| The time unit"second"is defined as:"The second,symbol s,is the SI unit of time.It is defined by taking the fixed numerical value of the caesium frequencyΔνcs,the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom,to be 9192631770 when expressed in the unit Hz,which is equal to s-1."Cesium atomic fountain clock is used to realize the definition of"second"directly.By applying the laser cooling technology,we trap the caesium atoms in the center of the magneto optical trap firstly,then throw up the cold atomic cloud vertically by changing the laser frequency detuning.The cold atomic cloud flies up and down twice through Ramsey cavity,realizing a Ramsey transition.By scanning the microwave frequency fed into Ramsey cavity,and recording atomic transition probability with laser at the same time,we achieve normalized Ramsey transition fringes.Using a computer to control and adjust of microwave frequency,so that the atomic transition probabiity is always maximum.Then the microwave frequency is completely equal to the ground state transition frequency of caesium atom,and the output microwave is the standard clock transition signal.The output microwave frequency in ceasium atomic fountain clock is not equal to the frequency in second definition.For the caesium atom in second definition is in a state without interference,while with the influence of external physical field and its own motion state,the atomic transition frequency would deviate from the defined frequency,which is the so-called frequency shift.For example,the magnetic field induced second-order Zeeman frequency shift,the atomic collision induced cold atomic collision frequency shift,the ambient temperature induced black-body radiation frequency shift.In order to realize the definition of“second”more accurately,we need to evaluate every frequency shift with the frequency uncertainty.The total frequency shift of caesium atomic fountain clock is the sum of each frequency shift,and the total frequency uncertainty is obtained from the operation of each frequency shift uncertainty.The smller the single frequency shift uncertainty is,the smaller the total frequency uncertainty of the clock is,and the higher the performance of the clock becomes.The magnetic field plays an important role during each fountain cycle,including the stages of cooling,state selection,free evolution,and Ramsey transition.However,magnetic field will lead to some magnetic-field-dependent frequency shifts—second-order Zeeman frequency shift,Majorana transition frequency shift,Ramsey and Rabi frequency pulling shift,which are the main frequency shifts that limit the performance improvement of caesium atomic fountain clock.This dissertation focuses on the evaluation of second-order Zeeman frequency shift and Majorana transition frequency shift,and the research content is divided into three parts.Firstly,according to the requirements of cesium atomic fountain clock for the magnetic field,we systematically design a magnetic field system.Then evaluate the second-order Zeeman frequency shift and Majorana transition frequency shift based on this magnetic field system.The specific research contents are as follows:1.Design and measurement of the magnetic field system.Combining with the requirements of the magnetic field in different zones of the caesium atomic fountain clock,and applying the classical electromagnetic field theory,we design the magnetic field system in the method of finite element analysis.Based on the international common magnetic field compensation method,position-adjustable compensation coils are designed in the magneto optical trap,and a uniform near-zero magnetic field is obtained by precisely adjusting the coils’position.This design weakens the influence on the upper selective C field and the magnetic shieldings’entrance magnetic field.At the same time,the atoms’temperature after polarization gradient cooling under this magnetic field meets caesium atomic fountain clock requirement.In the state selection zone,a uniform state selection C field is obtained by designing a non-uniform compensating magnetic field,which improves the atomic state selection efficiency.By winding a small-sized axial compensation coil at the entrance of the magnetic shieldings,we realize the compensation of magnetic field locally with small current.Which avoids the occurrence of large gradient near-zero magnetic field,and suppresses the atomic Majorana transition.The atomic interrogating and free flight zones are surrounded by four layers of high-performance cylindrical magnetic shieldings,which ae used to shield the earth’s magnetic field and the external electromagnetic field.A double-wound C-field solenoid is designed and placed inside the magnetic shieldings closely,with a current provided by a high-precision power supply.A stable and uniform static magnetic field——C field is obtained,which helps to reduce the uncertainty of second-order Zeeman frequency shift.The magnetic field on the atomic flight trajectory is measured and optimized with a uniaxial magnetometer before the vacuum