Stabilizing open quantum systems by Markovian reservoir engineering

physical models including two- and four-level atoms, (truncated) harmonic oscillators, and composite and decomposable systems. It is shown how these criteria could be exploited in principle for quantum reservoir engineeing via coherent control and direct feedback to stabilize the system to a desired steady state. We also discuss the question of limit points of the dynamics. Despite the non-existence of isolated centers, open quantum systems can have nontrivial invariant sets. These invariant sets are center manifolds that arise when the Bloch superoperator has purely imaginary eigenvalues and are closely related to decoherence-free subspaces.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  Romeo Ortega,et al.  Lagrangian and Hamiltonian Methods for Nonlinear Control 2006 , 2007 .

[3]  B. Baumgartner,et al.  Analysis of quantum semigroups with GKS–Lindblad generators: I. Simple generators , 2007, 0710.5385.

[4]  Dla Polski,et al.  EURO , 2004 .

[5]  P. Zoller,et al.  Preparation of entangled states by quantum Markov processes , 2008, 0803.1463.

[6]  E. Sudarshan,et al.  Zeno's paradox in quantum theory , 1976 .

[7]  J. J. Hope,et al.  Controlling entanglement by direct quantum feedback , 2008, 0807.1144.

[8]  Stefano Mancini,et al.  Towards feedback control of entanglement , 2005 .

[9]  S. G. Schirmer,et al.  Implementation of fault-tolerant quantum logic gates via optimal control , 2009, 0907.1635.

[10]  Xiaoting Wang,et al.  Entanglement generation between distant atoms by Lyapunov control , 2009, 0906.1830.

[11]  E. Knill,et al.  DYNAMICAL DECOUPLING OF OPEN QUANTUM SYSTEMS , 1998, quant-ph/9809071.

[12]  Stefano Mancini,et al.  Engineering an interaction and entanglement between distant atoms , 2004 .

[13]  David E. Evans.  Irreducible quantum dynamical semigroups , 1977 .

[14]  Lorenza Viola,et al.  Quantum Markovian Subsystems: Invariance, Attractivity, and Control , 2007, IEEE Transactions on Automatic Control.

[15]  Peter L. Knight,et al.  Driving atoms into decoherence-free states , 1999, QELS 2000.

[16]  Herbert Spohn,et al.  Approach to equilibrium for completely positive dynamical semigroups of N-level systems , 1976 .

[17]  Lorenza Viola,et al.  Analysis and synthesis of attractive quantum Markovian dynamics , 2008, Autom..

[18]  E. Davies,et al.  Quantum stochastic processes II , 1970 .

[19]  B. Baumgartner,et al.  Analysis of quantum semigroups with GKS–Lindblad generators: II. General , 2008, 0806.3164.

[20]  Herbert Spohn,et al.  An algebraic condition for the approach to equilibrium of an open N-level system , 1977 .

[21]  Wiseman,et al.  Quantum theory of continuous feedback. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[22]  G. Lindblad.  On the generators of quantum dynamical semigroups , 1976 .

[23]  Paul Glendinning,et al.  Stability, instability and chaos , by Paul Glendinning. Pp. 402. £45. 1994. ISBN 0 521 41553 5 (hardback); £17.95 ISBN 0 521 42566 2 (paperback) (Cambridge). , 1997, The Mathematical Gazette.

[24]  A. Frigerio.  Quantum dynamical semigroups and approach to equilibrium , 1977 .

[25]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[26]  H. M. Wiseman,et al.  Feedback-stabilization of an arbitrary pure state of a two-level atom , 2001 .

[27]  G. J. Milburn,et al.  Dynamical creation of entanglement by homodyne-mediated feedback (9 pages) , 2004, quant-ph/0409154.

[28]  J. J. Hope,et al.  Stabilizing entanglement by quantum-jump-based feedback , 2007 .

[29]  A. Frigerio,et al.  Stationary states of quantum dynamical semigroups , 1978 .