Stimulated emission of a laser photon by the excited states of a three-level atom

We study the stimulated emission spectra arising from the emission of a laser photon by two excited states of a three-level atom interacting with a laser field at low intensities. The lifetimes of the stimulated photons emitted by the two excited states are much longer than those emitted spontaneously, while the intensities of the induced peaks take negative values indicating that amplification occurs at low frequencies. The ratio of the intensities of the light emitted by the excited states |3 > and |2 > of the atom is proportional to (₃/₂)^1/2, where ₃ and ₂ are the radiative decay rates of the spontaneously emitted photons by the excited states |3 > and |2 > into the ground state |1 > of the atom, respectively. An absorption spectrum is induced into the ground state of the atom by the laser field. The competition between induced absorption and stimulated emission at low frequencies without population inversion is considered in the low-intensity limit of the laser field. It is shown that for values of ₃/₂ > 1 the relative intensity (height) of the induced peak takes positive values implying that the process of the induced absorption dominates. As the ratio ₃/₂ increases, the height of the induced peak decreases and vanishes for values of ₃/₂ < 400. For values of ₃/₂ > 400, the height of the induced peak becomes negative indicating that the process of the stimulated emission (amplification) is likely to occur at low frequencies. The computed spectra are graphically presented and discussed.Issued as NRCC No. 39088     

Simultaneous position and state measurement of Rydberg atoms

We present a technique for state-selective position detection of cold Rydberg atoms. Ground state Rb atoms in a magneto-optical trap are excited to a Rydberg state and are subsequently ionized with a tailored electric field pulse. This pulse selectively ionizes only atoms in e.g. the 54d state and not in the 53d state. The released electrons are detected after a slow flight towards a micro channel plate. From the time of flight of the electrons the position of the atoms is deduced. The state selectivity is about 20:1 when comparing 54d with 53d and the one-dimensional position resolution ranges from 6 to 40 μm over a range of 300 μm. This state selectivity and position resolution are sufficient to allow for the observation of coherent quantum excitation transport.     

Nonlinear resonances and phase transitions of two-ion Coulomb clusters in a Paul trap: Calculations without laser cooling

The mechanism responsible for transitions of laser-cooled trapped ions from an ordered crystal state to an irregular cloud state has been discussed controversially. A numeric and analytic study of the relative motion of two trapped ions without laser cooling is performed and compared with the results of previous simulations involving the laser. It turns out that the system without laser, in spite of its simplicity, already exhibits a non-monotonic dependence of crystal stability on trap parameters, which is linked to the presence of low-order nonlinear resonances.     

Studies of trapped strontium ions in low magnetic fields

The effect of weak magnetic fields ( 1 mT) on small clouds and single ions of strontium has been studied. The fluorescence rate and hence the cooling efficiency is sharply reduced for fields of less than around 0.2 mT. The magnetic field also splits the various levels involved through the Zeeman effect. In particular, the² S _1/2–² D _5/2 transition at 674 nm, which is the basis for a potential optical frequency standard, is split into a maximum of 10 components, depending upon the experimental geometry. This is studied for various configurations of the magnetic field and 674 nm laser polarization. The implication for frequency-standards work is that the standard will need to be operated in a small but highly stable field.     

Ion formation in laser-irradiated cesium vapor

We study theoretically the formation of Cs⁺ and during cw laser radiation resonant with 6s-7p transition of Cs atomic vapor. This is done by numerically solving rate equations for the evolution of atomic state and electron populations. The results of calculations for the atomic and molecular ions density at different values of laser power clarified that the associative ionization and Penning ionization process play an important role for producing the and Cs⁺, respectively, during the plasma formation. Also, the results showed that laser power of the order of 150 mW and 40-50 ns irradiation time are optimal in producing a fully ionized plasma.     

