Degenerate Atomic Levels Research Articles

Double-Λ electromagnetically induced transparency with degenerate atomic levels

The general expression for the transformation matrix of the two input weak arbitrarily polarized probe fields passing through the medium under the conditions of double-Λ electromagnetically induced transparency is obtained for arbitrary values of the amplitudes, phases and polarizations of the control fields and arbitrary values of the angular momenta of resonant levels. The conditions are found for the two input weak probe fields linearly polarized in perpendicular planes to exchange their polarizations after the passage through the medium without absorption. The polarization rotation of the probe fields is studied for the atoms being initially in the equilibrium state.

The dynamics of an atom-field system with degenerate atomic levels and a polarization-degenerate mode of the quantised field in a damped micro-cavity

The master equation for the atom-field system with degenerate atomic levels and two polarization modes of the quantized field in a damped micro-cavity is obtained in the basis of eigenvectors of the interaction operator. The solution for the lossless cavity is obtained. The analytic expressions for the probability of emission of the photon in the cavity by an excited atom and of the photon polarization matrix are derived in the ‘strong coupling’ and ‘bad cavity’ approximations for arbitrary values of angular momenta of atomic levels. The dependence of the photon polarization on the polarization of the short excitation pulse is studied.

Jaynes–Cummings model with degenerate atomic levels and two polarization modes of the quantized field

The Jaynes–Cummings model describing the interaction of two polarization modes of the quantized electromagnetic field with an isolated two-level atom with the levels degenerate in the projections of the angular momenta on the quantization axis is studied. The general expression for the evolution operator for such a model is obtained. The examples of low values of the level angular momenta or single photon in the cavity are discussed.

Fluctuation properties of laser light after interaction with an atomic system: Comparison between two-level and multilevel atomic transitions

The complex internal atomic structure involved in radiative transitions has an effect on the spectrum of fluctuations (noise) of the transmitted light. A degenerate transition has different properties in this respect than a pure two-level transition. We investigate these variations by studying a certain transition between two degenerate atomic levels for different choices of the polarization state of the driving laser. For circular polarization, corresponding to the textbook two-level atom case, the optical spectrum shows the characteristic Mollow triplet for strong laser drive, while the corresponding noise spectrum exhibits squeezing in some frequency ranges. For a linearly polarized drive, corresponding to the case of a multilevel system, additional features appear in both optical and noise spectra. These differences are more pronounced in the regime of a weakly driven transition: whereas the two-level case essentially exhibits elastic scattering, the multilevel case has extra noise terms related to spontaneous Raman transitions. We also discuss the possibility to experimentally observe these predicted differences for the commonly encountered case where the laser drive has excess noise in its phase quadrature.

Mixed Rabi Jaynes–Cummings model of a three-level atom interacting with two quantized fields

The quantum Rabi model describes the ultrastrong interaction of a two-level atom coupled to a single quantized bosonic mode. As compared to the Jaynes–Cummings model, in the Rabi model the absorption and emission processes do not need to satisfy energy conservation and the usual rotating wave approximation (RWA) breaks down. As a result, the atom-field dynamics in the Hilbert space splits into two independent parity chains, exhibiting a collapse-revival pattern and exact periodic dynamics in the limit of degenerate atomic levels. Here we introduce a mixed Rabi Jaynes–Cummings model by considering a three-level atom interacting with two quantized bosonic fields, in which the RWA is made for one transition (with a weak atom-field coupling) but not for the other one (with an ultrastrong atom-field coupling). As a result, we show that the field in the weak coupled atomic transition can be used as a tool to control the atom-field dynamics of the other (strong coupled) transition, thus realizing an effective two-level quantum Rabi model with a controllable field. In particular, a periodic temporal dynamics of the atom-field state can be realized by appropriate tuning of the weak control field, even for non-degenerate atomic levels. A photonic simulator of the mixed Rabi Jaynes–Cummings model, based on light transport in evanescently coupled optical waveguide lattices, is also briefly discussed.

Electromagnetically induced transparency with degenerate atomic levels

For the coherently driven Λ-type three-level systems the general expression for the susceptibility tensor at the frequency of the weak probe field is obtained for the arbitrary polarization of the strong coupling laser field and arbitrary values of the angular momenta of resonant atomic levels. The dependence of the relative difference in the group velocities of the two polarization components of the probe field on the polarization of the coupling field is studied.

Plasma formulary interactive

We present an interactive, Web-based application that provides a comfortable access to evaluating, comparing, and plotting of a multitude of different plasma and atomic physics parameters, grouped by the unit dimensions. A special attention is devoted to the Stark broadening which is calculated with a good accuracy for transitions between degenerate atomic levels. The list of the entities calculated encompasses over one hundred entries and is easily expandable. The application is built using open-source components and is compatible with a majority of modern browsers.

