Applied Mathematics in Quantum Computing, Solid-State Physics and Quantum Optics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: closed (10 June 2025) | Viewed by 1125

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Department of Physical Sciences, Hellenic Naval Academy, Hadjikyriakou Avenue, T.K, 185 39 Piraeus, Greece
Interests: quantum theory in low-dimensional structures; collective excitations; quantum computing
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Special Issue Information

Dear Colleagues,

During the last decades, theoretical and experimental efforts have been made in the field of quantum computing research by using the fundamental properties of low dimensional solid-state structures and quantum optics. Numerical algorithms and the mathematical investigation of the possible quantum computing structures are the focal points of quantum information in worldwide research.

In this Special Issue, the main principles of quantum computing are addressed by means of both mathematically rigorous formalism and numerical algorithms. Quantum effects, e.g., decoherence, dephasing, fidelity and collective excitations in solids, as well as quantum structures, e.g., quantum gates/quantum bits (qbits) and quantum computing algorithms, are among the topics included in this Issue. 

We welcome submissions from outstanding scholars, including but not limited to related research fields.

Dr. Vasilios N. Stavrou
Guest Editor

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Keywords

  • quantum bits
  • quantum gates, dephasing & decoherence
  • quantum entanglement
  • quantum computing algorithms
  • collective excitations
  • hybrid quantum structures
  • quantum cavities
  • waveguides time-dependent Schrödinger equation
  • optical cavities
  • Maxwel–Bloch equations
  • quantum theory of light

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Published Papers (1 paper)

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21 pages, 5274 KB  
Article
Drive-Loss Engineering and Quantum Discord Probing of Synchronized Optomechanical Squeezing
by Hugo Molinares and Vitalie Eremeev
Mathematics 2025, 13(13), 2171; https://doi.org/10.3390/math13132171 - 3 Jul 2025
Viewed by 458
Abstract
In an optomechanical system (OMS), the dynamics of quantum correlations, e.g., quantum discord, can witness synchronized squeezing between the cavity and mechanical modes. We investigate an OMS driven by two coherent fields, and demonstrate that optimal quantum correlations and squeezing synchronization can be [...] Read more.
In an optomechanical system (OMS), the dynamics of quantum correlations, e.g., quantum discord, can witness synchronized squeezing between the cavity and mechanical modes. We investigate an OMS driven by two coherent fields, and demonstrate that optimal quantum correlations and squeezing synchronization can be achieved by carefully tuning key parameters: the cavity-laser detunings, loss rates, and the effective coupling ratio between the optomechanical interaction and the amplitude drive. By employing the steady-state solution of the covariance matrix within the Lyapunov framework, we identify the conditions under which squeezing becomes stabilized. Furthermore, we demonstrate that synchronized squeezing of the cavity and mechanical modes can be effectively controlled by tuning the loss ratio between the cavity and mechanical subsystems. Alternatively, in the case where the cavity is driven by a single field, we demonstrate that synchronized squeezing in the conjugate quadratures of the cavity and mechanical modes can still be achieved, provided that the cavity is coupled to a squeezed reservoir. The presence of this engineered reservoir compensates the absent driving field, by injecting directional quantum noise, thereby enabling the emergence of steady-state squeezing correlations between the two modes. A critical aspect of our study reveals how the interplay between dissipative and driven-dispersive squeezing mechanisms governs the system’s bandwidth and robustness against decoherence. Our findings provide a versatile framework for manipulating quantum correlations and squeezing in OMS, with applications in quantum metrology, sensing, and the engineering of nonclassical states. This work advances the understanding of squeezing synchronization and offers new strategies for enhancing quantum-coherent phenomena in dissipative environments. Full article
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