One-photon Resonance Research Articles

Coherent propagation of an optical pulse in a fibre waveguide containing quasiresonant impurities. Adiabatic following approximation

An analysis is made of the propagation of ultrashort pulses in a fibre waveguide doped with resonant impurities. Equations describing the evolution of a pulse in the case of one-photon and two-photon resonances are derived on condition that the Rabi frequency is considerably less than the detuning from an exact resonance. The influence of impurity atoms on the parameters of a pulse and on the characteristics of its evolution (ultrashort pulse duration, 'soliton threshold', and ultrashort pulse collapse threshold) is determined. The corrections to these quantities have different signs for different types of resonance.

Fluorescence intensity and squeezing in a driven three-level atom: Ladder case.

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.

Observation of the SCI radical by resonance-enhanced multiphoton ionisation spectroscopy

Three hitherto unobserved vibrational levels of the b′3Σ–u electronic state of P2 have been identified via the rotationally resolved, one-photon resonance enthancements they provide in the multiphoton ionisation spectrum of this radical. Analysis yields an extended set of spectroscopic constants for the b′3Σ–u state and a first estimate of the relative strengths of the parallel and perpendicular contributions to the P2(b′3Σ–u–X 1Σ+g) transition moment. One additional, particularly intense but unresolved feature observed at an excitation wavelength of ca. 320.75 nm is tentatively assigned in terms of a two-photon resonance involving a Rydberg state of P2 with 1Σ+g symmetry.

Influence of the phase-matching conditions on the spectrum of four-photon light scattering at a one-photon resonance

An analysis is made of the influence of the phase matching conditions on the four-photon scattering spectrum at a one-photon resonance under various focusing conditions. An analytic expression is obtained for the phase matching integral in the limiting cases of hard focusing and strong absorption in a medium with the cubic nonlinearity. A study is made of the influence of one-photon resonances on the form of the spectrum of four-photon scattering by excited and preionisation states of atoms. Calculations are reported of the four-photon scattering spectra in which allowance is made for the interference of the resonant and nonresonant components of the third-order nonlinear susceptibility. A method for the normalisation of the experimental four-photon scattering spectra under one-photon resonance conditions is proposed; this method allows for the distortions associated with the influence of the phase mismatch and of one-photon absorption.

Time-resolved multiphoton ionization study of the 102 nm state of NO

We have used subpicosecond deep UV laser pulses (near 205 nm) in a time-resolved (2+1) multiphoton ionization study of the two-photon state of NO at 102 nm via a one-photon resonance with the A 2Σ+(3sσ) (ν=2) state. The two-photon excited state lifetime exhibits a strong pressure dependence from which the collisionless lifetime and the bimolecular depopulation or quenching rate constant were obtained. The large quenching rate constant strongly suggests that the state is a medium (10–12) n Rydberg level in the series converging to the ground electronic state of NO+. The subnanosecond collisionless lifetime implies that this state is subject to predissociation and/or autoionization.

Rydberg series of krypton excited from the 5p[3/2]1,2 states

We have studied high Rydberg states of krypton which are excitable from the 5p[3/2] states with J=1 and 2, using one-photon resonant, two-photon ionization beginning with the metastable 5s[3/2]2 state. An analysis of the ns and nd Rydberg state energies has allowed us to determine the ionization potential of Kr to an accuracy which is better than previous work, and resolves a discrepancy between previous laser-based and conventional spectroscopic results. The use of these intermediate states for the excitation of Rydberg states makes it possible to observe high members of series such as (n+2)s[3/2]1 and nd[1/2]1 which cannot be efficiently excited from the 5p' intermediate states which have been used in previous works.

Squeezing in two-atom resonance fluorescence induced by two-photon coherences

We examine squeezing properties of resonance fluorescence from two interacting atoms. Previous theoretical analyses of this model have predicted squeezing on one-photon resonance. Here we show that it is possible to obtain squeezing in two-atom resonance fluorescence through two-photon transitions induced by a cooperative atomic interaction. The squeezing occurs near a two-photon resonance and is not sensitive to the duration of the detection time in comparison with the decay time of the subradiant state. Moreover, squeezing near a two-photon resonance is completely independent of the direction of observation in respect to the atomic axis and can be significantly larger than that previously found on one-photon resonance.

