Three and Four-Body Interactions in Spin-Based Quantum Computers

In the effort to design and to construct a quantum computer, several leading proposals make use of spin-based qubits. These designs generally assume that spins undergo pairwise interactions. We point out that, when several spins are engaged mutually in pairwise interactions, the quantitative strengths of the interactions can change and qualitatively new terms can arise in the Hamiltonian, including four-body interactions. In parameter regimes of experimental interest, these coherent effects are large enough to interfere with computation, and may require new error correction or avoidance techniques.Comment: 5 pages incl. 4 figures. To appear in Phys. Rev. Lett. For an expanded version including detailed calculations see http://xxx.lanl.gov/abs/cond-mat/030201

Quantum derivation of the use of classical electromagnetic potentials in relativistic Coulomb excitation

We prove that a relativistic Coulomb excitation calculation in which the classical electromagnetic field of the projectile is used to induce transitions between target states gives the same target transition amplitudes, to all orders of perturbation theory, as would a calculation in which the interaction between projectile and target is mediated by a quantized electromagnetic field.Comment: 1 .zip file containing LaTex source plus three figures as .eps file

High energy cosmic-ray interactions with particles from the Sun

Cosmic-ray protons with energies above $10^{16}$ eV passing near the Sun may interact with photons emitted by the Sun and be excited to a $\Delta^+$ resonance. When the $\Delta^+$ decays, it produces pions which further decay to muons and photons which may be detected with terrestrial detectors. A flux of muons, photon pairs (from $\pi^0$ decay), or individual high-energy photons coming from near the Sun would be a rather striking signature, and the flux of these particles is a fairly direct measure of the flux of cosmic-ray nucleons, independent of the cosmic-ray composition. In a solid angle within $15^\circ$ around the Sun the flux of photon pairs is about \SI{1.3e-3}{} particles/(km$^2\cdot$yr), while the flux of muons is about \SI{0.33e-3}{} particles/(km$^2\cdot$yr). This is beyond the reach of current detectors like the Telescope Array, Auger, KASCADE-Grande or IceCube. However, the muon flux might be detectable by next-generation air shower arrays or neutrino detectors such as ARIANNA or ARA. We discuss the experimental prospects in some detail. Other cosmic-ray interactions occuring close to the Sun are also briefly discussed.Comment: 8 pages, 11 figure

Photon-Mediated Interaction between Two Distant Atoms

We study the photonic interactions between two distant atoms which are coupled by an optical element (a lens or an optical fiber) focussing part of their emitted radiation onto each other. Two regimes are distinguished depending on the ratio between the radiative lifetime of the atomic excited state and the propagation time of a photon between the two atoms. In the two regimes, well below saturation the dynamics exhibit either typical features of a bad resonator, where the atoms act as the mirrors, or typical characteristics of dipole-dipole interaction. We study the coherence properties of the emitted light and show that it carries signatures of the multiple scattering processes between the atoms. The model predictions are compared with the experimental results in J. Eschner {\it et al.}, Nature {\bf 413}, 495 (2001).Comment: 18 pages, 15 figure

A new look at the problem of gauge invariance in quantum field theory

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.Comment: Accepted by Physica Scripta. 27 page

Strongly correlated wave functions for artificial atoms and molecules

A method for constructing semianalytical strongly correlated wave functions for single and molecular quantum dots is presented. It employs a two-step approach of symmetry breaking at the Hartree-Fock level and of subsequent restoration of total spin and angular momentum symmetries via Projection Techniques. Illustrative applications are presented for the case of a two-electron helium-like single quantum dot and a hydrogen-like quantum dot molecule.Comment: 9 pages. Revtex with 2 GIF and 1 EPS figures. Published version with extensive clarifications. A version of the manuscript with high quality figures incorporated in the text is available at http://calcite.physics.gatech.edu/~costas/qdhelproj.html For related papers, see http://www.prism.gatech.edu/~ph274c

Primordial helium recombination II: two-photon processes

Interpretation of precision measurements of the cosmic microwave background (CMB) will require a detailed understanding of the recombination era, which determines such quantities as the acoustic oscillation scale and the Silk damping scale. This paper is the second in a series devoted to the subject of helium recombination, with a focus on two-photon processes in He I. The standard treatment of these processes includes only the spontaneous two-photon decay from the 2^1S level. We extend this treatment by including five additional effects, some of which have been suggested in recent papers but whose impact on He I recombination has not been fully quantified. These are: (i) stimulated two-photon decays; (ii) two-photon absorption of redshifted HeI line radiation; (iii) two-photon decays from highly excited levels in HeI (n^1S and n^1D, with n>=3); (iv) Raman scattering; and (v) the finite width of the 2^1P^o resonance. We find that effect (iii) is highly suppressed when one takes into account destructive interference between different intermediate states contributing to the two-photon decay amplitude. Overall, these effects are found to be insignificant: they modify the recombination history at the level of several parts in 10^4.Comment: 19 pages, 11 figures, to be submitted to PR

Perfect Reflection of Light by an Oscillating Dipole

We show theoretically that a directional dipole wave can be perfectly reflected by a single point-like oscillating dipole. Furthermore, we find that in the case of a strongly focused plane wave up to 85 % of the incident light can be reflected by the dipole. Our results hold for the full spectrum of the electromagnetic interactions and have immediate implications for achieving strong coupling between a single propagating photon and a single quantum emitter.Comment: 3 figure

Size-dependence of Strong-Coupling Between Nanomagnets and Photonic Cavities

The coherent dynamics of a coupled photonic cavity and a nanomagnet is explored as a function of nanomagnet size. For sufficiently strong coupling eigenstates involving highly entangled photon and spin states are found, which can be combined to create coherent states. As the size of the nanomagnet increases its coupling to the photonic mode also monotonically increases, as well as the number of photon and spin states involved in the system's eigenstates. For small nanomagnets the crystalline anisotropy of the magnet strongly localized the eigenstates in photon and spin number, quenching the potential for coherent states. For a sufficiently large nanomagnet the macrospin approximation breaks down and different domains of the nanomagnet may couple separately to the photonic mode. Thus the optimal nanomagnet size is just below the threshold for failure of the macrospin approximation.Comment: 10 pages, 7 figure

Radiation from accelerated perfect or dispersive mirrors following prescribed relativistic asymptotically inertial trajectories

We address the question of radiation emission from both perfect and dispersive mirrors following prescribed relativistic trajectories. The trajectories considered are asymptotically inertial: the mirror starts from rest and eventually reverts to motion at uniform velocity. This enables us to provide a description in terms of in and out states. We calculate exactly the Bogolubov alpha and beta coefficients for a specific form of the trajectory, and stress the analytic properties of the amplitudes and the constraints imposed by unitarity. A formalism for the description of emission of radiation from a dispersive mirror is presented.Comment: 7 figure