Experimental Determination of the Landé g-Factors for 5s~2 ~1S and 5s5p ~3P States of the ~(87)Sr Atom

We present an experimental determination on the Lande g-factors for the 5 s~2 ~1 S_0 and 5 s5 p ~3 P_0 states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the ~(87)Sr optical lattice clock. The Zeeman shift of the 5 s5 p ~3 P_0-5 s~2 ~1 S_0 forbidden transition is measured with the π-polarized andσ~±-polarized interrogations at different magnetic field strengths. Moreover, in the g-factor measurement with the σ~±-transition spectra, it is unnecessary to calibrate the external magnetic field. By this means, the ground state 5 s~2 ~1 S_0 g-factor for the ~(87)Sr atom is-1.306(52) ×10~(-4), which is the first experimental determination to the best of our knowledge, and the result matches very well with the theoretical estimation. The differential g-factorδg between the 5 s5 p~3 P_0 state and the 5 s~2 ~1 S_0 state of the ~(87)Sr atoms is measured in the experiment as well,which are-7.67(36) ×10~(-5) with π-transition spectra and-7.72(43) X 10-5 with σ~±-transition spectra, in good agreement with the previous report [Phys. Rev. A 76(2007) 022510]. This work can also be used for determining the differential g-factor of the clock states for the optical clocks based on other atoms.     

Observation of the ~1S_0-~3P_0 optical clock transition in cold ~(199)Hg atoms

We report on the observation of the highly forbidden ~1S_0–~3P_0 optical clock transition in laser-cooled ~(199) Hg atoms.More than 95% depletion of cold ~(199)Hg atoms is detected in the magneto-optical trap. Using the free-of-field detection method, the AC Stark shift from the cooling laser is removed from the in-field spectroscopy. At low-power clock laser pumping, the linewidth of the clock spectroscopy is approximately 450 k Hz(full width at half-maximum), which corresponds to a Doppler broadening at the atom temperature of 60 μK. We determine the ~1S_0–~3P_0transition frequency to be 1,128,575,290.819(14) MHz by referencing with a hydrogen maser and measuring with a fiber optical frequency comb. Moreover, a weak Doppler-free signal is observed.     

Calculations of atomic polarizability for beryllium using MCDHF method

Based on the fully relativistic multiconfiguration Dirac-Hartree-Fock(MCDHF) method and the corresponding program package GRASP2018,a new program for calculating the polarizabilities is developed.As the first application,the static electric-dipole polarizabilities of the ground state 2 s~2 ~1 S_0 and excited state 2 s2 p ~3 P_0 of beryllium are calculated.By means of these polarizabilities,the blackbody radiation(BBR) shift of the 2 s2 p ~3 P_0→2 s~2 ~1 S_0 clock transition is determined.The present results agree very well with other available theoretical results.     

Direct Laser Cooling Al~+ Ion Optical Clocks

The Al~+ ion optical clock is a very promising optical frequency standard candidate due to its extremely small black-body radiation shift. It has been successfully demonstrated with the indirect cooled, quantum-logic-based spectroscopy technique. Its accuracy is limited by second-order Doppler shift, and its stability is limited by the number of ions that can be probed in quantum logic processing. We propose a direct laser cooling scheme of Al~+ ion optical clocks where both the stability and accuracy of the clocks are greatly improved. In the proposed scheme,two Al~+ traps are utilized. The first trap is used to trap a large number of Al~+ ions to improve the stability of the clock laser,while the second trap is used to trap a single Al~+ ion to provide the ultimate accuracy. Both traps are cooled with a continuous wave 167 nm laser. The expected clock laser stability can reach9.0×10~(-17)/τ~(1/2). For the second trap, in addition to 167 nm laser Doppler cooling, a second stage pulsed 234 nm two-photon cooling laser is utilized to further improve the accuracy of the clock laser. The total systematic uncertainty can be reduced to about 1×10~(-18). The proposed Al~+ ion optical clock has the potential to become the most accurate and stable optical clock.     

