Eigenvalues and Eigenstates of Quantum Rabi Model

• URL: http://arxiv.org/abs/2104.12771v2
• Date: Mon, 13 Feb 2023 16:36:22 GMT
• Title: Eigenvalues and Eigenstates of Quantum Rabi Model
• Authors: Andrei Ivanov
• Abstract summary: We present an approach to the exact diagonalization of the quantum Rabi Hamiltonian. It is shown that the obtained eigenstates can be represented in the basis of the eigenstates of the Jaynes-Cummings Hamiltonian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The scientific interest in the analytical solution of the quantum Rabi model is due to the widespread use of this simple model in quantum optics, quantum computing, cavity QED, and nanoelectromechanical systems. This interest is related to the need for the theoretical description of the interaction of a two-level system with a quantum oscillator in the case when the rotating wave approximation fails. In this Letter, we present an approach to the exact diagonalization of the quantum Rabi Hamiltonian. This approach is based on the properties of the Pauli operators and allows us to readily solve the stationary Schrodinger equation for a two-level system. First, we demonstrate the applicability of the approach to the Jaynes-Cummings Hamiltonian to get the well-known solution. Then, we obtain the eigenvalues and eigenstates for the quantum Rabi Hamiltonian using the proposed approach. It is shown that the obtained eigenstates can be represented in the basis of the eigenstates of the Jaynes-Cummings Hamiltonian.

Related papers

• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Effective Description of the Quantum Damped Harmonic Oscillator: Revisiting the Bateman Dual System [0.3495246564946556]
  We present a quantization scheme for the damped harmonic oscillator (QDHO) using a framework known as momentous quantum mechanics. The significance of our study lies in its potential to serve as a foundational basis for the effective description of open quantum systems.
  arXiv  Detail & Related papers  (2023-09-06T03:53:09Z)
• Quantum model of hydrogen-like atoms in hilbert space by introducing the creation and annihilation operators [0.0]
  An analytical approach with series is extensively used based on wave mechanics theory in most of quantum textbooks. We will illustrate how systematically making an appropriate groundwork to discover the coherent states can lead to providing the energy quantization and normalized radial wave functions attached to the matrix representation.
  arXiv  Detail & Related papers  (2023-08-25T14:42:55Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Hybrid Quantum-Classical Eigensolver Without Variation or Parametric Gates [0.0]
  We present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space. A process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given.
  arXiv  Detail & Related papers  (2020-08-26T02:31:24Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Construction of quantum wavefunctions for non-separable but integrable two-dimensional Hamiltonian systems by means of the boundary values on the classical caustics [0.0]
  It is possible to construct the quantum wave functions for non-separable but integrable two-dimensional Hamiltonian systems. The method is applied both to the Schrodinger equation, and to the quantum Hamilton-Jacobi equation.
  arXiv  Detail & Related papers  (2020-04-28T10:43:28Z)
• Direct reconstruction of the quantum master equation dynamics of a trapped ion qubit [0.0]
  We introduce a method that reconstructs the dynamical equation of open quantum systems, directly from a set of expectation values of selected observables. We benchmark our technique both by a simulation and experimentally, by measuring the dynamics of a trapped $88textSr+$ ion under spontaneous photon scattering.
  arXiv  Detail & Related papers  (2020-03-10T13:09:00Z)

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.