Displaced and Squeezed Number States

We show that the binomial states (BS) of Stoler {\it et al.} admit the ladder and displacement operator formalism. By generalizing the ladder operator formalism we propose an eigenvalue equation which possesses the number and the squeezed states as its limiting solutions. The explicit forms of the solutions, to be referred to as the {\it generalized binomial states} (GBS), are given. Corresponding to the wide range of the eigenvalue spectrum these GBS have as widely different...

A recent proposal of new sets of squeezed states is seen as a particular case of a general context admitting realistic physical Hamiltonians. Such improvements reveal themselves helpful in the study of associated squeezing effects. Coherence is also considered.

In the second part of our review (for the first part see quant-ph/0108080), we discuss a physical model for generation of "truncated" coherent and squeezed states in finite-dimensional Hibert spaces.

The original canonical coherent states could be defined in several ways. As applications for other sets of coherent states arose, the rules of definition were correspondingly changed. Among such rule changes were a change of group and relaxation of the analytic nature of the labels. Recent developments have done away with the group connections altogether and thereby allowed sets of coherent states to be defined that are temporally stable for a wide variety of dynamical system...

This paper develops a method of manipulating the squeezed atom state to generate a few-photon state whose phase or photon-number fluctuations are prescribed at our disposal. The squeezed atom state is a collective atomic state whose quantum fluctuations in population difference or collective dipole are smaller than those of the coherent atom state. It is shown that the squeezed atom state can be generated by the interaction of atoms with a coherent state of the electromagneti...

We analyze the properties and dynamics of generalized squeezed states. We find that, in stark contrast to displacement and two-photon squeezing, higher-order squeezing leads to oscillatory dynamics. The state is squeezed in the initial stages of the dynamics but the squeezing reverses at later stages, and the state reverts almost completely back to the initial state. We analyze various quantities to verify that the oscillatory dynamics is physical and not a mathematical artef...

We describe a six-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs....

This is a brief review of various families of coherent and squeezed states (and their generalizations) for a charged particle in a magnetic field, that have been constructed for the past 50 years. Although the main attention is paid to the Gaussian states, various families of non-Gaussian states are also discussed, and the list of relevant references is provided.

A new class of states of light is introduced that is complementary to the well-known squeezed states. The construction is based on the general solution of the three-term recurrence relation that arises from the saturation of the Schr\"odinger inequality for the quadratures of a single-mode quantized electromagnetic field. The new squeezed states are found to be linear superpositions of the photon-number states whose coefficients are determined by the associated Hermite polyno...

This book chapter reports on theoretical protocols for generating nonclassical states of light and mechanics. Nonclassical states are understood as squeezed states, entangled states or states with negative Wigner function, and the nonclassicality can refer either to light, to mechanics, or to both, light and mechanics. In all protocols nonclassicallity arises from a strong optomechanical coupling. Some protocols rely in addition on homodyne detection or photon counting of lig...