Ionization of a hydrogen atom from its ground state by a coherent bichromatic laser field

We study the “coherent phase control” between the three-photon ionization by a fundamental laser field and the one-photon ionization by its third harmonic for a hydrogen atom in its ground state. The relative phase δ of the harmonic field with respect to the fundamental laser radiation “modulates” the interference between the two ionization channels, which is important near the crossing points between the ionization rates of the two individual processes. Numerical results for the total ionization rate and for the angular distribution of the photoelectrons as a function of the phase δ are presented for frequencies located in the vicinity of the atomic resonances corresponding to the absorption of two laser photons. Received 31 August 2000 and Received in final form 6 February 2001     

Saturation intensity for ultrashort-pulse X-ray laser schemes

Analytic expressions are obtained for the saturation intensity in X-ray laser schemes based on short-pulse high-intensity drivers. For field-ionized plasma schemes, the specific mean saturation intensityJ _sat is time independent and depends only on atomic transition probabilities, level degeneracies, and transition energies. The analytic expression is found to be in good agreement with a detailed numerical calculation. Integrating over space and frequency gives a saturation intensityI _sat of order 2 × 10¹¹ W/cm² for lasing in Li-like Ne at 98 . The low input energy requirements for this scheme (< 1 J), associated with using a confocal geometry, give energy efficiencies of order 10^–6 and greater. For inner-shell photo-ionization schemes, an accurate expression for a time-dependent saturation intensity is obtained. This scheme is calculated to have high saturation intensities,I _sat 10¹³ W/cm², at short wavelengths (5–15 ). The requirement of a line focus geometry leads to higher input energies (5 J) and the short duration of lasing (50 fs) results in lower energy efficiencies ( 10^–7). Repetition rates are important in determining appropriate applications for both schemes.     

Laser preparation of polarized nuclei: Absorption of one polarized photon is enough and no high spectral resolution is needed to achieve 100% polarization

A new method to prepare photoions with the polarized nuclear spin is proposed. Selected total electron momentum state |J,mJ〉$|J,m_J〉$ is excited by short (pico- or (sub)nanosecond) spectrally broad laser pulse which does not resolve a hyperfine structure thus preparing a superposition of all sublevels of the total angular momentum F   of an atom. Initially unpolarized nuclear spin state becomes highly polarized in a course of subsequent free quantum evolution, and at appropriate time an atom is ionized by another short laser pulse. For the case of nuclear spin I=1/2$I=1/2$, absorption of only one polarized photon is needed to achieve 100% nuclear polarization.     

Laser collimation of an Fe atomic beam on a leaky transition

We report results of the first laser collimation of a thermal beam of Fe atoms on the leaky ⁵D₄ ⁵F₅ transition, with both parallel linear ^xx and crossed linear ^xy laser polarization configurations. The measured atomic beam divergence is compared to a rate-equation model and a quantum Monte Carlo model. The experimental values for the divergence are limited by the finite laser line width, which is comparable to the natural line width of the Fe atom. In general, flux decreases with higher intensities, showing the effect of the leaky transition. At the best beam collimation _RMS = 0.17 mrad, which is for a detuning of = – and a saturation parameter of s = 6, the flux decreased to approximately 70%. Highest flux was measured for a detuning of = –2 and s = 4, reaching 135% of the uncooled value. From our measurements we estimate the total leak rate to be 1/(240 ± 40), which is in good agreement with the literature value of 1/244. The crossed linear polarization configuration is the better choice, with a slightly better collimation but the same atomic beam flux. Plugging of the largest leak would increase the flux to at least 80% of the closed transition value, resulting in better contrast for atom lithography.     

Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap

We present an investigation of sub-Doppler effects in a cesium magneto-optical trap. First, a simple one-dimensional theoretical model of the trap is developed for aJ _g = 1 J _e = 2 transition. This model predicts the size of the trapped atom cloud and temperature as a function of laser intensity and detuning. In the limit of small magnetic field gradients, the trap temperature is found to be equal to the molasses temperature and a minimum size for the trap is calculated. We then describe several experiments performed in a three-dimensional cesium trap to measure the trap parameters, spring constant, friction coefficient, temperature and density. Whilst the temperature of the trapped atoms is found to be equal to the molasses temperature, in agreement with theory, the trap spring constant is found to be two orders of magnitude smaller than the one-dimensional prediction, a value close to that predicted by Doppler models. The maximum density is found to be on the order of 10¹² atoms/cm³ or one atom per optical wavelength on average. When the number of trapped atoms becomes large, the temperature begins to increase dramatically. This excess temperature depends in a very simple way on the atom number, laser intensity and detuning, suggesting that its origin lies in multiple photon scattering within the trap.     

