parosc_p.xmds

<?xml version="1.0"?>
<!--Example parametric oscilator simulation using +P function-->
<!--Pump has been adiabatically eliminated, to give a 2-photon loss-->

<simulation>

  <name>parosc_p</name>

  <author>Joel Corney</author>
  <description>
    Example parametric oscilator simulation using +P function
    Pump has been adiabatically eliminated, to give a 2-photon loss
  </description>

  <prop_dim>t</prop_dim>
  <error_check>yes</error_check>
  <stochastic>yes</stochastic>
  <paths>1000</paths>
  <use_mpi>no</use_mpi>
  <seed>1 2</seed>
  <noises>2</noises>

  /***********/
  <globals>
  /***********/
  <![CDATA[
    const double Pi = 2.0*asin(1.0);
    
    /*Simulation Parameters*/
    const double kappa1 = 1;    /*Damping of alpha-mode*/
    const double kappa2 = 500;  /*Damping of gamma-mode*/
    const double g = 10;        /*Parametric coupling*/
    const double epsilon = 75;   /*Driving*/
    
    /*Scaled parameters*/
    const double lambda = g*epsilon/kappa2;
    const double h = g/sqrt(2*kappa2);
  ]]>
  </globals>

  /*************/
  <field>
  /*************/
    <name>main</name>
    <samples>1</samples>
 
    /***MAIN***/
    <vector>
      <name>main</name>
      <type>complex</type>
      <components>alpha1 alpha2</components>
      <fourier_space>no</fourier_space>    
      <![CDATA[
        /* NB: We take the '2' variables to be the conjugates */
        alpha1 = rcomplex(sqrt((lambda- kappa1)/(h*h)),0.0);
        alpha2 = rcomplex(sqrt((lambda- kappa1)/(h*h)),0.0);    
      ]]>
    </vector>        
  </field>

  /******************/
  <sequence>
  /******************/
    <integrate>
      <algorithm>SIIP</algorithm>
      <interval>500</interval>
      <lattice>50000</lattice>
      <samples>1000</samples>
      <iterations>4</iterations>
      <vectors>main</vectors>
      <![CDATA[
        complex s1 = c_sqrt(lambda - h*h*alpha1*alpha1);        /*Noise Correlations*/
        complex s2 = c_sqrt(lambda - h*h*alpha2*alpha2);        /*Noise Correlations*/

        dalpha1_dt = (h*h/2 - kappa1)*alpha1 + (lambda - h*h*alpha1*alpha1)*alpha2
                      + s1*n_1 ;
        dalpha2_dt = (h*h/2 - kappa1)*alpha2 + (lambda - h*h*alpha2*alpha2)*alpha1
                      + s2*n_2;
      ]]>
    </integrate>
  </sequence>

  /**************/
  <output>
    <filename>parosc_p.xsil</filename>
    <group>
      <sampling>
       <vectors>main</vectors>
        <moments>N_alpha N_alphai alpha_x alpha_y alpha_x2 alpha_y2</moments>
        <![CDATA[
          N_alpha = alpha1*alpha2 ;
          N_alphai = imag(alpha1*alpha2);
          alpha_x = (alpha1 + alpha2)/2;
          alpha_y = (alpha1 - alpha2)/(2*i);
          alpha_x2 = (alpha1 + alpha2)*(alpha1 + alpha2)/4.0 + 1.0/4.0;
          alpha_y2 = -(alpha1 - alpha2)*(alpha1 - alpha2)/4.0 + 1.0/4.0;
        ]]>
      </sampling>
    </group>
   </output>
</simulation>