# Laser-dressed vacuum polarization in a Coulomb field

## Abstract

We investigate quantum electrodynamic effects under the influence of an external, time-dependent electromagnetic field, which mediates dynamic modifications of the radiative corrections. Specifically, we consider the quantum electrodynamic vacuum-polarization tensor under the influence of two external background fields: a strong laser field and a nuclear Coulomb field. We calculate the charge and current densities induced by a nuclear Coulomb field in the presence of a laser field. We find the corresponding induced scalar and vector potentials. The induced potential, in first-order perturbation theory, leads to a correction to atomic energy levels. The external laser field breaks the rotational symmetry of the system. Consequently, the induced charge density is not spherically symmetric, and the energy correction therefore leads to a ''polarized Lamb shift.'' In particular, the laser generates an additional potential with a quadrupole moment. The corresponding laser-dressed vacuum-polarization potential behaves like 1/r{sup 3} at large distances, unlike the Uehling potential, which vanishes exponentially for large r. The energy corrections are of the same order of magnitude for hydrogenic levels, irrespective of the angular momentum quantum number. The induced current leads to a transition dipole moment which oscillates at the second harmonic of the laser frequency and is mediated by second-ordermore »

- Authors:

- Budker Institute of Nuclear Physics, 630090 Novosibirsk (Russian Federation)
- (Germany)

- Publication Date:

- OSTI Identifier:
- 20786440

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.052104; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; CHARGE DENSITY; COULOMB FIELD; CURRENT DENSITY; DIPOLE MOMENTS; ELECTROMAGNETIC FIELDS; HARMONIC GENERATION; LAMB SHIFT; LASER RADIATION; MAGNETIC FIELDS; PERTURBATION THEORY; PHOTON-ATOM COLLISIONS; PHOTONS; POTENTIALS; QUADRUPOLE MOMENTS; QUANTUM ELECTRODYNAMICS; RADIATIVE CORRECTIONS; ROTATIONAL STATES; SYMMETRY; TIME DEPENDENCE; VACUUM POLARIZATION

### Citation Formats

```
Milstein, A. I., Terekhov, I. S., Jentschura, U. D., Keitel, C. H., and Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg.
```*Laser-dressed vacuum polarization in a Coulomb field*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Milstein, A. I., Terekhov, I. S., Jentschura, U. D., Keitel, C. H., & Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg.
```*Laser-dressed vacuum polarization in a Coulomb field*. United States. doi:10.1103/PHYSREVA.72.0.

```
Milstein, A. I., Terekhov, I. S., Jentschura, U. D., Keitel, C. H., and Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg. Tue .
"Laser-dressed vacuum polarization in a Coulomb field". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786440,
```

title = {Laser-dressed vacuum polarization in a Coulomb field},

author = {Milstein, A. I. and Terekhov, I. S. and Jentschura, U. D. and Keitel, C. H. and Max-Planck-Institut fuer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg},

abstractNote = {We investigate quantum electrodynamic effects under the influence of an external, time-dependent electromagnetic field, which mediates dynamic modifications of the radiative corrections. Specifically, we consider the quantum electrodynamic vacuum-polarization tensor under the influence of two external background fields: a strong laser field and a nuclear Coulomb field. We calculate the charge and current densities induced by a nuclear Coulomb field in the presence of a laser field. We find the corresponding induced scalar and vector potentials. The induced potential, in first-order perturbation theory, leads to a correction to atomic energy levels. The external laser field breaks the rotational symmetry of the system. Consequently, the induced charge density is not spherically symmetric, and the energy correction therefore leads to a ''polarized Lamb shift.'' In particular, the laser generates an additional potential with a quadrupole moment. The corresponding laser-dressed vacuum-polarization potential behaves like 1/r{sup 3} at large distances, unlike the Uehling potential, which vanishes exponentially for large r. The energy corrections are of the same order of magnitude for hydrogenic levels, irrespective of the angular momentum quantum number. The induced current leads to a transition dipole moment which oscillates at the second harmonic of the laser frequency and is mediated by second-order harmonic generation in the vacuum-polarization loop. In the far field, at distances r>>1/{omega} from the nucleus ({omega} is the laser frequency), the laser induces mutually perpendicular electric and magnetic fields, which give rise to an energy flux that corresponds to photon fusion leading to the generation of real photons, again at the second harmonic of the laser. Our investigation might be useful for other situations where quantum field theoretic phenomena are subjected to external fields of a rather involved structure.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 5,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}