Effect of Laser Cooling on Frequency Standard of Single Ca^＋ Ion Trapped in a Radio-Frequency Paul Trap

The source of systematic frequency shift of single-ion optical frequency standard of^40 Ca^＋ ion trapped in endcap trap and laser-cooled to a few of mK is analysed and calculated. Second-order Doppler shift, Stark shift due to micromotion and thermal motion, blackbody Stark shift and ac Stark shift are calculated for the ground state and excited 3d ^2D5/2 state. The Hertz-level measurement of the optical clock frequency in a single ^40Ca^＋ ion can be performed.     

Precision spectroscopy with a single ~(40)Ca~+ ion in a Paul trap

Precision measurement of the 4s2S1/2–3d2D5/2clock transition based on40Ca+ion at 729 nm is reported. A single40Ca+ion is trapped and laser-cooled in a ring Paul trap, and the storage time for the ion is more than one month. The linewidth of a 729 nm laser is reduced to about 1 Hz by locking to a super cavity for longer than one month uninterruptedly.The overall systematic uncertainty of the clock transition is evaluated to be better than 6.5×10-16. The absolute frequency of the clock transition is measured at the 10-15 level by using an optical frequency comb referenced to a hydrogen maser which is calibrated to the SI second through the global positioning system(GPS). The frequency value is 411 042 129776 393.0(1.6) Hz with the correction of the systematic shifts. In order to carry out the comparison of two40Ca+optical frequency standards, another similar40Ca+optical frequency standard is constructed. Two optical frequency standards exhibit stabilities of 1×10-14τ-1/2with 3 days of averaging. Moreover, two additional precision measurements based on the single trapped40Ca+ion are carried out. One is the 3d2D5/2state lifetime measurement, and our result of 1174(10) ms agrees well with the results reported in [Phys. Rev. A 62 032503(2000)] and [Phys. Rev. A 71 032504(2005)]. The other one is magic wavelengths for the 4s2S1/2–3d2D5/2clock transition; λ|m j|=1/2= 395.7992(7) nm and λ|m j|=3/2=395.7990(7) nm are reported, and it is the first time that two magic wavelengths for the40Ca+clock-transition have been reported.     

Frequency-Shift of a Frequency Stabilized Laser Based on Zeeman Effect

We introduce a new method of frequency-shifting for a diode laser in laser cooling experiments, the method is based on the Zeeman egect of^87 Rb atoms. The laser frequency is stabilized by absorption spectrum line of atoms in magnetic field. We show that a magnetic field can be added up to 10^-2T. The corresponding frequency shift is 10^2 MHz and the response time is about 1ms. The large range of the frequency shift is suffcient for laser-cooling experiments.     

Observation of Spin Polarized Clock Transition in 87Sr Optical Lattice Clock

Atomic clocks operating at optical frequencies, with much better accuracy compared with microwave atomic clocks, have been assumed to be the next- generation time and frequency standards, Many applications will benefit from this lower frequency un- certainty of optical clocks, such as the re-definition of ＇the second＇, i.e. one of the seven base units of the international system of units （SI）, test of the time variation of fundamental physical constants and rel- ativity geodesy. Recently, the neutral atom lattice clock has achieved a lower frequency uncertainty com- pared with the optical ion clock, mainly due to the im- provement of the clock laser frequency stability refer- enced to a long high-finesse ULE cavity and the more accurate evaluation of black-body radiation shift. Strontium is an excellent candidate for the neutral atom optical clock. For the fermionic isotope of stron- tium, it has intrinsically less collision shift and the first order Zeeman shift can be removed by an inter- leaved probing approach.Recently, through the pre-cise measurement of the polarizability of strontium, the black body radiation （BBR） shift of the stron- tium lattice clock, which remains to be the limitation factor of its total frequency uncertainty, is reduced to a lower 10^-18 value.The instability of the strontium lattice clock has reached 3.1 × 10-16/√T, showing the significant advantage over the single ion optical clock. The total systematic uncertainty has reached 6.4 × 10^-18 in fractional frequency, which is the best among all optical clocks until now.     

A Radio Frequency Field Guide Using Field Induced Adiabatic Potential

We study the behaviour of atoms in a field with both static magnetic field and radio frequency （rf） magnetic field. We calculate the adiabatic potential of atoms numerically beyond the usually rotating wave approximation, and it is pointed that there is a great difference between using these two methods. We find the preconditions when RWA is valid. In the extreme of static field almost parallel to rf field, we reach an analytic formula. Finally, we apply this method to 87 Rb and propose a guide based on an rf field on atom chip.     

