A squeezed coherent state is more general than the coherent state, but its properties are similar. Like the coherent state, the squeezed state is the eigenfunction of an operator, . This operator is a linear combination of the creation and destruction operators. The mixing of the operators is controlled by means of a variable, r, which is called the squeezing parameter:
This operator is called the Boguliubov transform. Notice that if r=0, then eq:q18 becomes the destruction operator. Therefore, one does not need two different methods to compute squeezed coherent and coherent states. A coherent state is a special case of a squeezed state. The eigenvalue of is which is analogous to the coherent state's :
If r=0 then is . In general is complex, but as with one can assume without loss of generality that is real. The principle difference between the coherent and squeezed coherent state is that the variances of momentum and position are not constant. One of these variances may be made arbitrarily small by setting the squeezing parameter. The trade--off is that the other variance becomes arbitrarily large. The optics community has shown interest in these field states because of this property. Fiber optic cables transmit data via a laser beam which is a good approximation of a coherent state. Although more and more noise is removed from optical signals by advances in microelectronics and optics, a quantum uncertainty noise limit will ultimately be reached. A squeezed coherent beam could breach the quantum noise barrier.
One of the problems with this technology is that the squeezing is periodic as seen in Figure .
Figure: The Squeezed Coherent State in Phase Space
Every one--fourth of a period the squeezed variance changes. One can transmit data on either the magnetic or electric field, but the data must be written to and read off the field. This process requires a phase--sensitive field detection device called a homodyne detector. The construction of these detectors is currently an important research topic.
The central properties of squeezed coherent light are listed in the table below in terms of the squeezing parameter and .[19,20]