Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition

• URL: http://arxiv.org/abs/2504.20730v2
• Date: Wed, 30 Apr 2025 13:39:28 GMT
• Title: Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition
• Authors: Giuseppe Patera, Alessandro Pugliese,
• Abstract summary: "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems.<n>We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors.<n>We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
• Score: 49.1574468325115
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Bloch-Messiah decomposition (BMD) is a fundamental tool in quantum optics, enabling the analysis and tailoring of multimode Gaussian states by decomposing linear optical transformations into passive interferometers and single-mode squeezers. Its extension to frequency-dependent matrix-valued functions, recently introduced as the "analytic Bloch-Messiah decomposition" (ABMD), provides the most general approach for characterizing the driven-dissipative dynamics of quantum optical systems governed by quadratic Hamiltonians. In this work, we present a detailed study of the ABMD, focusing on the typical behavior of parameter-dependent singular values and of their corresponding singular vectors. In particular, we analyze the hitherto unexplored occurrence of avoided and genuine crossings in the spectrum of quantum noise, the latter being manifested by nontrivial topological Berry phases of the singular vectors. We demonstrate that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors and suggesting the presence of genuine crossings in nearby systems. We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings. As a notable example, we show that such control can be exploited to generate broad, flat-band squeezing spectra -- a desirable feature for enhancing degaussification protocols. This study provides new insights into the structure of multimode quantum correlations and offers a theoretical framework for experimental exploitation of complex quantum optical systems.

Related papers

• Spectral truncation of out-of-time-ordered correlators in dissipative system [44.99833362998488]
  Out-of-time-ordered correlators (OTOCs) have emerged as powerful tools for diagnosing quantum chaos and information scrambling.<n>We investigate the spectral decomposition of OTOCs in open quantum systems using the dissipative modified kicked rotator (DMKR) as a paradigmatic model.<n>Our results provide a quantitative framework for understanding OTOCs in dissipative quantum systems and suggest new avenues for experimental exploration in open quantum platforms.
  arXiv  Detail & Related papers  (2025-03-05T17:22:25Z)
• Covariant non-perturbative pointer variables for quantum fields [44.99833362998488]
  We derive and renormalize the integro-differential equation that governs the detector pointer-variable dynamics.<n>Our formal solution, expressed in terms of Green's functions, allows for the covariant, and causal analysis of induced observables on the field.
  arXiv  Detail & Related papers  (2025-02-03T11:53:31Z)
• Quench Spectroscopy for Dissipative and (Non)-Hermitian Quantum Lattice Models [0.0]
  We extend the quench spectroscopy method to dissipative and isolated non-Hermitian quantum lattice models. We first investigate theoretically the dynamics of the open Bose-Hubbard chain confined in the superfluid phase induced by a sudden global quench. We then discuss the applicability of the quench spectroscopy to non-Hermitian transverse-field Ising chain confined in the paramagnetic phase.
  arXiv  Detail & Related papers  (2024-12-01T01:24:11Z)
• Towards quantum computing Feynman diagrams in hybrid qubit-oscillator devices [0.0]
  We show that experiments in hybrid qubit-oscillator devices can be seen through the lens of functional calculus and path integrals. This connection suggests an expansion of the characteristic function in terms of Feynman diagrams. We discuss how these ideas can be generalized to finite temperatures via the Schwinger-Keldysh formalism.
  arXiv  Detail & Related papers  (2024-11-07T19:17:00Z)
• Simulating a quasiparticle on a quantum device [0.0]
  We propose a variational approach to explore quasiparticle excitations in interacting quantum many-body systems. We benchmark the proposed algorithm via numerical simulations performed on the one-dimension transverse field Ising chain. We show that the localized quasiparticle states constructed with VQE contain accessible information on the full band of quasiparticles.
  arXiv  Detail & Related papers  (2024-09-13T05:39:13Z)
• Nonlinear dynamical Casimir effect and Unruh entanglement in waveguide QED with parametrically modulated coupling [83.88591755871734]
  We study theoretically an array of two-level qubits moving relative to a one-dimensional waveguide. When the frequency of this motion approaches twice the qubit resonance frequency, it induces parametric generation of photons and excitation of the qubits. We develop a comprehensive general theoretical framework that incorporates both perturbative diagrammatic techniques and a rigorous master-equation approach.
  arXiv  Detail & Related papers  (2024-08-30T15:54:33Z)
• Stochastic Model of Qudit Measurement for Superconducting Quantum Information Processing [0.0]
  This thesis focuses on modeling the dispersive measurement of a transmon qutrit in an open quantum system using quadrature detections. Research has demonstrated the possibility of driving higher-order transitions in a transmon or designing innovative multimode superconducting circuits.
  arXiv  Detail & Related papers  (2023-12-03T03:57:49Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Stochastic modeling of superconducting qudits in the dispersive regime [0.0773931605896092]
  This work focuses on modeling the dispersive quadrature measurement in an open quantum system. We verify our model with a series of experimental results on a transmon-type qutrit.
  arXiv  Detail & Related papers  (2023-10-29T00:39:47Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)

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.