Suppression of servo error uncertainty to 10~(-18) level using double integrator algorithm in ion optical clock

A universal locking model for single ion optical clocks was built based on a simple integrator and a double integrator.Different integrator algorithm parameters have been analyzed in both numerical simulations and experiments. The frequency variation measured by the comparison of two optical clocks coincides well with the simulation results for different second integrator parameters. According to the experimental results, the sensitivity of the servo error influenced by laser frequency drift with the addition of a double integrator was suppressed by a factor of 107. In a week-long comparison of optical clocks, the relative uncertainty of the servo error is determined to be 1.9 × 10~(-18), which is meaningful for the systematic uncertainty of the transportable single ~(40)Ca~+ ion optical clock entering the 10~(-18) level.     

Measurement of 129Xe frequency shift due to Cs–129Xe collisions

Enhancement factor K0, which characterizes NMR and EPR frequency shifts for Cs-129Xe, is measured for the first time. The enhancement factor r-o was measured to be （702±41） at 80 ℃ and （653±20） at 90 ℃, using the NMR frequency shift, detected by atomic magnetometer at a low magnetic field of 100 nT. This result is useful for predicting the EPR frequency shifts for Cs and the NMR frequency shifts for 129Xe in spin-exchange cells.     

Excitonic Absorption of Semiconductor Nanorings under Terahertz Fields

The optical absorption of GaAs nanorings （NRs） under adc electric field and a terahertz （THz） ac electric field applied in the plane containing the NRs is investigated theoretically. The NRs may enclose some magnetic flux in the presence of a magnetic field perpendicular to the NRs plane. Numerical calculation shows that the excitonic effects are essential to correctly describe the optical absorption in NRs. The applied lateral THz electric field, as well as the dc field leads to reduction, broadening and splitting of the exciton peak. In contrast to the presence of a dc field, significant optical absorption peak arises below the zero-field bandgap in the presence ofa THz electric field at a certain frequency. The optical absorption spectrum depends evidently on the frequency and amplitude of the applied THz field and on the magnetic flux threading the NRs. This promises potential applications of NRs for magneto-optical and THz electro-optical sensing.     

All-fiber-based laser with 200 mHz linewidth

We demonstrate the frequency stabilization of a 1.55 μm erbium-doped fiber laser by locking it to a 5-km-long optical fiber delay line(FDL). The stabilized laser is characterized via comparison with a second identical laser system. We obtain a fractional frequency stability of better than 3 × 10~(-15) over time scales of 1–10 s and a laser linewidth of 0.2 Hz, which is the narrowest linewidth of an FDL-stabilized laser observed to date.     

Automatic compensation of magnetic field for a rubidium space cold atom clock

When the cold atom clock operates in microgravity around the near-earth orbit, its performance will be affected by the fluctuation of magnetic field. A strategy is proposed to suppress the fluctuation of magnetic field by additional coils, whose current is changed accordingly to compensate the magnetic fluctuation by the linear and incremental compensation. The flight model of the cold atom clock is tested in a simulated orbital magnetic environment and the magnetic field fluctuation in the Ramsey cavity is reduced from 17 nT to 2 nT, which implied the uncertainty due to the second order Zeeman shift is reduced to be less than 2×10~(-16). In addition, utilizing the compensation, the magnetic field in the trapping zone can be suppressed from 7.5 μT to less than 0.3 μT to meet the magnetic field requirement of polarization gradients cooling of atoms.     

Ferromagnetic resonance frequency shift model of laminated magnetoelectric structure tuned by electric field

Based on Smith-Beljers theory and classical laminate theory, an explicit model is proposed for the ferromagnetic resonance （FMR） frequency shift of a stress-mediumed laminated magnetoelectric structure tuned by an electric field. This model can effectively predict the experimental phenomenon that the FMR frequency increases under a parallel magnetic field and decreases under a perpendicular magnetic field when the electric field ranges from - 10 kV/m to 10 kV/m. Besides, this theory further shows that the FMR frequency increases monotonically as the angle between the direction of the external magnetic field and the outside normal direction of the laminated structure increases, and the frequency will increase as great as 7 GHz. In addition, when the angle reaches a certain critical value, the external electric field fails to tune the FMR frequency. When the angle is above the critical value, the increase of the electric field induces the FMR frequency to increase, and the opposite scenario happens when it is below the critical value. When the angle is 90~ （parallel magnetic field）, the FMR frequency is the most sensitive to the change of the electric field.     

Application of Electron-Shelving Detection via 423 nm Transition in Calcium-Beam Optical Frequency Standard

A new scheme of small compact optical frequency standard based on thermal calcium beam with application of 423 nm shelving detection and sharp-angle velocity selection detection is proposed. Combining these presented techniques, we conclude that a small compact optical frequency standard based on thermal calcium beam will outperform the commercial caesium-beam microwave dock, like the 5071 Cs clock （from Hp to Agilent, now Symmetricom company）, both in accuracy and stability.     

