Entanglement generation in uniformly accelerating atoms: Reexamination of the Unruh effect

The master equation describing the completely positive time evolution of a uniformly accelerated two-level system in weak interaction with a scalar field in the Minkowski vacuum is derived and explicitly solved. The moving system is found to be subjected to dissipation that drives its density matrix to a purely thermal equilibrium state, exhibiting a nonvanishing probability of spontaneous excitation, this phenomenon being usually referred to as the Unruh effect. Remarkably, when the uniformly accelerating system is composed by two, independent two-level atoms, the corresponding asymptotic, equilibrium state turns out to be entangled.

[1]  H. Spohn.  Kinetic equations from Hamiltonian dynamics: Markovian limits , 1980 .

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

[3]  Lorentz-covariant reduced-density-operator theory for relativistic-quantum-information processing , 2002, quant-ph/0207053.

[4]  Herbert Spohn,et al.  The proper form of the generator in the weak coupling limit , 1979 .

[5]  Daniel R. Terno,et al.  Quantum Information and Relativity Theory , 2002, quant-ph/0212023.

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

[7]  Radiative energy shifts of an accelerated two-level system. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[8]  G. Sewell.  Quantum fields on manifolds: PCT and gravitationally induced thermal states , 1982 .

[9]  W. Unruh,et al.  What happens when an accelerating observer detects a Rindler particle , 1984 .

[10]  K. Lendi,et al.  Evolution matrix in a coherence vector formulation for quantum Markovian master equations of N-level systems , 1987 .

[11]  W. Unruh.  Notes on black-hole evaporation , 1976 .

[12]  Andrzej Kossakowski,et al.  Properties of Quantum Markovian Master Equations , 1978 .

[13]  E. Davies,et al.  Markovian master equations. II , 1976 .

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

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

[16]  Entanglement induced by a single-mode heat environment , 2001, quant-ph/0109052.

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

[18]  S. Takagi.  Vacuum Noise and Stress Induced by Uniform Acceleration Hawking-Unruh Effect in Rindler Manifold of Arbitrary Dimension , 1986 .

[19]  Complete positivity and the neutral kaon system , 1998 .

[20]  P. Davies.  Scalar production in Schwarzschild and Rindler metrics , 1975 .

[21]  W. Wootters,et al.  Entanglement of a Pair of Quantum Bits , 1997, quant-ph/9703041.

[22]  Complete positivity and dissipative factorized dynamics , 2002, quant-ph/0208023.

[23]  Completely positive dynamics of correlated neutral kaons , 1997, hep-ph/9711240.

[24]  H. Bethe.  The Electromagnetic shift of energy levels , 1947 .

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

[26]  States insensitive to the Unruh effect in multilevel detectors , 1997, gr-qc/9707058.

[27]  Nonpositive evolutions in open system dynamics , 2003, quant-ph/0303027.

[28]  A. M. Basharov.  Decoherence and entanglement in radiative decay of a diatomic system , 2002 .

[29]  William K. Wootters,et al.  Entanglement of formation and concurrence , 2001, Quantum Inf. Comput..

[30]  L. Jakóbczyk.  Entangling two qubits by dissipation , 2002 .

[31]  E. Davies,et al.  Markovian master equations , 1974 .

[32]  Testing Complete Positivity , 1997, quant-ph/9706032.

[33]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.