Non-markovian entanglement dynamics of quantum continuous variable systems in thermal environments

We study two continuous variable systems (or two harmonic oscillators) and investigate their entanglement evolution under the influence of non-Markovian thermal environments. The continuous variable systems could be two modes of electromagnetic fields or two nanomechanical oscillators in the quantum domain. We use the quantum open system method to derive the non-Markovian master equations of the reduced density matrix for two different but related models of the continuous variable systems. The two models both consist of two interacting harmonic oscillators. In model A, each of the two oscillators is coupled to its own independent thermal reservoir, while in model B the two oscillators are coupled to a common reservoir. To quantify the degrees of entanglement for bipartite continuous variable systems in Gaussian states, logarithmic negativity is used. We find that the dynamics of the quantum entanglement is sensitive to the initial states, the oscillator-oscillator interaction, the oscillator-environment interaction and the coupling to a common bath or to different, independent baths.

[1]  A. Leggett,et al.  Dynamics of the dissipative two-state system , 1987 .

[2]  G. Milburn,et al.  Ion trap transducers for quantum electromechanical oscillators , 2005, quant-ph/0501037.

[3]  Entanglement and purity of two-mode Gaussian states in noisy channels (10 pages) , 2003, quant-ph/0310087.

[4]  Seth Lloyd,et al.  Macroscopic entanglement by entanglement swapping. , 2006, Physical review letters.

[5]  Kimble,et al.  Unconditional quantum teleportation , 1998, Science.

[6]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .

[7]  F. Illuminati,et al.  Extremal entanglement and mixedness in continuous variable systems , 2004, quant-ph/0402124.

[8]  J. Eisert,et al.  Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom , 2004, quant-ph/0402004.

[9]  A. Cleland,et al.  Nanometre-scale displacement sensing using a single electron transistor , 2003, Nature.

[10]  Guang-Can Guo,et al.  Influence of noise on the fidelity and the entanglement fidelity of states , 1997 .

[11]  B. Camarota,et al.  Approaching the Quantum Limit of a Nanomechanical Resonator , 2004, Science.

[12]  Stefano Mancini,et al.  Entangling macroscopic oscillators exploiting radiation pressure. , 2002, Physical review letters.

[13]  Miles P. Blencowe,et al.  Quantum electromechanical systems , 2004 .

[14]  C. Fabre,et al.  Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation , 2005, quant-ph/0507067.

[15]  Daniel Braun,et al.  Creation of entanglement by interaction with a common heat bath. , 2002, Physical review letters.

[16]  T. Hiroshima.  Decoherence and entanglement in two-mode squeezed vacuum states. , 2000, quant-ph/0006100.

[17]  Fabio Benatti,et al.  Environment induced entanglement in Markovian dissipative dynamics. , 2003, Physical review letters.

[18]  H. J. Kimble,et al.  Quantum teleportation of light beams , 2003 .

[19]  Paz,et al.  Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise. , 1992, Physical review. D, Particles and fields.

[20]  M. D. LaHaye,et al.  Cooling a nanomechanical resonator with quantum back-action , 2006, Nature.

[21]  K. Audenaert,et al.  Entanglement properties of the harmonic chain , 2002, quant-ph/0205025.

[22]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[23]  M. Roukes.  Nanoelectromechanical systems face the future , 2001 .

[24]  Timothy C. Ralph,et al.  Experimental investigation of continuous-variable quantum teleportation , 2002, quant-ph/0207179.

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

[26]  N. Cerf,et al.  Quantum key distribution using gaussian-modulated coherent states , 2003, Nature.

[27]  Horace P. Yuen,et al.  Classical noise-based cryptography similar to two-state quantum cryptography , 1998 .

[28]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.

[29]  Cirac,et al.  Inseparability criterion for continuous variable systems , 1999, Physical review letters.

[30]  Optimized teleportation in Gaussian noisy channels , 2003, quant-ph/0309097.

[31]  M. Blencowe,et al.  Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box. , 2002, Physical review letters.

[32]  Christoph Simon,et al.  Towards quantum superpositions of a mirror , 2004 .

[33]  Dirk-Gunnar Welsch,et al.  Entanglement generation and degradation by passive optical devices , 2001 .

[34]  S. Braunstein,et al.  Quantum Information with Continuous Variables , 2004, quant-ph/0410100.

[35]  Entanglement oscillations in non-Markovian quantum channels , 2007, quant-ph/0702055.

[36]  A. Leggett,et al.  Quantum tunnelling in a dissipative system , 1983 .

[37]  Jakub S. Prauzner-Bechcicki,et al.  LETTER TO THE EDITOR: Two-mode squeezed vacuum state coupled to the common thermal reservoir , 2002 .

[38]  Simón.  Peres-horodecki separability criterion for continuous variable systems , 1999, Physical review letters.

[39]  F. Benatti,et al.  Entangling oscillators through environment noise , 2006 .

[40]  J Eisert,et al.  Towards quantum entanglement in nanoelectromechanical devices. , 2004, Physical review letters.

[41]  Jonathan J. Halliwell,et al.  Disentanglement and decoherence by open system dynamics , 2004 .

[42]  M. Plenio.  Logarithmic negativity: a full entanglement monotone that is not convex. , 2005, Physical review letters.

[43]  Disentanglement by dissipative open system dynamics , 2003, quant-ph/0312099.