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

et al. 2020

Lobachevskii J Math

Self Cite

Due to complexity of the systems and processes it addresses, the development of computational quantum physics is influenced by the progress in computing technology. Here we overview the evolution, from the late 1980s to the current year 2020, of the algorithms used to simulate dynamics of quantum systems. We put the emphasis on implementation aspects and computational resource scaling with the model size and propagation time. Our minireview is based on a literature survey and our experience in implementing different types of algorithms.

Section: Discussionmentioning

confidence: 99%

Modeling Complex Quantum Dynamics: Evolution of Numerical Algorithms in the HPC Context

Meyerov

Liniov

et al. 2020

Lobachevskii J Math

Self Cite

“…The distance between the trajectories is calculated as the absolute difference between the two corresponding observables θ . We implement a high-performance realization of the quantum jumps method 27 to generate M r = 10 2 different trajectories for every considered set of model parameters. We first integrate each trajectory up to time t 0 = 10T in order to propagate the model system into the asymptotic regime, and then we follow the dynamics of fiducial and auxiliary trajectories up to time t = 10T .…”

Section: Methodsmentioning

confidence: 99%

Chaotic spin-photonic quantum states in an open periodically modulated cavity

Yusipov

Денисов

Chaos: An Interdisciplinary Journal of Nonlinear Science

2021

When applied to dynamical systems, both classical and quantum, time periodic modulations can produce complex nonequilibrium states which are often termed 'chaotic'. Being well understood within the unitary Hamiltonian framework, this phenomenon is less explored in open quantum systems. Here we consider quantum chaotic state emerging in a leaky cavity, when an intracavity photonic mode is coherently pumped with the intensity varying periodically in time. We show that a single spin, when placed inside the cavity and coupled to the mode, can moderate transitions between regular and chaotic regimes -that are identified by using quantum Lyapunov exponents -and thus can be used to control the degree of chaos. In an experiment, these transitions can be detected by analyzing photon emission statistics.A passage connecting Chaos Theory 1 and many-body quantum physics is provided by the mean-field ideology 2-4 and different semiclassical approximations 5,6 . They declare that, when the number N of quantum degrees of freedoms is systematically increased, the exponentially complex evolution of a quantum model can be approximated with a fixed size system of classical non-linear differential equations. These equations model the dynamics of the expectation values of relevant observables and the model becomes exact in the thermodynamic limit N → ∞. A degree of chaos in the original quantum system can be quantified by calculating standard classical quantifiers (usually maximal Lyapunov exponents 6,7 ) for the corresponding classical system. In the case of an open quantum system, the mean-field approach can be realized on the level of density matrices 8 . Alternatively, the adjoint form of a Markovian master equation, governing the evolution of the system density matrix 4 , can be employed [9][10][11] . What if we are dealing with an open model and do not want (or simply do not have a possibility) to go into the (semi)classical limit or resort to a mean-field description? When the evolution of the system is modeled with a master equations of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form 4 , a recently proposed idea of quantum Lyapunov exponents 12 provides a possibility to quantify the degree of chaos in a straightforward manner. Here we implement this idea and demonstrate how chaotic regimes of a system with N 1 states (a photonic mode in an open cavity) can be controlled by coupling it to a single spin.

“…(1) at time t p for the initial density matrix . We make use of the recently developed high-performance realization of the method 53 and generate different trajectories for averaging, leaving time for relaxation towards an asymptotic state, and following the dynamics for up to .…”

Section: Model and Methodsmentioning

confidence: 99%

Quantum Neimark-Sacker bifurcation

Yusipov

2019

Sci Rep

Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddle-node, and period doubling classical bifurcations. Here, making use of the periodically modulated open quantum dimer model, we report and investigate a quantum Neimark-Sacker bifurcation. Its classical counterpart is the birth of a torus (an invariant curve in the Poincaré section) due to instability of a limit cycle (fixed point of the Poincaré map). The quantum system exhibits a transition from unimodal to bagel shaped stroboscopic distributions, as for Husimi representation, as for observables. The spectral properties of Floquet map experience changes reminiscent of the classical case, a pair of complex conjugated eigenvalues approaching a unit circle. Quantum Monte-Carlo wave function unraveling of the Lindblad master equation yields dynamics of single trajectories on “quantumtorus” and allows for quantifying it by rotation number. The bifurcation is sensitive to the number of quantum particles that can also be regarded as a control parameter.