This work presents a theoretical framework to study the non-Markovian dynamics of a two-level quantum emitter interacting with a broadband squeezed electromagnetic reservoir, and both one- and two-photon interaction processes are incorporated. Mathematical modeling uses a time-convolution less projection operator technique. This yields a time-local master equation. The coefficients of this equation are derived from integrals over the reservoir's squeezed correlation functions: and . The model is validated through rigorous numerical simulation of the resulting dynamical equations. Testing involves computing key physical observables: the transient emission spectrum and the field linear entropy . These predictions are systematically analyzed against variations in squeezing parameters , coupling strengths , and detector bandwidth . The results confirm that the model successfully captures phase-dependent decoherence, spectral modulation, and purity oscillations. Notably, two-photon processes suppress decoherence under strong squeezing. The consistency between analytical derivations and numerical outcomes validates the framework. It is established as a predictive tool for quantum optics in engineered nonclassical environments. This study directly connects engineered reservoir properties specifically its nonclassical photon statistics to observable, time-dependent quantum phenomena. The findings offer fundamental insights and a predictive tool for quantum control, sensing, and information processing in tailored electromagnetic environments.
This work presents a theoretical framework to study the non-Markovian dynamics of a two-level quantum emitter interacting with a broadband squeezed electromagnetic reservoir, and both one- and two-photon interaction processes are incorporated. Mathematical modeling uses a time-convolution less projection operator technique. This yields a time-local master equation. The coefficients of this equation are derived from integrals over the reservoir's squeezed correlation functions: and . The model is validated through rigorous numerical simulation of the resulting dynamical equations. Testing involves computing key physical observables: the transient emission spectrum and the field linear entropy . These predictions are systematically analyzed against variations in squeezing parameters , coupling strengths , and detector bandwidth . The results confirm that the model successfully captures phase-dependent decoherence, spectral modulation, and purity oscillations. Notably, two-photon processes suppress decoherence under strong squeezing. The consistency between analytical derivations and numerical outcomes validates the framework. It is established as a predictive tool for quantum optics in engineered nonclassical environments. This study directly connects engineered reservoir properties specifically its nonclassical photon statistics to observable, time-dependent quantum phenomena. The findings offer fundamental insights and a predictive tool for quantum control, sensing, and information processing in tailored electromagnetic environments.
This work develops a control-oriented theoretical framework for the manipulation of transient emission spectra and field-state purity in a qubit interacting with a broadband squeezed reservoir. We model the joint qubit-field dynamics using a time-resolved open quantum system formalism. This establishes a direct, quantitative connection between transient spectral characteristics, quantum purity evolution, and controllable system parameters. The analysis reveals that nonclassical reservoir properties, particularly squeezing-induced correlations, strongly influence both spectral deformation and coherence redistribution during the early-time dynamics. Building on this foundation, the work explores practical control strategies aimed at engineering the system’s dynamical response. Pulse shaping and time-dependent modulation of qubit-reservoir coupling offer effective control tools. These regulate spectral broadening, suppress unwanted decoherence, and accelerate convergence toward stabilized operating regimes. In addition, feedback-assisted qubit probing protocols are investigated as a means of monitoring and controlling field purity while minimizing measurement back-action on the squeezed mode. Our results show that well-designed control loops can balance information extraction and disturbance. This enables efficient regulation of nonclassical field properties. The proposed approach highlights transient spectral measurements as a powerful diagnostic and control resource, linking observable emission features to underlying quantum correlations and purity dynamics. From an engineering perspective, the framework offers practical guidelines. These guide the design of feedback-stabilized quantum emitters and reservoir-engineered coherence control. These findings are directly relevant to emerging quantum technologies, including cavity and circuit quantum electrodynamics, quantum sensing, and quantum communication systems operating in nonclassical environments.
