Chapter 2 Page 9: The sentence
”The present chapter will provide some tools for the calculation of the interferometric phase shift. The first part illustrates the derivation of the temporal evolution of a three-level atom in a light field, and we will use the results to evaluate the output of a three-pulses Raman interferometer.
The second part explains how laser phase noise will affect the interferometer phase. In the present derivation, [38, 69] will be loosely followed. In this chapter Φ will indicate the phase shift between the atomic wave packets at the output of the interferometer and Φ the Raman lasers phase difference.” has been replaced with
“The present chapter will provide some tools for the calculation of the interferometric phase shift, mainly following [38, 69]. The first part illustrates the derivation of the temporal evolution of a three-level atom in a light field, and we will use the results to evaluate the output of a three-pulses Raman interferometer. The second part explains how laser phase noise will affect the interferometer phase. In this chapter Φ will indicate the phase shift between the atomic wave packets at the output of the interferometer and Φ the Raman lasers phase difference.”
Page 15: The sentence
“the system evolution equations are the following:” has been replaced with
“the system evolution equations are the following [38]:” Page 16
The sentence
“Results are presented in table 2.1.” has been replaced with
“Results are presented in table 2.1 [38].” The sentence
“Finally it is worth pointing out that noninteracting atoms does not interfere at the end of the interferometer.”
has been replaced with
“Finally it is worth pointing out that atoms not undergoing the central π pulse will not interfere at the end of the interferometer.”
Page 20: The sentence
“it is convenient to rewrite the equations 2.23 in the matrix form:” has been replaced with
“it is convenient to rewrite the equations 2.23 in the matrix form [38, 69]:” Page 22:
The sentence
“…depicted in figure 2.6 and its analytical expression is:” has been replaced with
“…depicted in figure 2.6 and its analytical expression is [38, 69]:” Page 23:
The sentence
“In performing the calculations we assumed that the resonance condition is verified for all three pulses. Due to the Doppler effect this assumption is not true for typical values of T used. In order to preserve
the resonance condition, we add a linear frequency ramp α on one of the two Raman lasers. Consequently, the equation 2.45 becomes:”
has been replaced with
“In these calculations, the resonance condition is assumed to be verified for all three pulses. Due to the Doppler effect this assumption is not true for typical values of T used. In order to preserve the resonance condition, a linear frequency ramp α is added on one of the two Raman lasers. Consequently, the equation 2.45 becomes [38]:”
Page 25 The sentence
“Thus the transfer function of the interferometer has the following expression:” has been replaced with
“Thus the transfer function of the interferometer has the following expression [38, 69]:” The sentence
“In particular, we are going to develop the calculations for the Raman phase noise and for seismic vibrations.”
has been replaced with
“In particular, we will see below the calculations for the Raman phase noise and for seismic vibrations.”
Page 28 The sentence
“Replacing this equation into equation 2.60 the Allan variance simplifies to give finally:” has been replaced with
“Replacing this equation into equation 2.60 the Allan variance simplifies to give finally [38, 69]:” Page 29
The sentence
“It is also possible to calculate the Allan variance from the equation 2.63 also in presence of acceleration noise:”
has been replaced with
“It is also possible to calculate the Allan variance from the equation 2.63 also in presence of acceleration noise [38, 69]:”
