Topology shared between classical metamaterials and interacting superconductors

• URL: http://arxiv.org/abs/2207.10045v1
• Date: Wed, 20 Jul 2022 17:18:33 GMT
• Title: Topology shared between classical metamaterials and interacting superconductors
• Authors: Po-Wei Lo, Chao-Ming Jian, and Michael J Lawler
• Abstract summary: Supersymmetry has been studied at a linear level between normal modes of metamaterials described by rigidity matrices and non-interacting quantum Hamiltonians. Recently, insight into the behavior of nonlinear mechanical systems was found by defining topological indices via the Poincar'e-Hopf index. We establish a connection between isostatic mechanical metamaterials and supersymmetric quantum systems, such as electrons coupled to phonons in metals and superconductors.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Supersymmetry has been studied at a linear level between normal modes of metamaterials described by rigidity matrices and non-interacting quantum Hamiltonians. The connection between classical and quantum was made through the matrices involved in each problem. Recently, insight into the behavior of nonlinear mechanical systems was found by defining topological indices via the Poincar\'e-Hopf index. It turns out, because of the mathematical similarity, this topological index shows a way to approach supersymmetric quantum theory from classical mechanics. Using this mathematical similarity, we establish a topological connection between isostatic mechanical metamaterials and supersymmetric quantum systems, such as electrons coupled to phonons in metals and superconductors. Firstly, we define $Q_{net}$ for an isostatic mechanical system that counts the minimum number of zero-energy configurations. Secondly, we write a supersymmetric Hamiltonian that describes a metal or a superconductor interacting with anharmonic phonons. This Hamiltonian has a Witten index, a topological invariant that captures the balance of bosonic and fermionic zero-energy states. We are able to connect these two systems by showing that $Q_{net}=W$ under very general conditions. Our result shows that (1) classical metamaterials can be used to study the topology of interacting quantum systems with aid of supersymmetry, and (2) with fine-tuning between anharmonicity of phonons and couplings among Majorana fermions and phonons, it is possible to realize such a supersymmetric quantum system that shares the same topology as classical mechanical systems.

Related papers

• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Markovian dynamics for a quantum/classical system and quantum trajectories [0.0]
  We develop a general approach to the dynamics of quantum/classical systems. An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative.
  arXiv  Detail & Related papers  (2024-03-24T08:26:54Z)
• Schr\"odinger cat states of a 16-microgram mechanical oscillator [54.35850218188371]
  The superposition principle is one of the most fundamental principles of quantum mechanics. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr"odinger cat states of motion. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states.
  arXiv  Detail & Related papers  (2022-11-01T13:29:44Z)
• Measuring quantum geometric tensor of non-Abelian system in superconducting circuits [21.82634956452952]
  We use a four-qubit quantum system in superconducting circuits to construct a degenerate Hamiltonian with parametric modulation. We reveal its topological feature by extracting the topological invariant, demonstrating an effective protocol for quantum simulation of a non-Abelian system.
  arXiv  Detail & Related papers  (2022-09-26T01:08:39Z)
• Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers [0.0]
  We establish relations between the quantum metric and the topological invariants of generic Dirac Hamiltonians. We show that topological indices are bounded by the quantum volume determined by the quantum metric. This work suggests unexplored topological responses and metrological applications in a broad class of quantum-engineered systems.
  arXiv  Detail & Related papers  (2021-06-01T21:10:48Z)
• Spin Entanglement and Magnetic Competition via Long-range Interactions in Spinor Quantum Optical Lattices [62.997667081978825]
  We study the effects of cavity mediated long range magnetic interactions and optical lattices in ultracold matter. We find that global interactions modify the underlying magnetic character of the system while introducing competition scenarios. These allow new alternatives toward the design of robust mechanisms for quantum information purposes.
  arXiv  Detail & Related papers  (2020-11-16T08:03:44Z)
• Self-organized topological insulator due to cavity-mediated correlated tunneling [0.0]
  We discuss a model where topology emerges from the quantum interference between single-particle dynamics and global interactions. The onset of quantum interference leads to spontaneous breaking of the lattice translational symmetry. The emerging quantum phase is a topological insulator and is found at half fillings.
  arXiv  Detail & Related papers  (2020-11-03T13:23:06Z)
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions [1.2433211248720717]
  The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness. We define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. We demonstrate an equivalent formalism of computation using a general time independent Hamiltonian.
  arXiv  Detail & Related papers  (2020-08-06T07:53:28Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Topological photon pairs in a superconducting quantum metamaterial [44.62475518267084]
  We use an array of superconducting qubits to engineer a nontrivial quantum metamaterial. By performing microwave spectroscopy of the fabricated array, we experimentally observe the spectrum of elementary excitations. We find not only the single-photon topological states but also the bands of exotic bound photon pairs arising due to the inherent anharmonicity of qubits.
  arXiv  Detail & Related papers  (2020-06-23T07:04:27Z)
• Quantum decoherence by Coulomb interaction [58.720142291102135]
  We present an experimental study of the Coulomb-induced decoherence of free electrons in a superposition state in a biprism electron interferometer close to a semiconducting and metallic surface. The results will enable the determination and minimization of specific decoherence channels in the design of novel quantum instruments.
  arXiv  Detail & Related papers  (2020-01-17T04:11:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.