不同版本频标作业other quantum frequency standards

1、 Quantum Frequency StandardsWhat is the quantum projection noise limit?The state of the atoms that we want to interrogate is a superposition of two eigenstates, the probability of finding the atom in the state cannot be determined. When the projection operator acting on the superposition state, the

2、variance of which can be easily calculated as. In our case of the Fountain Clock, the measurement is usually performed at the sides of the center frequency in the Ramsey interference pattern. The broadened uncertainty can then be defined as , where N is the total number of the atoms in the interroga

3、tion and is the frequency of the interrogating laser. The total number of particles converges over the time domain.The expression for the probability in excited state using the Ramsey method: .With the variance we could estimate the maximum frequency uncertainty, i.e. the Quantum Projection Noise. T

4、 is the interval time between two interactions. From the result, we conclude that increasing the interrogating atoms and the interval time can reduce the Quantum Projection Noise. The noise is a type of shot noise. Calculate the spontaneous decay rate between the two hyperfine levels of the ground s

5、tate of and There is no Electric Dipole Transition and Electric quadruple Transition between hyperfine levels. We only calculate the spontaneous decay rate due to the Magnetic Dipole Transition here. Using the popular transition probability formula for Magnetic Dipole Transition, (2-1)where for 133C

6、s ground state the two hyperfine levels denoted as and , and for 87Rb ground state the two hyperfine levels denoted as and . The diagram is shown as follows,On the case of 133Cs, , , the spontaneous decay rate between the two hyperfine levels of the ground state is. For 87Rb, , so the spontaneous de

7、cay rate between the two hyperfine levels of the ground state is .Explain the origin of Majorana pulling in atomic clock.As with atoms with a non-zero nuclear spin, the ground state will be split into several magnetic sub-state in an external magnetic field. In different sub-energy levels with the r

8、espective said the State and the static magnetic field, and compare the direction of the atomic magnetic moment. If the atoms through the field of non-uniform size and direction of travel along the path of change, there will be two kinds of different situations. If the field change is not too fast,

9、the atomic magnetic moment will follow the magnetic field changes, we call it adiabatic process. However, non-adiabatic process refers to the atom could not follow the magnetic field proposed, and the transition will occur in different sub-state, when we define the direction of the magnetic field of

10、 quantum axis. This is the so-called Majorana transition between the sub-state of the same hyperfine level.In atomic clock with such atoms, if Majorana Transition occurs, it would change the sub-state of the ground state and shift the clock frequency mF=0mF=0. That is the origin of Majorana pulling

11、in atomic clock.Comparing with (3.96), why there is a PI in (7.11)?Consider two subsequent interactions of durationof a two-level atom with an interrogating field where these two interaction times are separated by a time T where the field is switched off. Ramsey calculated the probability to find th

12、e two-level system in the excitedstate after the second interaction as (4-1)We make the approximation ,Using detectors, we can transit the probability formula to signal formula , (4-3)Then, we get *In (3.96), in the expression of the Allen deviation In (7.11), the Allen deviation is expressed as So

13、the in (7.11) is derived from Equation *.Write a program in Mathematic or Matlab to plot a Ramsey interference pattern using reasonable Cs-clock parameters.In a Cs atomic clock, the atoms in the Ramsey conditions in the upper levels of the probability of，Where is the Rabi frequency，The velocity dist

14、ribution is is the most probable velocity.According to Ref1, the detected fluorescence is So the Matlab code is pasted belowdy=5e-3;y=1;rho=1e2;r (1e4)=0;for i=1:1e4 x=-5+10/1e4*i; sum=0; for k=1:1e3 temp=(sin (sqrt (1 + x2)*y)/(k*dy)2*cos (x*rho)/(2*k*dy)2 + (2*x2*sin (sqrt (1 + x2)*y)/(2*k*dy)4*sin (x*rho)/(2*k*dy)2)/(1 + x2) - (2*x2*sin (sqrt (1 + x2)*y)/(k*dy)*sin (sqrt (1 + x2)*y)/(k*dy)2*sin (x*rho)/(k*dy)/sqrt(1 + x2)*2* (k*dy)3*dy)/(1 + x2)*2.7(k*dy)2); sum=sum+temp; end r (i)=sum;endthe corresponding pattern Reference1 C