Recoil Shift Research Articles

Precise measurement of the D2 S1(0) vibrational transition frequency

We report the absolute frequency of the vibrational transition in the electronic ground state of D. Deuterium molecules in the state in a molecular beam are excited to using a narrow-linewidth continuous-wave laser stabilised to an optical frequency comb; a strong static electric field in the excitation region induces a transition dipole moment, greatly enhancing the transition strength. Molecules excited to are state-selectively ionised using a pulsed ultraviolet laser and mass-selectively detected. Spectra recorded by scanning the infrared laser frequency are fit with a multi-Gaussian model that accounts for the intensities and relative frequencies of all hyperfine components at the static electric field strength used in the measurement. Zero-field absolute transition frequencies were determined from fits of 28 spectra recorded at nine different field strengths. Statistical uncertainty and systematic uncertainties due to the field plate spacing and relative intensities of the hyperfine components comprise the bulk of the overall uncertainty. We determine an absolute S(0) transition frequency of 94,925,100,487(17) kHz after correcting for the photon recoil and second-order Doppler shifts. This value agrees with other recent experimental measurements and a theoretical prediction, but with a lower fractional uncertainty of only 0.2 ppb.

Inclusion of the recoil shift in Doppler-broadened measurements of CO2 transition frequencies

We report an important correction to recently reported 12C16O2 transition frequencies and derived spectroscopic constants. A total of 44 previously reported frequencies corresponding to transitions in the (30012 ← 00001) and (30013 ← 00001) band with uncertainties as low as 200 Hz are modified by including the effect of photon-absorption-induced recoil shifts. This shifting mechanism decreases all the transition frequencies by approximately 1.7 kHz.

Pure quartic solitons in dispersion-engineered aluminum nitride micro-cavities.

Pure quartic soliton (PQS) is a new class of solitons demonstrated in recent years and provides innovations in nonlinear optics and its applications. Generating PQSs in micro-cavities offers a novel way to achieve coherent microcombs, presenting a promising application potential. Here we numerically investigate the PQS generation in a dispersion-engineered aluminum nitride (AlN) micro-cavity. To support PQS, a well-designed shallow-trench waveguide structure is adopted, which is feasible to be fabricated. The structure exhibits a dominant fourth-order dispersion reaching up to -5.35×10-3 ps4/km. PQSs can be generated in this AlN micro-cavity in the presence of all-order-dispersion and stimulated Raman scattering. Spectral recoil and soliton self-frequency shift are observed in the PQS spectrum. Furthermore, we find that due to the narrow Raman gain spectrum of crystalline AlN, the PQS evolves directly to chaos rather than turning into a breather. The threshold pump power with which the PQS turns into chaos is also theoretically calculated, which squares with the simulation results.

Quantitative simulation of a magneto-optical trap operating near the photon recoil limit

We present a quantitative model for magneto-optical traps operating on narrow transitions, where the transition linewidth and the recoil shift are comparable. We combine a quantum treatment of the light scattering process with a Monte-Carlo simulation of the atomic motion. By comparing our model to an experiment operating on the transition in strontium, we show that it quantitatively reproduces the cloud size, position, temperature and dynamics over a wide range of operating conditions, without any adjustable parameters. We also present an extension of the model that quantitatively reproduces the transfer of atoms into a far off-resonance dipole trap, highlighting its use as a tool for optimizing complex cold atom experiments.

Systematic Effects in Atomic Fountain Clocks

We describe recent advances in the accuracies of atomic fountain clocks. New rigorous treatments of the previously large systematic uncertainties, distributed cavity phase, microwave lensing, and background gas collisions, enabled these advances. We also discuss background gas collisions of optical lattice and ion clocks and derive the smooth transition of the microwave lensing frequency shift to photon recoil shifts for large atomic wave packets.

Determining the band gap and mean kinetic energy of atoms from reflection electron energy loss spectra.

Reflection electron energy loss spectra from some insulating materials (CaCO3, Li2CO3, and SiO2) taken at relatively high incoming electron energies (5-40 keV) are analyzed. Here, one is bulk sensitive and a well-defined onset of inelastic excitations is observed from which one can infer the value of the band gap. An estimate of the band gap was obtained by fitting the spectra with a procedure that includes the recoil shift and recoil broadening affecting these measurements. The width of the elastic peak is directly connected to the mean kinetic energy of the atom in the material (Doppler broadening). The experimentally obtained mean kinetic energies of the O, C, Li, Ca, and Si atoms are compared with the calculated ones, and good agreement is found, especially if the effect of multiple scattering is taken into account. It is demonstrated experimentally that the onset of the inelastic excitation is also affected by Doppler broadening. Aided by this understanding, we can obtain a good fit of the elastic peak and the onset of inelastic excitations. For SiO2, good agreement is obtained with the well-established value of the band gap (8.9 eV) only if it is assumed that the intensity near the edge scales as (E - Egap)(1.5). For CaCO3, the band gap obtained here (7 eV) is about 1 eV larger than the previous experimental value, whereas the value for Li2CO3 (7.5 eV) is the first experimental estimate.

