Abstract
We experimentally and numerically investigated elastic waves in parallel arrays of elastically coupled one-dimensional acoustic waveguides composed of aluminum rods coupled along their length with epoxy. The elastic waves in each waveguide take the form of superpositions of states in the space of direction of propagation. The direction of propagation degrees of freedom is analogous to the polarization of a quantum spin; hence, these elastic waves behave as pseudospins. The amplitude in the different rods of a coupled array of waveguides (i.e., the spatial mode of the waveguide array) refer to the spatial degrees of freedom. The elastic waves in a parallel array of coupled waveguides are subsequently represented as tensor products of the elastic pseudospin and spatial degrees of freedom. We demonstrate the existence of elastic waves that are nonseparable linear combinations of tensor products states of pseudospin/ spatial degrees of freedom. These elastic waves are analogous to the so-called Bell states of quantum mechanics. The amplitude coefficients of the nonseparable linear combination of states are complex due to the Lorentzian character of the elastic resonances associated with these waves. By tuning through the amplitudes, we are able to navigate both experimentally and numerically a portion of the Bell state Hilbert space.
Highlights
The phenomenon of quantum entanglement [1] has generated great scientific interest and value right from the beginning of quantum mechanics
We have shown an analogy between the propagation of elastic waves on an elastic pseudospin and quantum phenomena [18,23,24,25,26]
By only tuning a single input, the relative excitation amplitudes of chains 1 and 2, we can navigate a sizeable portion of the Hilbert space of nonseparable states
Summary
The phenomenon of quantum entanglement [1] has generated great scientific interest and value right from the beginning of quantum mechanics. Quantum entanglement can be considered as combining two characteristics of quantum system, namely nonlocality and nonseparability. The realization of nonlocality is uniquely the province of quantum phenomena; recently, classical systems able to capture the characteristic of nonseparability [3,4,5,6,7] between different degrees of freedom of the same physical manifestation. In the field of optics, degrees of freedom of photon states that span different Hilbert spaces can be made to interact in a way that leads to local correlations [5,7,8,9,10,11,12,13,14,15,16,17]. Little attention has been paid to the nonseparability of sound waves; yet, remarkable new behaviors of sound, analogous to quantum physics, such as the notions of elastic pseudospin [18,19,20,21,22,23,24,25,26,27] and Zak/Berry phase [28,29,30,31,32,33,34,35,36], are emerging
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