Heisenberg's Uncertainty Relations and Quantum Optics

Abstract

We present a brief review of the impact of the Heisenberg uncertainty relations on quantum optics. In particular we demonstrate how almost all coherent and nonclassical states of quantum optics can be derived from uncertainty relations.1 Introduction: Heisenberg Uncertainty Relations:-Heisenberg's uncertainty relations had tremendous impact in the field of quantum optics particularly in the context of the construction of coherent and other classes of states for different physical systems and in the reconstruction of quantum states. We present very general arguments based on the equality sign in the Heisenberg uncertainty relations to demonstrate a very large class of coherent and nonclassical states for a wide variety of quantum systems such as single mode and two mode radiation fields, quantized motion of trapped ions, collection of spins, and two level atoms. The resulting states for spin systems are especially interesting as these have varied applications starting from the dynamics of a collection of two level atoms to two component Bose condensates. Additionally, spins in such states have strong entanglement. Consider a quantum mechanical system with two physical observables represented by hermitain operators A and B satisfying the commutation relation

On Heisenberg Uncertainty Relationship, Its Extension, and the Quantum Issue of Wave-Particle Duality

“…, when the quantum objects are complementarily manifested either as wave or particle ) nor with the wave-particle equivalency in free evolution (that is not necessarily related with free motion but with quantum existence independent of any experiment or observation). Nevertheless, possible generalizations and reformulation of HUR were suggested during the last decade by the modern quantum mathematics [10–12], optics [13], information theory [14–16], still without establishing the HUR description in the absence of commutation rules [17,18] or versions of Schwarz inequality [19,20]. …”