Bethe-Salpeter approach for relativistic positronium in a strong magnetic field

We study the electron-positron system in a strong magnetic field using the differential Bethe-Salpeter equation in the ladder approximation. We derive the fully relativistic two-dimensional form that the four-dimensional Bethe-Salpeter equation takes in the limit of asymptotically strong constant and homogeneous magnetic field. An ultimate value for the magnetic field is determined, which provides the full compensation of the positronium rest mass by the binding energy in the maximum symmetry state and vanishing of the energy gap separating the electron-positron system from the vacuum. The compensation becomes possible owing to the falling to the center phenomenon that occurs in a strong magnetic field because of the dimensional reduction. The solution of the Bethe-Salpeter equation corresponding to the vanishing energy-momentum of the electron-positron system is obtained.Comment: 35 pages, minor correction

Positronium collapse and the maximum magnetic field in pure QED

A maximum value for the magnetic field is determined, which provides the full compensation of the positronium rest mass by the binding energy in the maximum symmetry state and disappearance of the energy gap separating the electron-positron system from the vacuum. The compensation becomes possible owing to the falling to the center phenomenon. The maximum magnetic field may be related to the vacuum and describe its structure.Comment: 4 pages, accepted for publication in Phys. Rev. Letter

Magnetic field driven instability of charged center in graphene

It is shown that a magnetic field dramatically affects the problem of supercritical charge in graphene making any charge in gapless theory supercritical. The cases of radially symmetric potential well and Coulomb center in an homogeneous magnetic field are considered. The local density of states and polarization charge density are calculated in the first order of perturbation theory. It is argued that the magnetically induced instability of the supercritical Coulomb center can be considered as a quantum mechanical counterpart of the magnetic catalysis phenomenon in graphene.Comment: 10 pages, 4 figures; to be published in PR

Electric field of a pointlike charge in a strong magnetic field and ground state of a hydrogenlike atom

In an external constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length, we consider the modification of the Coulomb potential of a point charge owing to the vacuum polarization. We establish a short-range component of the static interaction in the Larmour scale, expressed as a Yukawa-like law, and reveal the corresponding "photon mass" parameter. The electrostatic force regains its long-range character in the Compton scale: the tail of the potential follows an anisotropic Coulomb law, decreasing away from the charge slower along the magnetic field and faster across. In the infinite-magnetic-field limit the potential is confined to an infinitely thin string passing though the charge parallel to the external field. This is the first evidence for dimensional reduction in the photon sector of quantum electrodynamics. The one-dimensional form of the potential on the string is derived that includes a delta-function centered in the charge. The nonrelativistic ground-state energy of a hydrogenlike atom is found with its use and shown not to be infinite in the infinite-field limit, contrary to what was commonly accepted before, when the vacuum polarization had been ignored. These results may be useful for studying properties of matter at the surface of extremely magnetized neutron stars.Comment: 45 pages, 6 figures, accepted to Phys. Rev.

Experimental Implementation of the Deutsch-Jozsa Algorithm for Three-Qubit Functions using Pure Coherent Molecular Superpositions

The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of Li$_{2}$ rovibrational eigenstates. The function's character, either constant or balanced, is evaluated by first imprinting the function, using a phase-shaped femtosecond pulse, on a coherent superposition of the molecular states, and then projecting the superposition onto an ionic final state, using a second femtosecond pulse at a specific time delay

Dynamics, correlations and phases of the micromaser

The micromaser possesses a variety of dynamical phase transitions parametrized by the flux of atoms and the time-of-flight of the atom within the cavity. We discuss how these phases may be revealed to an observer outside the cavity using the long-time correlation length in the atomic beam. Some of the phase transitions are not reflected in the average excitation level of the outgoing atom, which is the commonly used observable. The correlation length is directly related to the leading eigenvalue of the time evolution operator, which we study in order to elucidate the phase structure. We find that as a function of the time-of-flight the transition from the thermal to the maser phase is characterized by a sharp peak in the correlation length. For longer times-of-flight there is a transition to a phase where the correlation length grows exponentially with the flux. We present a detailed numerical and analytical treatment of the different phases and discuss the physics behind them.Comment: 60 pages, 18 figure files, Latex + \special{} for the figures, (some redundant figures are eliminated and others are changed

Investigation of the electromagnetically induced transparency in era of cosmological hydrogen recombination

Investigation of the cosmic microwave background formation processes is one of the most actual problem at present time. In this paper we analyze the response of the hydrogen atom to the external photon fields. Field characteristics are defined via conditions corresponding to the recombination era of universe. Approximation of three-level atom is used to describe the "atom - fields" interaction. It is found that the phenomena of the electromagnetically induced transparancy takes place in this case. Consideration of EIT phenomena makes it necessary to update astrophysical description of the processes of the cosmic microwave background formation and, in particular, Sobolev escape probability. Additional terms to the optical depth in definition of Sobolev escape probability on the level about 1% are found.Comment: 16 pages, 4 figures, 1 Tabl