Exact decoherence via an internal degree of freedom of the apparatus in the measurement of energy observable of a quantum harmonic oscillator

John Paul Besagas^1*, Eric Galapon¹

¹National Institute of Physics, University of the Philippines Diliman, Quezon City, Philippines

* Presenter:John Paul Besagas, email:jabesagas@up.edu.ph

Environment-induced decoherence theory (EIDT) is a formalism of standard quantum mechanics which provides the quantum-to-classical transition of the joint state of the system and measuring instrument in a quantum measurement process. This transition occurs by the interaction of the instrument with the large number of degrees of freedom of an environment. However, EIDT faces the issues of approximate suppression of the relevant coherences and approximately orthogonal pointer states, so that the emergent classicality is not exact and the outcomes are still subject to ambiguities. A recent paper [E.A. Galapon {\it EPL} {\bf 113} 60007 (2016)] discusses an isolated system-apparatus measurement model at which exact decoherence can be achieved at a finite measurement time. This is accomplished by separating the probe and the pointer of the measuring apparatus, keeping the probe off from observation and preparing these two subsystems of the apparatus into a momentum-limited initial state. In this work, we demonstrate how the scheme is put into effect in the specific example of measuring the energy observable of the quantum harmonic oscillator. We obtain the joint state of the quantum harmonic oscillator, probe and pointer as a function of measurement interaction time by solving the von Neumann equation for the joint state of the quantum harmonic oscillator, probe and pointer as a function of measurement interaction time. This apparoach is different from the one that is used in the original work. Here, we are able to obtain the same form of the joint state of the composite system and verify the conditions for exact decoherence and exactly orthogonal states as well as the decoherence and orthogonality times when we impose momentum-limited initial states on the apparatus probe and pointer.

Keywords: Foundations of quantum mechanics, measurement theory, decoherence, quantum statistical methods, Fundamental test of quantum mechanics