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Photonic and Phononic Properties of Engineered Nanostructures

Experimental demonstration of pseudospin behavior and classical entanglement in a phononic structure (Conference Presentation)

Pierre Alix Deymier, Lázaro Calderín, Arif Hasan, Trevor D. Lata, Pierre Lucas, Keith Runge

Published Mar 10, 2020• 0 citations
Publisher

Abstract

We present experimental and theoretical demonstrations of quantum-like behavior in phononic structures. This demonstration extends the notion of classical “entanglement” or classical “nonseparability” to the emerging field of phononics, opens the door for acoustic analogues to true quantum system in quantum information processing, since the preparation and control of entangled superposition of states is an essential ingredient for harnessing the second quantum revolution.

DOI
10.1117/12.2554413

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We present experimental and theoretical demonstrations of quantum-like behavior in phononic structures. This demonstration extends the notion of classical “entanglement” or classical “nonseparability” to the emerging field of phononics, opens the door for acoustic analogues to true quantum system in quantum information processing, since the preparation and control of entangled superposition of states is an essential ingredient for harnessing the second quantum revolution.
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The creation of multilevel quantum states, qudits, has revolutionized concepts for quantum computing. Classical systems that capture behavior analogous to quantum systems have been demonstrated. In this spirit, we consider a three-level classical analogue of the qudit composed of coupled acoustic waveguides. Here, we demonstrate both the experimental realization of a three-level classical analogue of the qudit and the creation and tuning of nonseparable superpositions of two of these analogues, which are classically “entangled.” Measurements of velocities and transmission inform our assignment of these nonseparable states.
We develop quantum acoustics as an independent quantum discipline. The elementary bosonic quantum is the phonon, obtained by canonical quantization of the elastic displacement field of a medium. The central replacement is c → cs, ε0 → ρ0, μ0 → 1/K, ℏ → ℏ, while the Planck constant is not replaced. Phonons obey canonical commutation relations, Bose–Einstein statistics with vanishing chemical potential, and energy quantization E = ℏω. The optical–acoustic dictionary is exact at the level of canonical quantization, mode algebra, Fock, coherent, squeezed, thermal and entangled states, and at the level of linear interference in the long-wavelength, single-branch, dissipationless limit. Multi-branch, dispersive, dissipative and finite-lifetime effects are handled by the generalized dictionary stated in Chapter 56. Quantum acoustics contains a macroscopic quantum branch, but it is not identical to macro- scopic quantum mechanics. The manuscript covers classical elasticity, variational principles, canonical quantization, phonon field algebra, propagators, Green functions, wave–particle duality, Bose–Einstein statistics, blackbody radiation, Debye heat capacity, acoustic quantum constants, acoustic Bekenstein–Hawking entropy, phonon thermodynamics, phonon BEC, phonon lasers, superfluidity, Fock, coherent, squeezed, thermal, entangled and non-classical states, beam splitters, Mach–Zehnder interferometers, Fabry–Perot cavities, Hong–Ou–Mandel interference, second-order coherence, phonon qubits, single- and two-qubit gates, quantum algorithms, quantum error correction and surface-code thresholds, quantum computing architecture, quantum networks and repeaters, quantum simulation, quantum sensing, topological phononic crystals, the SSH phonon model, two-dimensional topological phononic insulators, three-dimensional phonon Weyl semimetals, non-Hermitian acoustics and the phonon skin effect, non-Bloch band theory, topological defect classification, acoustic metrics, acoustic horizons, acoustic Hawking radiation, acoustic black- hole entropy and the information paradox, acoustic cosmology, phonon–graviton mixing, gravitational-wave coupling, the phonon analogy of dark matter and dark energy, surface acoustic wave resonators, optomechanical systems, superconducting qubit–phonon hybrid systems, Bose–Einstein condensates, phononic crystals, acoustic metamaterials, gravitational-wave detectors, the complete optical–acoustic dictionary, the generalized dictionary for multi-branch, dispersive, dissipative and finite-lifetime phonons, and strong-field QED vacuum and media as an analogue of multi-refringent, dispersive and dissipative media. Acoustic Hawking radiation has been observed in Bose–Einstein condensates by Steinhauer (2016). All definitions, derivations, mathematical details, experimental proposals and comparison factors are presented with explicit assumptions and complete proofs.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.