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Geometric phase of entanglement for non-adiabatic, two-photon optical vortex evolution in a dielectric trap
DeWolf-Moura, Tyjal
DeWolf-Moura, Tyjal
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2022
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Abstract
Despite the attention it has commanded, the resources it has garnered, and the promising theoretical
and technological milestones it has passed, quantum computing is in its infancy. A wide range of
paradigms are currently being explored, motivated by the need to strike a balance between controllable
interactions within the system and isolation from interactions with the environment. Within each of these,
strategies that exploit geometric holonomies to store and process information seem especially promising,
because they offer a measure of protection against environmental degradation. This tactic has yet to
receive much attention for optical quantum computing however. In fact, there is a dearth of information
associated with the geometric phase accumulation of entangled photon states|a linchpin for carrying out
universal holonomic quantum logic.
A theoretical investigation has therefore been carried out that elucidates the relationship between
photon entanglement and geometric phase. While intended to be helpful to quantum computing, the focus
is on basic science. A particularly simple setting is chosen in which photons propagate along an axis while
being laterally confined by a harmonic trap. Treating the propagation axis as time, linear combinations of
two-dimensional modes are used to construct optical vortices that orbit about the trap center. Two-photon
entangled states are created in terms of these, and the geometric phase is calculated over a single, shared
orbital period. This setting makes it possible to scrutinize the relationship between the degree of
entanglement and the geometric phase accumulated.
Attention is focused on the Geometric Phase of Entanglement (GPE), defined as the geometric phase
above and beyond that accumulated by each single-photon state independently. General requirements were
identified for which a GPE is supported. A set of especially tractable problems were then explored to
show how the GPE is influenced by vortex tilt, orbit radius, and degree of entanglement.
The insights obtained comprise a foundation for subsequent experimental investigations. Towards that
end, particular attention was also given to explain how the requisite two-photon states can be produced
and to identify two physical settings for which the harmonic trap can be realized: a sequence of cylindrical
lenses; and multi-mode dielectric fibers.
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