is at the heart of the theory of open quantum systems, is crucial for further progress in the development of controllable large-scale quantum systems. However, existing approaches to account for complex system-environment interaction in the presence of memory effects are either based on heuristic and oversimplified principles or give rise to computational difficulties. In practice, one can leverage on available experimental data and replace first-principles simulations with a data-driven analysis that is often much simpler. Inspired by recent advances in data analysis and machine learning, we propose a data-driven approach to the analysis of the non-Markovian dynamics of open quantum systems. Our method allows, on the one hand, capturing the most important characteristics of open quantum systems such as the effective dimension of the environment and the spectrum of the joint system-environment quantum dynamics, and, on the other hand, reconstructing a predictive model of non-Markovian quantum dynamics, and denoising the measured quantum trajectories. We demonstrate the performance of the proposed approach with various models of open quantum systems, including a qubit coupled with a finite environment, a spin-boson model, and the damped Jaynes-Cummings model.

Generalizing the framework of Dominy-Shabani-Lidar for the reduced dynamics

Consider an open quantum system S , interacting with its environment E. Whether the reduced dynamics of the system can be given by a linear map, or not, is an important subject, in the theory of open quantum systems. Dominy, Shabani and Lidar have proposed a general framework for linear Hermitian reduced dynamics. They have considered the case that both the system and the environment are finite dimensional. Their framework can be generalized to include the case that the environment is infinite dimensional too. In this paper, after demonstrating this generalization, we discuss the role of the convexity of the set, of possible initial states of the system-environment, in their framework. Next, we give a proof for the existence of the operator sum representation, for arbitrary linear Hermitian map. This proof enables us to prove the Choi-Jamiołkowski and the Jamiołkowski isomorphisms, straightforwardly.

Thermalization by off-shell processes: The virtues of small virtuality

We study the thermalization of a scalar field $\mathrm{\ensuremath{\Phi}}$ coupled to two other scalar fields ${\ensuremath{\chi}}_{1,2}$ that constitute a bath in thermal equilibrium. For a range of masses the $\mathrm{\ensuremath{\Phi}}$ propagator features threshold and infrared divergences, a vanishing residue at the (quasi)particle pole, and vanishing on-shell decay rates thereby preventing the equilibration of $\mathrm{\ensuremath{\Phi}}$ with the bath via on-shell processes. Inspired by the theory of quantum open systems we obtain a quantum master equation for the reduced density matrix of $\mathrm{\ensuremath{\Phi}}$ that includes the time dependence of bath correlations, yielding time dependent rates in the dynamics of relaxation and allowing virtual processes with an energy ${q}_{0}$ whose difference from the on-shell energy is of $\mathcal{O}(1/t)$ at long time $t$. These off-shell processes lead to thermalization despite vanishing $S$-matrix rates. In the case of threshold divergences we find that a thermal fixed point is approached as ${e}^{\ensuremath{-}\sqrt{t/{t}^{*}}}$ with the relaxation time ${t}^{*}$ becoming shorter at high temperature as a consequence of stimulated emission and absorption. In the infrared case, the thermal fixed point is approached as ${e}^{\ensuremath{-}\ensuremath{\gamma}(t)}$, where $\ensuremath{\gamma}(t)$ features a crossover between $\mathrm{ln}(t)$ and $t$ behavior for $t\ensuremath{\gg}1/T$. The vanishing of the residue and the crossover in relaxational dynamics in this case is strikingly reminiscent of the orthogonality catastrophe in heavy impurity systems. The results yield more general lessons on thermalization via virtual processes.

Toward exact predictions of spin-phonon relaxation times: An ab initio implementation of open quantum systems theory.

