67 research outputs found
Evolution equation for multi-photon states in turbulence
The recently developed Wigner functional theory is used to formulate an
evolution equation for arbitrary multi-photon states, propagating through a
turbulent atmosphere under arbitrary conditions. The resulting evolution
equation, which is obtained from an infinitesimal propagation approach, is in
the form of a Fokker-Planck equation for the Wigner functional of the state and
therefore incorporates functional derivatives. We show consistency with
previously obtained solutions from different approaches and consider possible
ways to find additional solutions for this equation.Comment: 22 pages, no figures, to appear in J. Phys.
Non-Markovian evolution of photonic quantum states in atmospheric turbulence
The evolution of the spatial degrees of freedom of a photon propagating
through atmospheric turbulence is treated as a non-Markovian process. Here, we
derive and solve the evolution equation for this process. The turbulent medium
is modeled by a sequence of multiple phase screens for general turbulence
conditions. The non-Markovian perspective leads to a second-order differential
equation with respect to the propagation distance. The solution for this
differential equation is obtained with the aid of a perturbative analysis,
assuming the turbulence is relatively weak. We also provide another solution
for more general turbulence strength, but where we introduced a simplification
to the differential equation.Comment: 12 pages, no figure
Optical vortex trajectories in an astigmatic and elliptical Gaussian beam
An optical vortex, produced at one point in an optical beam, would propagate
through an optical system to another point where the vortex can be used for
some purpose. However, asymmetrical optical elements in such a system can cause
astigmatism or at least distroy the rotational symmetry of the beam, which may
affect the propagation of the vortex in an undesirable way. While an optical
vortex in a rotationally symmetric, stigmatic Gaussian beam retains its initial
morphology for as far as it propagates, the morphology of an optical vortex in
an asymmetric or astigmatic Gaussian beam changes. The vortex can even be
replaced by another with the opposite topological charge. We consider the
behavior of single noncanonical vortices propagating in Gaussian beams that are
asymmetric and/or astigmatic. General expressions for the vortex trajectories
are provided. The locations of the flip planes and the evolution of the
anisotropy of the vortex are considered for different non-ideal situations.Comment: 8 pages, 4 figure
Infinitesimal propagation equation for decoherence of an OAM entangled biphoton in atmospheric turbulence
We derive a first order differential equation for the decoherence of an
orbital angular momentum entangled biphoton state propagating through a
turbulent atmosphere. The derivation is based on the distortion that orbital
angular momentum states experience due to propagation through a thin sheet of
turbulent atmosphere. This distortion is treated as an infinitesimal
transformation leading to a first order differential equation, which we call an
infinitesimal propagation equation. The equation is applied to a simple qubit
case to show how the entanglement decays.Comment: 12 pages, 3 figures, expanded version of arXiv:1009.1956. Minor
corrections to improve clarit
Infinitesimal propagation equation for atmospheric decoherence with multiphoton correlations
Previously a set of coupled first order differential equations were derived
for the decoherence of a pair of spatial mode entangled photons, propagating
along different paths through turbulence. Here we extend this analysis to the
situation where both photons travel along the same path, which introduces the
effect of multiple photon correlations. The resulting equation now contains
additional terms that take these multiphoton correlations into account. At the
same time, we provide a more thorough formulation of the quantized field,
starting from a Lorentz invariant formulation, which is then explicitly broken
by the choice of a particular propagation direction. The effect of the latter
improvement in the quantization on the form of the final equation is minimal.Comment: 10 pages, 1 Figures, extension of work done in arXiv:1102.5166v
Lindblad equation for the decay of entanglement due to atmospheric scintillation
The quantum state for the spatial degrees of freedom of photons propagating
through turbulence is analyzed. The turbulent medium is modeled by a single
phase screen for weak scintillation conditions and by multiple phase screens
for general scintillation conditions. In the former case the process is
represented by an operator product expansion, leading to an integral expression
that is consistent with current models. In the latter case the evolution of the
density operator is described by a first order differential equation with
respect to the propagation distance. It is shown that this differential
equation has the form of a Lindblad master equation. Additionally, it is shown
that this differential equation can take on the form of the infinitesimal
propagation equation.Comment: 17 pages, 1 figure. Accepted for publication in J. Phys.
Decoherence of orbital angular momentum entanglement in a turbulent atmosphere
The evolution of an entangled photon state propagating through a turbulent
atmosphere is formulated in terms of a set of coupled first order differential
equations, by using an infinitesimal propagation approach. The orbital angular
momentum (OAM) basis is used to described the density matrix of the state.
Although the analysis is done in the paraxial limit for a monochromatic optical
field, the formalism is comprehensive in the sense that it does not require any
assumptions about the strength of the turbulence and it can incorporate any
spectral model for the turbulence. As a comparative example the case of
entangled qubit OAM biphoton states is considered.Comment: 4 pages, 1 figure, a few minor change
Quantifying entanglement of parametric down-converted states in all degrees of freedom
The amount of entanglement that exists in a parametric down-converted state
is investigated in terms of all the degrees of freedom of the state. We
quantify the amount of entanglement by the Schmidt number of the state,
represented as a pure bipartite state by tagging the down-converted photons in
terms of orthogonal states of polarization with the aid of type II
phase-matching. To facilitate our calculations, we use a Wigner functional
approach, which allows the incorporation of the full infinite dimensional
spatiotemporal degrees of freedom. A quantitative example with reasonably
achievable experimental conditions is considered to demonstrate that extremely
large Schmidt numbers are achievable.Comment: 6 pages, 2 figure
Combining spatio-temporal and particle-number degrees of freedom
Quadrature bases that incorporate spatio-temporal degrees of freedom are
derived as eigenstates of momentum dependent quadrature operators. The
resulting bases are shown to be orthogonal for both the particle-number and
spatio-temporal degrees of freedom. Using functional integration, we also
demonstrate the completeness of these quadrature bases.Comment: 14 pages, no figures, accepted versio
Optical orbital angular momentum under strong scintillation
The evolution of classical optical fields propagating through atmospheric
turbulence is investigated under arbitrary conditions. We use the single-phase
screen (SPS) method and the infinitesimal propagation equation (IPE), a
multi-phase screen (MPS) method, to compute the optical power fractions
retained in an input Laguerre-Gauss (LG) mode or transferred to higher order LG
modes. Although they show the same trend while the scintillation is weak, the
IPE and SPS predictions deviate when the strength of scintillation passes a
certain threshold. These predictions are compared with numerical simulations of
optical fields propagating through turbulence. The simulations are performed
using an MPS model, based on the Kolmogorov theory of turbulence, for different
turbulence conditions to allow comparison in both weak and strong
scintillation. The numerical results agree well with the IPE results in all
conditions, but deviate from the SPS results for strong scintillation.Comment: 9 pages, 3 figure
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