in contrast to previous experiments
that stripped spatial entanglement
prior to coupling.
When both photons are coupled into
a single waveguide, the spatial correlation function at the output is separable
and localization of each photon is
observed. Alternatively, when the two
photons are in the spatially extended
entangled state, they emerge from the
array with their spatial correlation
intact. Neither photon, considered
separately (while tracing over the
other), localizes in the usual sense.
But the pair co-localizes in correlation
space, i.e., the photons always exit
together from the same waveguide
element. It will be interesting to study
the effects of quantum entanglement
in higher-dimensional random settings
where Anderson localization phenomena also occur.
In 1958, Philip Anderson suggested that a quantum mechanical wave function
may undergo localization in a disordered
lattice as a result of interference between
different paths arising from multiple
scattering. While direct evidence of this
localization remains elusive in solid
state physics, its optical analogue may
be realized in random arrays of coupled
waveguides. 1, 2 The propagation of quantum light in such photonic environments
has been theoretically investigated. 3, 4
One of the most interesting predictions
of these studies is the possibility of a
new type of localization, which occurs
when correlated two-photon states—such
as Einstein-Podolsky-Rosen entangled
photon pairs—are launched in a disordered lattice. We recently demonstrated
two-photon Anderson co-localization in
a waveguide array. 5
The array consists of identical,
evanescently coupled waveguides,
laser-written in silica glass. We varied
the inter-waveguide spacing to introduce disorder in the coupling coefficients. Optical spontaneous parametric
downconversion was used to produce
photon pairs which were imaged onto
the waveguide array. Two different
two-photon quantum states were considered: 1) a Fock state Z2L injected into
a single waveguide; and 2) a spatially
extended entangled state in which the
photon pair is coupled together into
any one of these waveguides. The two
photons are separated at the output
and detected in coincidence to produce
a correlation map. It was essential to
maintain the Einstein-Podolsky-Rosen
spatial entanglement when launching
the two photons onto the chip. This is
Entangled photon pairs are generated at a nonlinear crystal (NLC) and imaged onto the
input face of the waveguide array. Using a beam splitter (BS), two copies of the output
face of the array are imaged onto the planes of two scanning multimode fibers connected
to single photon counting modules (SPCM) leading to a coincidence circuit. (Inset) The
measured photon coincidence maps as functions of the waveguide positions x1 and x2 for
(a) single-waveguide input and (b) multi-waveguide input with photon pairs in a spatially
extended entangled correlated state.
A.F. Abouraddy, D.N.
Christodoulides, L.A. Martin
and B.E.A. Saleh
CREOL University of Central
Florida, Orlando, Fla., U.S.A.
G. Di Giuseppe
CREOL and University of
F. Dreisow, R. Keil, S. Nolte, A.
Perez-Leija and A. Szameit
Friedrich Schiller University,
1. T. Schwartz et al. Nature 446,
2. Y. Lahini et al. Phys. Rev. Lett.
100, 013906 (2008).
3. Y. Lahini et al. Phys. Rev. Lett.
105, 163905 (2010).
4. A.F. Abouraddy et al. Phys. Rev.
A 86, 040302(R) (2012).
5. G. Di Giuseppe et al. Phys. Rev.
Lett. 110, 150503 (2013).
Observing Anderson Co-Localization
of Entangled Photon Pairs
Waveguide array NLC BS
(a) Separable state (b) Entangled state