Quantum physics inspired optical effects in tight-binding lattices: Phase-controlled photonic transport

Abstract

A theoretical proposal for photonic transport in an array of waveguides is presented. By coupling phase-displaced inputs into adjacent waveguides, and calculating the expectation value of the position space operator, we demonstrate directed motion in this system. The one way photonic transport arises from interferences due to the phase differences in the inputs to the waveguides.2

A photonic crystal realization of a phase driven two-level atom

“…It is also known that an infinite lattice, considering ω 0 = 0 with a twowaveguides input with a phase difference between them, i.e. E(t = 0) = E 0 (0) + e iφ E 1 (0) with φ = 0 and E 0,1 (0) ∈ R, shows a ratchet-like behavior controlled by the phase φ [30]. In our idea of classical simulation of a radiation-matter interaction system, it may be possible to argue that the case ω 0 = 0 corresponds to emulating a hot trapped ion coupled to just the phase of a bosonic mode; such an argument has been used in the quantum Rabi problem [26].…”

“…Such an initial state produces a break in the symmetry of the breather mode of a single input for φ = 0 [30]. This breaking in the propagation symmetry is accompanied by a variable center of mass of the beam,…”

Disorder effects in tunable waveguide arrays with parity-symmetric tunneling

“…Bromberg and co-workers have investigated quantum and classical correlations when two photons are coupled to either the same waveguide or to adjacent waveguides [3], and Lahini and co-workers [12] have studied a similar problem in disordered lattices. More recently, coupling of two phase-displaced wavepackets into adjacent waveguides has been used to propose a form of the quantum ratchet [8]. Motivated by these works, we next explore the effects of disorder and α-dependent clean-system spectrum on an input wave packet that is localized to two waveguides with a relative phase θ between them, |ψ θ (0) = |p + e iθ |q / √ 2, with 1 ≤ p, q ≤ N .…”

“…This interest is a result of being able to observe quantum phenomena on a length-scale of a few millimeters, the typical length of a waveguide, as the discrete Schrödinger equation for a particle on a lattice is identical to the longitudinal component of the Helmholtz equation for the electric field in an array of waveguides [9,10]. Non-classical states of light have also been used to study quantum properties of light propagating through waveguide arrays [2,3,8,11]. In particular, the quantum correlations of two non-interacting indistinguishable particles propagating simultaneously have shown the effect of their initial separation on propagation of the particles in clean [12] and disordered [13] systems.…”

“…In recent years, arrays of evanescently coupled waveguides have attracted considerable interest as versatile structures suitable for the study of quantum and condensed matter phenomena such as Bloch oscillations, Zener tunneling [5], Dirac zitterbewegung [6], quantum random walks [7], and quantum ratchets [8]. This interest is a result of being able to observe quantum phenomena on a length-scale of a few millimeters, the typical length of a waveguide, as the discrete Schrödinger equation for a particle on a lattice is identical to the longitudinal component of the Helmholtz equation for the electric field in an array of waveguides [9,10].…”