Spontaneous emission from two-level atoms interacting with a squeezed vacuum field is examined, taking account of possible different interatomic separations. It is shown that the steady-state atomic population depends on whether the interatomic separations are comparable to or much smaller than the resonant wavelength. For the extended system the squeezed vacuum introduces a dependence of the atomic population on the interatomic separations. For large interatomic separations the atomic population is identical to that for the thermal field, which is the same for two independent atoms. For small interatomic separations the atomic population is higher than that for the thermal field. This is in contrast to the small-sample model in which the interatomic separation is ignored. In this case the final atomic population in the squeezed vacuum is the same as that for the independent atoms in the squeezed vacuum. Moreover, this population differs from that for the thermal field for which the atomic population is lower than that for the independent atoms. This difference is due to the interatomic correlations whose presence depends on whether the interatomic separation is or is not included. For the extended system the interatomic correlations are induced by the squeezed field and vanish for the thermal field. For the small-sample model, however, the interatomic correlations are induced by the thermal field and the squeezed vacuum changes these correlations in such a way that for the minimum-uncertainty squeezed states these correlations vanish. We also discuss the effect of the interatomic separation on the two-photon transitions and the normalized intensity correlation function in the two-atom system interacting with the squeezed vacuum field.
Spontaneous emission from two-level atoms interacting with a squeezed vacuum field is examined, taking account of possible different interatomic separations. It is shown that the steady-state atomic population depends on whether the interatomic separations are comparable to or much smaller than the resonant wavelength. For the extended system the squeezed vacuum introduces a dependence of the atomic population on the interatomic separations. For large interatomic separations the atomic population is identical to that for the thermal field, which is the same for two independent atoms. For small interatomic separations the atomic population is higher than that for the thermal field. This is in contrast to the small-sample model in which the interatomic separation is ignored. In this case the final atomic population in the squeezed vacuum is the same as that for the independent atoms in the squeezed vacuum. Moreover, this population differs from that for the thermal field for which the atomic population is lower than that for the independent atoms. This difference is due to the interatomic correlations whose presence depends on whether the interatomic separation is or is not included. For the extended system the interatomic correlations are induced by the squeezed field and vanish for the thermal field. For the small-sample model, however, the interatomic correlations are induced by the thermal field and the squeezed vacuum changes these correlations in such a way that for the minimum-uncertainty squeezed states these correlations vanish. We also discuss the effect of the interatomic separation on the two-photon transitions and the normalized intensity correlation function in the two-atom system interacting with the squeezed vacuum field.
Using the formalism developed earlier, we treat spontaneous emission from a three-level atom (ladder system) interacting with a broadband squeezed vacuum field. We obtain expressions for the transient and steady-state populations of the atomic levels with the conditions that the atom interacts with either a multimode perfect squeezed vacuum field, or a three-dimensional vacuum field in which the squeezed modes lie within a solid angle over which squeezing is propagated. The results are compared with those obtained for the atom interacting with a thermal field. We show that in the perfect case the first excited state is not populated when the squeezed vacuum field is in a minimum-uncertainty squeezed state. Moreover, the second excited state can have a steady-state population larger than 1/2. These features are completely absent when the atom interacts with the thermal field. In addition, for a low-intensity squeezed vacuum field the population in the second excited state exhibits a linear rather than quadratic dependence on the intensity of the squeezed vacuum field. In the three-dimensional case the presence of unsqueezed modes considerably reduces the effect of squeezing on spontaneous emission. However, a significant reduction in a population of the first excited state and a population larger than 1/2 in the second excited state can be achieved provided the squeezing is propagated over a large solid angle. We also discuss the effect of the two-photon detuning between the double carrier frequency of the squeezing and atomic transition frequency ${\mathrm{\ensuremath{\omega}}}_{3}$ on the steady-state atomic population.
We analyze the pairwise atomic states that are produced when a system of two atoms is irradiated by a squeezed vacuum field. Included in the analysis is the three-dimensional squeezed vacuum field propagated over a solid angle \ensuremath{\Omega}, the interatomic separation r12, the microscopic Fabry-P\'erot cavity, and the role played by an imperfect coupling between the cavity modes and squeezed input modes. It is shown that the steady state of the system in free space is the pairwise atomic state when the atoms interact with a perfect squeezed dipole wave and the interatomic separations are much smaller than the resonant wavelength (Dicke model). With the interatomic separations comparable to the resonant wavelength or with an imperfect squeezed dipole wave, the system decays to a state that is not the pairwise atomic state. The effect of squeezed vacuum field on the system is now manifested by the selective population of the collective atomic states. For atoms inside a microscopic Fabry-P\'erot cavity the pairwise atomic states are produced with an imperfect squeezed dipole wave. This can occur even for small solid angles \ensuremath{\Omega}. However, this effect is sensitive to mode matching between internal and external fields. It is shown that with a Gaussian profile for the input squeezed modes the steady state is not the pairwise atomic states, but a significant reduction of the population in the symmetric state still can be observed.
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
The time evolution of the populations of the collective states of a two-atom system in a squeezed vacuum can exhibit quantum beats. We show that the effect appears only when the carrier frequency of the squeezed field is detuned from the atomic resonance. Moreover, we find that the quantum beats are not present for the case in which the two-photon correlation strength is the maximum possible for a field with a classical analog. We also show that the population inversion between the excited collective states, found for the resonant squeezed vacuum, is sensitive to the detuning and the two-photon correlations. For large detunings or a field with a classical analog there is no inversion between the collective states. Observation of the quantum beats or the population inversion would confirm the essentially quantum-mechanical nature of the squeezed vacuum.
We show that atoms interacting with a squeezed radiation field reservoir can exhibit phase-dependent population decay and relax into a highly correlated pure state, in striking difference to decay in a heat bath. We use a Heisenberg operator treatment of radiative transitions in a broadband squeezed light field described as a quantum white-noise field with correlated fluctuations to describe the modified decay of a single atom, and of two atoms cooperatively decaying in a squeezed vacuum. We compare this decay with that generated by a broadband thermal field which lacks the essential field-mode correlations characteristic of squeezing.