Squeezed States for General Systems

Generalized Intelligent States (coherent and squeezed states) are derived for an arbitrary quantum system by using the minimization of the so-called Robertson-Schr\"odinger uncertainty relation. The Fock-Bargmann representation is also considered. As a direct illustration of our construction, the P\"oschl-Teller potentials of trigonometric type will be shosen. We will show the advantage of the Fock-Bargmann representation in obtaining the generalized intelligent states in an ...

Squeezed states are one of the most useful quantum optical models having various applications in different areas, especially in quantum information processing. Generalized squeezed states are even more interesting since, sometimes, they provide additional degrees of freedom in the system. However, they are very difficult to construct and, therefore, people explore such states for individual setting and, thus, a generic analytical expression for generalized squeezed states is ...

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....

With the successes of the Laser Interferometer Gravitational-wave Observatory, we anticipate increased interest in working with squeezed states in the undergraduate and graduate quantum-mechanics classroom. Because squeezed-coherent states are minimum uncertainty states, their wavefunctions in position and momentum space must be Gaussians. But this result is rarely discussed in treatments of squeezed states in quantum textbooks or quantum optics textbooks. In this work, we sh...

This article presents a squeezing transformation for quantum systems associated to finite vector spaces. The physical idea of squeezing here is taken from the action of the usual squeezing operator over wave functions defined on a real line, that is, a transformation capable to diminish (or enhance) the mean square deviation of a centered distribution. As it is discussed, the definition of such an operator on finite dimensional vector spaces is not a trivial matter, but, on t...

Characteristic uncertainty relations and their related squeezed states are briefly reviewed and compared in accordance with the generalizations of three equivalent definitions of the canonical coherent states. The standard SU(1,1) coherent states are shown to be the unique states that minimize the Schroedinger uncertainty relation for every pair of the three generators and the Robertson relation for the three generators. The characteristic uncertainty inequalities are natural...

In these notes, we discuss squeezed states using the elementary quantum language based on one-dimensional Schr\"odinger equation. No operators are used. The language of quantum optics is mentioned only for a hint to solve a differential equation. Sections II and III (squeezed vacuum and pure squeezed states) can be used in a standard undergraduate course on quantum mechanics after discussion of a harmonic oscillator. Section IV discusses density matrix of mixed squeezed state...

Using the f-deformed oscillator formalism, we introduce two types of squeezed coherent states for a Morse potential system (Morse-like squeezed coherent states) through the following definitions: i) as approximate eigenstates of a linear combination of f-deformed ladder operators and ii) as deformed photon-subtracted coherent states. For the states thus constructed we analyze their statistical properties, their uncertainty relations, and their temporal evolution on phase spac...

Ladder operators for the hyperbolic Rosen-Morse (RMII) potential are realized using the shape invariance property appearing, in particular, using supersymmetric quantum mechanics. The extension of the ladder operators to a specific class of rational extensions of the RMII potential is presented and discussed. Coherent states are then constructed as almost eigenstates of the lowering operators. Some properties are analyzed and compared. The ladder operators and coherent states...

A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and t...