deletions | additions       diff --git a/subsection_Quadrature_Noise_The_motion__.tex b/subsection_Quadrature_Noise_The_motion__.tex  index f977812..d6713c6 100644  --- a/subsection_Quadrature_Noise_The_motion__.tex  +++ b/subsection_Quadrature_Noise_The_motion__.tex 
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\[f(t) = X(t) cos(\omega_c t) + Y(t) sin(\omega_c t)\]  Where $X(t)$ is the in-phase component, $Y(t)$ is the quadrature component and $\omega_c$ is the "carrier" frequency, this is easily verified using the FT of the signal,  \[F(\omega) = X(\omega) + i Y(\omega)\] frequency.  As in the case of the harmonic oscillator, it's impossible to exactly determine $X(t)$ and $Y(t)$ for a given $t$ - there's an amount of uncertainty that can be due to classicalnoise  or quantum uncertainty relations. noise.  The quadrature components usually satisfy the uncertainty relation   \[\Delta X \Delta Y \geq 1 \]  States that minimize this relation are called coherent states, it's possible to decrease the uncertainty in one quadrature component at the expense of the other - these are called squeezed-coherent states.  The light generated by the OPO is squeezed, we can write the generated light signal  \[f(t) = A_s e^{i\omega_s t} + A_i e^{i \omega_i t} \]  In steady state,   \[ A_s \approx A_i\]  Also, we may write the frequencies in the form,  \[ \omega_{s, i} = \omega_p/2 \pm \delta \]  From the above eqs, eqs we get,  \[f(t) = A e^{i\omega_p/2 t}(e^{i \delta t} + e^{- i \delta t}) = 2A cos(\delta t) e^{i\omega_p/2 t} \]  The signal is squeezed - the quadrature component is attenuated and the in-phase component is amplified.   
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