Polarization and intensity spectra for Mg-Ne and Mg-Ar fractional collisions.

Extensive experimental studies of Mg-Ne and Mg-Ar fractional collisions are reported. In the fractional-collision process, two-color, two-photon absorption takes place during a single binary collision. Polarization and relative intensity spectra were measured in an approximately \ifmmode\pm\else\textpm\fi{}50-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range around the atomic Mg 3s $^{1}$${\mathit{S}}_{0}$\ensuremath{\rightarrow}3p $^{1}$${\mathit{P}}_{1}$\ensuremath{\rightarrow}5s $^{1}$${\mathit{S}}_{0}$ two-photon resonance. The generally-weak-field spectra show a remarkable phenomenology associated with the relative linear-polarization directions of the two exciting laser beams and with their separate detunings from atomic one-photon resonance. The polarization and relative absorption spectra display effects due to relative detuning, multiple Condon points, and laser intensity. Details of our experimental approach, and spectra for the process in Mg-Ar and Mg-Ne are presented and discussed. The data are seen to contain information on the short-range collision dynamics of the Mg--rare-gas pairs, and on the development of the alignment over the course of the collision.

Theory of laser-induced associative ionization of ultracold Na.

The rate coefficient for the laser-induced associative-ionization reaction of ultracold Na in an optical trap is calculated as a function of the trap laser detuning from the Na${(}^{2}$${\mathit{S}}_{1/2}$,F=2)\ensuremath{\rightarrow}Na${(}^{2}$${\mathit{P}}_{3/2}$,F=3) resonance. Aided by a knowledge of the excited-state potential-energy curves and of the nature of the free-atom optical-pumping process, we propose the following mechanism, which we call photoassociative ionization (PAI): 2Na${(}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}}^{+}$)${\ensuremath{\rightarrow}}^{\mathrm{\ensuremath{\Elzxh}}\mathrm{\ensuremath{\omega}}}$${\mathrm{Na}}_{2}^{\mathrm{*}}$(${0}_{\mathit{g}}^{\mathrm{\ensuremath{-}}}$ and ${1}_{\mathit{g}}$)${\ensuremath{\rightarrow}}^{\mathrm{\ensuremath{\Elzxh}}\mathrm{\ensuremath{\omega}}}$${\mathrm{Na}}_{2}^{\mathrm{*}\mathrm{*}}$(${1}_{\mathit{u}}$)\ensuremath{\rightarrow}${\mathrm{Na}}_{2}^{+}$+${\mathit{e}}^{\mathrm{\ensuremath{-}}}$. Maxima in the calculated PAI rate coefficient occur at detunings that are simultaneously one-photon resonant with bound levels of the long-range ${0}_{\mathit{g}}^{\mathrm{\ensuremath{-}}}$ state and two-photon resonant with the lower rotational levels of a vibrational level lying 9 GHz below the dissociation threshold of the autoionizing ${1}_{\mathit{u}}$ state. The calculated PAI spectrum (PAI rate coefficient versus trap-laser detuning) displays a series of broad peaks between -0.5 and -4 GHz detuning and a cutoff at -5 GHz detuning, as does the experimentally measured spectrum of Lett et al. [Phys. Rev. Lett. 67, 2139 (1991)].The broad widths of the peaks in the PAI spectrum is due in part to the orientation averaging of the collision vector with respect to the electric-field vector and to the optical pumping of the ${\mathrm{Na}}_{2}$\ensuremath{\rightarrow}${\mathrm{Na}}_{2}^{\mathrm{*}}$ rovibronic transition. The calculated PAI rate coefficient at -0.6 GHz detuning is a factor of 4 higher than the experimental value. Fine-structure-changing transitions play a role in the doubly excited states, because of the ${1}_{\mathit{u}}$ avoided crossing, but not in the intermediate states, because they have gerade symmetry and the only states that have been shown to undergo fine-structure-changing transitions with large probability have ungerade symmetry. Several predictions based on the proposed model and suggestions for future experiments are discussed.

