Effective Atomic Density Research Articles

Investigation of cold atom collision frequency shift measured by rapid adiabatic passage in cesium fountain clock

Cold collision frequency shift is one of the major systematic effects which limit the frequency uncertainty of the cesium fountain atomic clock. It is proportional to the effective atomic density, which is defined as the average density over the initial spacial and velocity distribution. The measurement of the frequency shift is based on a differential method, in which the fountain clock is operated with two different atomic densities, i.e. high density and low density, in turn. The clock frequency without collision shift can be achieved by linear extrapolation with the frequencies and density ratios of two states. For the density ratio is estimated with the atom number, it plays a crucial role in generating atoms with same density distribution for reducing systematic uncertainty in cold collision frequency shift estimation. The rapid adiabatic passage method is used in Cesium fountain clock to realize homogeneous transition probability, which modulates the amplitude and frequency of microwave continuously to prepare atom sample. To investigate the precision of this method, theoretical analysis and experimental measurement are both used here. An equation of deviation is derived from the time evolution of Bloch vector. The vector rotates at angular speed <i>Ω</i> with the rotation axis processing at lower angular speed. The deviations in the two directions on the surface of Bloch sphere are determined by the equations which are similar to wave equations, and can be simplified into wave equations when the deviations are sufficiently small. It is shown in the equations that the deviations are stimulated by angular velocity and angular acceleration of the precession, and is inversely proportional to the square of <i>Ω</i>. Further calculation shows that the deviation becomes smaller when the amplitude of microwave frequency and Rabi frequency are close to each other. It is then confirmed experimentally. The effects of some other parameters, such as the pulse length and time delay, on transition probability are also measured, showing that the RAP method is insensitive to these parameters up to a large scope. The precision of RAP method is dominated by three factors. The first factor is the product of rotating angular speed <i>Ω</i> and pulse length <i>T</i>, i.e. <i>ΩT</i>: The increase of <i>ΩT</i> can reduce the uncertainty to a satisfactory degree. The second factor is the uncertainty of resonant frequency, so the measurement is required to be precise. The third factor is the unexpected atoms which are not selected by the microwave, and may be attributed to pulling light. After optimizing the parameters, the ratio of low density to high density can approach to 0.5 with 3 × 10<sup>–3</sup> uncertainty, which leads to a systematic relative uncertainty of cold collision shift up to 1.6 × 10<sup>–16</sup>.

Experimental investigation on diagnosing effective atomic density in gas-type target by using proton energy loss

The investigations of interaction processes between ion beams and gas and between ion beams and plasma play important roles in atomic physics, astrophysics, high energy density physics, and inertial confinement fusion.The atomic density of target is one of the key experimental parameters which may determine the interaction mechanism and experimental results.How to precisely diagnose the atomic density of target in different matter states, like gas phase and plasma phase, is challenging work on the experiments in laboratory.Conventionally the vacuum gauges are used to measure the pressure inside the gas target, but the accuracy is limited for a complex target system and they can hardly work in a strong radiation surrounding, especially in plasma where the high temperature can physically damage the gauges.Therefore we propose a new method to measure the atomic densities for both gas target and plasma target based on the heavy ion beam accelerator facility at the Institute of Modern Physics, Chinese Academy of Sciences.In our experiment the protons are extracted from an electron cyclotron resonance ion source (ECRIS) and accelerated to 100 keV then transmitted to the target.A two-stage differential pumping system is constructed to keep 10-7 mbar order of magnitude in beam line when the gas is filled into the target area where the pressure could increase to higher than 1 mbar.A 45 dipole magnet is used to bend the protons which have passed through the gas.The energy is determined by the different positions of protons at the position-sensitive detector which is placed at the end of magnet.Consequently the energy losses of protons at different pressures are obtained.There have been proposed many theories for calculating the energy loss of protons in gas, and we chose the very popular code named SRIM to simulate the experimental case. Finally the effective linear atomic density of target along the ion beam trajectory in the target area is obtained.For comparison, the conventional vacuum gauges (one is the hot cathode gauge-IonIVac ITR 90 and the other is capacitance diaphragm gauge-Varian CDG-500) are simultaneously used in the experiment.The results show that the recalibrated effective pressure obtained by the energy loss is close to the pressure measured by Varian CDG-500 but much lower than the pressure from IonIVac ITR 90.Only after the detection efficiency correction, could the corrected results of IonIVac ITR 90 be coincident with the effective pressure obtained according to energy loss.Moreover we find that the effective atomic density determined by the protons energy loss shows that these advantages over the conventional gauges are not only the high accuracy and reliability but also the in-situ measurement, high temporal resolution and the ability to work in the complex radiation and hot plasma environment.These properties may play a great role in the experimental researches and relevant topics.

