Cooperative and interference effects in the resonance fluorescence of two identical three-level atoms at high photon densities

The excitation spectrum of two identical three-level atoms is considered when a strong electromagnetic field operates resonantly between two levels of the atoms. While undergoing the transition into the excited state, the atoms interact through their dipole-dipole interaction and radiate to each other as well, and subsequently, they decay radiatively into another excited state. For such a system, the spectral functions are calculated describing the cooperative and interference spectra for the symmetric and antisymmetric modes arising from the decay of the atoms from one excited state into another. In the absence of the pump field, the spectral function for the symmetric modes consists of two peaks, which are described by Lorentzian lines peaked at the frequencies ω = ω₂₃ + V_AB and ω = ω₂₃ ? V_AB and having spectral widths of the order of γ⁰₂₁ + γ⁰₂₃ and γ⁰₂₃, respectively, where ω₂₃ is the transition frequency between the two excited states, V_AB is the dipole-dipole interaction and $\text{1}\text{2}\text{γ}{}^0{}_{21}$ is the natural width for a photon spontaneously emitted from the 2 → 1 transition of an isolated atom. The splitting of the central peak for the transition in question and the broadening of the spectral widths are due entirely to the dipole-dipole and radiative interactions between the atoms. The spectral function for the antisymmetric modes describes a stable mode at the frequency ω = ω₂₃ ? V_AB, which has a delta-function distribution, and a Lorentzian line peaked at the frequency ω = ω₂₃ + V_AB and has a spectral width of the order of γ⁰₂₁. In the presence of the pump field, the spectral function for the symmetric modes contains, in addition to the central peaks, two pairs of sidebands, one pair of which is induced by the pump field with an energy shift equal to $\text{Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, while the other pair of sidebands is due to the dipole-dipole interaction between the atoms; the probability of occurrence of the latter pair of sidebands is proportional to $\text{V}{}_{\mathrm{AB}}\text{/Ω}{}_{\mathrm{<mtext>a</mtext>}}$, while the induced energy shift is equal to $\text{3Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, where $\text{√2Ω}{}_{\mathrm{<mtext>a</mtext>}}$ is the induced by the laser field energy shift (Rabi frequency) for a single two-level atom. The spectral widths for both pairs of sidebands are of the order of γ⁰₂₁ + γ⁰₂₃. The excitation spectrum of the antisymmetric modes consists of, in addition to the central peaks, a pair of stable sidebands, which have delta-function distributions, and two pairs of sidebands, which are similar but sharper than those for the symmetric modes. Detail comparisons are given between the one- and two-atom excitation spectra for the systems under investigation.     

One- and two-photon resonance fluorescence of a three-level atom at high photon densities

We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.     

Resonance fluorescence spectrum of a three-level atom. II. Numerical results

Numerical computations are presented for the excitation spectra arising from the interaction between a three-level atom in the cascade configuration and a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered when the laser field is at resonance with the equally spaced levels of the atom as well as a function of the detunings. The physical process of optical amplification occurs without population inversion and it is more pronounced when the laser field is detuned than when it is at resonance. The shapes of the spectral lines for a number of side-bands are of the absorption-amplification type rather than that of the absorption one. In the presence of detunings as well as in the cooperative two-photon cascade process, the resulting spectra are far more complicated than those occuring at resonance. Results of numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically.     

Cooperative effects in the two atom resonance fluorescence spectrum

We consider the resonance fluorescence spectrum of two similar interacting atoms in the limit of high photon densities. The excitation spectrum of the symmetric modes contains two sidebands in addition to the usual three peaks which are analogous to those of the isolated atom. These two new sidebands are due entirely to the cooperative behaviour of the two atoms and vanish when the atoms are far apart. The energy shifts and spectral widths for these two sidebands are two and five times larger than those for the isolated atom respectively. The probability of occurrence of these sidebands depends on the parameters V_AB/Ω and γ²₀/Ω², where V_AB is the dipole-dipole interaction energy, γ₀ is the spontaneous emission probability and Ω is the Rabi frequency. The asymmetric broadening of both sidebands depends on the parameter γ₀/Ω. The possibility to measure the dipole-dipole energy through the observation of these sidebands is discussed.     