Detection and characterization of gas-phase GaCl using resonance enhanced multiphoton ionization

We report resonance enhanced multiphoton ionization (REMPI) spectra of gas-phase gallium monochloride (GaCl) produced with laser light tuned between 330 and 430 nm. The spectra originate from one, two, and three photon resonances with electronic states that reside between 29 500 and 80 000 cm−1. We have assigned five Rydberg series comprised of 20 new electronic states. Each state exhibits a short vibrational progression. A least-squares fit of the unperturbed Rydberg state origins yields the adiabatic ionization potential, IPa(GaCl)=80 540±10 cm−1. We have also identified bands that originate from one-photon resonances with the previously known a 3Π state. We conservatively estimate the REMPI detection sensitivity for GaCl to be 109 molecules cm−3 (laser pulse)−1.

COLLECTIVE EFFECTS IN RESONANCE PROPERTIES OF A SYSTEM OF N TWO-LEVEL ATOMS

We consider resonance properties of an assembly of N two-level atoms interacting with an intense photon beam. The atoms are assumed to be noninteracting with each other except via the action of the electromagnetic field. Using the phase representation of the radiation field and the boson description of the atom system we calculate the one-photon resonance frequency for two kinds of the system: a beam of atoms moving with uniform velocity and a Boltzmann atom gas. The resonance frequency shift is found to be dependent on the total number of atoms and the initial preparation of the atom system. Numerical results show that the collective shift is of the same magnitude as the Bloch-Siegert one.

A study of the S 2(X 3Σ −g) molecule by multiphoton ionization spectroscopy

In this work the S 2 molecule has been studied using resonance enhanced multiphoton ionization (MPI) spectroscopy in the single-photon wavelength region 285–320 nm. This has resulted in the first spectroscopic observation of a gerade Rydberg state of S 2. The observed bands, which show spin—orbit structure, have been assigned to a two-photon resonant process, 3Δ g(3dπ←X 3Σ − g. Transitions to three vibrational levels (ν′ = 0, 1, 2) of the excited state have been recorded. This has enabled determination of vibrational constants ( ω e and ω eχ e) and the spin—orbit coupling constant of the 3Δ g state, whilst rotational constants ( B ν′) were derived from band head separations. A band in the MPI spectrum of S 2 corresponding to the one-photon resonance B 3Σ − u, ν′=8←X 3Σ − g, ν″=0 has also been observed. This has been detected in both the S + 2 and S + mass channels. Possible mechanisms for production of these ions via the B 3Σ − u state are discussed.

Photoelectron spectroscopy from the à 1A u state of acetylene: The bending vibrations of C2H+2 X 2Πu

Photoelectron spectra are reported for one-photon resonant, two-photon ionization of acetylene via a number of vibronic levels of the à 1Au state. Because the à 1Au state is trans bent and the X 2Πu ground state of the ion is linear, ionization from the à 1Au levels produces a long progression in the trans-bending vibration of the ion. The X 2Πu state is split by the Renner–Teller interaction along the trans-bending coordinate; the analysis of the photoelectron spectra allows the determination of the Renner–Teller parameters and leads to reassignments of the cis and trans-bending vibrations in earlier photoelectron studies.

Collisionless excitation of NH3 molecules via one- and two-photon transitions by multimode radiation of TEA CO2-laser

The excitation of ammonia by one- and two-photon transitions by TEA CO2-laser radiation has been studied under collisionless conditions. It has been shown that the experimental results of two-photon excitation of 14NH3 molecules in the 2v 2 a(1, 1) ← a(1, 1) transition by the 10P(24) CO2-laser line, the frequency offset of which is ≈ 0.02cm−1, can be described well by modelling the laser radiation as a broadband chaotic field. The experimental results of one-photon excitation in 14NH3 and 15NH3 [4], with the offset values exceeding the CO2-laser linewidth, can be also described well with the use of a chaotic field with a continuous spectrum. In the case of a nearly exact one-photon resonance, however, the excitation efficiency of molecules depends critically on the real mode structure of the CO2-laser radiation.

Ultrafast, room-temperature, resonance-enhanced third-order optical susceptibility tensor of an AlGaAs/GaAs quantum well

The ultrafast, room-temperature, resonance-enhanced third-order nonlinear susceptibility tensor of an AlGaAs/ GaAs quantum well is determined. A single 6-nm GaAs quantum well embedded in a waveguide of 382-nm mode size increases the |chi((3))| from a bulk-material level of 8 x 10(-11) esu +/-20% to 6 x 10(-10) esu +/-20%. The anisotropy of the diagonal elements |chi((3))(1111), |chi((3))(2222)| and their correlation with the off-diagonal elements |chi((3))(1212)|, |chi((3))(2121)| are consistent with the one-photon resonance mechanism.