High and low thermal conductivity of amorphous macromolecules

We measure the thermal conductivity, heat capacity and sound velocity of thin films of five polymers, nine polymer salts, and four caged molecules to advance the fundamental understanding of the lower and upper limits to heat conduction in amorphous macromolecules. The thermal conductivities vary by more than one order of magnitude, from $0.06\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ for [6,6]-phenyl-C71-butyric acid methyl ester to $0.67\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ for poly(vinylphosphonic acid calcium salt). Minimum thermal conductivity calculated from the measured sound velocity and effective atomic density is in good agreement with the thermal conductivity of macromolecules with various molecular structures and intermolecular bonding strength.

Local spins: improved Hilbert-space analysis

The decomposition of <Ŝ(2)> for a general wave function has been carried out in the framework of the Hilbert-space analysis. The one and two-center components fulfill all physical requirements imposed to date. An inherent ambiguity of the Hilbert-space decomposition of a two-electron quantity, in particular using a Mulliken-type scheme, is also discussed in detail. The formalism of effective atomic densities has allowed us to derive in a simple manner appropriate expressions for the decomposition of <Ŝ(2)> in the framework of Hilbert space analysis that are consistent with Mulliken population analysis and related quantities. Using a particular mapping we have derived the Hilbert-space expressions also in the framework of Löwdin population analysis in a straightforward manner. The numerical results obtained with the latter formalism have proved to be more robust and reliable.

Enhanced four-wave mixing in mercury isotopes, prepared by stark-chirped rapid adiabatic passage

We demonstrate significant enhancement of four-wave mixing in coherently driven mercury isotopes to generate vacuum-ultraviolet radiation at 125 nm. The enhancement is accomplished by preparation of the mercury atoms in a state of maximum coherence, i.e. maximum nonlinear-optical polarization, driven by Stark-chirped rapid adiabatic passage (SCRAP). In this technique, a pump laser at 313 nm excites the two-photon transition between the ground state 6s 21 S0 and the target state 7s 1 S0 in mercury. A strong, offresonant radiation field at 1064 nm generates dynamic Stark shifts. These Stark shifts serve to induce a rapid adiabatic passage process on the two-photon transition. During the process a coherent superposition of the two states is established, which enhances the nonlinear-optical polarization in the medium to the maximum possible value. The maximum coherence permits efficient four-wave mixing of a pump laser and an additional probe laser at 626 nm. The efficiency is further enhanced, as the SCRAP process allows to stimulate the complete set of different mercury isotopes to participate in the frequency conversion process. This enlarges the effective atomic density of the medium. Thus, we observe the generation of vacuum-ultraviolet radiation at 125 nm enhanced by more than one order of magnitude with respect to conventional frequency conversion. Parallel to the frequency conversion process, we monitored the evolution of the population in the medium by laser-induced fluorescence. These data demonstrate efficient coherent population transfer by SCRAP.

Ion transmission and characterization of ordered nanoporous alumina

Ordered nanoporous alumina samples with a pore diameter of 70 nm, an array period of 100 nm and several thicknesses were considered as possible masks for pattern transfer by MeV ion lithography. A simple procedure for the sample alignment using a 2 MeV He + beam was utilized. The energy distributions of transmitted ions as well as backscattering spectra were studied in aligned and non-aligned orientations. The best transmission, comparable to the relative surface area covered by pores, was reached for 2 μm thick samples and was independent on ion species. Although the transmission for thicker membranes was generally lower, it significantly depended on the quality of each individual sample. The presented ion beam technique can therefore be used as a tool for the characterization of porous materials. The acceptance angle for transmission through pores and the effective atomic density of samples can be obtained from the experimental data and it is shown that nanoporous alumina can be used as a mask for MeV ion lithography.