High-order synthetic dimensions in waveguide photonic lattices
Parallelizing high-dimensional random walks

Date:
July 6, 2020
Source:
Forschungsverbund Berlin
Summary:
Scientists have recently shown that a multitude of high-dimensional
synthetic lattices naturally emerge in (abstract) photon-number
space when a multiport photonic lattice is excited by N
indistinguishable photons.



FULL STORY ==========================================================================
In physics, a very intuitive way of describing the evolution of a
system proceeds via the specification of functions of the spatiotemporal coordinates.

Yet, there often exist other degrees of freedom in terms of which the
physical entities pertaining to a variety of structures can be seen to
evolve and that are not amenable to a description via spatial coordinates.


==========================================================================
Yet, there often exist other degrees of freedom in terms of which the
physical entities pertaining to a variety of structures can be seen to
evolve and that are not amenable to a description via spatial coordinates.

This is precisely the idea of synthetic dimensions: coexisting frameworks
in which a wavefunction, defined in specific degrees of freedom, takes
another form that "lives" in a domain with much higher dimensions than
what the structures' (apparent) geometry would suggest. This approach
is rather appealing as it can be used to access and probe dimensions
beyond our 3- dimensional world, e.g. 5-dimensional or 8-dimensional, etc.

In our recent work we have shown that a multitude of high-dimensional
synthetic lattices naturally emerge in (abstract) photon-number space
when a multiport photonic lattice is excited by N indistinguishable
photons. More precisely, the Fock-representation of N-photon states
in systems composed of M evanescently coupled single-mode waveguides
yields to a new layer of abstraction, where the associated states can
be visualized as the energy levels of a synthetic atom.

In full analogy with ordinary atoms, such synthetic atoms feature allowed
and disallowed transitions between its energy levels.

These concepts have far-reaching implications as they open a route to the simultaneous realization of, in principle, an infinite number of lattices
and graphs with different numbers of nodes and many dimensions. This possibility is rather appealing for realizing parallel quantum random
walks where the corresponding walkers can perform different numbers
of steps on different, planar and nonplanar, multidimensional graphs
that depend on the number of photons involved in each process. These
quantum walks can be implemented, for instance, by exciting a simple four-waveguide system with a standard quantum light source comprising
infinite coherent superpositions of states, e.g. a coherent state
|a. Similarly, the symmetric excitation of a two-waveguide system with identical photons, when properly viewed in abstract space, feature the phenomena of discrete diffraction and Bloch oscillations.


========================================================================== Story Source: Materials provided by Forschungsverbund_Berlin. Note:
Content may be edited for style and length.


========================================================================== Journal Reference:
1. Konrad Tschernig, Roberto de J. Leo'n-Montiel, Armando Pe'rez-Leija,
Kurt
Busch. Multiphoton synthetic lattices in multiport waveguide arrays:
synthetic atoms and Fock graphs. Photonics Research, 2020; 8 (7):
1161 DOI: 10.1364/PRJ.382831 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/07/200706113920.htm

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