9,984 research outputs found
Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric
An ad hoc quantization scheme for the electromagnetic field in a weakly
dispersive, transparent dielectric leads to the definition of canonical and
kinetic forms for the momentum of the electromagnetic field in a dispersive
medium. The canonical momentum is uniquely defined as the operator that
generates spatial translations in a uniform medium, but the quantization scheme
suggests two possible choices for the kinetic momentum operator, corresponding
to the Abraham or the Minkowski momentum in classical electrodynamics. Another
implication of this procedure is that a wave packet containing a single dressed
photon travels at the group velocity through the medium. The physical
significance of the canonical momentum has already been established by
considerations of energy and momentum conservation in the atomic recoil due to
spontaneous emission, the Cerenkov effect, the Doppler effect, and phase
matching in nonlinear optical processes. In addition, the data of the Jones and
Leslie radiation pressure experiment is consistent with the assignment of one
?k unit of canonical momentum to each dressed photon. By contrast, experiments
in which the dielectric is rigidly accelerated by unbalanced electromagnetic
forces require the use of the Abraham momentum.Comment: 21 pages, 1 figure, aip style, submitted to PR
Alternative approach to electromagnetic field quantization in nonlinear and inhomogeneous media
A simple approach is proposed for the quantization of the electromagnetic
field in nonlinear and inhomogeneous media. Given the dielectric function and
nonlinear susceptibilities, the Hamiltonian of the electromagnetic field is
determined completely by this quantization method. From Heisenberg's equations
we derive Maxwell's equations for the field operators. When the nonlinearity
goes to zero, this quantization method returns to the generalized canonical
quantization procedure for linear inhomogeneous media [Phys. Rev. A, 43, 467,
1991]. The explicit Hamiltonians for the second-order and third-order nonlinear
quasi-steady-state processes are obtained based on this quantization procedure.Comment: Corrections in references and introductio
Dispersive response of atoms trapped near the surface of an optical nanofiber with applications to quantum nondemolition measurement and spin squeezing
We study the strong coupling between photons and atoms that can be achieved
in an optical nanofiber geometry when the interaction is dispersive. While the
Purcell enhancement factor for spontaneous emission into the guided mode does
not reach the strong-coupling regime for individual atoms, one can obtain high
cooperativity for ensembles of a few thousand atoms due to the tight
confinement of the guided modes and constructive interference over the entire
chain of trapped atoms. We calculate the dyadic Green's function, which
determines the scattering of light by atoms in the presence of the fiber, and
thus the phase shift and polarization rotation induced on the guided light by
the trapped atoms. The Green's function is related to a full
Heisenberg-Langevin treatment of the dispersive response of the quantized field
to tensor polarizable atoms. We apply our formalism to quantum nondemolition
(QND) measurement of the atoms via polarimetry. We study shot-noise-limited
detection of atom number for atoms in a completely mixed spin state and the
squeezing of projection noise for atoms in clock states. Compared with
squeezing of atomic ensembles in free space, we capitalize on unique features
that arise in the nanofiber geometry including anisotropy of both the intensity
and polarization of the guided modes. We use a first principles stochastic
master equation to model the squeezing as function of time in the presence of
decoherence due to optical pumping. We find a peak metrological squeezing of ~5
dB is achievable with current technology for ~2500 atoms trapped 180 nm from
the surface of a nanofiber with radius a=225 nm.Comment: To be appeared on PR
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