Squeezed States for General Systems

In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schr\"...

After beginning with a short historical review of the concept of displaced (coherent) and squeezed states, we discuss previous (often forgotten) work on displaced and squeezed number states. Next, we obtain the most general displaced and squeezed number states. We do this in both the functional and operator (Fock) formalisms, thereby demonstrating the necessary equivalence. We then obtain the time-dependent expectation values, uncertainties, wave-functions, and probability de...

A closed form expression for the higher-power coherent states (eigenstates of $a^{j}$) is given. The cases j=3,4 are discussed in detail, including the time-evolution of the probability densities. These are compared to the case j=2, the even- and odd-coherent states. We give the extensions to the "effective" displacement-operator, higher-power squeezed states and to the ladder-operator/minimum-uncertainty, higher-power squeezed states. The properties of all these states are d...

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 general algorithm has been given for the generation of Coherent and Squeezed states, in one-dimensional hamiltonians with shape invariant potential, obtained from the master function. The minimum uncertainty states of these potentials are expressed in terms of the well-known special functions.

In this paper we use the Lie algebra of space-time symmetries to construct states which are solutions to the time-dependent Schr\"odinger equation for systems with potentials $V(x,\tau)=g^{(2)}(\tau)x^2+g^{(1)}(\tau)x +g^{(0)}(\tau)$. We describe a set of number-operator eigenstates states, $\{\Psi_n(x,\tau)\}$, that form a complete set of states but which, however, are usually not energy eigenstates. From the extremal state, $\Psi_0$, and a displacement squeeze operator de...

We introduce a new method for constructing squeezed states for the 2D isotropic harmonic oscillator. Based on the construction of coherent states in [1], we define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the SU(2) coherent states. The new ladder operators are used for generalizing the squeezing operator to 2D and the SU(2) coherent states play the role of the Fock states in the expansion of the 2D s...

We present an operator theoretic side of the story of squeezed states regardless the order of squeezing. For low order, that is for displacement (order 1) and squeeze (order 2) operators, we bring back to consciousness what is know or rather what has to be known by making the exposition as exhaustive as possible. For the order 2 (squeeze) we propose an interesting model of the Segal-Bargmann type. For higher order the impossibility of squeezing in the traditional sense is pro...

Minimum-uncertainty squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples we deal with nonlinear generalizations of quadrature squeezed states and deformed nonlinear squeezed states. In this manner one may derive those squeezed states which are directly related to given observables. This can be useful for optimi...

It was at the dawn of the historical developments of quantum mechanics when Schr\"odinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as coherent states today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowaday...