Supersqueezed states from squeezed states

Michael Martin Nieto

Published Jan 1, 1993• 2 citations

Abstract

Using super-Baker-Campbell-Hausdorff relations on the elements of the supergroup OSP(2/2), we derive the supersqueeze operator and the supersqueezed states, which are the supersymmetric generalization of the squeezed states of the harmonic oscillator.

Related papers

Supersqueezed states

V. Alan Kostelecký, Michael Martin Nieto, D. Rodney Truax

We derive the supersqueeze operator for the supersymmetric harmonic oscillator, using Baker-Campbell-Hausdorff relations for the supergroup OSP(2/2). Combining this with the previously obtained superdisplacement operator, we derive the supersqueezed states. These are the supersymmetric generalization of the squeezed states of the harmonic oscillator.

arXiv:hep-ph/9211335Physical Review AAug 1, 199317 citations

Generalized coherent and squeezed states based on the h(1)⊕su(2) algebra

Nibaldo Alvarez-Moraga, Véronique Hussin

States which minimize the Schrödinger–Robertson uncertainty relation are constructed as eigenstates of an operator which is an element of the h(1)⊕su(2) algebra. The relations with supercoherent and supersqueezed states of the supersymmetric harmonic oscillator are given. Moreover, we are able to compute general Hamiltonians which behave like the harmonic oscillator Hamiltonian or are related to the Jaynes–Cummings Hamiltonian.

arXiv:math-ph/0503062Journal of Mathematical PhysicsMay 1, 200217 citations

Supercoherent states

B. W. Fatyga, V. Alan Kostelecký, Michael Martin Nieto +1 more

A general approach is presented for constructing coherent states for supersymmetric systems. It uses Rogers's supermanifold formulation of supergroups to extend the group-theoretic method. Supercoherent states are explicitly obtained for the supersymmetric harmonic oscillator. They are shown to be eigenstates of the supersymmetric annihilation operator and to be minimum-uncertainty states. Two more-complex situations with extended physical supersymmetries are also considered: an electron moving in a constant magnetic field, and the electron-monopole system. The supercoherent states for these systems are found using super Baker-Campbell-Hausdorff relations and their interpretation is elucidated.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsFeb 15, 199155 citations

COHERENT STATES AND SQUEEZED STATES, SUPERCOHERENT STATES AND SUPERSQUEEZED STATES

Michael Martin Nieto

This article reports on a program to obtain and understand coherent states for general systems. Most recently this has included supersymmetric systems. A byproduct of this work has been studies of squeezed and supersqueezed states. To obtain a physical understanding of these systems has always been a primary goal. In particular, in the work on supersymmetry an attempt to understand the role of Grassmann numbers in quantum mechanics has been initiated.

arXiv:hep-th/9212116WORLD SCIENTIFIC eBooksApr 1, 19944 citations

Functional forms for the squeeze and the time-displacement operators

Michael Martin Nieto

Using Baker - Campbell - Hausdorff relations, the squeeze and harmonic-oscillator time-displacement operators are given in the form , where , , and are explicitly determined. The applications are discussed.

arXiv:quant-ph/9605032Quantum and Semiclassical Optics Journal of the European Optical Society Part BOct 1, 199620 citations

Supercoherent states and physical systems

V. Alan Kostelecký, Michael Martin Nieto, B. W. Fatyga +1 more

A method is developed for obtaining coherent states of a system admitting a supersymmetry. These states are called supercoherent states. The presented approach is based on an extension to supergroups of the usual group-theoretic approach. The example of the supersymmetric harmonic oscillator is discussed, thereby illustrating some of the attractive features of the method. Supercoherent states of an electron moving in a constant magnetic field are also described.

Jan 1, 19920 citations