% Squeezed vacuum state (Sec. II.E)
%   |xi> = 1/sqrt(cosh r) * sum_n (-1)^n sqrt((2n)!)/(2^n n!) e^{i n theta} (tanh r)^n |2n>
% A superposition of the even number states only.

clear;            % Clear memory
clc;              % Clear the command window/screen
d = 20;
I = eye(d);
r = 0.3;          % squeezing parameter
theta = pi/4;     % squeezing direction
Sqz = 0;          % initialization
for x = 0:(d/2)-1
  p = (1/sqrt(cosh(r)))*sqrt(prod(1:(2*x)))/(2^x*prod(1:x));
  Sqz = Sqz + p*(-1)^x*exp(i*x*theta)*(tanh(r))^x*I(:,2*x+1);
end
Sqz                 % squeezed vacuum state output
N_sqz = norm(Sqz)   % check norm (should be 1)