system is packaged.The final measurement results show that the magntetic field strength and gradient are 17 n T and 70 n T/cm at the center of the magneto-optical trap,2400 n T and100 n T/cm in state selection zone,greater than 56 n T and 10 n T/cm at the entrance of the magnetic shieldings.The C field strength fluctuates less than 1 n T in the range of42 cm above the Ramsey cavity,and the magnetic field of each zone meets the experimental requirements of caesium atomic fountain clock with a high indicator.2.Research on measuring cold atom temperature by knife-edge method.To evaluate the effect of polarization gradient cooling on atoms in the improved magnetic field system,two methods are used to measure the cold atom temperature.First,a new method of knife-edge,is used to measure the cold atom temperature.This method is realized by modeling based on the relationship between the temperature and size of cold atomic cloud.In the experiment,we design and build a device for temperature measurement,setting a honrizontal laser at different hights of the atomic trajectory.By controlling the size of the upper supersaturated resonant laser irradiated on the cold atomic cloud,and using the lower laser to measure the residual atomic number,we obtain the atom temperature as（7.5±0.49）μK.At the same time,the traditional time-of-flight method is used to measure cold atom temperature,which is in good agreement with the temperature measurement result of the knife-edge method.The accuracy of the knife-edge method is verified,and the magnetic field performance meets the requirement of cesium atomic fountain clock for cold atom temperature.3.Theoretical study and evaluation of second-order Zeeman frequency shift.According to Breit-Rabi formula,we describe the generation mechanism of second-order Zeeman frequency shift,analyze and discuss the influence of C field spatial uniformity,timing stability and calculation error on the uncertainty of second-order Zeeman frequency shift.In the experiment,using atoms as the probe,we firstly measure the magnetic field in the free flight zone by two methods:atomic low-frequency transition and magnetic sensitive Ramsey transition.The average of C-field is 167.85n T,with a variation of less than 0.5 n T over 30 cm.According to the second-order Zeeman frequency shift formula,the frequency shift is calculated as 131.03×10-15,and the uncertainty of the second-order Zeeman frequency shift induced by the calculation error is estimated to be 1.0×10-19.Then,during NTSC-F2 normal operation,the fountain clock is locked on the central fringe of the magnetic sensitive Ramsey transition for ten consecutive days,and monitor the variation of the central frequency with time.The uncertainty of second-order Zeeman frequency shift induced by the uniformity and stability of the C field is 0.07×10-15,and the stability of the clock transition frequency induced by the stability of the C field is less than 2.6×10-17.The evaluation of second-order Zeeman frequency shift of NTSC-F2 is completed,and the uncertainty of this frequency shift is reduced by 3/4 compared with that of NTSC-F1,which further verifies the improvement of the spatial uniformity and time stability of the C field in NTSC-F2.4.Intensive study and evaluation of the Majorana transition frequency shift.Firstly, the adiabatic transition conditions of atoms are discussed,and the influence of magnetic field gradient and strength on the adiabatic transition of atoms are analyzed.By constructing a physical model,using quantum method,we calculate and analyze the changes of the atomic state after Majorana transition in the low frequency magnetic field,and obtain Majorana transition frequency shift formula.Then,according to the structural parameters and current parameters of the NTSC-F2 magnetic field system,we simulate the radial and axial magnetic field distributions at the entrance of magnetic shieldings in the method of finite element analysis.Combining the simulation results of NTSC-F2 magnetic field system and applying Monte Carlo method to simulate the colc atomic cloud position and temperature distribution,we obtain the relationship between Majorana transition frequency shift and the magnetic field at the entrance of the magnetic shieldings and the population of initial atomic state.Experimentally,the initial asymmetric populated atomic state is prepared by the dual-frequency state selection method for the first time,and the direct measurement of Majorana transition frequency shift is realized.The relationship between Marjorana transition frequency shift and the magnetic field at the entrance of the magnetic shieldings is obtained,and the measurement results are in good agreement with the previous simulated results.Finally,according to the simulated and measured results,the current of compensation coil at the entrance of the magnetic shieldings is selected to be 220μA during NTSC-F2 normal operation,and the uncertainty of Majorana transition frequency shift is evaluated to be 4.57×10-18. |
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