Three-photon Transition Research Articles

Multiphoton transitions in a macroscopic quantum two-state system.

We have observed multiphoton transitions between two macroscopic quantum-mechanical superposition states formed by two opposite circulating currents in a superconducting loop with three Josephson junctions. Resonant peaks and dips of up to three-photon transitions were observed in spectroscopic measurements when the system was irradiated with a strong rf-photon field. The widths of the multiphoton absorption dips are shown to scale with the Bessel functions in agreement with theoretical predictions derived from the Bloch equation or from a spin-boson model.

Three-photon resonant atomic excitation in spatially incoherent laser beams

Two-color excitation by spatially coherent and incoherent laser beams has been used to study three-photon-resonant excitation and subsequent ionization of xenon in conditions, when internally generated sum-frequency field plays an important role in excitation of atomic resonances through interfering one-photon excitation pathway. We show that the incoherence in one of the pumping fields reduces the efficiency of generated sum-frequency field, and thus suppresses the interference between the three- and the one-photon excitation channels. The degree of suppression is controlled by varying the crossing angle between coherent and incoherent laser beams. We show that ionization profiles can be analyzed on the basis of the well-studied interference of one- and three-photon transition amplitudes, but with pumping field decomposed into multiple small-scale uncorrelated domains where coherent process of four-wave mixing occurs. The gain length for a coherent process in these domains depends on the coherence degree and excitation geometry. It gives a possibility of controlling the contribution of coherent processes to the excitation of multiphoton resonances.

Three-photon transitions from ground state to bound states in atomic hydrogen

In this paper, we present an efficient alternative method for the evaluation of the three-photon transition matrix element in the dipole approximation from the ground state to bound states in atomic hydrogen. This method is a variation of the Dalgarno–Lewis method for the treatment of the second-order Stark effect in the hydrogen atom. In this approach, the infinite double sum over the complete set of states including the continuum states present in the third-order perturbation theory result is treated exactly. The closed analytical expression obtained for the matrix element, as a function of incident photon energy, clearly displays all singularities present in the original third-order perturbation theory result.

Multiphoton Excitation of an Ozone Molecule in Laser Fields

The multiphoton excitation of O3 molecules in laser fields is discussed using the second quantization and unitary transformations. It is successful to derive the total Hamiltonian (including the stretch-vibration Hamiltonian of an ozone molecule, the laser fields Hamiltonian and the interaction Hamiltonian between O3 and laser fields), the transition probabilities from the ground state to excited states and the expressions for the average number of photons absorbed by molecules from laser fields. The calculated stretch-vibration energy spectrum of O3 molecules is in good agreement with that of experiments. There are two peaks of single-photon transition at 1042.5 and 1103.0 cm-1, respectively. The three peaks of the two-photon transition are at 1027.5, 1055.5 and 1101.0 cm-1 respectively. The peaks at 1014.5, 1028.0, 1043.0 and 1100.5 cm-1 are four peaks of the three-photon transition. The amplitudes of the three-photon transition probability are about 6 orders of magnitude less than those of the two-photon transition which are about 14 orders of magnitude less than those of the single-photon transition. The laser field intensity is taken as 5×10-2 W/cm2, which is different from 109 W/cm2 in the former researches. This theoretical model can be used to discuss the multiphoton excitation for all of the molecules with a C2v symmetry, but inadequate to calculate the n-photon (n≥4) transition. In the computational process, it is found that the transition probability changes with the intensity of the laser field, which needs further research in the future.

Resonance ionization spectroscopy of stable strontium isotopes and 90Sr via 5s 2 1S 0→5s5p 1P 1→5s5d 1D 2→5s11f 1F 3→Sr +

Single-, double- and triple-resonance ionization in the 5s 2 1S 0→5s5p 1P 1→5s5d 1D 2 →5s11f 1F 3→Sr + system of strontium was investigated to achieve an efficient and highly selective ionization scheme for ultra-trace detection of the radioisotope 90Sr. Isotope shifts and hyperfine structure for all stable isotopes of Sr were measured in all three resonant transitions. Good agreement with previous data was found in the 5s 2 1S 0→5s5p 1P 1 transition and precision was improved by approximately one order of magnitude. Isotope shifts, including that for 90Sr, and hyperfine structure in the two- and three-photon transitions were measured for the first time. The double- and triple-resonance schemes were characterized with respect to their isotopic selectivity for detection of 90Sr. The double-resonance process offers an optical selectivity of 2×10 4, while unfavorable isotope shifts in the triple-resonance process limit its selectivity to ∼100. Using double-resonance ionization combined with mass spectrometric detection, an overall detection efficiency of >10 −5, a selectivity >10 10, and a detection limit of 0.7 fg 90Sr in samples with a 10 10 excess of stable Sr isotopes have been demonstrated.