Realization of Closed-Loop Operation of Optical Lattice Clock Based on ~(171)Yb

We report the realization of closed-loop operation of an optical lattice clock based on ~(171)Yb atoms. We interrogate the ~1 S_0→~3 P_0 clock transition using single Rabi pulses of 578 nm laser light. The two π-transitions from mF=±1/2 ground states are alternatively interrogated,and the clock laser frequency is locked to the center of the two resonances. The in-loop error signal stability of the clock reaches 3×10~(-17) for an average time of 3500 s. We also perform interleaved operations of the clock with two independent servo loops, and the fractional frequency difference averages down to 2×10~(-16) in 7200 s.     

Forbidden transition properties of fine-structure 2p~3 ~4S_(3/2)–2p~3 ~2D_(3/2,5/2) for nitrogen-like ions

Based on relativistic wave functions from multiconfiguration Dirac–Hartree–Fock and configuration interaction calculations, E2 and M1 transition probabilities of 2p~3 ~4S_(3/2)–2 p~3 ~2D_(3/2,5/2) are investigated in the nitrogen-like sequence with7 ≤ Z ≤ 16. The contributions of the electron correlations, Breit interaction, and the quantum electrodynamic(QED) effects on the transition properties are analyzed. The present results can be used for diagnosing plasma. In addition, several N-like ions can also be recommended as a promising candidate for a highly charged ion(HCI) clock with a quality factor(Q) of transition as high as 10~(20).     

Improvement of Stability of ~(40)Ca~+ Optical Clock with State Preparation

Stability is one of most important performances of an atomic clock. Here we describe our recent work on improving the stability of our 40 Ca+ optical clock. State preparation is adopted to transfer the ion to the groundstate magnetic sublevel of the clock transition, after the quenching laser transfers the ion to the ground state at each cycle. Using this method,the stability for ~(40)Ca~+ optical clock is improved to about 6.3 × 10~(-15)/τ~(1/2).Compared with 1.0 × 10~(-14)/τ~(1/2) in previous work, the averaging time is decreased to reach a given level of statistical uncertainty in a clock comparison.     

Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals

A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however,there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional(3 D) secular spectra of trapped ions using molecular dynamics simulations. The 3 D resonance peaks of the ~(40)Ca~+ – ~(27)Al~+ pair obtained by using this method were in good agreement with the 3 D in-and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%.The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the ~(40)Ca~+ – ~(27)Al~+ pair was primarily determined by its axial in-phase coupling. In addition,the frequencies and amplitudes of the ion pair's resonance modes(in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the ~(40)Ca~+ – ~(27)Al~+ pair were slightly weaker than those of the ~(24)Mg~+– ~(27)Al~+ pair, but significantly stronger than those of ~9Be~+ – ~(27)Al~+ . However, the Doppler cooling limit temperature of ~(40)Ca~+ is comparable to that of ~9Be~+ but lower than approximately half of that of ~(24)Mg~+. Furthermore, laser cooling systems for ~(40)Ca~+ are more reliable than those for ~(24)Mg~+and ~9Be~+ . Therefore, ~(40)Ca~+ is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of ~(27)Al~+ and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable ~(27)Al~+ optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.     

Binding Energy of an Exciton Bound to Ionized Acceptor in Quantum Dots

Binding energiesfor an exciton (X ) trapped in the two-dimensional quantum dot by a negative ion located on the z axis at a distance from the dot plane are calculated by using the method of few-body physics.This configuration is called a barrier (A-,X) center.The dependence of the binding energy of the ground state of the barrier (A-,X)center on the electron-to-hole mass ratio for a few values of the distance d between the fixed negative ion on the z axis and the dot plane is obtained.We find that when d → 0,the barrier (A-,X) center has not any bound state.We also studied the stability and binding energy of the ground state of the barrier (A-,X) center in a parabolic quantum dot as a function of the distance d between the fixed negative ion on the z axis and the dot plane.``     

Generation of Two－Mode Nonclassical States via Dispersive Interaction in Trapped－Ion Cavity Quantum Electrodynamics

We propose a simple method to generate a practical SU(2)-Schroedinger-cat state of a single trapped-ion vibration mode and the light field state, using the method based on a quantum system, which is composed of the onedimensional trapped-ion motion and a single cavity field mode. Moreover, the method proposed can be used for the generation two-mode maximal quantum entangled state. The detection of such a state is also briefly discussed.     