Evaluation of second-order Zeeman frequency shift in NTSC-F2

Caesium atomic fountain clock is a primary frequency standard, which realizes the duration of second. Its performance is mostly dominated by the frequency accuracy, and the C-field induced second-order Zeeman frequency shift is the major effect, which limits the accuracy improvement. By applying a high-precision current supply and high-performance magnetic shieldings, the C-field stability has been improved significantly. In order to achieve a uniform C-field, this paper proposes a doubly wound C-field solenoid, which compensates the radial magnetic field along the atomic flight region generated by the lead-out single wire and improves the accuracy evaluation of second-order Zeeman frequency shift. Based on the stable and uniform C-field, we launch the selected atoms to different heights and record the magnetically sensitive Ramsey transition|F = 3, mF=-1 → |F = 4, mF=-1 central frequency, obtaining this frequency shift as 131.03×10~(-15) and constructing the C-field profile(σ = 0.15 n T). Meanwhile, during normal operation, we lock NTSC-F2 to the central frequency of the magnetically sensitive Ramsey transition |F = 3, mF=-1 → |F = 4, mF=-1 fringe for ten consecutive days and record this frequency fluctuation in time domain. The first evaluation of second-order Zeeman frequency shift uncertainty is 0.10×10~(-15). The total deviation of the frequency fluctuation on the clock transition induced by the C-field instability is less than 2.6×10~(-17). Compared with NTSC-F1, NTSC-F2, there appears a significant improvement.     

Magnetic field measurement based on a stimulated two-photon Raman transition

The magnetic field in the microwave interaction zone of the fountain atomic clock was measured by stimulated Raman transitions.By measuring the two-photon transition frequency between the Zeeman levels of the two ground states,we achieved a magnetic field measurement accuracy of the order of 0.28 nT.This method is immune to the Doppler shift and the AC Stark shift.The second order Zeeman shift of the fountain clock is 170.7×10-15,with the uncertainty of 7.2×10-16.     

An Yb-fiber frequency comb phase-locked to microwave standard and optical reference

We present a fully stabilized Yb-fiber frequency comb locked to a microwave standard and an optical reference separately. The carrier-envelope offset frequency is generated by a standard f–2f interferometer with 40 dB signal-tonoise ratio. The offset frequency and the repetition rate are stabilized simultaneously to the radio frequency reference for more than 30 hours, and the fractional Allan deviation of the comb is the same as the microwave standard of 10^-12 at 1 s.Alternatively, the comb is locked to an ultra-stable optical reference at 972 nm using an intracavity electro-optic modulator,exhibiting a residual integrated phase noise of 458 mrad(1 Hz–10 MHz) and an in-loop tracking stability of 1.77× 10^-18 at 1 s, which is significantly raised by six orders comparing to the case locked to the microwave frequency standard.     

Frequency Resonance in Stochastic Systems

The phenomenon of frequency resonance,which is usually related to deterministic systems.is investigated in stochastic systems.We show that for those autonomous systems driven only by white noise,if the output power spectrum exhibits a nonzero peak frequency,then applying a periodic signal just on this noise-induced central frequency can also induce a resonance phenomenon,which we call the frequency stochastic resonance.The effect of such a resonance in a coupled stochastic system is shown to be much better than that in a single-oscillator system.     

Effects of an applied low frequency field on the dynamics of a two-level atom interacting with a single-modefield

The effects of an applied low frequency field on the dynamics of a two-level atom interacting with a single-mode field are investigated. It is shown that the time evolution of the atomic population is mainly controlled by the coupling constants and the frequency of the low frequency field, which leads to a low frequency modulation function for the time evolution of the upper state population. The amplitude of the modulation function becomes larger as the coupling constants increase. The frequency of the modulation function is proportional to the frequency of the low frequency field, and decreases with increasing coupling constant.     

Stabilization and Shift of Frequency in an External Cavity Diode Laser with Solenoid-Assisted Saturated Absorption

A simple method to realize both stabilization and shift of the frequency in an external cavity diode laser （ECDL） is reported. Due to the Zeeman effect, the saturated absorption spectrum of Rb atoms in a magnetic field is shifted. This shift can be used to detune the frequency of the ECDL, which is locked to the saturated absorption spectrum. The frequency shift amount can be controlled by changing the magnetic field for a specific polarization state of the laser beam. The advantages of this tunable frequency lock include low laser power requirement, without additional power loss, cheapness, and so on.     

Simulation and experiments of rf tuning of a 201.5 MHz four-rod RFQ cavity

A four-rod radio frequency quadruple (RFQ) cavity has been built for the Peking University Neutron Imaging Facility (PKUNIFTY). The rf tuning of such a cavity is important to make the field distribution flat and to tune the cavity's resonant frequency to its operating value. Plate tuners are used to tune the RFQ, which have an effect on both the cavity frequency and field distribution. The rf performance of the RFQ and the effect of plate tuners are simulated. Based on the simulation, a code RFQTUNING is designed, which gives a fast way to tune the cavity. With the aid of the code the cavity frequency is tuned to 201.5 MHz and the flatness deviation of the field distribution is reduced to less than 5%.