What to see and what not to see in three-photon absorption: (3+1) REMPI of HBr

Hönl–London type approximation expressions are derived for transition strengths of the Ω′=0,1,2,3, ←Ω″=0 (Σ, Π, Δ and Φ←Σ) three-photon transitions for diatomic molecules belonging to Hund’s case (a) and intermediate (a)–(b) coupling schemes. These are used to demonstrate what may be seen and what may not be seen in three-photon absorption spectra. The forms are used to simulate room temperature (3+1)REMPI spectra of HBr, for different electronic transitions. The analysis as well as comparison with (2+1)REMPI spectra is used to demonstrate the usefulness of three-photon absorption spectroscopy to identify excited states and to derive spectroscopic parameters. A Rydberg state, not observed in single or two-photon absorption, with band origin 82 837 cm−1 was identified and analyzed for the first time. It was assigned as the L1Φ(3) ((σ2π3)5dδ)) state, (0,0) band.

Absorption spectrum of a strongly driven atom in a detuned squeezed vacuum

We present numerical and analytical results for the Mollow probe absorption spectrum of a coherently driven two-level system in a narrow bandwidth squeezed vacuum field. The spectra are calculated for the case where the Rabi frequency of the driving field is much larger than the natural linewidth and the squeezed vacuum carrier frequency is detuned from the driving laser frequency. The driving laser is on resonance. We show that in a detuned squeezed vacuum the standard Mollow features are each split into triplets. The central components of each triplet are weakly dependent on the squeezing phase but the sidebands strongly depend on the phase and can have dispersive or absorptive/emissive profiles. We also derive approximate analytical expressions for the spectral features and find that the multi-peak structure of the spectrum can be interpreted either via the eigenfrequencies of a generalized Floquet Hamiltonian or in terms of three-photon transitions between dressed states involving a probe field photon and a correlated photon pair from the squeezed vacuum field.

Derivation of coupled cluster excited states response functions and multiphoton transition moments between two excited states as derivatives of variational functionals

Based on an analysis of the second residues of the coupled cluster ground state response functions, general expressions are derived for multiphoton transition moments between two excited states and for excited states response functions. The second residues are rewritten as derivatives of variational functionals and computational efficient expressions are obtained in accordance with the 2n+1 and 2n+2 rules. For the excited state response functions secular divergent terms are removed by reformulating the expressions that are identified from the second residues of the ground state response functions as derivatives of an excited state quasienergy Lagrangian. Explicit expressions are given for coupled cluster one-, two- and three-photon transition moments between two excited states and for excited states first-order properties and linear and quadratic response functions.

Three-photon ionization of Ca

The two- and three-photon resonant ionization of Ca has been studied. Calcium atoms in the thermal atomic beam were ionized from the ground state by three-photon absorption. The ion signals exhibited resonances attributed to the two-photon transition and three-photon transitions due to , , and , autoionizing states. A simple theoretical model was used to reproduce the main features of the observed spectra due to the two-photon resonant ionization.

Phase lag near the resonances in (ω1,ω3) coherent control

Molecular phases are computed near the resonances in the (ω1,ω3) coherent control scheme for excitations to predissociating final states. We show that the phase factors for the one- and three-photon transition amplitudes are identical, giving a vanishing molecular phase, when the intermediate manifolds consist only of discrete states and when the final continuum states do not interact. The phase lag between the dissociation products identically vanishes across the resonance in this case. On the other hand, when there is contribution of the intermediate continuum states, the imaginary part of the three-photon transition operator can give different phase factors for the one- and three-photon transition amplitudes, yielding very important effects of the molecular phase in (ω1,ω3) coherent control. It is also shown that couplings between the final continuum states can give different molecular phase for different product channels in the absence of the effects of the intermediate continuum states, exhibiting the phase lag of the products near resonances. We demonstrate that the phase lag may show minimum near the top of the resonance, as was observed in Gordon and co-workers’ recent observations [Zhu et al., Science 270, 77 (1995)] on the phase lag in HI coherent control experiments, indicating that the observed phase lag is due to the effects of the molecular phase.

