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

Abstract

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.

Versatile wideband balanced detector for quantum optical homodyne tomography

“…whereâ(t) is the time dependent photon annihilation operator [14]. In a practical HD, the relationship between the quadrature measurement and the output current is more complex.…”

Spatial, spectral, and temporal coherence of ultraintense twin beams

“…We also note that several quantifiers of entanglement dimensionality have been compared in [13,38,39]. The number of paired modes effectively present in any physical variable of the twin beam can be estimated by the corresponding Fedorov ratio K ∆ [40]. It is defined as the ratio of the width ∆n s of the signal-field intensity profile and the width ∆C s of the corresponding intensity cross-correlation function in a given variable, i.e.…”

The localized quantum vacuum field

“…The transition takes place with energy and momentum conservation, the emitted photon and the recoiled atom in the ground state being entangled. Atom recoil during spontaneous transitions to the ground state has been experimentally observed [7], and the wavefunction of the photon-ground state atom has been analytically computed in [3] in terms of a s ingle-photon state 〉 k 1 | with a wavefunction in the coordinate representation…”

“…Since the photon is afterwards re-absorbed, it is not spatially separated enough from the negative-energy particle in order to assure localized interactions of the negative-energy particle alone. The entangled state is a consequence of energy-and momentum-conservation laws at transition, as for the case of the excited-ground state transition in [3].…”

“…Then, the total energy of the quantum electromagnetic field is given by 2 / quantum number that labels the different excited states of a harmonic oscillator with mass, this ambiguous conceptual issue constitutes the first of many paradoxes associated to quantum vacuum. Note for completeness that the wavefunction of a single photon is not the same as the wavefunction of the first excited state of a quantum oscillator (see [2,3] and the references therein); it can be meaningfully defined if a relaxed definition of localizability of quantum systems is employed.…”