Sum and difference frequency generation in a two-level system with permanent dipole moments.

We calculate the sum- and difference-frequency-generation (SFG and DFG) susceptibilities, ${\mathrm{\ensuremath{\chi}}}^{(2)}$(-(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$);${\mathrm{\ensuremath{\omega}}}_{1}$,${\mathrm{\ensuremath{\omega}}}_{2}$) and ${\mathrm{\ensuremath{\chi}}}^{(2)}$(-(${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$);${\mathrm{\ensuremath{\omega}}}_{1}$,-${\mathrm{\ensuremath{\omega}}}_{2}$), of a homogeneously broadened two-level system with permanent dipole moments in the presence of pump fields at frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$. Both SFG and DFG susceptibilities have two maxima at frequencies corresponding to the one- and two-photon resonances of the two-level system. Knowledge of the magnitude of one of the maxima of either SFG or DFG is sufficient for determining the magnitude of the second peak of that process and also the two peaks of the other process. In both processes the peak at the two-photon resonance has dominant contributions arising from off-diagonal elements of the density matrix. The interference between these contributions is constructive in SFG and destructive in DFG. Therefore, SFG is more efficient at the two-photon resonance than DFG. An expression for the ratio between these peaks is obtained. The peak of the spectrum of each process corresponding to the one-photon resonance has two main contributions, one of which is diagonal and the other off diagonal. In DFG the interference between the two contributions is constructive and in SFG the interference is destructive. Hence, DFG is more efficient in the vicinity of the one-photon resonance. However, since the off-diagonal contributions to SFG and DFG on the one-photon resonance are equal in magnitude (and differ by a phase difference of \ensuremath{\sim}\ensuremath{\pi}) the efficiencies of the two processes are equal when the duration of the pulses is comparable to or shorter than ${\mathit{T}}_{1}$.

Nondegenerate multiwave mixing in polydiacetylene: phase conjugation with frequency conversion

We present an analysis of optical phase conjugation with frequency doubling in terms of nondegenerate six-wave mixing fifth-order nonlinear susceptibility. We show how the Bragg phase-matching condition is achieved at small angles. The process under picosecond-pulse conditions in a polydiacetylene solution pumped at two-photon resonance and probed at one-photon resonance is experimentally demonstrated. Results are discussed in terms of a one-dimensional quantum three-level system. The proximity of one- and two-photon resonance in conjugated polymers makes these polymers efficient nonlinear-optical materials for this original application. The experiment permits artifact-free measurement of the two-photon state recovery time of the red form of polydiacetylene.

Multiresonance CARS spectra of quinizarin in chloroform solution

Some properties of multiresonance CARS spectra of polyatomic molecules in condensed phases are briefly discussed with reference to the possible effects of having a transfer of population under one-photon resonance conditions. Some experimental results are presented for the case of quinizarin in chloroform solution at room temperature. The observation of vibrational resonances of the first excited state as well as evidences of the participation of higher excited states to the multiresonant processes clearly indicate the need to go beyond the usual four level system description of the CARS spectra.

Gauge relation between self-induced transparency theory and principal chiral models

The gauge relations between generalised reduced Maxwell-Bloch equations and field equations of some principal chiral models are established. One-photon resonance in two-level and three-level media and also two-photon resonance are considered.

Two-photon optical bistability of polar molecules inserted in a solid matrix: Phonon effects

Single-beam two-photon optical bistability in a Fabry-Perot cavity filled with molecules which change permanent dipole moment upon electronic excitation is analysed under the mean-field and plane-wave approximations. One-photon resonances are discarded. These molecules are assumed to be in a solid matrix. Phonon effects are then taken into account. The Bloch equations of the system are further coupled by a term that is dependent on the electron-phonon interaction, leading to shifts in the switching thresholds which modify the optical bistability character. Such a term becomes irrelevant when the difference between the dipole moments is much greater than the transition dipole moment.