Dissipation of System and Atom in Two-Photon Jaynes–Cummings Model with Degenerate Atomic Levels

The method of perturbative expansion of master equation is employed to study the dissipative properties of system and of atom in the two-photon Jaynes-Cummings model (JCM) with degenerate atomic levels. The numerical results show that the degeneracy of atomic levels prolongs the period of entanglement between the atom and the field. The asymptotic value of atomic linear entropy is apparently increased by the degeneration. The amplitude of local entanglement and disentanglement is suppressed. The better the initial coherence property of the degenerate atom, the larger the coherence loss.

The effect of degenerate atomic levels on the field state dissipation in two-photon Jaynes-Cummings model

The dissipation of the field in the two-photon Jaynes-Cummings model (JCM) with degenerate atomic levels was studied. The initial degenerate atomic state affects the field coherence loss. When the degenerate atom is initially in an equal probability superposition state, the field coherence loss is smallest. It is found that the degeneracy of the atomic level increases the period of entanglement between the atom and the field. When the degeneracy was considered, the coherence properties of the field could be affected by the reservoir qualitatively, if a nonlinear two-photon process is involved. This is different from the dissipation of one-photon JCM with degenerate atomic levels.

The Fermi model as a key for understanding excited state potential energy curves

The interaction of a Rydberg electron with a ground-state atom is modelled using the Fermi approximation to obtain long-range potentials for various excited diatomic molecules. Particular attention is paid to the cases of degenerate and near-degenerate atomic Rydberg levels. Extensive comparisons are performed with recent ab initio calculations for 1Σ + and 3Σ + states of NaH and He 2, for up to the ninth state of a specified symmetry in the former. Overall, good qualitative and in some cases, quantitative agreement is found. For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several atomic states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single non-zero potential emerges from the remaining flat manifold. Such behaviour explains, for example, the presence of high barriers at large distances seen in ab initio calculations for the 1,3Σ + 4f states of NaH. For NaH, the Fermi results are generally better for the weaker triplet interactions than the singlets. In case of near-degenerate levels, the weaker interactions are normally described better than the stronger interaction, where avoided crossings (not included in this simple model) may be important. The Fermi model is also shown to yield a physically sound diabatic approach for excited states of diatomic molecules, allowing for a deeper understanding of the unusual shapes of the adiabatic curves. Limitations of the Fermi model are also discussed.

Undulations in potential curves analyzed using the Fermi model: LiH, LiHe, LiNe, andH2examples

The interaction of a Rydberg electron with a ground-state atom is modeled using the Fermi approximation to obtain long-range potentials for various excited diatomic molecules. Particular attention is paid to cases of degenerate and near-degenerate atomic Rydberg levels. Extensive comparisons are performed with recent ab initio calculations for 1 Σ + and 3 Σ + states of LiH and H 2 , also 2 Σ + states of LiHe, for up to the ninth state of a specified symmetry. Results for LiNe are also discussed. Overall, good qualitative and in some cases quantitative agreement is found. For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single nonzero potential emerges from the remaining flat manifold. Such behavior explains, for example, the presence of high barriers at large distances seen in ah initio calculations for the 1 , 3 Σ + g , u n=3 states of molecular hydrogen. For the systems involving H the Fermi results are generally better for the weaker, triplet interactions than the singlets. In the case of near-degenerate levels the weaker interactions are normally described better than the stronger interaction, where avoided crossings (not included in this simple model) may be important. In LiHe, where the interactions are weaker, generally for separations larger than about 10a 0 the Fermi model obtains barrier positions within 1a 0 and maxima within 10 cm - 1 . For LiNe, because of the very small scattering length for electrons in neon, largely qualitative results are obtained. The Fermi model is also shown to yield a physically sound diabatic approach for excited states of diatomic molecules, allowing for a deeper understanding of the unusual shapes of the adiabatic curves. Limitations of the Fermi model are also discussed.

The dissipative dynamics of the Jaynes-Cummings model with degenerate atomic levels

We studied the dissipative dynamics of a degenerate-level atom interacting with a single linearly polarized mode field in the dispersive approximation. It is found that the degeneracy of the atomic levels affects the dissipation of the system, of the atom and the field. The period of entanglement becomes much longer than that in the usual Jaynes-Cummings model dissipation. The degeneracy of the atomic level increases the maximum value of the degree of the statistical mixture.

Sums of products of Coulomb wave function over degenerate states

The sums of products of Coulomb wave function over degenerate states are expressed in terms of quadratic forms that depend on the wave function of only one state with zero orbital angular momentum l = m = 0. These sums are encountered in many fields in the physics of atoms and molecules, for example, in investigations of the perturbation of degenerate atomic energy levels of a small potential well, a delta-function potential. The sums were found in an investigation of the limit of the Coulomb Green's function G(r, r', E), where the energy parameter E approaches an atomic energy level: E --> E-n, E-n = -Z(2)/2n(2). The Green's function found by L. Hostler and R. Pratt in 1963 was used. The result obtained is a consequence of the degeneracy of the Coulomb energy levels, which in turn is due to the four-dimensional symmetry of the Coulomb problem. (C) 2000 MAIK "Nauka/Interperiodica".

