Open systems of interacting quantum fields

Fang Gao, Roberto Rey-de-Castro, Yaoxiong Wang +2 more

Many systems under control with an applied field also interact with the surrounding environment. Understanding the control mechanisms has remained a challenge, especially the role played by the interaction between the field and the environment. In order to address this need, here we expand the scope of the Hamiltonian-encoding and observable-decoding (HE-OD) technique. HE-OD was originally introduced as a theoretical and experimental tool for revealing the mechanism induced by control fields in closed quantum systems. The results of open-system HE-OD analysis presented here provide quantitative mechanistic insights into the roles played by a Markovian environment. Two model open quantum systems are considered for illustration. In these systems, transitions are induced by either an applied field linked to a dipole operator or Lindblad operators coupled to the system. For modest control yields, the HE-OD results clearly show distinct cooperation between the dynamics induced by the optimal field and the environment. Although the HE-OD methodology introduced here is considered in simulations, it has an analogous direct experimental formulation, which we suggest may be applied to open systems in the laboratory to reveal mechanistic insights.

Thibaut Lacroix

Ricardo Castro Santis

Quantum Open System Theory is nowadays a highly developed field which involves, on the mathematical side, many mathematical concepts such as operator theory, semigroups of operators on certain Banach spaces (algebras), classical and quantum stochastic differential equations. Inside Quantum Open System Theory there is the theory of quantum continual measurements: a quantum system is monitored with continuity in time. This is surely an open system because, apart from possible interactions with the external environment like a thermal bath, the system is interacting with the measuring apparatus. The typical field in which a theory of continual measurements is needed is quantum optics: when light emitted by some system is observed (by counting of photons - direct detection - or through some interference mechanism - heterodyne and homodyne detection) a continual measurement is performed.

Konstantin A. Makarov, Eduard Tsekanovskiı̆

Fangfang Meng, Shuang Cong

Abstract State transition control of open quantum systems is a research hotspot and difficulty. The control method in the light of the Lyapunov stability theory is a common method. Current research shows that if the open quantum systems meet the constraints that the free Hamiltonian is strong regular and the interaction Hamiltonian is fully connected, by devising appropriate control fields in the light of the Lyapunov stability theory, the open quantum system can move to the desired final state. In view of the fact that most practical open quantum systems do not meet these two constraints, this paper propose a control method. The implicit function perturbation terms are introduced into the control fields to resolve the problem that the open quantum systems do not meet these two convergence constraints. And the main control fields are devised in the light of the Lyapunov stability theory to make the state transition of the open quantum systems converging to the desired final state.

Alexander A. Lisyansky, E. S. Andrianov, Alexey P. Vinogradov +1 more