Recoil Effects in Valence Band Photoemission of Organic Solids

Recoil effects in valence band X-ray photoelectron spectroscopy (XPS) are studied for both abb-trifluorostyrene and styrene molecular crystal systems. The gradual changes of XPS spectra excited by several photon energies are theoretically investigated within the tight-binding approximation and harmonic approximation of lattice vibrations and have been explained in terms of not only atomic mass but also atomic orbital (AO) population. The recoil effect of valence band photoemission strongly depends on the population and partial photoionization cross section (PICS) of AOs as well as the masses of composite atoms. In abb-trifluorostyrene F 2p dominant bands show the recoil shift close to free F atom recoil shift, and C 2s dominant bands show that to free C atom recoil shift, whereas the mixed bands of C and F give rise to the peak asymmetries due to their different recoil shifts. For these systems, hydrogen contribution is negligibly small which is in contrast to our previous results for the crystals composed of small organic molecules. We also discuss some potential uses of the recoil shifts for these systems.

Recoil effects for valence and core photoelectrons inV3Si

Hard and soft x-ray photoelectron spectroscopy was performed for core and valence electrons in V${}_{3}$Si. The recoil effects on the photoelectron emission were observed not only in the case of the Si 2$p$ core level, but also for the valence band, although such effects were not observed for the V 2$p$ and V 3$p$ core levels. The valence-band results are compared with the results of the theoretical model calculation based on the tight-binding cluster approximation and harmonic approximation for lattice vibrations. The Si 2$p$ core-level results interpreted as due to the single nucleus recoil effects are consistent with the interpretation of those of the valence electrons calculated on these approximations. From the ${E}_{\mathrm{B}}$ dependence of the valence-band recoil shifts, useful information is obtained on the Si 3$p$ partial density of states near the Fermi level.

Recoil Effects in Valence Photoemission from Simple Molecules and Clusters

We discuss recoil effects from extended molecular orbitals in simple molecular crystals excited by high-energy X-ray photons. Because of Debye-Waller factors the interference effects between photoelectron waves emanating from different atomic sites can be neglected, and the Gelius formula is safely used, which provides us with simple expression of photoemission bands. This formula can explain the recoil energy shift and energy dependence of the intensity of each level. We apply it to the photoemission bands from acetylene and diacetylene molecular crystals in the energy range from 125 to 1200 eV. Hydrogen recoil shift is much larger than carbon, however it is hard to observe recoil effect due to the hydrogen recoil because of its quite small photoionization cross section even in this intermediate energy region. Additionally, we expect that useful information which is obtained from the energy dependence of these bands: the C 2s and 2p components in each molecular orbital can be estimated roughly from the energy dependence. [DOI: 10.1380/ejssnt.2012.128]

Site-specific recoil effect in hard X-ray photoelectron spectroscopy of the valence band of compound crystals

Abstract The recoil effect of photoelectrons for the valence bands of compound crystals is studied theoretically. In the hard X-ray excitation of valence bands, the photoelectron spectrum changes according to the change of the excitation energy due to two origins: the energy dependence of the ionization cross sections of the atomic orbitals, and the recoil effect. In the case of compound materials with large mass differences among the component atoms, the spectrum is decomposed into the sum of the partial density of states with respective recoil shifts and broadenings. This indicates the possibility to get information on the partial density of states in the valence band through the mass dependent recoil effect of the spectrum.

On the recoil and Doppler shifts

The recoil shift due to the finite mass of an absorbing atom is, when viewed in the right way, simply part of the total Doppler shift. This is true both in the low speed and relativistic limits and also for the reflection of light from a low-mass mirror.

Do all nuclei recoil on photoemission in compounds?

Hard and soft x-ray photoelectron spectroscopy was performed for core and valence electrons in solid compounds containing V and O atoms. The single-nucleus recoil effects on photoelectron emission were observed in the form of recoil shifts for all core levels and the valence band in a heavy Fermion material LiV2O4, whereas such shifts were negligible in VO2 even in the high-temperature metal phase. The valence band recoil shifts of V5O9 and V2O3 metal are found to be in between. These differences in the valence band are ascribable to the difference in the relative spectral weight of the O 2p component near the Fermi level.

