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SUMMARY:**WITHDRAWN** Observing the effects of Time Ordering in Single Pho
ton Frequency Conversion
DTSTART;VALUE=DATE-TIME:20150617T204500Z
DTEND;VALUE=DATE-TIME:20150617T210000Z
DTSTAMP;VALUE=DATE-TIME:20200222T004006Z
UID:indico-contribution-841507@indico.cern.ch
DESCRIPTION:Speakers: Nicolas Quesada (University of Toronto)\nFrequency c
onversion (FC) is one of the most common nonlinear processes used in quant
um optics. \nThis process has the property that the Hamiltonian that gover
ns it does not commute with itself at different times\, and hence time ord
ering becomes an important aspect in the description of its dynamics. \nRe
cently\, it has been shown that the Magnus expansion provides an appropria
te description of the effects of time ordering in several nonlinear quantu
m optical processes[1-2]. \nOne of the most important results derived from
the use of the Magnus expansion in nonlinear optics is that the joint con
version amplitude (JCA) that governs the conversion processes in FC become
s a nonlinear function of the classical pump electric field because of tim
e ordering effects. \nIn the low pump intensity regime\, and assuming that
the joint conversion amplitude can only upconvert one Schmidt frequency m
ode\, one can show that the probability of upconversion is $\\sin ^2\\vare
psilon$ where $\\varepsilon$ is linearly related to the peak electric fiel
d of the pump. As the intensity is increased time ordering corrections cre
ate more Schmidt frequency modes\, with a dependence on the electric field
of the pump is nonlinear.\nWith these observations in mind\, we predict t
hat efficiencies of maximum $80\\%$ can be achieved by using intensities t
hat make $\\sin^2 \\varepsilon \\approx 1$. The inability to achieve $100\
\%$ conversion is due to two effects:\n\n\n1. None of the Schmidt function
s of the full JCA\, including time ordering\, will perfectly match the pro
file of the initial photon that is matched to the low pump intensity JCA.\
n\n\n2. The parameter $\\varepsilon$ that determines the ``rotation angle'
' of the single photon is\, because of ordering effects\, a nonlinear fun
ction of the electric field.\n\n\nWe also find that these nonlinearities c
an also help achieve unit efficiencies by harnessing more than one of Schm
idt mode of the high pump intensity JCA. \nWith this observations in mind
we propose an experiment where these nonlinear effects can be observed and
used to achieve near unit efficiency FC.\n\n\n[1] N. Quesada and J.E. Sip
e\, Phys. Rev. A **90**\, 063840 (2014).\n[2] N. Quesada and J.E. Sipe\, t
o appear in Phys. Rev. Lett. (2015) (arXiv:1410.0012 ).\n\nhttps://indico.
cern.ch/event/355942/contributions/841507/
LOCATION:University of Alberta CCIS L2-200
URL:https://indico.cern.ch/event/355942/contributions/841507/
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