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arXiv:1001.0986 · Physical Review B

Classical and quantum interference in multiband optical Bloch oscillations

Stefano Longhi

Published Jun 4, 2009• 9 citations
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Abstract

Classical and quantum interference of light propagating in arrays of coupled waveguides and undergoing multiband optical Bloch oscillations (BOs) with negligible Zener tunneling is theoretically investigated. In particular, it is shown that Mach-Zehnder-like interference effects spontaneously arise in multiband BOs owing to beam splitting and subsequent beam recombination occurring in one BO cycle. As a noteworthy example of quantum interference, we discuss the doubling of interference fringes in photon counting rates for a correlated photon pair undergoing two-band BOs, a phenomenon analogous to the manifestation of the de Broglie wavelength of an entangled biphoton state observed in quantum Mach-Zehnder interferometry.

DOI
10.1103/physrevb.79.245108

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Classical and quantum interference of light propagating in arrays of coupled waveguides and undergoing multiband optical Bloch oscillations (BOs) with negligible Zener tunneling is theoretically investigated. In particular, it is shown that Mach-Zehnder-like interference effects spontaneously arise in multiband BOs owing to beam splitting and subsequent beam recombination occurring in one BO cycle. As a noteworthy example of quantum interference, we discuss the doubling of interference fringes in photon counting rates for a correlated photon pair undergoing two-band BOs, a phenomenon analogous to the manifestation of the de Broglie wavelength of an entangled biphoton state observed in quantum Mach-Zehnder interferometry.
Atoms undergoing Bloch oscillations (BOs) in an accelerating optical lattice acquire momentum of two photon recoils per BO. This technique provides a large momentum transfer tool for atom optics, but its full exploitation for atom interferometric sensors requires both experimental and theoretical characterization of associated phases. Each BO involves a Landau-Zener crossing with multiple crossings inducing interference known as Stückelberg interference. We develop a multipath Stückelberg interferometer and investigate atomic phase evolution during BOs, up to 100 photon recoil momentum transfer. We compare to numerically calculated single-particle Schrödinger evolution, demonstrate highly coherent BO sequences, and assess phase stability requirements for BO-enhanced precision interferometry in fundamental physics and sensing applications. Published by the American Physical Society 2024
We report on experiments investigating quantum transport and band interferometry of an atomic Bose-Einstein condensate in an optical lattice with a two-band miniband structure, realized with a Fourier-synthesized optical lattice potential. Bloch-Zener oscillations, the coherent superposition of Bloch oscillations and Landau-Zener tunneling between the two bands, are observed. When the relative phase between paths in different bands is varied, an interference signal is observed, demonstrating the coherence of the dynamics in the miniband system. Measured fringe patterns of this Stückelberg interferometer allow us to interferometrically map out the band structure of the optical lattice over the full Brillouin zone.
Atomic media are important in optics research since they can be conveniently manipulated and controlled due to easy selection of atomic levels, laser fields, and the active adjustment of many system parameters. In this paper, we investigate optical Bloch oscillation, Zener tunneling, and Bloch–Zener oscillation in atomic media both theoretically and numerically. We use two coupling fields to prepare the dynamical optical lattice through interference. To induce a transverse force, we make the frequency difference between the two coupling fields increase linearly along the longitudinal coordinate. These phenomena have potential application for beam splitters and optical interconnects, and are helpful for investigating quantum analogies.
Light trapping in photonic lattices at a linear defect shows interesting nonclassical behavior when probed by maximally path-entangled NNN-photon states (NOON states). In particular, photon coincidences of localized light at the defect oscillate at a spatial frequency that is NNN times faster than the classical beating spatial frequency of the defect modes, resembling the $\ensuremath{\lambda}/N$ oscillations of NOON states encountered in Mach-Zehnder interferometry. Analytical results of quantum interference are presented for an exactly solvable tight-binding waveguide array.
Interference effects of photon pairs propagating through two-dimensional lattices of evanescently coupled waveguides are theoretically analyzed for input states of independent and path-entangled photons. Their correlation unveils characteristic Hong-Ou-Mandel interferences as well as more complex phenomena unique to these structures. Furthermore, purely classical states of light are used to simulate these quantum interferences in intensity correlation experiments. The results suggest that waveguide arrays can be employed as convenient devices for manipulating quantum states of light.