We present a two-mode squeezed Jaynes–Cummings model, built upon the formalism of pair coherent states (PCSs), to investigate the dynamics of a two-level atom interacting with a two-mode quantized field. By solving the time-dependent Schrödinger equation under the rotating-wave approximation, we elucidate the system’s quantum evolution, with particular emphasis on how the squeezing degree and photon number difference modulate atomic population inversion and entanglement. We further quantify the nonclassical traits of the two-mode squeezed PCSs via Mandel’s parameter and the violation of the Cauchy–Schwarz inequality, highlighting their sensitivity to model parameters. These findings illuminate the subtle interplay of squeezing, photon statistics, and entanglement in advanced quantum optical systems.
We present a two-mode squeezed Jaynes–Cummings model, built upon the formalism of pair coherent states (PCSs), to investigate the dynamics of a two-level atom interacting with a two-mode quantized field. By solving the time-dependent Schrödinger equation under the rotating-wave approximation, we elucidate the system’s quantum evolution, with particular emphasis on how the squeezing degree and photon number difference modulate atomic population inversion and entanglement. We further quantify the nonclassical traits of the two-mode squeezed PCSs via Mandel’s parameter and the violation of the Cauchy–Schwarz inequality, highlighting their sensitivity to model parameters. These findings illuminate the subtle interplay of squeezing, photon statistics, and entanglement in advanced quantum optical systems.
We considered the anti-Jaynes-Cummings (AJC) interaction of a two-level atom in an initial ground state interacting with a field mode in an initial squeezed coherent state at arbitrary values of squeeze parameter r and provided the Jaynes-Cummings (JC) interaction as a comparison. We analysed the degree of entanglement (DEM) measured by the von Neumann entropy and the nature of the field quantified by the Mandel Q parameter in relation to the atomic population inversion during the AJC interaction and separately the corresponding JC interaction. We noted in our examples that at r>1.4, photon statistics evolved to super-Poissonian from sub-Poissonian during the respective AJC, JC interactions. Further, for high values of r, the form of the time evolution of atomic population inversion depicted enhanced ringing revivals at the collapse region in comparison to the case of an initial coherent state. What is more, at higher values of r the time evolution of DEM showed more rapid oscillations and recorded higher values, concurrently, an increase in the degree of mixedness.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of the radiation field is investigated, as the state of the field is gradually changed from a coherent state to a squeezed coherent state. The effect of mild squeezing on the coherent light is shown to be striking: the photon number distribution gets localized and it peaks maximally for a particular value of squeezing. The atomic inversion retains its structure for a longer time. The mean linear entropy shows that the atom has a tendency to get disentangled from field within the collapse region and also in the revival region, for mild squeezing. These properties are absent for the case of a coherent state or for an excessively squeezed coherent state. We also elucidate a connection between these properties and the photon statistics of the mildly squeezed coherent state; these states have the minimum variance and are also maximally sub-Poissonian.
We develop a model to investigate the behavior of atomic coupler consists
of two waveguides, each of which includes a localized or a trapped
atom with a two-mode pair coherent state source. The waveguides are
placed close enough to each other to allow energy exchange between
them. The two atoms, in the different waveguides, are located adjacent
to each other. In each waveguide, one mode propagates along and interacts
with the atom inside in a standard way as the Jaynes- Cummings
model (JCM). The atom-mode system, in each waveguide, interacts with
the other one via the evanescent wave. Pair coherent states (PCS) are
one of the most important states in quantum information theory since
it includes sufficient entanglement causing the violation of the Bell inequality.
Moreover, the PCS possesses prominent nonclassical properties
such as sub-Poissonian statistics, correlation in the number fluctuations,
squeezing and violations of the Cauchy Schwartz inequalities
The coherent states in the parity deformed analog of standard boson Glauber coherent states are generated, which admit a resolution of unity with a positive measure. The quantum-mechanical nature of the light field of these para-Bose states is studied, and it is found that para-Bose order plays an important role in the nonclassical behaviors including photon antibunching, sub-Poissonian statistics, signal-to-quantum noise ratio, quadrature squeezing effect, and multi-peaked number distribution. Furthermore, we consider the Jaynes-Cummings model of a two-level atom in a para-Bose cavity field with the initial states of the excited and Glauber coherent ones when the atom makes one-photon transitions, and obtain exact energy spectrum and eigenstates of the deformed model. Nonclassical properties of the time-evolved para-Bose atom-field states are exhibited through evaluating the fidelity, evolution of atomic inversion, level damping, and von Neumann entropy. It is shown that the evolution time and the para-Bose order control these properties.
We study interaction between a pair of indistinguishable two-level atoms and the single-mode cavity field. It is supposed that the pair of two-level atoms is laser cooled and trapped into the ground vibrational state, in which vibrational quantum number ⟨nv⟩=0 . Two Jaynes–Cummings models are investigated. One is the Jaynes–Cummings model with intensity-dependent coupling and the another is the two-photon Jaynes–Cummings model of a pair of indistinguishable two-level atoms. It should be noted that in the present model, at initial moment t=0 , in intensity-dependent Jaynes–Cummings model the cavity field is prepared in Holstein–Primakoff SU(1,1) CS, while in two-photon Jaynes–Cummings model it is prepared in the squeezed vacuum state. Moreover, at initial moment t=0 , pair of atoms is supposed to be in the first excited state ∣e1⟩ in both models. By using exact analytical solutions for state-vectors of the coupled atom-field systems amplitude-squared squeezing of the quantized cavity field is examined as a function of the ∣ξ∣ parameter. In this situation, in both models higher-order squeezing has the tendency towards oscillations, but exact periodicity of these oscillations is violated by the analogy with the second-order squeezing.
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