Helicity Amplitude Analysis of Z_c(3900)~± in e~+e~- →π~+π~-J/ψ

It is crucial to determine the spin and parity(J~P) of Z_c(3900)~± for understanding its structure.We perform a helicity amplitude analysis on Z_c(3900)~± in the process e~+e~-→π~+π~-J/φ with the hypotheses J~P= 0~-,1~+,1~-,2~+ and 2~-.To estimate the significance of J~P = 1~+ over other hypotheses,we perform a Monte Carlo simulation study,and we also discuss the prospect of measuring the spin parity in the future experiment with a large data sample.     

Order Parameter of a Nanometre-Scale S-Wave Superconducting Grain in Quantum Tunnelling Process： Frequency Space Analysis

A nano-scale s-wave superconducting grain, coupled to a normal metallic contact through a tunnelling junction, is placed in an external magnetic field. We suppose that effect of this quantum tunnelling on the Fourier transform of the order parameter is in the form of a small additive correction to the BCS order parameter. At the first order approximation in terms of this correction term and by using an instanton method, the related Green functions （in frequency space） are obtained. By establishing a self-consistent configuration an analytic formula for the order parameter is also found. We also show that a departure from superconductivity can be captured by this formula. This change of state is indeed a manifestation of a quantum transition induced by quantum fluctuations. In this sense, this is an advantage of our simple method which, like other more elaborate methods, can detect a quantum transition in the state of the grain.     

Improvement of the short-term stability of atomic fountain clock with state preparation by two-laser optical pumping

To improve the signal to noise ratio(SNR) and the short-term stability of cesium atomic fountain clocks, the work of two-laser optical pumping is presented theoretically and experimentally. The short-term stability of the NIM6 fountain clock has been improved by preparing more cold atoms in the |F = 4, mF= 0〉 clock state with a shortened cycle time.Two π-polarized laser beams overlapped in the horizontal plane have been applied after launching, one is resonant with|F = 4〉→ |F = 4〉 transition and the other is resonant with |F = 3〉→ |F = 4〉 transition. With optical pumping, the population accumulated in the |mF= 0〉 clock state is improved from 11% to 63%, and the detection signal is increased by a factor of 4.2, the SNR of the clock transition probability and the short-term stability are also improved accordingly.     

The Role of α_1(1260) in π~-p→α_1~-(1260)p and π~-p → π~-ρ~0p Reactions Near Threshold

We report on a theoretical study of the π~-ρ→α1(1260)p and π~-ρ→π~-ρ~0p reactions near threshold within an effective Lagrangian approach.The production process is described by t-channel ρ~0 meson exchange.For the π~-ρ→π~- ρ~0p reaction,the final π~-ρ~0 results from the decay of the α1(1260) resonance,which is assumed as a dynamically generated state from the K* K and ρπ coupled channel interactions.We calculate the total cross section of the π~-ρ→α1(1260)p reaction.It is shown that,with the coupling constant of the α1(1260) to ρπ channel obtained from the chiral unitary theory and a cut off parameter Δρ~1.5 GeV in the form factors,the experimental measurement can be reproduced.Furthermore,the total and differential cross sections of π~p→α1(1260)p→π~ρ~0p reaction are evaluated,and it is expected that our model calculations can be tested by future experiments.These reactions are important for the study of the α1(1260) resonance and would provide further constraints on the properties of the α1(1260) state.     

Dynamics of the CH4+ O(~3 P) → CH_3(ν= 0) + OH(■= 0) reaction

The dynamics of the ground-state reaction of CH_4+ O(~3P) → CH_3(ν = 0) + OH( ν= 0) have attracted a great deal of attention both theoretically and experimentally. This rapid communication represents extensive quasi-classical trajectory calculations of the vibrational distributions on a unique full-dimensional ab initio potential energy surface for the title reaction, at the collision energy of relevance to previous crossed molecular beam experiments. The surface is constructed using the all electrons coupled-cluster singles and doubles approach plus quasi-perturbative triple excitations with optimized basis sets. A modified Shepard interpolation method is also employed for the construction. Good agreement between our calculations and the available experimental results has been achieved, opening the door for accurate dynamics on this surface.     

