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Research in Computing Science

Sudden Death of Entanglement of two Quantum Dots Embedded in its Own Cavity

S. Sánchez-Sánchez, José Javier Sánchez Mondragón, F. R. Castillo Soria, Victor Ivan Moreno Oliva, E. Román Hernández

Published Dec 31, 2017• 0 citations
Publisher

Abstract

Entanglement of quantum systems is a key aspect to understanding the dynamics and behavior of mixed systems (density matrix) as bipartite quantum bits (qubits).Thus we need to have a reliable and accurate way to measure the entanglement degree of the system, i.e., how it evolves, so that raises several approaches to meet these demands.A quantifiable measure widely used is the "entanglement of formation" of a mixed state, defined as the minimum number required of "singlets" to create a set of pure states that represents the density matrix of the system.In this paper we consider a system of two semiconductor quantum dots embedded in its own cavity and coupled to the internal mode field of cavity type Jaynes-Cummings.The entanglement between the two quantum dots is investigated, and we show analytically that entanglement has very interesting, effects such as time evolution including the effect called sudden death.

DOI
10.13053/rcs-131-1-13

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Entanglement of quantum systems is a key aspect to understanding the dynamics and behavior of mixed systems (density matrix) as bipartite quantum bits (qubits).Thus we need to have a reliable and accurate way to measure the entanglement degree of the system, i.e., how it evolves, so that raises several approaches to meet these demands.A quantifiable measure widely used is the "entanglement of formation" of a mixed state, defined as the minimum number required of "singlets" to create a set of pure states that represents the density matrix of the system.In this paper we consider a system of two semiconductor quantum dots embedded in its own cavity and coupled to the internal mode field of cavity type Jaynes-Cummings.The entanglement between the two quantum dots is investigated, and we show analytically that entanglement has very interesting, effects such as time evolution including the effect called sudden death.
The Entanglement of quantum systems is a key aspect in order to understand the dynamics and behavior of mixed systems (density matrix) as bipartite systems of quantum bits (q-bits). A quantifiable measure widely used is the "entanglement of formation" of a mixed state, defined as the minimum number of singlets needed to create an ensemble of pure states that represents the density matrix of the system. Considering a double quantum dot system coupled cavity type Jaynes-Cummings investigate the entanglement between two quantum dots, immersed each in its own cavity, showing analytically that entanglement has a very interesting effects such as temporal evolution including the so-called sudden death effect.
The time evolution of entanglement between two quantum dots (QDs) trapped inside a cavity driven by a coherent quantized field is studied. In the presence of dissipation, entanglement shows many interesting features such as sudden death and revival, and finite steady state value after sudden death. We also investigate dependence of entanglement on dot variables and its relation to bistability. It is found that entanglement vanishes when the cavity field intensity approaches the upper branch of the bistability curve. When the cavity is driven by a modulated field in the presence of dissipation, it can periodically generate entanglement, which is much larger than the maximum value attained in the steady-state for this system but the dots are never fully entangled.
Based on the exactly analytic solution obtained of the intensity-dependent Jaynes–Cummings model for a certain class of initial entangled mixed states, we explore the time evolution of the entanglement between two atoms, initially non-locally correlated and separately interacting with two distinct cavities. The results show that entanglement sudden death is dependent on the different initial states of atoms, and the length of the time interval for the zero entanglement is invariant for a certain class of initial mixed states.
The entanglement dynamics of system, where atoms A and B interact with single mode cavity fields a and b respectively, is studied. The interaction between atom A and cavity a may be described by using the typical Jaynes–Cummings model, while that between the atom B and cavity b filled with a Kerr medium is of a two-photon process. For a certain initial atom entanglement state, there is an entanglement sudden death effect between the two atoms. The Kerr medium in the cavity b can effectively prevent the undesirable entanglement sudden death from occurring. Also, from the viewpoint of the population dynamics, we discuss why the Kerr medium can do so.