• Quantum foudation entanglement concurrent hybrid

When and how does a classical apparatus interact with a quantum sys-
tem? What kind of quantum effects can we observe macroscopically? Those
and many other questions are under investigation, the real problem being
the deep relations between quantum and classical mechanics. The dynam-
ics of quantum-classical hybrids, formulated by [1], is an attempt to treat
these questions. This theory is based on the phase space representation of
quantum mechanics by Heslot [2].The basic idea is to generalize the classical
and the quantum mechanical phase spaces through the introduction of the
Cartesian product space with a generalized Poisson bracket.
Our goal is to analyze the dynamics of entanglement of two q-bits in this
hybrid theory.
Precisely, we analyze a system of two q-bits coupled with a harmonic oscilla-
tor. We formulate our discussion in the Tavis-Cummings model [3]. Foremost
we study the dynamics of the q-bits and accordingly we describe the evolu-
tion of entanglement using the concurrence [4]. Then, beginning with the
Tavis-Cummings model, we “promote” the quantum harmonic oscillator to
a classical one. The quantum Hamiltonian becomes a hybrid one. Some
motivations that led us to choose this system are: the abundance of interest-
ing aspects of this model, and its possible relevance for the development of
quantum information protocols. We have decided to use a numerical proce-
dure, in order to solve the hybrid equations of motion. The q-bit-oscillator
coupling produces a back-reaction on the harmonic oscillator that can be
experimentally relevant, providing a testbed for the hybrid theory. Also, we
have demonstrated that the concurrence is an invariant of the hybrid system.
Furthermore, we discuss a possible experimental application, the hybrid cool-
ing. We can, in principle, use the hybrid coupling to construct a new kind
of cooling system, as we will illustrate in the thesis work.