The influence of quantum interference effects on the resonance fluorescence spectra of a degenerate three-level atom

The resonance fluorescence spectra of a degenerate three-level atom of the V-type in the field of an intense monochromatic wave with an arbitrary polarization composition are investigated. Analytical expressions are derived for the resonance fluorescence spectra, and the angular distribution of spontaneous fluorescence of atoms is analyzed for the D-line emitted by vapors of alkali atoms. It is shown that the number of lines in the spectrum may decrease in the case of the linear polarization of spontaneous radiation. The radiation relaxation operator is obtained for the D-line of alkali metals in the case when an atom is near the metal surface. Interference effects for such systems are analyzed.     

Squeezed states in resonance fluorescence of two interacting atoms

The possible existence of so-called “squeezed” states in two-atom resonance fluorescence is discussed in Lehmberg's master equation approach. It is shown that squeezing strongly depends on interatomic separations r₁₂. For large r₁₂ one of the quadrature components is squeezed, and as r₁₂ decreases its squeezing decreases in order to appear in the other quadrature component for certain value of r₁₂. For very small r₁₂ fluctuations in both components tend to zero.     

Enhamcement of photon antibunching by interference II. Polarization effects

As one expects photon antibumching is a small effect for great mean photon numbers. In addition perceptible k-photon absorption (k≥2) which produces photon antibunching, needs large mean photon numbers. In order to measure a great anticorrelation effect in a Hanbury Brown-Twiss experiment we have to reduce the intensity by interference. How this can be accomplished with the help of polarizers is shown in this paper. This method is in certain analogy to the principles of the polarization spectroscopy.     

光腔中两原子共振荧光的相干性质

研究了置于光腔中的两个二能级原子，在强相干场驱动下的共振荧光光场的辐射场相干性质，发现在坏腔条件下，可以通过调节光腔与相干场的频率来提高一阶可见度和减小二阶关联函数.这是因为改变光腔与相干场的频率会引起原子修饰态布居数的改变，导致一阶可见度和二阶关联函数发生显著变化. 关键词： 光腔 两个二能级原子 一阶可见度 二阶关联函数     

Collective effects in the self-interference of a single photon emitted by two atoms

Collective effects in the spontaneous emission pattern of two identical two-level atoms a fixed distance apart and sharing initially a single excitation are investigated. It is shown that the interference can take place even when it is known for certain which atom is excited initially. This interference is due solely to the atomic coherence established through multiple photon absorptions and reemissions and will disappear if it is ignored. The interference patterns with and without collective effects are compared for symmetric and antisymmetric initial states. The dark center from an antisymmetric state is shown both analytically and numerically.     

Influence of interference effects of spontaneous emission on the behavior and spectra of resonance fluorescence of a three-level atom in a strong wave field

An investigation is made of the influence of quantum interference processes accompanying radiative relaxation of excited states on the population dynamics, total intensity, and spectra of the resonance fluorescence of three-level V-type atoms. Analytic expressions are obtained for the total intensity and spectra of the resonance fluorescence taking into account the off-diagonal nature of the radiative relaxation operator. It is shown that quantum interference process can substantially alter the total spontaneous emission intensity of the atoms and the population dynamics of the atomic levels, as well as the resonance fluorescence spectra.     

Antibunching,sub-poissonian photon statistics and finite bandwidth effects in resonance fluorescence

It is demonstrated that, although the fluorescent photons from a driven two-level atom always exhibit antibunching, they need not obey sub-poissonian statistics. The maximum sub-poissonian excursion of the normalized second factorial moment (〈(Δn)²〉 ? 〈n〉)/〈n〉 occurs in the transient regime where it can approach the value -1. Effect s of finite bandwidth of excitation on photon statistics are also investigated and it is shown that the photon number distribution may be narrower with finite bandwidth excitation than with coherent excitation.     