Spin-phonon coupling is the main driver of spin relaxation and decoherence in solid-state semiconductors at finite temperature. Controlling this interaction is a central problem for many disciplines, ranging from magnetic resonance to quantum technologies. Spin relaxation theories have been developed for almost a century but often use a phenomenological description of phonons and their coupling to spin, resulting in a nonpredictive tool and hindering our detailed understanding of spin dynamics. Here, we combine time-local master equations up to the fourth order with advanced electronic structure methods and perform predictions of spin-phonon relaxation time for a series of solid-state coordination compounds based on both transition metals and lanthanide Kramers ions. The agreement between experiments and simulations demonstrates that an accurate, universal, and fully ab initio implementation of spin relaxation theory is possible, thus paving the way to a systematic study of spin-phonon relaxation in solid-state materials.

Efficiency of photonic state tomography affected by fiber attenuation

In this article, we investigate the efficiency of photonic state tomography in the presence of fiber attenuation. The theoretical formalism of the photon loss is provided by implementing methods from the theory of open quantum systems. The quantum state is reconstructed from photon counts obtained for symmetric informationally complete positive operator-valued measures. The number of photons that reach the detectors is numerically modeled by the binomial distribution, which describes the loss of light caused by the medium. This approach allows us to study the quality of state tomography versus the length of the fiber. In particular, we focus on entangled qubits and qutrits, which are sent through fibers of different lengths. The amount of entanglement detected by the measurement scheme is quantified and presented on graphs. The results demonstrate how the quality of photonic tomography depends on the distance between the source and the receiver.

Continuous variable quantum teleportation of a thermal state in a thermal environment

The analytical formula for the fidelity of teleportation from Alice to Bob of a thermal state used as an input state is derived using the characteristic function approach. As a resource state it is used a continuous-variable two-mode bosonic state shared between Alice and Bob and the system is placed in a contact with a general environment. The quantum fidelity depends on the average thermal photon number of the input sate and on the parameters of the resource state and environment. In order to evaluate the parameters required for a successful quantum teleportation of a thermal state we estimate the evolution of the entanglement and fidelity of teleportation in the case when Alice and Bob share an initial squeezed thermal state in contact with a thermal bath. We work in the framework of the theory of open quantum systems based on completely positive dynamical semigroups and we use the Gorini–Kossakowski–Lindblad–Sudarshan master equation in order to describe the evolution of the system. The conditions for a successful quantum teleportation are the fidelity of teleportation larger than the threshold value of the classical fidelity of teleportation and entanglement present in the resource state. In order to assure the fulfillment of these conditions it is necessary to select the time of teleportation and to adjust the parameters characterizing the system (squeezing between the modes of the resource state, their average numbers of thermal photons and frequencies), and the temperature of the thermal reservoir. It is shown that in similar physical conditions, the fidelity of teleportation of the thermal states is larger than that one for a coherent state.

Quantum dynamics of dissipative Kerr solitons

Dissipative Kerr solitons arising from parametric gain in ring microresonators are usually described within a classical mean-field framework. Here, we develop a quantum-mechanical model of dissipative Kerr solitons in terms of the Lindblad master equation and study the model via the truncated Wigner method, which accounts for quantum effects to leading order. We show that, within this open quantum system framework, the soliton experiences a finite coherence time due to quantum fluctuations originating from losses. Reading the results in terms of the theory of open quantum systems allows us to estimate the Liouvillian spectrum of the system. It is characterized by a set of eigenvalues with a finite imaginary part and a vanishing real part in the limit of vanishing quantum fluctuations. This feature shows that dissipative Kerr solitons are a specific class of dissipative time crystals.

Triplet-radical spin entanglement: potential of molecular materials for high-temperature quantum information processing

Recently, spin-bearing molecules have been experimentally demonstrated to have great potential as building blocks for quantum information processing due to their substantial advantages including tunability, portability, and scalability. Here, we propose a theoretical model based on the theory of open quantum systems for spin dynamics in a molecule containing one radical, which can interact with the triplet state arising from another part of the molecule owing to optical excitation and intersystem crossing. With the initial state being a classical mixture of a radical frac{1}{2}-spin, the exchange interaction between the radical and the triplet produces a spin coherent state, which could potentially be used for a qubit-qutrit quantum entangling gate. Our calculations for the time-resolved electron paramagnetic resonance spectra showed good qualitative agreement with the related experimental results for radical-bearing molecules at high temperature (~77 K, the boiling point of liquid nitrogen). This work therefore lays a solid theoretical cornerstone for optically driven quantum gate operations in radical-bearing molecular materials, aiming toward high-temperature quantum information processing.

