H. S. Eisenberg

Spatial optical solitons in waveguide arrays

We overview theoretical and experimental results on spatial optical solitons excited in arrays of nonlinear waveguides. First, we briefly summarize the basic properties of the discrete nonlinear Schrodinger (NLS) equation frequently employed to study spatially localized modes in arrays, the so-called discrete solitons. Then, we introduce an improved analytical model that describes a periodic structure of thin-film nonlinear waveguides embedded into an otherwise linear dielectric medium. Such a model of waveguide arrays goes beyond the discrete NLS equation and allows studying many new features of the nonlinear dynamics in arrays, including the complete bandgap spectrum, modulational instability of extended modes, different types of gap solitons, the mode oscillatory instability, the instability-induced soliton dynamics, etc. Additionally, we summarize the recent experimental results on the generation and steering of spatial solitons and diffraction management in waveguide arrays. We also demonstrate that many effects associated with the dynamics of discrete gap solitons can be observed in a binary waveguide array. Finally, we discuss the important concept of two-dimensional (2-D) networks of nonlinear waveguides, not yet verified experimentally, which provides a roadmap for the future developments of this field. In particular, 2-D networks of nonlinear waveguides may allow a possibility of realizing useful functional operations with discrete solitons such as blocking, routing, and time gating.

Nonlinearly induced escape from a defect state in waveguide arrays

We experimentally investigate the linear and nonlinear optical properties of a nonuniform waveguide array. By reducing the width of a single waveguide, we decrease its effective index and induce waveguiding along the defect. Due to the positive nonlinearity, the index difference is reduced for increasing power levels with the result that the field escapes. Waveguiding is suppressed by the action of the nonlinearity.

Quantum entanglement of a large number of photons

A bipartite multiphoton entangled state is created through stimulated parametric down-conversion of strong laser pulses in a nonlinear crystal. It is shown how detectors that do not resolve the photon number can be used to analyze such multiphoton states. Entanglement of up to 12 photons is detected using both the positivity of the partially-transposed density matrix and a newly derived criteria. Furthermore, evidence is provided for entanglement of up to 100 photons. The multiparticle quantum state is such that even in the case of an overall photon collection and detection efficiency as low as a few percent, entanglement remains and can be detected.

Optical discrete solitons in waveguide arrays. 2. Dynamic properties

An AlGaAs waveguide array below the half-bandgap is used to investigate experimentally basic dynamic features of discrete systems. In particular, nonlinear locking of a discrete soliton to its input waveguide was observed for certain input conditions. We also investigated the soliton dynamics as a function of the position of the initial excitation and found that small shifts from the centers of symmetries of the structure could be greatly enhanced. Both effects depend on the geometry of the array and on the beam size.

Optical discrete solitons in waveguide arrays. I. Soliton formation

We investigate the generation of discrete spatial solitons in arrays of coupled waveguides. Light was launched into the center of the array, and different beam sizes and array geometries were tested. At low power, the propagating field spreads as it couples to more waveguides. When the intensity is increased, localization is observed around the input waveguides, leading to the formation of a discrete soliton. For wide input beams, exciting a few waveguides, soliton splitting, which is due to instability induced by multiphoton absorption, is observed. All of these effects are described well by a coupled-mode formalism.

Entanglement Swapping between Photons that have Never Coexisted

The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the nonlocality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spacelike separation, but also to particles with timelike separation. In order to demonstrate these principles, we generated and fully characterized an entangled pair of photons that have never coexisted. Using entanglement swapping between two temporally separated photon pairs, we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed two-photon state demonstrates that entanglement can be shared between timelike separated quantum systems.

Interactions of discrete solitons with structural defects.

We investigated the interaction of discrete solitons with defect states fabricated in arrays of coupled waveguides. We achieved attractive and repulsive defects by decreasing and increasing, respectively, the spacing of one pair of waveguides in an otherwise uniform array. Linear and nonlinear propagation in the same samples show distinctly different properties. The role of the Peierls-Nabarro potential in the interaction of the soliton with the defect is discussed.

Multiphoton Path Entanglement by Nonlocal Bunching

Multiphoton path entanglement is created without applying postselection, by manipulating the state of stimulated parametric down-conversion. A specific measurement on one of the two output spatial modes leads to the nonlocal bunching of the photons of the other mode, forming the desired multiphoton path entangled state. We present experimental results for the case of a heralded two-photon path entangled state and show how to extend this scheme to higher photon numbers.

Nonlinear interferometry via fock-state projection

We use a photon-number-resolving detector to monitor the photon-number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical nonlinearities. Following a scheme by Bentley and Boyd [Opt. Express 12, 5735 (2004).10.1364/OPEX.12.005735], we explore this effect to demonstrate interference patterns a factor of 5 smaller than the Rayleigh limit.

Measurements of the dependence of the photon-number distribution on the number of modes in parametric down-conversion

Optical parametric down-conversion (PDC) is a central tool in quantum optics experiments. The number of collected down-converted modes greatly affects the quality of the produced photon state. We use Silicon Photomultiplier (SiPM) number-resolving detectors in order to observe the photon-number distribution of a PDC source, and show its dependence on the number of collected modes. Additionally, we show how the stimulated emission of photons and the partition of photons into several modes determine the overall photon number. We present a novel analytical model for the optical crosstalk effect in SiPM detectors, and use it to analyze the results.