Optogalvanic spectra of calcium in the 6090–6760 Å region

Optogalvanic spectra of some 30 transitions of calcium originating from the ground state as well as from several excited states (4s4p ^1,3P, 4s3d ^1,3D, 4s5p ³P, 3d4p ³D, ³F) have been investigated using laser-irradiation of a low-current glow discharge in a thermionic diode. The influence of various experimental parameters such as bias field, oven temperature and buffer gas pressure on the spectra are reported. Seven previously unreported transitions are recorded including four forbidden transitions which violate the J selection rules. An interesting anomaly observed in the non-statistical population of the 4s3d ³D_3,2,1 multiplet is discussed where the populations of ³D₃:³D₂:³D₁ are in the ratio of 94:5:1. A possible explanation is based on avoided crossing between potential energy curves of the Ca-Ar molecule.     

Non-adiabatic quantum molecular dynamics: General formalism and case study H<Subscript>2</Subscript><Superscript>+</Superscript> in strong laser fields

In Rydberg atoms subject to static and harmonic collinear electric fields, intrashell transition can be induced by the first order perturbation from a small perpendicular electric or magnetic field, or by effects of the second order in the major fields. Both mechanisms lead to resonances that are suppressed under certain conditions, and high-frequency interference oscillations in case of non-adiabatic field switching. Recent measurements of microwave ionization signals show very rich and fascinating structures similar to the ones predicted for intrashell mixing. We show that the observed ionization structures may be explained by diabatic electric-field ionization and the consistent use of perturbation theory for intrashell mixing. In particular, the dominant oscillation frequency is successfully interpreted in terms of interference between first and second order transition amplitudes. New predictions are provided. The present approach gives a comprehensive picture of intrashell transitions, which may be tested in future experiments designed to observe such transitions directly. Received 2 May 2002 / Received in final form 23 September 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: Valentin.Ostrovsky@pobox.spbu.ru RID="b" ID="b"e-mail: horsdal@ifa.au.dk     

Phase properties of a Jaynes-Cummings model with Stark shift and Kerr medium

Phase properties of the field interacting with a two-level atom in a lossless cavity Jaynes-Cummings model, taking into account the level shifts produced by Stark effect with an additional Kerr medium for one-mode are studied using the phase formalism of Pegg and Barnett. It is shown in particular that phase properties of the field reflect the collapse and revival phenomena. The results for the time evolution of the phase probability distribution and the phase fluctuations are obtained. The effect of Stark shift on the phase properties in both the absence and presence of a Kerr medium is analyzed. Phase localization is found for certain choice of the parameters. Received: 27 March 1998 / Revised: 8 June 1998 / Accepted: 9 June 1998     

Two dimension selective coherent population trapping controlled by a phase shift

Two-dimensional laser cooling based on velocity-selective coherent population trapping is investigated theoretically for the J _g=1J _e=0 atomic transition. Wavevectors and polarizations of three laser beams are chosen to realize a coherent superposition of three degenerate ground states. For the first time in laser cooling, use is made of the electric field phases to realize coherent population trapping selective in two dimensions. Numerical solutions and analytic estimates are presented for laser cooling of helium atoms.     

