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Journal of Physics Conference Series

Density matrix of strongly coupled quantum dot – microcavity system

Nguyen Van Hop

Published Sep 1, 2009• 1 citation
Publisher

Abstract

Any two-level quantum system can be used as a quantum bit (qubit)-the basic element of all devices and systems for quantum information and quantum computation. Recently it was proposed to study the strongly coupled system consisting of a two-level quantum dot and a monoenergetic photon gas in a microcavity-the strongly coupled quantum dot-microcavity (QD-MC) system for short, with the Jaynes-Cumming total Hamiltonian, for the application in the quantum information processing. Different approximations were applied in the theoretical study of this system. In this work, on the basis of the exact solution of the Schrodinger equation for this system without dissipation we derive the exact formulae for its density matrix. The realization of a qubit in this system is discussed. The solution of the system of rate equation for the strongly coupled QD-MC system in the presence of the interaction with the environment was also established in the first order approximation with respect to this interaction.

DOI
10.1088/1742-6596/187/1/012066

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Any two-level quantum system can be used as a quantum bit (qubit)-the basic element of all devices and systems for quantum information and quantum computation. Recently it was proposed to study the strongly coupled system consisting of a two-level quantum dot and a monoenergetic photon gas in a microcavity-the strongly coupled quantum dot-microcavity (QD-MC) system for short, with the Jaynes-Cumming total Hamiltonian, for the application in the quantum information processing. Different approximations were applied in the theoretical study of this system. In this work, on the basis of the exact solution of the Schrodinger equation for this system without dissipation we derive the exact formulae for its density matrix. The realization of a qubit in this system is discussed. The solution of the system of rate equation for the strongly coupled QD-MC system in the presence of the interaction with the environment was also established in the first order approximation with respect to this interaction.
The Jaynes-Cummings model, describing the interaction between a single two-level system and a photonic mode, has been used to describe a large variety of systems, ranging from cavity quantum electrodynamics, trapped ions, to superconducting qubits coupled to resonators. Recently there has been renewed interest in studying the quantum strong-coupling (QSC) regime, where states with photon number greater than one are excited. This regime has been recently achieved in semiconductor nanostructures, where a quantum dot is trapped in a planar microcavity. Here we study the quantum strong-coupling regime by calculating its photoluminescence (PL) properties under a pulsed excitation. We discuss the changes in the PL as the QSC regime is reached, which transitions between a peak around the cavity resonance to a doublet. We particularly examine the variations of the PL in the time domain, under regimes of short and long pulse times relative to the microcavity decay time.
The theory of the quantum information transmission between two semiconductor two-level quantum dots as two qubits through an intermediary photon gas in a cavity is presented. The reduced density matrix of each two-level quantum dot is the quantum information encoded into this qubit. The quantum information exchange between two distant qubits imbedded in the photon gas is performed in the form of the mutual dependence of their reduced density matrices due to the interaction between the electrons in the qubits and the photon gas. The system of rate equations for the reduced density matrix of the two-qubit system is derived. From the solution of this system of equations it follows the mutual dependence of the reduced density matrices of two distant qubits.
Light-matter interaction on the level of single emitters and single photons has attracted significant scientific interest in recent years. Of particular interest is strong coupling of single emitters in solid state systems and its application to quantum information processing. Due to the enormous progress in semiconductor technology it has become feasible to demonstrate strong coupling of single quantum dots in high-Q microcavity systems. Although it has been argued in these studies that it is very unlikely that several degenerated quantum dots contributed to the observed Rabi-splitting, it was not verified that the system had one and only one emitter. In this work we present proof that the emission from a strongly-coupled QD- microcavity system is dominated by a single quantum emitter.
The master equation for the microcavity-quantum dot coupled system is established based on the quantum regression theorem,and the time-dependent evolution of the density matrix of the two-level system for a quantum dot in a microcavity is studied under pumping by laser pulses.The characteristics such as the number of emitted photons and the second-order corelation function are derived from the density matrixes.Parameters of the microcavity and the pumping conditions are optimized for single-photon sources.The relativity between the microcavity decay rate and coupling coefficient is critical for single photon emission.
Abstract The general theory of the time-resolved luminescence of the coupled system consisting of a single-mode microcavity and a two-level quantum dot containing one electron placed inside this microcavity is presented. It is based on the study of the time evolution of the density matrix of a larger system consisting of one electron in the two-level quantum dot, single-mode photons in the microcavity and external photons in a spatial region in which the emitted photons are detected. The decoherence of the system is taken into account in the Markov approximation. The explicit analytical form of the time dependence of the intensity of the emitted photon beam is established. It depends not only on the physical parameters of the system but also contains the matrix elements determining the initial condition of the luminescence process.
Abstract The theory of coherent oscillations of the matrix elements of the density matrix of the two-state system as a quantum bit is presented. Different calculation methods are elaborated in the case of a free quantum bit. Then the most appropriate methods are applied to the study of the density matrices of the quantum bits interacting with a classical pumping radiation field as well as with the quantum electromagnetic field in a single-mode microcavity. The theory of decoherence of a quantum bit in Markovian approximation is presented. The decoherence of a quantum bit interacting with monoenergetic photons in a microcavity is also discussed. The content of the present work can be considered as an introduction to the study of the quantum dynamics of quantum bits.