Spontaneous recoil effects of optical pumping on trapped atoms

The recoil effects of spontaneous photon emissions during optical pumping of a trapped three-level atom are exactly calculated. Without resort to the Lamb-Dicke approximation, and considering arbitrary detuning and saturation of the pump laser, the density of recoil shifts in phase space is derived. It is shown that this density is not of Gaussian shape, and that it becomes isotropic in phase space only for a branching ratio corresponding to fluorescence scattering but unfavorable for optical pumping. The dependence of its anisotropy on the laser saturation is discussed in the resonant case, and the mapping of moments of the atom's center-of-mass motion due to the pumping is presented. Moreover, it is shown how optimum parameters for protecting the center-of-mass quantum state from pump-induced disturbance depend on the specific property to be protected.

Cover Picture: Highly Coherent Spectroscopy of Ultracold Atoms and Molecules in Optical Lattices (ChemPhysChem 3/2008)

The cover picture shows strontium atoms which are laser cooled to a microkelvin temperature and held in an optical lattice trap. The trap consists of a series of microtraps at the antinodes of the optical standing wave. The intense blue light in the background is the fluorescence of the atoms when they are laser cooled or detected. The clock transition is in red. In their Concept article Zelevinsky et al. (page 375) show that an ultrastable laser recovers a high-resolution spectrum of the narrow, forbidden optical clock transition with a linewidth of 2 Hz. Spectroscopy is performed without recoil shifts, Doppler effects, or ac Stark shifts from the trapping light.

Rayleigh scattering from a trapped bose condensate and the corresponding recoil atom velocity distribution

An approach has been developed that allows the Rayleigh scattering cross section to be calculated with allowance for the quantum character of motion of the center of mass of the trapped scattering particles. The shape of the line of light scattering from a Bose condensate in a parabolic trap has been studied. A shift of the scattering line center is equal to the recoil shift, while the line width depends on the chemical potential of the Bose gas and on the relaxation time of the velocity of the above-condensate recoil particles. A velocity distribution function in the beam of recoil atoms formed in the course of induced Rayleigh scattering is determined. It is shown that, under the typical experimental conditions, the characteristic width Δv/v of the recoil velocity distribution in this beam is on the order of 10−3 at a velocity v on the order of several centimeters per second.

A study of the cross sections and the spin observables for proton-12C elastic scattering in momentum space in the intermediate energy region

The differential cross sections and the spin observables of p-12C elastic scattering in the whole intermediate energy region are calculated using the KMT multiple scattering theory with microscopic momentum space optical potential which incorporates the spin dependence of the NN and p-12C interactions. The theory takes into consideration the antisymmetrized NN amplitudes, nucleon recoil and binding energy shifts, Lorentz invariant angle transformations, t matrices with on-shell behavior from NN phase shifts,and off-shell behavior from a realistic separable potential model. Qualitative agreement is found in differential cross sections and polarization data for 200Ep<1000 MeV.

Difference between a Photon’s Momentum and an Atom’s Recoil

When an atom absorbs a photon from a laser beam that is not an infinite plane wave, the atom's recoil is less than variant Planck's k in the propagation direction. We show that the recoils in the transverse directions produce a lensing of the atomic wave functions, which leads to a frequency shift that is not discrete but varies linearly with the field amplitude and strongly depends on the atomic state detection. The same lensing effect is also important for microwave atomic clocks. The frequency shifts are of the order of the naive recoil shift for the transverse wave vector of the photons.

Observation of large atomic-recoil-induced asymmetries in cold atom spectroscopy

The atomic recoil effect leads to large (25 %) asymmetries in simple spectroscopic investigations of Ca atoms that have been laser-cooled to 10 microkelvin. Starting with spectra from the more familiar Doppler-broadened domain, we show how the fundamental asymmetry between absorption and stimulated emission of light manifests itself when shorter spectroscopic pulses lead to the Fourier transform regime. These effects occur on frequency scales much larger than the size of the recoil shift itself, and have not been observed before in saturation spectroscopy. These results are relevant to state-of-the-art optical atomic clocks based on freely expanding neutral atoms.

Recoil-free spectroscopy of neutral Sr atoms in the Lamb-Dicke regime.

Recoil-free as well as Doppler-free spectroscopy was demonstrated on the 1S0-3P1 transition of Sr atoms confined in a one-dimensional optical lattice. By investigating the wavelength and polarization dependence of the ac Stark shift acting on the 1S0 and 3P1(m(J)=0) states, we determined the wavelength where the Stark shifts for both states coincide. This Stark-free optical lattice, allowing the purturbation-free spectroscopy of trapped atoms, may keep neutral-atom based optical standards competitive with single-ion standards.

Spectroscopy with β2 p and β– ν recoil shifts

The beta-delayed proton emission from the lightest Ar-isotopes has been measured with a high-granularity, large solid-angle Si-detector setup. Although designed for the detection of beta-delayed two-proton and three-proton events, the setup also permitted measurement of proton energy shifts due to the beta–neutrino recoil. We discuss how spectroscopic information can be extracted from such measurements, even at the drip line. For the case of 31Ar, the ground-state spin could be determined as 5/2.