A planar array of three one-dimensional elastic waveguides mutually coupled periodically along their length and driven externally is shown theoretically and numerically to support nonseparable superpositions of states. These states are the product of Bloch waves describing the elastic displacement along the waveguides and spatial modes representing the displacement across the array of waveguides. For a system composed of finite length waveguides, the frequency, relative amplitude, and phase of the external drivers can be employed to selectively excite specific groups of discrete product modes. The periodicity of the coupling is used to fold bands enabling superpositions of states that span the complete Hilbert space of product states. We show that we can realize a transformation from one type of nonseparable superposition to another one that is analogous to a nontrivial quantum gate. This transformation is also interpreted as the complex conjugation operator in the space of the complex amplitudes of individual waveguides.

中文翻译：

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在周期耦合的一维波导阵列中导航不可分弹性态的希尔伯特空间

从理论上和数值上示出了三个一维弹性波导的平面阵列，该平面阵列沿其长度周期性地相互耦合并且被外部驱动以支持状态的不可分离的叠加。这些状态是Bloch波的产物，Bloch波描述了沿波导的弹性位移，而空间模则代表了跨波导阵列的位移。对于由有限长度波导组成的系统，可以使用外部驱动器的频率，相对幅度和相位来有选择地激发离散产品模式的特定组。耦合的周期性用于折叠带，从而实现跨越乘积状态的完整希尔伯特空间的状态的叠加。我们证明了我们可以实现从一种不可分离的叠加形式到另一种类似于非平凡量子门的转变。在单个波导的复振幅的空间中，这种变换也被解释为复共轭算子。