R-matrix Floquet theory of multiphoton processes: XIII. Resonances in multiphoton detachment

The results of calculations investigating the effects of autodetaching resonances on the multiphoton detachment spectra of are presented. The R-matrix Floquet method is used, in which the coupling of the ion with the laser field is described non-perturbatively. The laser field is fixed at an intensity of , while frequency ranges are chosen such that the lowest autodetaching states of the ion are excited through a two- or three-photon transition from the ground state. Detachment rates are compared, where possible, to previous results obtained using perturbation theory. An illustration of how non-lowest-order processes, involving autodetaching states, can lead to light-induced continuum structures is also presented. Finally, it is demonstrated that by using a frequency connecting the 1s and 2s states, the probability of exciting the residual hydrogen atom is significantly enhanced.

On the molecular phase in coherent control

Systematic analysis is carried out for molecular phase in (ω1,ω3) coherent control scheme. Two mechanisms for nonzero molecular phase are proposed. It is shown that the imaginary part of the three-photon transition operator, which is due to the contribution of the intermediate continuua, can give different phase factors for the one- and three-photon transition amplitudes, yielding very important effects of molecular phase in (ω1,ω3) coherent control. We also show that the interactions between the final continuum states can result in nonzero molecular phase, when the intermediate states are discrete. These findings are discussed in relation to Gordon and co-workers’ recent observations [Zhu et al., Science 270, 77 (1995)] on phase lag.

The polarization-angular structure and elliptical dichroism of the cross sections for three-photon bound-bound transitions in atoms

Using the electric dipole approximation, we present, in invariant form, the cross section of an arbitrary three-photon transition between the discrete states of an atom with total angular momenta Ji and Jf. The cross section contains scalar and mixed products of the photon polarization vectors, and invariant atomic parameters dependent only on the photon frequencies. We determine the number of independent atomic parameters at fixed values of Ji and Jf and obtain their explicit expressions in terms of the reduced composite dipole matrix elements. The polarization dependence of the cross sections is expressed in terms of the degrees l and ξ of linear and circular photon polarizations. We analyze the phenomenon of dissipation-induced circular dichroism in three-photon processes, i.e., the difference Δ of the cross sections for opposite signs of the degree of circular polarization of all the photons. We study in detail the case of two identical photons and the phenomenon of elliptical dichroism, when Δ∼lξ holds and dichroism occurs only when the photons are elliptically polarized, with 0<|ξ|<1. Finally, we discuss the dissipation-induced effects of atom polarization in three-photon processes involving linearly polarized or unpolarized photons.

Competing three-photon and one-photon transitions in cavity quantum electrodynamics.

We examine a model of two-channel cavity quantum electrodynamics (QED) consisting of three-photon and one-photon absorption processes, i.e., we present a cavity-QED version of a nonlinear optical balance. We give detailed numerical results for the evolution of the atomic populations and the number of photons at the fundamental and third harmonic frequencies. We also show the behavior of the system if the fields are treated semiclassically, and we find the quantum effects to be rather dominant.

Coupled quantum well semiconductors with giant electric field tunable nonlinear optical properties in the infrared

Coupled quantum wells present unique opportunities for engineering new semiconductors with large optical nonlinearities associated with intersubband transitions in the infrared. In this paper we report an in depth study of these properties in the AlInAs/GaInAs heterostructure material system grown by molecular beam epitaxy. We show that by judicious control of the tunnel coupling between wells and of the thickness of the latter one can design the wavefunctions and the energy levels in such a may that these new structures behave as quasi-molecules with extremely large dipole matrix elements and strongly field tunable nonlinear optical properties. Structures with giant nonlinear susceptibilities /spl chi//sup (2)/(2/spl omega/) and /spl chi//sup (3)/(3/spl omega/) (compared to the bulk constituents of the quantum wells) have been designed and demonstrated. They exhibit large linear Stark shifts of the intersubband transitions which have been used to efficiently tune the nonlinear susceptibilities. The second order nonlinear susceptibility |/spl chi//sup (2)/(2/spl omega/)| exhibits a peak as a function of the electric field corresponding to the energy levels being made equally spaced via the Stark effect. In a three-coupled-well structure triply resonant third harmonic generation has been observed. This process is associated with four equally spaced bound states. The corresponding |/spl chi//sub (3/spl omega/)//sup (3)/| (10/sup -14/ (m/V)/sup 2/ at 300 K and 4/spl times/10/sup -14/ (m/V)/sup 2/ at 30 K) is the highest measured third order noniinear susceptibility in any material. The equivalent of multiphoton ionization of a molecule has also been investigated in this structure. Electrons are photoexcited to a continuum resonance above the barrier via a three-photon transition enhanced by intermediate energy levels. The effect of this resonance on /spl chi//sup (3)/(3/spl omega/) as the electric field is varied is also investigated. Finally, appropriate figures of merit are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New method for determining three-photon transition tensor patterns for randomly oriented molecules

