Dynamic generation of maximally entangled photon multiplets by adiabatic passage

The adiabatic passage scheme for quantum state synthesis, in which atomic Zeeman coherences are mapped to photon states in an optical cavity, is extended to the general case of two degenerate cavity modes with orthogonal polarization. Analytical calculations of the dressed-state structure and Monte Carlo wave-function simulations of the system dynamics show that, for a suitably chosen cavity detuning, it is possible to generate states of photon multiplets that are maximally entangled in polarization. These states display nonclassical correlations of the type described by Greenberger, Horne, and Zeilinger (GHZ). An experimental scheme to realize a GHZ measurement using coincidence detection of the photons escaping from the cavity is proposed. The correlations are found to originate in the dynamics of the adiabatic passage and persist even if cavity decay and GHZ state synthesis compete on the same time scale. Beyond entangled field states, it is also possible to generate entanglement between photons and the atom by using a different atomic transition and initial Zeeman state.Comment: 22 pages (RevTeX), including 23 postscript figures. To be published in Physical Review

The use of exp(iS[x]) in the sum over histories

The use of $\sum \exp(iS[x])$ as the generic form for a sum over histories in configuration space is discussed critically and placed in its proper context. The standard derivation of the sum over paths by discretizing the paths is reviewed, and it is shown that the form $\sum \exp(iS[x])$ is justified only for Schrodinger-type systems which are at most second order in the momenta. Extending this derivation to the relativistic free particle, the causal Green's function is expressed as a sum over timelike paths, and the Feynman Green's function is expressed both as a sum over paths which only go one way in time and as a sum over paths which move forward and backward in time. The weighting of the paths is shown not to be $\exp(iS[x])$ in any of these cases. The role of the inner product and the operator ordering of the wave equation in defining the sum over histories is discussed.Comment: 22 pages, Latex, Imperial-TP-92-93-4

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

A master equation for a two-sided optical cavity.

Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same notion of photons as in linear optics scattering theory and consider a continuum of travelling-wave cavity photon modes. Our model predicts the same stationary state photon emission rates for the different sides of a laser-driven optical cavity as classical theories. Moreover, it predicts the same time evolution of the total cavity photon number as the standard standing-wave description in experiments with resonant and near-resonant laser driving. The proposed resonator Hamiltonian can be used, for example, to analyse coherent cavity-fiber networks [E. Kyoseva et al., New J. Phys. 14, 023023 (2012

Canonical Transformations and Path Integral Measures

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are discussed and used to show that the quantum mechanical version of the classical transformation does not leave the measure of the path integral invariant, instead inducing an anomaly. The relation to operator techniques and ordering problems is discussed, and special attention is paid to incorporation of the initial and final states of the transition element into the boundary conditions of the problem. Classical canonical transformations are developed to render an arbitrary power potential cyclic. The resulting Hamiltonian is analyzed as a quantum system to show its relation to known quantum mechanical results. A perturbative argument is used to suppress ordering related terms in the transformed Hamiltonian in the event that the classical canonical transformation leads to a nonquadratic cyclic Hamiltonian. The associated anomalies are analyzed to yield general methods to evaluate the path integral's prefactor for such systems. The methods are applied to several systems, including linear and quadratic potentials, the velocity-dependent potential, and the time-dependent harmonic oscillator.Comment: 28 pages, LaTe

Creation of maximally entangled photon-number states using optical fiber multiports

We theoretically demonstrate a method for producing the maximally path-entangled state (1/Sqrt[2]) (|N,0> + exp[iN phi] |0,N>) using intensity-symmetric multiport beamsplitters, single photon inputs, and either photon-counting postselection or conditional measurement. The use of postselection enables successful implementation with non-unit efficiency detectors. We also demonstrate how to make the same state more conveniently by replacing one of the single photon inputs by a coherent state.Comment: 4 pages, 1 figure. REVTeX4. Replaced with published versio

Engineering Entanglement between two cavity modes

We present scheme for generation of entanglement between different modes of radiation field inside high-Q superconducting cavities. Our scheme is based on the interaction of a three-level atom with the cavity field for pre-calculated interaction times with each mode. This work enables us to generate complete set of Bell basis states and GHZ state

Robust Entanglement in Atomic Systems via Lambda-Type Processes

It is shown that the system of two three-level atoms in $\Lambda$ configuration in a cavity can evolve to a long-lived maximum entangled state if the Stokes photons vanish from the cavity by means of either leakage or damping. The difference in evolution picture corresponding to the general model and effective model with two-photon process in two-level system is discussed.Comment: 10 pages, 3 figure