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.
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 \ensuremathω3 on the steady-state atomic population.
A complete treatment of a three-level ladder system interacting with a broadband squeezed vacuum field is presented. It is assumed that the ground state and the second excited state are decoupled in the electric-dipole approximation, and are tuned close to the sum frequency of the incident squeezed vacuum field. Using Zwanzig's projection-operator techniques, we derive the master equation, assuming that the system interacts with a broadband squeezed vacuum field in one or more dimensions. It is shown that, in the first case, the squeezed vacuum introduces new decay constants and frequency-shift parameters. These have the same dependence on the atom-radiation coupling parameter as the ordinary vacuum decay rate and frequency shift, the only major difference being that they are multiplied by the squeezing parameters M and N. In more dimensions, the decay constants and frequency-shift parameters depend on the solid angle \ensuremath{\Omega} over which the squeezing is propagated. For \ensuremath{\Omega}=0 these correspond to the usual Einstein A coefficients and Lamb shifts of the atomic levels, while for large \ensuremath{\Omega} they are similar to those for the one-dimensional squeezed vacuum.
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.
A theoretical study is made of the steady-state intensity and squeezing properties of the fluorescent light from a three-level-atom system in a ladder configuration, which is subject to spontaneous-emission decay to the electromagnetic-field vacuum. Two cases are examined: in the equispaced (ES) level case, the two atomic transition frequencies are nearly equal and two photon absorption processes occur from a single coherent laser field that couples both transitions and has a small detuning from each; in the non- equispaced (NES) level case, the atomic transition frequencies are rather different and two photon absorption processes occur from two coherent laser fields, each coupled to a single transition and in near resonance with it. In both cases, a situation of small two-photon detuning occurs. Optical Bloch equations for the atomic density matrix in rotating frames are given and matrix expressions for determining the steady-state populations and coherences are obtained. Analytic expressions are also given for special cases. The fluorescent intensity is obtained from the populations of the intermediate and upper states, with the normally ordered variance (NOV) for quadrature components of the fluorescent field involving, in addition, the atomic coherences. The fluorescent intensities are shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases.In both cases, the fluorescent intensities show the well known resonances from the upper state at zero two-photon detuning and from the intermediate state at zero one-photon detuning for the lower transition. However, further resonances are also found. The intermediate-state intensity displays a resonance at zero two-photon detuning. Also, the upper-state intensity shows a resonance at zero one-photon detuning for the upper transition, but only for the NES case; evidently, the transfer rate from upper to lower transition coherences destroys this resonance for the ES case. The time-averaged NOV is also shown graphically as a function of two-photon detuning for a variety of one-photon detunings and Rabi frequencies for the ES and NES cases. For the ES case, the quadrature frequency is chosen as the single laser frequency and for the NES case, it is chosen as either the average of the two laser frequencies or the lower transition laser frequency. Squeezing occurs near zero two-photon detuning for both ES and NES cases, though only for the quadrature frequency equal to the average laser frequency in the latter case. It also occurs near zero detuning for the lower transition for both cases, though only for the quadrature frequency equal to the lower transition laser frequency in the NES case. The squeezing minima show a splitting effect for large Rabi frequencies corresponding to two-photon or one-photon Rabi splitting of the dressed atom levels for the situation near two-photon or one-photon resonance, respectively. The large squeezing near two-photon resonance for moderate Rabi frequencies and large one-photon detuning corresponds to essentially pure three-level squeezing, while that near one-photon resonance for weak Rabi frequencies involves two-level squeezing.
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.
A three-level ladder atom driven by two coherent laser fields with rather different frequencies in various kinds of reservoirs is considered. Making use of the master equation and Bloch equation, we calculate numerically and show graphically the steady-state populations versus two-photon detuning. We also discuss and compare the two-photon and one-photon processes occurring for various cases. For a squeezed vacuum, only when the carrier frequency of the squeezed vacuum equals the average of frequencies of the two driving fields and the phase matching condition is fulfilled, will there be a strong two-photon resonant absorption from the squeezed vacuum, a characteristic different from absorption of photons from a classical field; Otherwise, the two-photon ab-sorption rate from the squeezed vacuum will be greatly diminished.
A three-level atom with two competing transitions can sense correlations between modes of an electromagnetic field with which it interacts. We examine the sensitivity of three-level atoms in ladder, \ensuremath{\Lambda}, and V configurations to correlations between modes in a broadband correlated reservoir of field modes. Our model of a correlated reservoir includes pairwise mode correlations around a center frequency. When such correlations are set to zero, the reservoir becomes a simple thermal heat bath, but in the opposite extreme when the modes are perfectly correlated, we recover a minimum-uncertainty broadband squeezed vacuum. We show that atomic populations are extremely sensitive to these correlations, and can, in the ladder system, become inverted as a result of the phase-sensitive noise. We also show how atomic population trapping is affected by mode correlations.