两个V型三能级原子系统的纠缠突然死亡与复苏

研究了在真空辐射场作用下,两个V型三能级原子系统的纠缠随时间的演化特性.发现当两原子间距较远,自发辐射会导致纠缠退化,甚至导致纠缠突然死亡,而原子激发态衰变的速率会影响纠缠死亡的时间;当两原子间距非常小,由于原子间的合作效应,死亡后的纠缠会在一段时间后复苏,初始的纠缠和复苏的纠缠由不同的原因引起.     

Interference in the virtual photon clouds of two hydrogen atoms

The possibility of interference effects between the clouds of two ground-state hydrogen atoms at large distances is considered. It is shown that no interference is present in the quantum average of the coarse-grained energy density operator at O(e²). Interference between the two clouds is shown to take place at O(e⁴).     

Imaging of s and d partial-wave interference in quantum scattering of identical bosonic atoms

We report on the direct imaging of s and d partial-wave interference in cold collisions of atoms. Two ultracold clouds of 87Rb atoms were accelerated by magnetic fields to collide at energies near a d-wave shape resonance. The resulting halos of scattered particles were imaged using laser absorption. By scanning across the resonance we observed a marked evolution of the scattering patterns due to the energy dependent phase shifts for the interfering s and d waves. Since only two partial-wave states are involved in the collision process the scattering yield and angular distributions have a simple interpretation in terms of a theoretical model.     

Dynamics of the collective spontaneous emission of two three-level atoms in a cavity

Based on the master equation for the density matrix, the collective spontaneous emission of two A-type three-level atoms interacting with two modes of a quantum electromagnetic field in a finite-Q cavity is studied. The evolution of the emission intensity for each mode is found for the case where both atoms are initially in the excited state.     

Detection of low gas densities by resonance fluorescence in the vacuum ultraviolet

An experimental arrangement is described which allows the detection of low gas densities by resonance fluorescence in the vacuum ultraviolet. As a light source a capillary discharge through helium was used. Fluorescence signals as a function of density have been measured in krypton, deuterium, and hydrogen, and the results have been compared with calculations. Detection limits of 3·10⁹ atoms/cm³ have been obtained.     

The fluorescence spectrum of a three-level atom in two-photon resonance with the laser field

The influence of the two-photon resonant interaction on the fluoresence spectrum of a three-level atom is studied. The levels in questions are the 1S, 2P and 3S states of a two-electron atom. It is shown, that in the case of exact two-photon resonance between the 1S–3S transition and the laser field, and when the 2P state is out of resonance, the fluorescence spectrum contains 4 lines. The properties of these lines are discussed.     

三能级原子与耦合腔相互作用系统中的纠缠特性

采用Negativity熵来度量两个子系统间的纠缠,利用数值计算方法研究了简并Λ型三能级原子和简并V型三能级原子与耦合腔共振相互作用系统中原子之间、腔场之间和原子与腔场间的纠缠特性.给出了系统初始激发数为1时系统态矢的演化公式;讨论了腔场间的耦合系数变化对纠缠特性的影响.研究结果表明:随腔场间的耦合系数增大,原子间的纠缠增强,腔场间的纠缠减弱.     

Interference effects in the scattering of identical atoms in a laser radiation field

The properties of the collision integral in a quantum Boltzmann-type kinetic equation are studied under the conditions of spatially nonuniform distributions of colliding particles interacting with an external electromagnetic field. The components of the nonlinear resonances and the velocity distribution of the excited atoms, which are due to polarization transitions, are determined on the basis of the Kazantsev collision integral.     

Phase-conjugation in two-level atoms: comparison of quantum interference theory to exact results

The analytically derived predictions of a recently developed theory on phase conjugate four wave mixing (FWM) in two-level atoms [Phys. Rev. A 60, 1672 (1999)], which interprets many of the signal features as a consequence of quantum interference between the probability amplitudes for photon emission from relevant dressed states, is compared to the results that one obtains from a non-perturbative, numerical calculation of the density matrix equations. The results delineate the regimes and assumptions under which the perturbative results are valid, and it is shown that despite the simplifying assumptions that are invoked for the dressed state theory, many of its predictions are in qualitative agreement with the exact, numerical results.