Abstract
We demonstrate theoretically, using multiple-time-scale perturbation theory, the existence of nonseparable superpositions of elastic waves in an externally driven elastic system composed of three one-dimensional elastic wave guides coupled via nonlinear forces. The nonseparable states span a Hilbert space with exponential complexity. The amplitudes appearing in the nonseparable superposition of elastic states are complex quantities dependent on the frequency of the external driver. By tuning these complex amplitudes, we can navigate the state’s Hilbert space. This nonlinear elastic system is analogous to a two-partite two-level quantum system.
Highlights
The notions of superposition of states and entanglement lay at the core of today’s second quantum revolution [1]
We have shown theoretically and experimentally that linear combinations of elastic states taking the form of tensor products of orbital angular momentum (OAM) and spinor amplitudes can form nonseparable states reminiscent of “entangled” Bell states [10]
We have used multiple-time-scale perturbation theory, to investigate the behavior of an externally driven elastic system composed of three coupled mass-spring chains
Summary
The notions of superposition of states and entanglement lay at the core of today’s second quantum revolution [1]. We demonstrated that the amplitude coefficients of the nonseparable superposition of states are complex due to dissipation in the constitutive elastic materials By tuning these complex amplitudes, we have shown that we can experimentally navigate a sizeable portion of the Bell state’s Hilbert space. We show that to first order in perturbation, if we excite two OAM plane wave states in each band, the elastic system can be visualized as a two-partite two-level system bands and two plane wave states in each band, the elastic system can be visualized as a two-partite which can support superpositions of nonlinear modes which span an exponentially complex Hilbert two-level system which can support superpositions of nonlinear modes which span an exponentially space.
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