skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Discriminating cascading processes in nonlinear optics: A QED analysis based on their molecular and geometric origin

Authors:
; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1349138
Grant/Contract Number:
FG02-04ER15571
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 95; Journal Issue: 3; Related Information: CHORUS Timestamp: 2017-03-30 11:32:18; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Bennett, Kochise, Chernyak, Vladimir Y., and Mukamel, Shaul. Discriminating cascading processes in nonlinear optics: A QED analysis based on their molecular and geometric origin. United States: N. p., 2017. Web. doi:10.1103/PhysRevA.95.033840.
Bennett, Kochise, Chernyak, Vladimir Y., & Mukamel, Shaul. Discriminating cascading processes in nonlinear optics: A QED analysis based on their molecular and geometric origin. United States. doi:10.1103/PhysRevA.95.033840.
Bennett, Kochise, Chernyak, Vladimir Y., and Mukamel, Shaul. Wed . "Discriminating cascading processes in nonlinear optics: A QED analysis based on their molecular and geometric origin". United States. doi:10.1103/PhysRevA.95.033840.
@article{osti_1349138,
title = {Discriminating cascading processes in nonlinear optics: A QED analysis based on their molecular and geometric origin},
author = {Bennett, Kochise and Chernyak, Vladimir Y. and Mukamel, Shaul},
abstractNote = {},
doi = {10.1103/PhysRevA.95.033840},
journal = {Physical Review A},
number = 3,
volume = 95,
place = {United States},
year = {Wed Mar 29 00:00:00 EDT 2017},
month = {Wed Mar 29 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevA.95.033840

Citation Metrics:
Cited by: 2works
Citation information provided by
Web of Science

Save / Share:
  • The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, themore » susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N{sup 2}.« less
  • We present a full quantum treatment of a five-level atomic system coupled to two quantum and two classical light fields. The two quantum fields undergo a cross-phase-modulation induced by electromagnetically induced transparency. The performance of this configuration as a two-qubit quantum phase gate for traveling single photons is examined. A trade-off between the size of the conditional phase shift and the fidelity of the gate is found. Nonetheless, a satisfactory gate performance is still found to be possible in the transient regime, corresponding to a fast gate operation.
  • The purpose of this paper is to present an introduction to the central aspects of the modulation equations of nonlinear geometric optics. That means regularity properties and existence in the large. 13 refs.
  • We construct infinitely accurate approximate solutions to systems of hyperbolic partial differential equations which model short wavelength dispersive nonlinear phenomena. The principal themes follow. (1) The natural framework for the study of dispersion is wavelength {epsilon} solutions of systems of partial differential operators in {epsilon}{partial_derivative}. The natural {epsilon}-characteristic equation and {epsilon}-eikonal equations are not homogeneous. This corresponds exactly to the fact that the speeds of propagation, which are called group velocities, depend on the length of the wave number. (2) The basic dynamic equations are expressed in terms of the operator {epsilon}{partial_derivative}{sub t}. As a result growth or decay tendsmore » to occur at the catastrophic rate e{sup ct/{epsilon}}. The analysis is limited to conservative or nearly conservative models. (3) If a phase {phi}(x)/{epsilon} satisfies the natural {epsilon}-eikonal equation, the natural harmonic phases, n{phi}(x)/{epsilon}, generally do not. One needs to impose a coherence hypothesis for the harmonics. (4) In typical examples the set of harmonics which are eikonal is finite. The fact that high harmonics are not eikonal suppresses the wave steepening which is characteristic of quasilinear wave equations. It also explains why a variety of monochromatic models are appropriate in nonlinear settings where harmonics would normally be expected to appear. (5) We study wavelength {epsilon} solutions of nonlinear equations in {epsilon}{partial_derivative} for times O(1). For a given system, there is a critical exponent p so that for amplitudes O({epsilon}{sup p}), one has simultaneously smooth existence for t=O(1), and nonlinear behavior in the principal term of the approximate solutions. This is the amplitude for which the time scale of nonlinear interaction is O(1). (6) The approximate solutions have residual each of whose derivatives is O({epsilon}{sup n}) for all n{gt}0. (Abstract Truncated)« less
  • We give a rigorous justification of geometric optics for a class of Kreiss well-posed semilinear boundary problems where both resonant interactions and glancing modes are present. Errors are o(1) in L{sup 2} as the wavelength tends to zero. We emphasize the features that distinguish boundary problems from hyperbolic problems in free space. These include: (1) the failure of coherence and symmetry hypotheses alone to guarantee existence of the exact solution on a fixed domain independent of the wavelength, (2) inconsistent transport equations for flaning modes connected with the presence of a glancing boundary layer, (3) the need to use (generalized)more » eigenvectors associated to nonreal eigenvalues in constructing approximate solutions and the related presence of an elliptic boundary layer, (4) and the appearance of unbounded families of projection operators (associated to eigenvalues of high multiplicity) in the profile equations. The difficulties in (1) and (4) are both handled by arguments that make use of the same hypothesis; namely, that the real zeros in {xi} of the principal symbol p({tau},{xi},{eta}) ({xi} is dual to {chi}, where {chi}=0 defines the boundary) have multiplicity at most two. As an essential tool we introduce the class of F{sub {infinity}}, m, s, {gamma} spaces, the natural spaces for obtaining energy estimates uniform with respect to wavelength in highly oscillatory boundary problems. 11 refs., 1 fig.« less