Spontaneous emission of a photon: Wave-packet structures and atom-photon entanglement

Spontaneous emission of a photon by an atom is described theoretically in three dimensions with the initial wave function of a finite-mass atom taken in the form of a finite-size wave packet. Recoil and wave-packet spreading are taken into account. The total atom-photon wave function is found in the momentum and coordinate representations as the solution of an initial-value problem. The atom-photon entanglement arising in such a process is shown to be closely related to the structure of atom and photon wave packets which can be measured in the coincidence and single-particle schemes of measurements. Two predicted effects, arising under the conditions of high entanglement, are anomalous narrowing of the coincidence wave packets and, under different conditions, anomalous broadening of the single-particle wave packets. Fundamental symmetry relations between the photon and atom single-particle and coincidence wave-packet widths are established. The relationship with the famous scenario of Einstein-Podolsky-Rosen is discussed.

[1]  Reid,et al.  Correlations in nondegenerate parametric oscillation: Squeezing in the presence of phase diffusion. , 1989, Physical review. A, General physics.

[2]  C H Monken,et al.  Multimode Hong-Ou-mandel interference. , 2003, Physical review letters.

[3]  Carlos H. Monken,et al.  Transfer of angular spectrum and image formation in spontaneous parametric down-conversion , 1998 .

[4]  C. Kurtsiefer,et al.  Observation of correlated atom-photon pairs on the single-particle level , 1997 .

[5]  Q. Su,et al.  Entanglement for pair production on the zeptosecond scale , 2005 .

[6]  Yanhua Shih,et al.  Identifying entanglement using quantum "ghost" interference and imaging , 2004, InternationalQuantum Electronics Conference, 2004. (IQEC)..

[7]  G. Kurizki,et al.  Proposal for translational entanglement of dipole-dipole interacting atoms in optical lattices. , 2003, Physical Review Letters.

[8]  K. Rzążewski,et al.  Spontaneous emission from an extended wavepacket , 1992 .

[9]  POSITION AND MOMENTUM ENTANGLEMENT OF DIPOLE-DIPOLE INTERACTING ATOMS IN OPTICAL LATTICES: THE EINSTEIN-PODOLSKY-ROSEN PARADOX ON A LATTICE , 2004, quant-ph/0409149.

[10]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[11]  John C Howell,et al.  Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion. , 2004, Physical review letters.

[12]  Joseph H. Eberly,et al.  Correlations and one-quantum pulse shapes in photon pair generation , 1993 .

[13]  L. Mandel,et al.  Optical Coherence and Quantum Optics , 1995 .

[14]  A. Akhiezer,et al.  QUANTUM ELECTRODYNAMICS. , 1965 .

[15]  M. S. Zubairy,et al.  Quantum optics: Frontmatter , 1997 .

[16]  C. K. Law.  Entanglement production in colliding wave packets , 2004 .

[17]  C. Monken,et al.  TRANSVERSE COHERENCE LENGTH OF DOWN-CONVERTED LIGHT IN THE TWO-PHOTON STATE , 1999 .

[18]  Quantum entanglement in photon-atom scattering , 2003 .

[19]  Packet narrowing and quantum entanglement in photoionization and photodissociation , 2003, quant-ph/0312119.

[20]  E. Wigner,et al.  Berechnung der natürlichen Linienbreite auf Grund der Diracschen Lichttheorie , 1930 .

[21]  K. Mishima,et al.  Entanglement in scattering processes , 2004 .

[22]  Rubin,et al.  Transverse correlation in optical spontaneous parametric down-conversion. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[23]  M C Teich,et al.  Role of entanglement in two-photon imaging. , 2001, Physical review letters.

[24]  Einstein localization in entangled light scattering , 2004 .

[25]  Law,et al.  Continuous frequency entanglement: effective finite hilbert space and entropy control , 2000, Physical review letters.

[26]  J H Eberly,et al.  Analysis and interpretation of high transverse entanglement in optical parametric down conversion. , 2004, Physical review letters.

[27]  Joseph H. Eberly,et al.  Measure of electron-electron correlation in atomic physics , 1994 .

[28]  Reid,et al.  Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification. , 1989, Physical review. A, General physics.

[29]  C. K. Law,et al.  Localized single-photon wave functions in free space. , 2002, Physical review letters.