Higher-nsqueezed states and factorization of the squeezing operator
Jeffrey J. Hamilton · Physical Review A · 1990
It is shown that n>0 simple-harmonic-oscillator squeezed states have the same time-evolution behavior as the fundamental (n=0) squeezed state. That is, the probability density \ensuremath{\Vert}\ensuremath{\psi}(x,t)${\mathrm{\ensuremath{\Vert}}}^{2}$ retains its original shape as time progresses, except that the scales of the ordinate and abscissa oscillate in a reciprocal manner with frequency 2\ensuremath{\omega}. This allows the time-evolved squeezing operator S${\mathrm{^}}_{\mathit{H}}$(\ensuremath{\lambda},t) to be written as a product of simple factors. Moreover, if a thermal distribution with density matrix \ensuremath{\rho}^ is squeezed, then the mixed squeezed state with minimum free energy has a density matrix given by a unitary transformation \ensuremath{\rho}${\mathrm{^}}_{\mathit{s}}$=S^(\ensuremath{\lambda})\ensuremath{\rho}^S^ $^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$(\ensuremath{\lambda}), where \ensuremath{\lambda} is a suitable squeezing parameter.