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arXiv:cond-mat/0502184 · Physical Review B

Electric field control and optical signature of entanglement in quantum dot molecules

Gabriel Bester, Alex Zunger

Published Oct 25, 2005• 37 citations
arXivHTMLPDF

Abstract

The degree of entanglement of an electron with a hole in a vertically coupled self-assembled dot molecule is shown to be tunable by an external electric field. Using atomistic pseudopotential calculations followed by a configuration interaction many-body treatment of correlations, we calculate the electronic states, degree of entanglement, and optical absorption. We offer a way to spectroscopically detect the magnitude of electric field needed to maximize the entanglement.

DOI
10.1103/physrevb.72.165334

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The degree of entanglement of an electron with a hole in a vertically coupled self-assembled dot molecule is shown to be tunable by an external electric field. Using atomistic pseudopotential calculations followed by a configuration interaction many-body treatment of correlations, we calculate the electronic states, degree of entanglement, and optical absorption. We offer a way to spectroscopically detect the magnitude of electric field needed to maximize the entanglement.
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Currently there is strong interest in realizing implementations of quantum computation and quantum cryptography in a solid state environment. One of the systems that are actively studied are semiconductor quantum dots (QDs). Due to their discrete energy level structure, they are often called artificial atoms, and they attract immediately interest of quantum information science since they allow to mimic the design developed for atomic physics systems such as ions in traps or atoms in cavities. However, despite of the similarities, one has to keep in main that any elementary excitation in a QD has a generic many-body character. An essential building block of a quantum processor is a quantum gate which entangles the states of two quantum bits. Recently it has been proposed that a pair of vertically aligned QDs could be used as an optically driven quantum gate: The quantum bits are individual carriers either on dot zero or dot one. The different dot indices play the same role as a "spin," therefore we term them "isospin." Quantum mechanical tunneling between the dots rotates the "isospin" and leads to superposition of two quantum dot states. The quantum gate is built when two different particles, an electron and a hole, are created optically. The two particles form entangled isospin states. The entanglement can be controlled by application of an electric field along the heterostructure growth direction. Here we present spectroscopic studies on single quantum dot molecules (QDMs) with different vertical separation between the dots that support the feasibility of this proposal. The comparison of the evolution of the excitonic recombination spectrum with the results of calculations allows us to demonstrate coherent tunneling of electrons and holes across the separating barrier and the formation of entangled exciton states. For a given barrier width, we find only small variations of the tunneling induced splitting between the entangled states demonstrating a good homogeneity within the obtained QDM ensembles.
Finding efficient methods for controlling entanglement is an important issue in quantum information processing. Here, we inspect theoretically possible ways for tuning orbital and spin entanglement of two interacting particles confined to a double quantum dot with spin-orbit coupling (SOC) which renders possible the coupling of spin to an external electric field. The entanglement in the spin part is sensitive to a transverse electric field. We show that through the field-induced SOC the entanglement of the spin subsystem can be slightly increased; the effect of a longitudinal electric field is more subtle: For a small interdot distance, a longitudinal electric field enhances substantially the entanglement of spins, while for a large interdot distance it has no impact. An external longitudinal electric field has a minor effect on the entanglement in the orbital part irrespective of the interdot distance. We trace back this observed phenomenon to a combined effect of the applied external electric field and the overlap of wave functions which is enhanced for decreasing interdot distances. As a result, at large interdot separation, the concurrence of the two-electron states turns insensitive to the applied electric field.
We give three methods for entangling quantum states in quantum dots. We do this by showing how to tailor the resonant energy (F\"orster-Dexter) transfer mechanisms and the biexciton binding energy in a quantum dot molecule. We calculate the magnitude of these two electrostatic interactions as a function of dot size, interdot separation, material composition, confinement potential, and applied electric field by using an envelope function approximation in a two-cuboid dot molecule. In the first implementation, we show that it is desirable to suppress the F\"orster coupling and to create entanglement by using the biexciton energy alone. We show how to perform universal quantum logic in a second implementation which uses the biexciton energy together with appropriately tuned laser pulses: by selecting appropriate material parameters high-fidelity logic can be achieved. The third implementation proposes generating quantum entanglement by switching the F\"orster interaction itself. We show that the energy transfer can be fast enough in certain dot structures that switching can occur on a time scale which is much less than the typical decoherence times.
Establishing the hybrid entanglement among a growing amount of matter and photonic quantum bits is necessary for scalable quantum computation and long-distance quantum communication. Here we demonstrate that charged excitonic complexes forming in strongly correlated quantum dot molecules are able to generate tripartite hybrid entanglement under proper carrier quantization. The mixed orbitals of the molecule construct multi-level ground states with sub-meV hole tunneling energy and relatively large electron hybridization energy. We show that appropriate size and interdot spacing keeps the electron particle weakly localized, opening extra recombination channels by correlating ground-state excitons. This allows for creation of higher order entangled states. Nontrivial hole tunneling energy, renormalized by multi-particle interactions, facilitates the realization of the energy coincidence among only certain components of the molecule optical spectrum. This translates to the emergence of favorable spectral components in a multi-body excitonic complex which sustain principal oscillator strengths throughout the electric field-induced hole tunneling process. We particularly analyze whether the level broadening of favorable spin configurations could be manipulated to eliminate the distinguishability of photons.