Squeezed states quantum optics

A suitable choice of the variational wave functions for various electron-phonon two-level systems is a long-standing problem in solid state physics as well as in quantum optics. For two-level reflection symmetric systems with intralevel electron-phonon interaction the approach with a variational two-center squeezed coherent phonon wave function was found to yield the lowest ground state energy. The two-center wave function was constructed as a linear combination of the phonon wave functions related to both levels introducing new VP. 

The Heisenberg uncertainty relation (9) imposes basic restrictions on the accuracy of the simultaneous measurement of the two quadrature components of the optical held. In the vacuum state the noise is isotropic and the two components have the same level of quantum noise. However, quantum states can be produced in which the isotropy of quantum fluctuations is broken—the uncertainty of one quadrature component, say, Q, can be reduced at the expense of expanding the uncertainty of the conjugate component, P. Such states are called squeezed states [5,6]. They may or may not be the minimum uncertainty states. Thus, for squeezed states... 

This work is intended as an attempt to present two essentially different constructions of harmonic oscillator states in a FD Hilbert space. We propose some new definitions of the states and find their explicit forms in the Fock representation. For the convenience of the reader, we also bring together several known FD quantum-optical states, thus making our exposition more self-contained. We shall discuss FD coherent states, FD phase coherent states, FD displaced number states, FD Schrodinger cats, and FD squeezed vacuum. We shall show some intriguing properties of the states with the help of the discrete Wigner function. 

The method described in the previous sections can be easily generalized to be useful for generation of various FD quantum-optical states different from the FD coherent state. Thus, we shall show an example of how to adapt our method to generate the FD squeezed vacuum [10]. In the first part of this work [see Eq. (78) in Ref. 1], we have defined the (,v + 1)-dimensional generalized squeezed vacuum to be... 

A more far-reaching phenomenon is the possibility of generating radiation in "squeezed" states [4.19]. Such radiation exhibits reduced noise below the quantum limit and could have important applications for optical communication and precision interferometric measurements of small displacements, e.g. in gravity-wave detection experiments. A considerable degree of "squeezing" has recently been experimentally demonstrated [4.20, 21]. Various aspects of modern quantum optics have been discussed in [4. 22-25]. 

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