Dynamics of Entropy Production Rate in Two Coupled Bosonic Modes Interacting with a Thermal Reservoir.

The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system.

Social Fröhlich condensation: preserving societal order through sufficiently intensive information pumping

PurposeThis paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modeling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature.Design/methodology/approachThe model of social Fröhlich condensation and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics).FindingsThe presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as Fröhlich condensation.Research limitations/implicationsThe model of social Fröhlich condensation is heavily based on theory of open quantum systems. Its consistent elaboration needs additional efforts.Practical implicationsEvidence of such phenomenon as social Fröhlich condensation is demonstrated by stability of modern informationally open societies.Social implicationsApproaching the state of Fröhlich condensation is the powerful source of social stability. Understanding its informational structure and origin may help to stabilize the modern society.Originality/valueApplication of the quantum-like model of Fröhlich condensation in social and political sciences is really the novel and original approach to mathematical modeling of social stability in society exposed to powerful information radiation from mass-media and Internet-based sources.

Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation.

The theory of open quantum systems lays the foundation for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this Letter, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure, we compactly represent quantum states with autoregressive neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of string states to partially restore the symmetry of the autoregressive neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one-dimensional and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain MonteCarlo method to sample restricted Boltzmann machines. Our Letter provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

Coherence dynamics in low-energy nuclear fusion

Low-energy nuclear fusion reactions have been described using a dynamical coupled-channels density matrix method, based on the theory of open quantum systems. For the first time, this has been combined with an energy projection method, permitting the calculation of energy resolved fusion probabilities. The results are benchmarked against calculations using stationary Schrödinger dynamics and show excellent agreement. Calculations of entropy, energy dissipation and coherence were conducted, demonstrating the capability of this method. It is evident that the presence of quantum decoherence does not affect fusion probability. This framework provides a basis for quantum thermodynamic studies using thermal environments.

Evolution of Gaussian Rényi-2 quantum correlations in a squeezed thermal environment

In this paper, we investigate, in the framework of the theory of open quantum systems, based on completely positive dynamical semigroups, the Markovian dynamics of Gaussian Rényi-2 correlations — quantum entanglement, quantum discord, mutual information and classical correlations in a system composed of two bosonic modes, interacting with a squeezed thermal bath. We show that the time evolution of the Rényi-2 correlations strongly depends on the parameters of the initial Gaussian squeezed thermal state of the considered system and on the parameters characterizing the squeezed thermal bath. It is shown that while Gaussian Rényi-2 entanglement is suppressed in a finite time, due to the interaction with the squeezed thermal bath, the correlations beyond entanglement — Gaussian Rényi-2 discord, classical correlations and mutual information undergo a freezing-like behavior, namely they decay only asymptotically, in the limit of large times. We also illustrate a fundamental hierarchy for bipartite Gaussian correlations.

Theory of multiple quantum coherence signals in dilute thermal gases

Manifestations of dipole–dipole interactions in dilute thermal gases are difficult to sense because of strong inhomogeneous broadening. Recent experiments reported signatures of such interactions in fluorescence detection-based measurements of multiple quantum coherence (MQC) signals, with many characteristic features hitherto unexplained. We develop an original open quantum systems theory of MQC in dilute thermal gases, which allows us to resolve this conundrum. Our theory accounts for the vector character of the atomic dipoles as well as for driving laser pulses of arbitrary strength, includes the far-field coupling between the dipoles, which prevails in dilute ensembles, and effectively incorporates atomic motion via a disorder average. We show that collective decay processes—which were ignored in previous treatments employing the electrostatic form of dipolar interactions—play a key role in the emergence of MQC signals.