26 research outputs found
Quantum synthesis of arbitrary unitary operators
Nature provides us with a restricted set of microscopic interactions. The
question is whether we can synthesize out of these fundamental interactions an
arbitrary unitary operator. In this paper we present a constructive algorithm
for realization of any unitary operator which acts on a (truncated) Hilbert
space of a single bosonic mode. In particular, we consider a physical
implementation of unitary transformations acting on 1-dimensional vibrational
states of a trapped ion. As an example we present an algorithm which realizes
the discrete Fourier transform.Comment: 6 RevTeX pages with 3 figures, submitted to Phys.Rev.A, see also
http://nic.savba.sk/sav/inst/fyzi/qo
High-order nonlinearities in the motion of a trapped atom
Published versio
Pfaffian pairing wave functions in electronic structure quantum Monte Carlo
We investigate the accuracy of trial wave function for quantum Monte Carlo
based on pfaffian functional form with singlet and triplet pairing. Using a set
of first row atoms and molecules we find that these wave functions provide very
consistent and systematic behavior in recovering the correlation energies on
the level of 95%. In order to get beyond this limit we explore the
possibilities of multi-pfaffian pairing wave functions. We show that a small
number of pfaffians recovers another large fraction of the missing correlation
energy comparable to the larger-scale configuration interaction wave functions.
We also find that pfaffians lead to substantial improvements in fermion nodes
when compared to Hartree-Fock wave functions.Comment: 4 pages, 2 figures, 2 tables, submitted to PR
N-Photon wave packets interacting with an arbitrary quantum system
We present a theoretical framework that describes a wave packet of light
prepared in a state of definite photon number interacting with an arbitrary
quantum system (e.g. a quantum harmonic oscillator or a multi-level atom).
Within this framework we derive master equations for the system as well as for
output field quantities such as quadratures and photon flux. These results are
then generalized to wave packets with arbitrary spectral distribution
functions. Finally, we obtain master equations and output field quantities for
systems interacting with wave packets in multiple spatial and/or polarization
modes.Comment: 20 pages, 8 figures. Published versio
Quantum versus classical descriptions of sub-Poissonian light generation in three-wave mixing
Sub-Poissonian light generation in the non-degenerate three-wave mixing is
studied numerically and analytically within quantum and classical approaches.
Husimi Q-functions and their classical trajectory simulations are analysed to
reveal a special regime corresponding to the time-stable sub-Poissonian
photocount statistics of the sum-frequency mode. Conditions for observation of
this regime are discussed. Theoretical predictions of the Fano factor and
explanation of the extraordinary stabilization of the sub-Poissonian photocount
behavior are obtained analytically by applying the classical trajectories.
Scaling laws for the maximum sub-Poissonian behavior are found. Noise
suppression levels in the non-degenerate vs degenerate three-wave mixing are
discussed on different time scales compared to the revival times. It is shown
that the non-degenerate conversion offers much better stabilization of the
suppressed noise in comparison to that of degenerate process.Comment: 9 pages, 12 figures, to be published in J. Optics
Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
A study of fermion nodes for spin-polarized states of a few-electron ions and
molecules with one-particle orbitals is presented. We find exact nodes
for some cases of two electron atomic and molecular states and also the first
exact node for the three-electron atomic system in state using
appropriate coordinate maps and wavefunction symmetries. We analyze the cases
of nodes for larger number of electrons in the Hartree-Fock approximation and
for some cases we find transformations for projecting the high-dimensional node
manifolds into 3D space. The node topologies and other properties are studied
using these projections. We also propose a general coordinate transformation as
an extension of Feynman-Cohen backflow coordinates to both simplify the nodal
description and as a new variational freedom for quantum Monte Carlo trial
wavefunctions.Comment: 7 pages, 7 figure
Linear optics substituting scheme for multi-mode operations
We propose a scheme allowing a conditional implementation of suitably
truncated general single- or multi-mode operators acting on states of traveling
optical signal modes. The scheme solely relies on single-photon and coherent
states and applies beam splitters and zero- and single-photon detections. The
signal flow of the setup resembles that of a multi-mode quantum teleportation
scheme thus allowing the individual signal modes to be spatially separated from
each other. Some examples such as the realization of cross-Kerr nonlinearities,
multi-mode mirrors, and the preparation of multi-photon entangled states are
considered.Comment: 11 pages, 4 eps-figures, using revtex
Reconstruction of motional states of neutral atoms via MaxEnt principle
We present a scheme for a reconstruction of states of quantum systems from
incomplete tomographic-like data. The proposed scheme is based on the Jaynes
principle of Maximum Entropy. We apply our algorithm for a reconstruction of
motional quantum states of neutral atoms. As an example we analyze the
experimental data obtained by the group of C. Salomon at the ENS in Paris and
we reconstruct Wigner functions of motional quantum states of Cs atoms trapped
in an optical lattice
Cavity QED with cold trapped ions
Published versio
Quantum description of light pulse scattering on a single atom in waveguides
We present a time dependent quantum calculation of the scattering of a
few-photon pulse on a single atom. The photon wave packet is assumed to
propagate in a transversely strongly confined geometry, which ensures strong
atom-light coupling and allows a quasi 1D treatment. The amplitude and phase of
the transmitted, reflected and transversely scattered part of the wave packet
strongly depend on the pulse length (bandwidth) and energy. For a transverse
mode size of the order of , we find nonlinear behavior for a few
photons already, or even for a single photon. In a second step we study the
collision of two such wave packets at the atomic site and find striking
differences between Fock state and coherent state wave packets of the same
photon number.Comment: to appear in Phys. Rev.