Vacuum breakdown in magnetic dipole wave by 10-PW class lasers.

The vacuum breakdown by 10-PW-class lasers is studied in the optimal configuration of laser beams in the form of an m-dipole wave, which maximizes the magnetic field. Using 3D PIC simulations we calculated the threshold of vacuum breakdown, which is about 10 PW. We examined in detail the dynamics of particles and identified particle trajectories which contribute the most to vacuum breakdown in such highly inhomogeneous fields. We analyzed the dynamics of the electron-positron plasma distribution on the avalanche stage. It is shown that the forming plasma structures represent concentric toroidal layers and the interplay between particle ensembles from different spatial regions favors vacuum breakdown. Based on the angular distribution of charged particles and gamma photons a way to experimentally identify the process of vacuum breakdown is proposed.

Particle trajectories, gamma-ray emission, and anomalous radiative trapping effects in magnetic dipole wave.

In studies of interaction of matter with laser fields of extreme intensity there are two limiting cases of a multibeam setup maximizing either the electric field or the magnetic field. In this work attention is paid to the optimal configuration of laser beams in the form of an m-dipole wave, which maximizes the magnetic field. We consider in such highly inhomogeneous fields the advantages and specific features of laser-matter interaction, which stem from individual particle trajectories that are strongly affected by gamma photon emission. It is shown that in this field mode qualitatively different scenarios of particle dynamics take place in comparison with the mode that maximizes the electric field. A detailed map of possible regimes of particle motion (ponderomotive trapping, normal radiative trapping, radial, and axial anomalous radiative trapping), as well as angular and energy distributions of particles and gamma photons, is obtained in a wide range of laser powers up to 300 PW, and it reveals signatures of radiation losses experimentally detectable even with subpetawatt lasers.

Machine learning approach to the Floquet-Lindbladian problem.

Similar to its classical version, quantum Markovian evolution can be either time-discrete or time-continuous. Discrete quantum Markovian evolution is usually modeled with completely positive trace-preserving maps, while time-continuous evolution is often specified with superoperators referred to as "Lindbladians." Here, we address the following question: Being given a quantum map, can we find a Lindbladian that generates an evolution identical-when monitored at discrete instances of time-to the one induced by the map? It was demonstrated that the problem of getting the answer to this question can be reduced to an NP-complete (in the dimension N of the Hilbert space, the evolution takes place in) problem. We approach this question from a different perspective by considering a variety of machine learning (ML) methods and trying to estimate their potential ability to give the correct answer. Complimentarily, we use the performance of different ML methods as a tool to validate a hypothesis that the answer to the question is encoded in spectral properties of the so-called Choi matrix, which can be constructed from the given quantum map. As a test bed, we use two single-qubit models for which the answer can be obtained using the reduction procedure. The outcome of our experiment is that, for a given map, the property of being generated by a time-independent Lindbladian is encoded both in the eigenvalues and the eigenstates of the corresponding Choi matrix.

Unfolding a quantum master equation into a system of real-valued equations: Computationally effective expansion over the basis of SU(N) generators.

Dynamics of an open N-state quantum system is often modeled with a Markovian master equation describing the evolution of the system density operator. By using generators of SU(N) group as a basis, the density operator can be transformed into a real-valued "coherence-vector." A generator of the dissipative evolution, so-called "Lindbladian," can be expanded over the same basis and recast in the form of a real matrix. Together, these expansions result is a nonhomogeneous system of N^{2}-1 real-valued linear ordinary differential equations. Now one can, e.g., implement standard high-performance algorithms to integrate the system of equations forward in time while being sure in exact preservation of the trace (norm) and Hermiticity of the density operator. However, when performed in a straightforward way, the expansion turns to be an operation of the time complexity O(N^{10}). The complexity can be reduced when the number of dissipative operators is independent of N, which is often the case for physically meaningful models. Here we present an algorithm to transform quantum master equation into a system of real-valued differential equations and propagate it forward in time. By using a specific scalable model, we evaluate computational efficiency of the algorithm and demonstrate that it is possible to handle the model system with N=10^{3} states on a single node of a computer cluster.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method.

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.