Coherence Control of Tunneling

Abstract

The phase space representation of quantum mechanics are well known as powerful tools for studying the correspondence between the density operator and classical distributions in phase space. This representation, known as the third formulation of quantum mechanics, is given in terms of the joint probability distribution (or more precisely the quasi-probability), and is independent of the conventional Hilbert space or the path integral formulations. In this representation on needs not choosing coordinate or momentum - it works in the full space, accommodating the uncertainty principle, and offering a unique insights into the classical limit of quantum theory [1]. Tunneling is a genuine quantum effect discovered long agosince the heyday of quantum mechanics. This manifests itself, for instance, as quantum particle passing through a classically forbidden barrier; the energy of the particle being smaller than that of the barrier. Although tunneling can be predicted in few simple systems, it remains a formidable task in a vast majority of quantum systems. Track Tunneling in a system maybe essential for understanding of its behavior. In this work, we want to make use of an indicator of quantumness (or non classicality) to control tunnelling in dynamical systems. This indicator [6], has been successfully tested in a large number of quantum states of infinite dimensional Hilbert space. It is based on the relative volume of the negative part of the Wigner function and is a quantitative measure of the degree to which a system is quantum. Attempts have been trying to link the negativity of the Wigner function with the entanglement of the analysed state on a composed Hilbert space [7]. To proceed, we will first review fundamentals of quantum mechanics in phase space focusing mainly on the role of different distribution functions. In particular, we will make use of the indicator of the Nonclassicality [6] to explore few quantum states including Fock states, Schrondinger cats, and so on. Then we will consider a tunnel model system such as ammonia (or Umbrella) for which coherent destruction of tunnelling has been revealed [8, 9]. Finally, we hope to have full control over this tunnelling model by means of that indicator [6]