Topology Classes of Flat U(1) Bundles and Diffeomorphic Covariant Representations of the Heisenberg Algebra

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat U(1) bundles over the configuration space manifold. In the case of Riemannian manifolds, these representations are also manifestly diffeomorphic covariant. The general discussion, illustrated by some simple examples in non relativistic quantum mechanics, is of particular relevance to systems whose configuration space is parametrised by curvilinear coordinates or is not simply connected, which thus include for instance the modular spaces of theories of non abelian gauge fields and gravity.Comment: 22 pages, no figures, plain LaTeX file; changes only in details of affiliation and financial suppor

Coherent and Squeezed Vacuum Light Interferometry: Parity detection hits the Heisenberg limit

The interference between coherent and squeezed vacuum light can produce path entangled states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer-Rao bound, which reaches the Heisenberg-limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.Comment: Change in the format from aps to iop since we decided to submit it to NJP; Minor changes in tex

Dynamic interference of photoelectrons produced by high-frequency laser pulses

The ionization of an atom by a high-frequency intense laser pulse, where the energy of a single-photon is sufficient to ionize the system, is investigated from first principles. It is shown that as a consequence of an AC Stark effect in the continuum, the energy of the photoelectron follows the envelope of the laser pulse. This is demonstrated to result in strong dynamic interference of the photoelectrons of the same kinetic energy emitted at different times. Numerically exact computations on the hydrogen atom demonstrate that the dynamic interference spectacularly modifies the photoionization process and is prominently manifested in the photoelectron spectrum by the appearance of a distinct multi-peak pattern. The general theory is shown to be well approximated by explicit analytical expressions which allow for a transparent understanding of the discovered phenomena and for making predictions on the dependence of the measured spectrum on the properties of the pulse.Comment: 5 figure

An efficient scheme for the deterministic maximal entanglement of N trapped ions

We propose a method for generating maximally entangled states of N two-level trapped ions. The method is deterministic and independent of the number of ions in the trap. It involves a controlled-NOT acting simultaneously on all the ions through a dispersive interaction. We explore the potential application of our scheme for high precision frequency standards.Comment: 4 pages, no figures, submitted to PRL, under review, Revised Version: Incorporated referee comment

Geometric phases for generalized squeezed coherent states

A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and the corresponding anholonomies deduced.Comment: 15 page

Path Integrals in Polar Field Variables in QFT

We show how to transform a $d$-dimensional Euclidean path integral in terms of two (Cartesian) fields to a path integral in terms of polar field variables. First we present a conjecture that states how this transformation should be done. Then we show that this conjecture is correct in the case of two toy models. Finally the conjecture will be proven for a general QFT model with two fields

The feasible generation of entangled photon states by using linear optical elements

We present a feasible scheme to produce a polarization-entangled photon states $\frac{1}{\sqrt{2}}(|H>|V>+|V>|H>)$ in a controllable way. This scheme requires single-photon sources, linear optical elements and photon detectors. It generates the entanglement of spatially separated photons. The interaction takes place in the photon detectors. We also show that the same idea can be used to produce the entangled $N$-photon state $\frac{1}{\sqrt{2}}(|0,N>+|N,0>)$Comment: to appear in PR

Dynamics of entropy and nonclassical properties of the state of a Λ\Lambda-type three-level atom interacting with a single-mode cavity field with intensity-dependent coupling in a Kerr medium

In this paper, we study the interaction between a three-level atom and a quantized single-mode field with $` `$intensity-dependent coupling$"$ in a $` `$Kerr medium$"$. The three-level atom is considered to be in a $\Lambda$-type configuration. Under particular initial conditions, which may be prepared for the atom and the field, the dynamical state vector of the entire system will be explicitly obtained, for arbitrary nonlinearity function $f(n)$ associated to any physical system. Then, after evaluating the variation of the field entropy against time, we will investigate the quantum statistics as well as some of the nonclassical properties of the introduced state. During our calculations we investigate the effects of intensity-dependent coupling, Kerr medium and detuning parameters on the depth and domain of the nonclassicality features of the atom-field state vector. Finally, we compare our obtained results with those of $V$-type three-level atoms.Comment: 18 pages, 7 Figure