## Tesi etd-10032013-031332 |

Thesis type

Tesi di laurea magistrale

Author

FRATINO, LORENZO

email address

lorenzo.fratino@gmail.com

URN

etd-10032013-031332

Title

Entaglement in a quantum-classical hybrid of two q-bits and one oscillator.

Struttura

FISICA

Corso di studi

FISICA

Commissione

**relatore**Prof. Elze, Hans Thomas

Parole chiave

- Quantum foudation entanglement concurrent hybrid

Data inizio appello

24/10/2013;

Consultabilità

completa

Riassunto analitico

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.

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.

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