The method and results are given for the tensor patterns and polarization ratios of three-photon absorption excited by single-laser for randomly oriented molecules. The ratio of oriented average of transition rate for circularly polarized light to that for linearly polarized light, Ω, can be obtained by the simple three-photon transition tensor. For transition of which the tensor has one independent element, we give the value of polarization ratio; for transition of which the tensor contains two independent elements, we also give the possible range of polarization ratio. These results may be helpful for the symmetry assignment of the excited states.

Generation of intense green light through amplified spontaneous emission in Er/sup 3+/-doped germanosilicate single-mode optical fiber pumped at 1.319 μm

Generation of intense 525 nm green light through amplified spontaneous emission (ASE) in monomode Er/sup 3+/-doped germanosilicate fiber pumped by a Nd:YAG laser operated at 1.319 /sub /spl mu//m is reported. The green emission band around 525 nm corresponds to the /sup 2/H/sub 11/2//spl rarr//sup 2/I/sub 15/2/ transition, and the pumping mechanism is accomplished by a first step resonant two-photon absorption exciting /sup 4/F/sub 9/2/ level and a second one-photon step excited-state absorption (/sup 4/I/sub 9/2/) which, with the /sup 2/H/sub 11/2/ state, is populated. The stepwise three-photon frequency upconversion process is enhanced via resonant two- and three-photon transitions connecting ions /sup 4/I/sub 15/2/ ground-state to the /sup 4/F/sub 9/2/ and /sup 4/F/sub 5/2/ excited-states levels, respectively, giving rise to amplified spontaneous emission from the /sup 2/H/sub 11/2/ level to the /sup 4/F/sub 15/2/ ground-state. Efficient third-harmonic generation at 439 nm in short lengths of fiber, in addition to the ASE mechanism, is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Resonance-enhanced multiphoton ionisation spectroscopy of thiirane

We present a new and more extensive interpretation of the vertical electronic spectrum of the thiirane molecule based on (i) analysis of observed two- and three-photon resonance enhancements in the wavelength-resolved multiphoton ionisation spectrum of jet-cooled thiirane and (ii) measurements of the kinetic energies of the photoelectrons accompanying the multiphoton ionisation process. Six Rydberg series are identified, including the four series identified in previous one-photon vacuum ultraviolet absorption studies of this molecule. Series assignments are offered based on the measured quantum defects, their relative two- and three-photon transition strengths and the dependence (if any) of the two-photon transition intensities upon changing from linearly to circularly polarised photoexcitation. Our analysis suggests that, as in H2S, many of the Rydberg orbitals have hybrid / character; it also points to the need for some revision of all previous interpretations of the electronic spectrum of the thiirane molecule.

Intensity and alignents of three-photon nonresonant transitions

In this paper we present the algebraic angular momentum recoupling method to treat three-photon nonresonant excitations. The expressions of the laser-induced fluorescence (LIF) intensity of a three-photon nonresonant excitation are obtained. Such a treatment can be extended to a 3+1 and up to an n+1 photon nonresonant excitation without recourse to coupling coefficients higher than the 9- j symbols. The recurrence relations of spherical tensor are also obtained. The table of spherical tensor operators in terms of angular momentum operators has been extended to k=8 by using this recurrence relation. The general form of the reduced matrix elements of higher order spherical tensor operators is also given.

Exact computation of the 9-j symbols

A useful algebraic for the 9- j symbol has been written for inconvinient use on a computer. A simple FORTRAN program for the exact computation of 9- j symbols has been written for the VAX with VMS version V5.4-1 according to this formula. The results agree with the approximate values in existing literature. Some specific values of 9- j symbols needed for the intensity and alignments of three-photon nonresonant transitions are tabulated. Approximate 9- j symbol values beyond the limitation of the computer can also be computed by this program. The computer code of the exact computation of 3- j, 6- j and 9- j symbols are through electronic mail upon request.