Electron-ion recombination and photoionization of Fe XXI

Results for electron-ion recombination and photoionization of , with emphasis in high-temperature region, are presented from ab initio unified method. The unified method, based on close coupling (CC) approximation and R-matrix method, (i) subsumes both the radiative recombination (RR) and dielectronic recombination (DR), (ii) enables self-consistent sets of photoionization and recombination cross sections from using an identical wavefunction for both the processes, and (iii) provides state-specific recombination rates of a large number of bound states. A large CC wavefunction expansion, which includes the ground and 28 core excitations of n=2 and 3 complexes and span a wide energy range, has been used. Compared to Δn=2-2, Δn=2-3 core excitations are found to introduce strong resonant structures and enhance the background photoionization cross sections (σ_PI) in the high-energy region. These features along with prominent photoexcitation-of-core (PEC) resonances at n=3 core thresholds have increased the unified total recombination rate coefficients (α_R(T)) at temperatures , region of maximum abundance of the ion in collisional equilibrium, by a factor of 1.6 over previous calculations. State-specific recombination rate coefficients α_R(nLS), which include both the RR and DR, are presented for the first time for 685 bound states with n?10 and l?9. The unified total recombination rate with photoelectron energy α_R(E) is presented and the role of low-energy near-threshold fine structure resonances is illustrated. The present results should provide a reasonably complete self-consistent set of recombination rates and photoionization cross sections for astrophysical modelings of high-temperature plasmas from optical to far-ultraviolet wavelength regions.     

Sub-Half-Wavelength Atom Localization via Coherent Control of Autler-Townes Spontaneous Spectrum

We show that it is possible to localize an atom in a half-wavelength region by relaxing the strict condition that the atom is prepared in a specific excited state as in the recently proposed scheme [Phys. Rev. A 65 （2002） 043819]. In particular, we consider a four-level atom, for which a weak exciting field transfers population from the ground state to the excited state and three control fields （one standing-wave field while two travelling-wave fields） couple the excited state and two auxiliary states. By tuning the exciting field and by varying the collective phase of the control fields, the atom is localized in one of the two half-wavelength regions with 50% detecting probability. The main advantage of the scheme is the experimental accessibility and controllability.     

Retrodiction for coherent communication with homodyne or heterodyne detection

Previous work on the retrodictive theory of direct detection is extended to cover the homodyne detection of coherent optical signal states and . The retrodictive input state probabilities are obtained by the application of Bayes' theorem to the corresponding predictive distributions, based on the probability operator measure (POM) elements for the homodyne process. Results are derived for the retrodictive information on the complex amplitude of the signal field obtainable from the difference photocount statistics of both 4-port and 8-port balanced homodyne detection schemes. The local oscillator is usually assumed much stronger than the signal but the case of equal strengths in 4-port detection is also considered. The calculated probability distributions and error rates are illustrated numerically for values of signal and local oscillator strengths that extend from the classical to the quantum regimes.     

Two-step laser excitation of the highly excited even-parity states of atomic mercury

We report term energies and quantum defects of highly excited even-parity states of mercury in the 83 876–84 140 cm^-1 energy range, employing a two-step laser excitation scheme via the S₀↦6s6p³P₁ inter-combination transition. Two dye lasers, pumped by a common Nd:YAG laser, were frequency doubled by BBO crystals and used to record the spectra in conjunction with a thermionic diode ion detector. Our new observations include the much extended D₂ (22 ≤n ≤52) series and a few members of the S₁ (24 ≤n ≤30) Rydberg series. Members of the D₂ Rydberg series with such a high n value are reported for the first time. The relative intensities of the D₂ and S₁ transitions (m = 4, 5 and 6) of group II-B elements excited from the P₁ inter-combination states are also discussed.     

Light-induced effect on the density distribution in a sample of cold trapped atoms

As it is known [1] an intense laser field can induce atom-atom interaction according to a dipole-dipole R ^–3 law. Such an interaction depends on the angle between light polarization and interatomic vector-position R. This angular dependence may produce an anisotropy in the spatial density distribution of the confined sample of cold atoms. We develop the main relations and apply them to the case of an atomic cloud of cold trapped neutral atoms with the density higher than or of the order of ^–3, where is the wavelength of light. The results presented here show the effect of such an interaction in a density regime of high experimental interest.