Coherent dynamics of two coupled quantum systems

Kazutomu Shiokawa, Raymond Kapral

The conditions under which an open quantum-mechanical system may be described by mixed quantum-classical dynamics are investigated. Decoherence is studied using influence functional methods in a model composite quantum system comprising two coupled systems, A and C, interacting with a harmonic bath with Ohmic and super-Ohmic spectral densities. Subsystem A is directly coupled to subsystem C, while C is coupled directly to the bath. Calculations are presented for a model where subsystem A is taken to be a two-level system which is bilinearly coupled to a single harmonic oscillator C subsystem. The loss of quantum coherence in each subsystem is discussed in the extreme nonadiabatic regime where the intrinsic dynamics of subsystem A is essentially frozen. Subsystem C is shown to lose its coherence rapidly, while subsystem A maintains coherence for longer time periods since C modulates the influence of the bath on A. Thus, one may identify situations where the coupled AC system evolution effectively obeys mixed quantum-classical dynamics.

V. M. Akulin

G. Flores-Hidalgo, Rudnei O. Ramos

James Russell Hamilton, Raphael David Levine, F. Remacle

Dynamical symmetries, time-dependent operators that almost commute with the Hamiltonian, extend the role of ordinary symmetries. Motivated by progress in quantum technologies, we illustrate a practical algebraic approach to computing such time-dependent operators. Explicitly we expand them as a linear combination of time-independent operators with time-dependent coefficients. There are possible applications to the dynamics of systems of coupled coherent two-state systems, such as qubits, pumped by optical excitation and other addressing inputs. Thereby, the interaction of the system with the excitation is bilinear in the coherence between the two states and in the strength of the time-dependent excitation. The total Hamiltonian is a sum of such bilinear terms and of terms linear in the populations. The terms in the Hamiltonian form a basis for Lie algebra, which can be represented as coupled individual two-state systems, each using the population and the coherence between two states. Using the factorization approach of Wei and Norman, we construct a unitary quantum mechanical evolution operator that is a factored contribution of individual two-state systems. By that one can accurately propagate both the wave function and the density matrix with special relevance to quantum computing based on qubit architecture. Explicit examples are derived for the electronic dynamics in coupled semi-conducting nanoparticles that can be used as hardware for quantum technologies.

Zhi‐Rong Zhong

We study the dynamics of a coupled cavity system composed of three cavities, and propose a scheme for the coherent manipulation of two collective atomic modes by a control atom. In the scheme, the control atom and two atomic ensembles interact with the local cavity mode, while the control atom is externally driven by a laser field. We show that under certain conditions, the dynamics of the whole system are reduced to an effective coherent coupling between the control atom and two collective atomic modes, while the cavity fields are only virtually excited. We also study the dynamics of the entanglement generation of the two distant collective atomic modes. The scheme provides a potential application for quantum-state engineering and quantum control.

V. M. Akulin