We distinguish between two forms of the _squeezed coherent state_ which are not necessarily equal, since the order with which we apply the squeezing and displacement operators matters! These are the _[[two photon coherent state]]_ which is derived from [the vacuum state](The%20vacuum%20state.md) as follows: $|\xi\rangle_\alpha=\hat{S}(\xi)\hat{D}(\alpha)|0\rangle$ ^b829e9 and the so called _ideal squeezed state_, which comes about from applying the [[displacement operator]] and [squeezing Operator](Squeezing%20Operator.md) in reverse order such that we obtain $|\alpha\rangle_\xi=\hat{D}(\alpha)\hat{S}(\xi)|0\rangle$ In the image below we compare pure and two photon coherent states as they appear in phase space.  Image adapted from Mandel L., Wolf E., _Optical Coherence and Quantum Optics_ #QuantumMechanics/StationaryStateQuantumSystems #QuantumMechanics/QuantumOptics