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Frontiers in Optics

Generation of Entangled Photon-States in a Quantum Dot

Christoph F. Wildfeuer, Jonathan P. Dowling

Published Jan 1, 2006• 0 citations
Publisher

Abstract

A quantum dot in a microcavity is a promising device to generate entangled photon pairs. We show an efficient scheme to obtain entangled two-mode N-photon states based on a two-mode Jaynes-Cummings model.
DOI
10.1364/ls.2006.ltui5

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A quantum dot interacting with two resonant cavity modes is described by a two-mode Jaynes-Cummings model. Depending on the quantum dot energy level scheme, the interaction of a singly doped quantum dot with a cavity photon generates entanglement of electron spin and cavity states or allows one to implement a SWAP gate for spin and photon states. An undoped quantum dot in the same structure generates pairs of polarization entangled photons from an initial photon product state. For realistic cavity loss rates, the fidelity of these operations is of order 80%.
We describe a mathematical solution for the generation of entangled N-photon states in two field modes. A simple and compact solution is presented for a two-mode Jaynes-Cummings model by combining the two field modes in a way that only one of the two resulting quasimodes enters in the interaction term. The formalism developed is then applied to calculate various generation probabilities analytically. We show that entanglement, starting from an initial field and an atom in one defined state may be obtained in a single step. We also show that entanglement may be built up in the case of an empty cavity and excited atoms whose final states are detected, as well as in the case when the final states of the initially excited atoms are not detected.
We propose a new method of generating nonclassical optical field states. The method uses a semiconductor device, which consists of a single quantum dot as active medium embedded in a p- i- n junction and surrounded by a microcavity. Resonant tunneling of electrons and holes into the quantum dot ground states, together with the Pauli exclusion principle, produce regulated single photons or regulated pairs of photons. We propose that this device also has the unique potential to generate pairs of entangled photons at a well-defined repetition rate.
We theoretically investigate fast and highly efficient entangled-photon generation by irradiating a quantum dot (QD) embedded in a microcavity with short laser pulses. We evaluate the optimized width and field strength of the pulses for achieving a high population of an excited state as an entangled-photon source. We also calculate the emission time of the entangled photon pair as a function of the cavity quality factor QQQ. The shortest emission time reaches 3/(4g)3/(4g)3/(4g) under the condition $Q={\ensuremath{\omega}}_{0}/(4g)$, where ggg is the coupling frequency between the cavity photon and excited states of the QD and ${\ensuremath{\omega}}_{0}$ is the excitation frequency of the QD. The QD-cavity system has a potential for fast and efficient generation of high-quality entangled-photon pairs.
Theoretical study on entangled photon generation from a quantum dot (QD) embedded in microcavity is briefly reviewed within a strong coupling regime. In this system, entangled photon pairs can be generated through the cascade photon emission via dressed states in the cavity quantum electrodynamics (CQED). Excitation levels of a QD are modeled by a V-type three-level system and four-level system including a biexciton. In contrast to the entangled-photon generation until now, all four Bell states can be generated from an identical cavity system by simply selecting applied-field polarizations and frequencies as characteristic features of the CQED. The CQED effects play a crucial role in providing a high degree of entanglement: (i) spectral fi ltering can be used to extract entangled photons due to the vacuum Rabi splitting and (ii) non-entangled co-polarized photons are strongly suppressed due to the photon blockade effect.