Stochastic Simulations of Dissipation in Quantum Optics: Quantum Superpositions

Gerasimos Angelatos, Hakan E. Türeci

B. M. Garraway, P. L. Knight

We show how nonclassical states can be constructed by interference amongst constituents in a superposition of basis states (chosen either from a Fock or coherent state basis). Such superpositions are fragile and highly susceptible to dissipation. We discuss the connection between ensemble averages and the evolution of individual realizations using quantum jump and quantum state diffusion models of conditioned measurements, each realization reflecting a particular measurement record. This allows us to distinguish between decoherence, localization and the deconstruction of superpositions into their components.

B. M. Garraway, P. L. Knight

Recent work on the dynamics of open systems has shown how the density operator may be unraveled into component state-vector trajectories using quantum-state diffusion or the quantum-jump model. In traditional dissipative environments the coherent evolution is stochastically perturbed by the action of the reservoir or environment, so that superposition states are dephased. We examine a system in which both coherent driving and dissipative damping involve the simultaneous creation and annihilation of pairs of photons. This has unusual consequences for the creation and decay of coherences. We analyze this problem using the two recently proposed simulation methods and compare the results of the simulation methods with each other and with density-matrix calculations. We also demonstrate the formation of Schr\"odinger ``cat'' states of the field through the action of dissipation and depict them using the Wigner and Husimi quasiprobability functions.

B. Shore

Pomorski, Krzysztof

The mathematical equivalence between finite state stochastic machine and non-dissipative and dissipative quantum tight-binding and Schroedinger model is derived. Stochastic Finite state machine is also expressed by classical epidemic model and can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results shows that quantum mechanical phenomena might be simulated by classical statistical model as represented by finite state stochastic machine. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of classical physics can be the base for possible incorporation of quantum technologies and in particular for quantum like computation and quantum like communication. The classical density matrix is derived and described by the equation of motion in terms of anticommutator. Existence of Rabi like oscillations is pointed in classical epidemic model. Furthermore the existence of Aharonov-Bohm effect in quantum systems can also be reproduced by the classical epidemic model or in broader sense by finite state stochastic machine. Every quantum system made from quantum dots and described by simplistic tight-binding model by use of position-based qubits can be effectively described by classical statistical model encoded in finite stochastic state machine with very specific structure of S matrix that has twice bigger size as it is the case of quantum matrix Hamiltonian. Furthermore the description of linear and non-linear stochastic finite state machine is mapped to tight-binding and Schroedinger model. The concept of N dimensional complex time is incorporated into tight-binding model, so the description of dissipation in most general case is possible.