Vector-light interference with a multimode N00N state

Multimode N00N states stand out as an excellent platform to explore higher-order quantum interference phenomena, with benefits in quantum-enhanced estimation of multiple parameters beyond classical limits. Here, we investigate higher-order polarization properties, geometric phase features, and associated wave-particle duality structures in double-slit vector-light interference involving a multimode N00N state. We particularly show that the interferometric polarization modulation and the accompanied geometric phase accumulation are <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>N</a:mi> </a:math> times faster for the multimode N00N state than for one-photon or classical light. We also formulate <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>N</b:mi> <b:mi>th</b:mi> </b:mrow> </b:math> -order extensions of the three wave-particle duality relations established for a single vector-light photon: the two via distinguishabilities and visibilities [A. Norrman , ], and the one via the geometric phase and which-path information ratio [E. Pillinen , ]. Our work contributes to the broader fundamental understanding of how vectorial quantum light acts in higher-order interference, with possible opportunities in precision metrology outside scalar-field regimes.