ABSTRACT T 0.1 Significance of the Study This study provides a comprehensive theoretical and numerical investigation of light emission from a two-level atom interacting with a squeezed vacuum field. By devel oping a model based on the squeezed Jaynes–Cummings Hamiltonian and formulating atomic evolution via the master equation, the work establishes a framework for un derstanding how quantum squeezing modifies atomic dynamics. Analysis of popula tion inversion and emission characteristics shows that squeezing can enhance or inhibit spontaneous emission, accelerate population oscillations, and induce spectral narrow ing, while the second-order correlation function g(2)(τ) reveals photon antibunching and nonclassical statistics. The study further examines two-atom systems coupled to a common squeezed vacuum, highlighting steady-state entanglement and nonclassical correlations in quadrature variances, emphasizing the role of squeezing as a quantum resource. Overall, these findings provide insight into the influence of squeezed reser voirs on spontaneous emission, coherence, photon correlations, and entanglement, with important implications for quantum optics, precision spectroscopy, quantum metrology, and quantum information processing. Keywords: Master equation; Power spectrum; Quantum entanglement;Spontaneous emission; Squeezed vacuum; Two-level atom
ABSTRACT T 0.1 Significance of the Study This study provides a comprehensive theoretical and numerical investigation of light emission from a two-level atom interacting with a squeezed vacuum field. By devel oping a model based on the squeezed Jaynes–Cummings Hamiltonian and formulating atomic evolution via the master equation, the work establishes a framework for un derstanding how quantum squeezing modifies atomic dynamics. Analysis of popula tion inversion and emission characteristics shows that squeezing can enhance or inhibit spontaneous emission, accelerate population oscillations, and induce spectral narrow ing, while the second-order correlation function g(2)(τ) reveals photon antibunching and nonclassical statistics. The study further examines two-atom systems coupled to a common squeezed vacuum, highlighting steady-state entanglement and nonclassical correlations in quadrature variances, emphasizing the role of squeezing as a quantum resource. Overall, these findings provide insight into the influence of squeezed reser voirs on spontaneous emission, coherence, photon correlations, and entanglement, with important implications for quantum optics, precision spectroscopy, quantum metrology, and quantum information processing. Keywords: Master equation; Power spectrum; Quantum entanglement;Spontaneous emission; Squeezed vacuum; Two-level atom
If a broadband squeezed vacuum is treated as a reservoir with respect to a two-level atom, the non-zero phase-dependent reservoir correlation functions characterizing the squeezed vacuum introduce `squeezing terms' to the master equation. These terms are responsible, for example, for the well known narrowing of the spectral lines in the resonance fluorescence spectrum of the atom. For a squeezed vacuum reservoir with finite bandwidth it is possible to derive the master equation that is consistent with the Born-Markov approximation by a two-step procedure which consists in dressing the atom first and next coupling it to the finite-bandwidth reservoir. The master equation is valid whenever the bandwidth of the reservoir is much broader than the atomic linewidth but not necessarily broader than the Rabi frequency. This procedure can be applied not only for the squeezed vacuum reservoir but also for the ordinary vacuum with the structure of the mode density that is not flat, e.g., modelled by a Lorentzian function as in a cavity. The master equation for this case, in the operator form, shows some similarities to the master equation for the squeezed vacuum reservoir due to the presence of the `squeezing-like terms'. The similarities and differences of the two master equations are discussed in this paper.
This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit systems undergoing pure dephasing, considering the effects of squeezing parameter, phase difference, and coupling strength within an Ohmic spectral density model. The decoherence factor shows how reservoir engineering influences coherence loss. Numerical results demonstrate that optimal squeezing and local bath configurations enhance QFI preservation, while collective couplings accelerate decay. We also examine the interplay with von Neumann entropy, highlighting their inverse correlation, where increased mixedness reduces metrological sensitivity.
Two-mode squeezed states as paradigmatic entangled resources have broad applications in quantum information processing. Here, we study the generation of stable optical-microwave squeezing in structured environments within a hybrid electro-optomechanical system, where a mechanical oscillator is simultaneously coupled to an optical cavity mode and a microwave mode of an LC resonator. Specifically, an effective Hamiltonian that captures the optical-microwave squeezing interaction is constructed by combining strongly modulated driving fields applied to both photonic modes with a mechanical parametric amplifier. Based on this effective model, the dynamical evolution of two-mode squeezing in structured environments is analyzed. It is remarkably shown that the non-Markovian noise can substantially enhance the squeezing level in comparison to the Markovian case, and that two-mode squeezing can persist even in the absence of external driving fields under non-Markovian conditions, thereby mitigating the detrimental effects of anti-squeezing. Furthermore, the persistence of the two-mode squeezed state is enhanced when the environmental spectral densities of the microwave and optical modes are identical. Our work provides a theoretical framework for generating and persisting two-mode squeezing in structured environments.