Electromagnetically induced absorption

A large increase in atomic absorption due to coherent interaction with resonant radiation is predicted for a closed transition between two degenerate atomic levels verifying $0<{F}_{g}<{F}_{e}{(F}_{g}$ and ${F}_{e}$ are the total angular momentum of the ground and the excited levels, respectively). In good agreement with the theoretical prediction, a total absorption enhancement by a factor 1.7 was obtained on the ${D}_{2}$ line of ${}^{85}\mathrm{Rb}\mathrm{}$ in a vapor cell experiment.

Nonlinear Theory of Many Effective Two-Photon Correlated-Spontaneous-Emission Lasers11The project supported by National Natural Science Foundation of China

In this paper, we transform the nonlinear density matrix equation for many effective two-photon correlated-spontaneous-emission laser field obtained recently by the author to the Fokker-Planck equation, and then discuss the inffluence of atomic coherences and the number of lower almost degenerate atomic levels on the lasing without inversion and noise reduction or phase squeezing of the field.

Influence of Atomic Phase Fluctuations on Field Squeezing and Brightness of Many Two-Photon Correlated-Spontaneous-Emission Lasers11The project supported by National Natural Science Foundation of China

We show in this paper that phase fluctuations of active atoms in many two-photon correlated spontaneous-emission lasers will reduce field squeezings and brightness of the squeezed light. But, under certain conditions of laser operation, the fluctuations of atomic phases between lower almost degenerate atomic levels could increase the squeezings and the brightness. We also show that, even for large phase fluctuations of the active atoms, almost perfect field squeezings and substantial brightness of the squeezed light can be obtained.

Phase and photon-number squeezings in a many-cascade two-photon correlated-spontaneous-emission laser

I show that, in the case of both one- and two-photon resonances, a many-cascade two-photon correlated-spontaneous-emission laser can generate light exhibiting phase and photon-number squeezings. Optimizing the mean photon number in the cavity with respect to a phase factor sin[1/2(n-1)\ensuremath{\theta}]/sin(1/2\ensuremath{\theta}), we find that the maximized mean photon number and its squeezing increase with increasing the top populations ${\mathrm{\ensuremath{\rho}}}_{\mathit{n}\mathit{n}}^{\mathit{a}}$ of the active atoms. However, the photon-number squeezing may decrease, increase, or not change when increasing the number n-1 of lower, almost degenerate atomic levels, depending on the relative phase \ensuremath{\theta} of lower atomic states determined by the optimization conditions. The phase squeezing has a maximum value with increasing n-1 and ${\mathrm{\ensuremath{\rho}}}_{\mathit{n}\mathit{n}}^{\mathit{a}}$.

Theory of saturation spectroscopy including effects of level degeneracy

A theory of saturation spectroscopy is developed which accounts for effects of level degeneracy. The theory can be applied to those situations in which a pump laser field of arbitrary strength and polarization acts between two manifolds of degenerate or nearly degenerate atomic levels, while a probe laser field of arbitrary strength and polarization acts between a coupled manifold of levels. As such, this theory of "three-level" systems could, in principle, include effects arising from level degeneracy, optical pumping, atomic motion, transient laser fields, different polarizations and strengths for pump and probe fields, and atomic transit across the laser fields. The present calculation, however, is limited to a study of optical pumping and field polarization effects for pump fields of arbitrary strength and weak probe fields interacting with a single velocity subclass of atoms. Probe absorption line shapes clearly display the effects of pump-field strength (Rabi splittings), pump-field polarization (positions and number of Rabi-split resonance peaks), pump-field detuning (positions of resonance peaks), and optical pumping (relative strengths of the resonance peaks). The calculation is carried out with the use of an irreducible tensor basis for the atomic density matrix although a standard ($m$-basis) calculation is included in an appendix.

Correlation effects in collisional depolarisation and redistribution of radiation

The author derives an expression for the spectrum of the radiation scattered by an atom that suffers binary collisions in the weak-field limit. The frequency of the incident radiation is in near-resonance with a multiplet transition. The authors accounts for strong atom-perturber correlations that are induced when the incident or the detected frequency is in the far wing of an absorption line. For an isolated transition between two degenerate atomic levels the model picture of quasistatic absorption followed by adiabatic reorientation of the excited state predicts a redistributed fluorescence line with a polarisation that is determined by geometrical factors.

Saturation-induced polarization preferences in two-mode oscillating gas lasers

Equations are derived describing the time evolution of the polarization parameters of a two-mode oscillating isotropic gas laser. The equations are presented in a form particularly well suited for investigating the cross-saturation effect on the polarization behavior of the two modes, and apply to all kinds of degenerate atomic levels and arbitrary resonator tunings. It is found as a general rule that mode-mode interaction results in modes whose polarizations are mutually orthogonal. An exception to this rule is found in the case of j→ j( j1) transitions, in which, under special tuning conditions two circularly polarized modes with the same sense of rotation from a stable solution as well.