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We present both the theoretical framework and experimental implementation of permutation gates using logical phi-bits, classical acoustic analogs of qubits. Logical phi-bits are nonlinear acoustic modes supported by externally driven acoustic metamaterials. Using a tensor product of modified Bloch sphere representations, we realize all possible two logical phi-bit permutations including SWAP and C-NOT. We also illustrate the scalability of a permutation for any number of logical phi-bits. Experimental demonstrations of these permutations require a single physical action on the driving conditions of the acoustic metamaterial. All logical phi-bits exist in the same physical system. We compare the phi-bit system with its quantum counterpart using Qiskit simulations, which illustrate the complexity of realizing these permutations in a quantum context. 

Abstract Cryptography is crucial in protecting sensitive information and ensuring secure transactions in a time when data security and privacy are major concerns. Traditional cryptography techniques, which depend on mathematical algorithms and secret keys, have historically protected against data breaches and illegal access. With the advent of quantum computers, traditional cryptography techniques are at risk. In this work, we present a cryptography idea using logical phi-bits, which are classical analogues of quantum bits (qubits) and are supported by driven acoustic metamaterials. The state of phi-bits displays superpositions similar to quantum bits, with complex amplitudes and phases. We present a representation of the state vector of single and multi-phi-bit systems. The state vector of multiple phi-bits system lies in a complex exponentially scaling Hilbert space and is used to encode information or messages. By changing the driving conditions of the metamaterial, the information can be encrypted with exceptional security and efficiency. We illustrate experimentally the practicality and effectiveness of encoding and encryption of a message using a 5 phi-bits system and emphasize the scalability of this approach to anNphi-bits system with the same processing time. 

Pyramidal antireflective structures were produced by hot embossing single- and double-sides of an amorphous GeSe₄optical element. The optical performances were measured across the wavelength range from 2 µm to 15 µm. The transmittance at normal incident angle was increased up to 75.6% and 79.8% for single and double-side embossing respectively. The experimental results were in close agreement with simulation performed using the rigorous coupled-wave analysis (RCWA). Theoretical models also predicted well the transmittance changes as a function of incident angle from 0 ° to 50 ° at a fixed laser wavelength of 5.1 µm. A Fabry-Perot interferometer consisting of two single surface embossed samples is proposed.