Direct observation of Landau-Zener tunneling in a curved optical waveguide coupler

An electromagnetic realization of Landau-Zener (LZ) tunneling is experimentally demonstrated in femtosecond-laser written waveguide couplers with a cubically bent axis. Quantitative measurements of light evolution inside the coupler, based on fluorescence imaging, enable to trace the detailed dynamics of the LZ process. The experimental results are in good agreement with the theoretical LZ model for linear crossing of energy levels with constant coupling of finite duration.

Figure 1

(Color online) (a) Schematic of a cubically curved directional coupler for the observation of LZ dynamics. (b) Fluorescence measurement of curved directional coupler with spacing $d=17\mu \text{m}$ and cubic profile $A=300\mu \text{m}$, $L_1=31.25\text{mm}$, (the arrow indicates the propagation direction).

Figure 2

(Color online) Schematic setups for (a) waveguide manufacturing and (b) fluorescence measurements.

Figure 3

(Color online) Experimental observation of the Landau-Zener tunneling process. The separation of the waveguides is $d=17\mu \text{m}$ resulting in a coupling rate ${\Omega }_0=0.063{\text{mm}}^{-1}$, the full bending amplitude is $A=300\mu \text{m}$ and the bending length is $L_1=31.25\text{mm}$. (a) Digitally straightened fluorescence image, (b) detuning ${\eta }^2{z}^{\prime }/{\Omega }_0$ of the waveguides due to the curvature normalized to the coupling constant ${\Omega }_0$ and (c) measured (solid) and theoretical (dashed) intensities ${\left|a_1\left(z^{\prime }\right)\right|}^2$ and ${\left|a_2\left(z^{\prime }\right)\right|}^2$ in the two waveguides plotted vs propagation distance in the reference frame $z^{\prime }$. State $|1⟩$ was excited initially.

Figure 4

(Color online) Same as Fig. 3 but for a full bending amplitude of $A=500\mu \text{m}$ resulting in incomplete power transfer to an average level of $\approx 50\%$.