Controlling entanglement by direct quantum feedback

We discuss the generation of entanglement between electronic states of two atoms in a cavity using direct quantum feedback schemes. We compare the effects of different control Hamiltonians and detection processes in the performance of entanglement production and show that the quantum-jump-based feedback proposed by us in Phys. Rev. A {\bf 76} 010301(R) (2007) can protect highly entangled states against decoherence. We provide analytical results that explain the robustness of jump feedback, and also analyse the perspectives of experimental implementation by scrutinising the effects of imperfections and approximations in our model.

[1]  Hood,et al.  The atom-cavity microscope: single atoms bound in orbit by single photons , 2000, Science.

[2]  Christoph Becher,et al.  Control and Measurement of Three-Qubit Entangled States , 2004, Science.

[3]  V. P. Belavkin,et al.  Measurement, filtering and control in quantum open dynamical systems , 1999 .

[4]  G Weihs,et al.  Experimental demonstration of four-photon entanglement and high-fidelity teleportation. , 2001, Physical review letters.

[5]  J. F. Poyatos,et al.  Quantum Reservoir Engineering with Laser Cooled Trapped Ions. , 1996, Physical review letters.

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

[7]  Stefano Mancini,et al.  Bayesian feedback versus Markovian feedback in a two-level atom , 2002 .

[8]  P. Bertet,et al.  Step-by-step engineered multiparticle entanglement , 2000, Science.

[9]  C. Hamley,et al.  Cavity QED with optically transported atoms , 2003, quant-ph/0309052.

[10]  R. Handel,et al.  Deterministic Dicke-state preparation with continuous measurement and control , 2004, quant-ph/0402137.

[11]  Jian Zou,et al.  Steady atomic entanglement with different quantum feedbacks , 2008 .

[12]  Daniel A. Lidar,et al.  Decoherence-Free Subspaces for Quantum Computation , 1998, quant-ph/9807004.

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

[14]  K. Lendi,et al.  Quantum Dynamical Semigroups and Applications , 1987 .

[15]  Wei Lu,et al.  Real-time detection of electron tunnelling in a quantum dot , 2003, Nature.

[16]  Joseph E. Reiner,et al.  Quantum feedback in a weakly driven cavity QED system , 2004 .

[17]  L. Davidovich,et al.  Decoherence, pointer engineering, and quantum state protection. , 2001, Physical review letters.

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

[19]  W. Wootters Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[20]  Milburn,et al.  Quantum theory of optical feedback via homodyne detection. , 1993, Physical review letters.

[21]  G. Agarwal Quantum statistical theories of spontaneous emission and their relation to other approaches , 1974 .

[22]  N V Morrow,et al.  Feedback control of atomic motion in an optical lattice. , 2002, Physical review letters.

[23]  Kishore T. Kapale,et al.  Generation of Werner states via collective decay of coherently driven atoms , 2006 .

[24]  C. Monroe,et al.  Experimental entanglement of four particles , 2000, Nature.

[25]  Klaus Mølmer,et al.  Monte Carlo wavefunctions in quantum optics , 1996 .

[26]  G. Milburn,et al.  Entanglement in the steady state of a collective-angular-momentum (Dicke) model , 2002 .

[27]  Michael Köhl,et al.  Correlations and counting statistics of an atom laser. , 2005, Physical review letters.

[28]  P. Zanardi,et al.  Noiseless Quantum Codes , 1997, quant-ph/9705044.

[29]  F. Schmidt-Kaler,et al.  Bell states of atoms with ultralong lifetimes and their tomographic state analysis. , 2004, Physical review letters.

[30]  T. Yu,et al.  Finite-time disentanglement via spontaneous emission. , 2004, Physical review letters.

[31]  K. Jacobs,et al.  FEEDBACK CONTROL OF QUANTUM SYSTEMS USING CONTINUOUS STATE ESTIMATION , 1999 .

[32]  G. Rempe,et al.  Normal-mode spectroscopy of a single-bound-atom-cavity system. , 2004, Physical review letters.

[33]  Jun Ye,et al.  Characterization of high-finesse mirrors: Loss, phase shifts, and mode structure in an optical cavity , 2001, quant-ph/0101103.

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

[35]  L. Lugiato,et al.  Optical bistability and cooperative effects in resonance fluorescence , 1978 .

[36]  C. J. Hood,et al.  Real-Time Cavity QED with Single Atoms , 1998 .

[37]  M. B. Plenio,et al.  Cavity-loss-induced generation of entangled atoms , 1999 .

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

[39]  Milburn,et al.  Interpretation of quantum jump and diffusion processes illustrated on the Bloch sphere. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[40]  Milburn,et al.  Quantum theory of field-quadrature measurements. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[41]  Andreas Buchleitner,et al.  Decoherence and multipartite entanglement. , 2004, Physical review letters.

[42]  A. D. Boozer,et al.  Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity. , 2006, Physical review letters.

[43]  Submicron positioning of single atoms in a microcavity. , 2005, Physical review letters.

[44]  G. Rempe,et al.  Trapping and observing single atoms in a blue-detuned intracavity dipole trap. , 2007, Physical review letters.

[45]  H. Weinfurter,et al.  Observation of three-photon Greenberger-Horne-Zeilinger entanglement , 1998, quant-ph/9810035.

[46]  S. V. Lawande,et al.  Exact steady-state density operator for a collective atomic system in an external field , 1979 .

[47]  B. Julsgaard,et al.  Experimental long-lived entanglement of two macroscopic objects , 2001, Nature.

[48]  Hideo Mabuchi,et al.  Real-Time Quantum Feedback Control of Atomic Spin-Squeezing , 2004, Science.

[49]  Christoph Becher,et al.  Feedback cooling of a single trapped ion. , 2006, Physical review letters.

[50]  H. Carmichael An open systems approach to quantum optics , 1993 .

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