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Register a new userCoherent States for the Isotropic and Anisotropic 2D Harmonic Oscillators
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In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. 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, where these are then used as the basis of expansion for Schrodinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density functions in configuration space.
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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 squeezed states. We discuss some properties of the 2D squeezed states.
Normally, the half-harmonic oscillator is active when $x>0$ and absent when $x<0$. From a canonical quantization perspective, this leads to odd eigenfunctions being present while even eigenfunctions are absent. In that case, only the usual odd eigenfunctions will appear if the wall slides to negative infinity. However, if an affine quantization is used, sliding the wall away shows that all the odd and even eigenfunctions are encountered, exactly like any full-harmonic oscillator. We provide numerical support for this.
We show that in the case of unknown {em harmonic oscillator coherent states} it is possible to achieve what we call {it perfect information cloning}. By this we mean that it is still possible to make arbitrary number of copies of a state which has {it exactly} the same information content as the original unknown coherent state. By making use of this {it perfect information cloning} it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We define the notion of a {em Measurement Fidelity}. We show that this information cloning gives rise, in the case of $1to N$, to a {em distribution} of {em measurement fidelities} whose average value is ${1over 2}$ irrespective of the number of copies originally made. Generalisations of this to the $Mto MN$ case as well as the measurement fidelities for Gaussian cloners are also given.
In this communication we investigate the quantum statistics of three harmonic oscillators mutually interacting with each other considering the modes are initially in Fock states. After solving the equations of motion, the squeezing phenomenon, sub-Poissonian statistics and quasiprobability functions are discussed. We demonstrate that the interaction is able to produce squeezing of different types. We show also that certain types of Fock states can evolve in this interaction into thermal state and squeezed thermal state governed by the interaction parameters.
We have withdrawn this paper due to a fatal flaw in eqn(38).
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