Optical Simulation of Neutrino Oscillations in Binary Waveguide Arrays

We theoretically propose and investigate an optical analogue of neutrino oscillations in a pair of vertically displaced binary waveguide arrays with longitudinally modulated effective refractive index. Optical propagation is modeled through coupled-mode equations, which in the continuous limit converge to two coupled Dirac equations for fermionic particles with different mass states, analogously to neutrinos. In addition to simulating neutrino oscillation in the noninteracting regime, our optical setting enables us to explore neutrino interactions in extreme regimes that are expected to play an important role in massive supernova stars. In particular, we predict the quenching of neutrino oscillations and the existence of topological defects, i.e., neutrino solitons, which in our photonic simulator should be observable as excitation of optical gap solitons propagating along the binary arrays at high excitation intensities.

Figure 1

Schematics of two vertically displaced BWAs for the simulation of neutrino oscillation. (a) Three-dimensional sketch of the structure. Neighbouring silica waveguides are offset, while every waveguide shows a longitudinally modulated effective index. Light is trapped by every waveguide in the transverse $x\text{−}y$ directions and propagates in the longitudinal $z$ direction. (b) Transverse section of the structure. Optical amplitudes of the upper ($A_n$) and lower ($B_n$) array are coupled to nearest neighbours. Horizontal and vertical coupling constants between nearest neighbour waveguides are denoted by ${\kappa }_H,{\kappa }_V$, respectively.

Figure 2

(a) Linear dispersion of the structure sketched in Fig. 1, supporting the linear modes $M_1,M_2,M_3,M_4$. (b) Linear dispersion of instantaneous mass eigenstates of neutrinos: energy $E$ as a function of momentum $p$. Full (dashed) lines represent the dispersion of neutrino (antineutrino) eigenstates, while blue (red) lines represent the dispersion of eigenstates with energies $E_{+}$ ($E_{-}$). Parameter values are $\kappa =0.5$, $\epsilon =0.3$, $m_a=0.5$, $m_b=0.25$.

Figure 3

Probabilities $P(A)$ [panel(a)] and $P(B)$ [panel (b)] of measuring the neutrino with flavors $A$ and $B$, respectively, as functions of the propagation length for several nonlinear coefficients $\gamma =0,0.01,0.1$, corresponding to the blue, green, and red curves. The other parameter values are $\kappa =1$, $\epsilon =0.001$, $m_a=0.01$, $m_b=0.012$.

Figure 4

Homogeneous nonlinear mode families not undergoing oscillation. Full (dashed) curves show the modulus of the spinor amplitudes $|A|$ ($|B|$) as functions of the energy $E$ (propagation constant in our optical analogy). Parameter values are $\kappa =1$, $\epsilon =0.001$, $m_a=0.01$, $m_b=0.012$, $\gamma =1$.

Figure 5

Coupled neutrino-antineutrino soliton with null energy $E=0$ (propagation constant in our optical analogy). Blue (red) markers depict the amplitude of odd (even) waveguide sites, related to the spinor component $A_2$ ($A_1$) in the continuous limit. In our calculations we have used the parameters $\kappa =1$, $\epsilon =0.01$, $m_a=0.1$, $m_b=0.12$, $\gamma =1$.