Experimental review of e~+e~-→ππh_c

We review the recent BESIII measurement of e~+e~-→ππh_c in which its line shape is studied between the center-of-mass energies of 3.9 to 4.42 Ge V and an iso-vector charmonium-like state Z_c(4020) is observed in the invariant mass of πhc at the BESIII experiment. The charged Z_c(4020)~± is the second observed Z_c state following Z_c(3900), while the Z_c(4020)~0 is the first observed neutral Z_c state. The line shape of σ(e~+e~-→ππh_c) is also reanalyzed in view of searching for the Y state and the existence of the Y(4220) state is confirmed and compared with the previous work of the BESIII experiment.     

An Ultraviolet Fiber Fabry-Perot Cavity for Florescence Collection of Trapped Ions

We demonstrate a fiber Fabry-Pérot cavity in the ultraviolet range, which covers the florescence wavelength for the ~2 P_(1/2) to ~2 S_(1/2) transition of Yb+ and is designed in the bad cavity limit for florescence collection. Benefiting from both the small cavity mode volume and the large atom dipole, a cavity with moderate finesse and high transmission still supports a good cooperativity, which is made and tested in experiment. Based on the measured experimental parameters, simulation performed on the cavity and ion shows a Purcell factor better than 2.5 and a single-mode fiber collection efficiency over 10%. This technology can support ultra-bright single photon sources based on trapped ions and can provide the possibility to link remote atoms as a quantum network.     

Super-resolution and super-sensitivity of entangled squeezed vacuum state using optimal detection strategy

Interference metrology is a method for achieving high precision detection by phase estimation. The phase sensitivity of a traditional interferometer is subject to the standard quantum limit, while its resolution is constrained by the Rayleigh diffraction limit. The resolution and sensitivity of phase measurement can be enhanced by using quantum metrology. We propose a quantum interference metrology scheme using the entangled squeezed vacuum state, which is obtained using the magic beam splitter, expressed as |ψ〉=(|ξ〉|0〉+|0〉|ξ〉)/(2+2/coshr)~(1/2), such as the N00 N state. We derive the phase sensitivity and the resolution of the system with Z detection, project detection, and parity detection. By simulation and analysis, we determine that parity detection is an optimal detection method, which can break through the Rayleigh diffraction limit and the standard quantum limit.     

Analysis of the coupling constants g_(a_0ηπ~0 )and g_(a_0η'π~0) with light-cone QCD sum rules

Abstract In this article, we take the point of view that the light scalar meson a_0(980) is a conventional qq state, and calculate the coupling constants g_(a_0ηπ~0) and g_(a_0η'π~0) with the light-cone QCD sum rules. The central value of the coupling constant g_(a_0ηπ~0) is consistent with that extracted from the radiative decay φ(1020) → a_0(980)γ→ηπ~oγ. The central value and lower bound of the decay width Γ_(α_0→ηπ~0) = 127_(-48)~(+84) MeV are compatible with the experimental data of the total decay width Γ_(α_0(980))= (50-100) MeV from the Particle Data Group with a very model dependent estimation (the decay width can be much larger), while the upper bound is too large. We give a possible explanation for the discrepancy between the theoretical calculation and experimental data.     

An improved strontium lattice clock with 10~(-16) level laser frequency stabilization

A clock laser based on a 30-cm-long ultrahigh finesse optical cavity was developed to improve the frequency stability of the Sr optical lattice clock at the National Institute of Metrology. Using this clock laser to probe the spin-polarized~(87)Sr atoms, a Rabi transition linewidth of 1.8 Hz was obtained with 500 ms interrogation time.Two independent digital servos are used to alternatively lock the clock laser to the ~1S_0(m_F=+9∕2)→~3P_0(m_F=+9∕2)transition. The Allan deviation shows that the short-term frequency stability is better than3.2 × 10~(-16)and averages down followed by 1.8 × 10~(-15)∕τ~(1/2).