Entanglement transfer from electron spins to photons in spin light-emitting diodes containing quantum dots

We show that electron recombination using positively charged excitons in single quantum dots provides an efficient method to transfer entanglement from electron spins onto photon polarizations. We propose a scheme for the production of entangled four-photon states of GHZ type. From the GHZ state, two fully entangled photons can be obtained by a measurement of two photons in the linear polarization basis, even for quantum dots with observable fine structure splitting for neutral excitons and significant exciton spin decoherence. Because of the interplay of quantum mechanical selection rules and interference, maximally entangled electron pairs are converted into maximally entangled photon pairs with unity fidelity for a continuous set of observation directions. We describe the dynamics of the conversion process using a master-equation approach and show that the implementation of our scheme is feasible with current experimental techniques.Comment: 5 pages, 2 figures. v2: Extended scheme, revised version. v3: Minor additions and extended title, published versio

Molecular spintronics: Coherent spin transfer in coupled quantum dots

Time-resolved Faraday rotation has recently demonstrated coherent transfer of electron spin between quantum dots coupled by conjugated molecules. Using a transfer Hamiltonian ansatz for the coupled quantum dots, we calculate the Faraday rotation signal as a function of the probe frequency in a pump-probe setup using neutral quantum dots. Additionally, we study the signal of one spin-polarized excess electron in the coupled dots. We show that, in both cases, the Faraday rotation angle is determined by the spin transfer probabilities and the Heisenberg spin exchange energy. By comparison of our results with experimental data, we find that the transfer matrix element for electrons in the conduction band is of order 0.08 eV and the spin transfer probabilities are of order 10%.Comment: 13 pages, 6 figures; minor change

Recipes for spin-based quantum computing

Technological growth in the electronics industry has historically been measured by the number of transistors that can be crammed onto a single microchip. Unfortunately, all good things must come to an end; spectacular growth in the number of transistors on a chip requires spectacular reduction of the transistor size. For electrons in semiconductors, the laws of quantum mechanics take over at the nanometre scale, and the conventional wisdom for progress (transistor cramming) must be abandoned. This realization has stimulated extensive research on ways to exploit the spin (in addition to the orbital) degree of freedom of the electron, giving birth to the field of spintronics. Perhaps the most ambitious goal of spintronics is to realize complete control over the quantum mechanical nature of the relevant spins. This prospect has motivated a race to design and build a spintronic device capable of complete control over its quantum mechanical state, and ultimately, performing computations: a quantum computer. In this tutorial we summarize past and very recent developments which point the way to spin-based quantum computing in the solid-state. After introducing a set of basic requirements for any quantum computer proposal, we offer a brief summary of some of the many theoretical proposals for solid-state quantum computers. We then focus on the Loss-DiVincenzo proposal for quantum computing with the spins of electrons confined to quantum dots. There are many obstacles to building such a quantum device. We address these, and survey recent theoretical, and then experimental progress in the field. To conclude the tutorial, we list some as-yet unrealized experiments, which would be crucial for the development of a quantum-dot quantum computer.Comment: 45 pages, 12 figures (low-res in preprint, high-res in journal) tutorial review for Nanotechnology; v2: references added and updated, final version to appear in journa

Electron-photon interaction in quantum dots : spin and entanglement

The interaction of electrons and photons lies at the heart of quantum physics. The most notable phenomena which are described by quantum physics but which obviously invalidate a classical description of the electromagnetic field - the photoelectric effect, the Compton effect, or the antibunching of photons emitted from a single atom, to mention a few - are intimately related to the interaction of electrons and photons. Electrons possess an internal degree of freedom, the spin. The spin S of an electron can be described as an internal angular momentum, leading to a magnetic moment m due to the electric charge of the electron. Stern and Gerlach have shown that the projection of m onto a quantization axis (defined by an external magnetic field in their experiment), e.g., along the z axis, is either mz = g�μB/2 (\spin up") or mz = g�μB=2 (\spin down"), where �μB � 9:2741 � 10-24 J/T is the Bohr magneton and g is the g-factor of the electron (g = 2 for free electrons). An electron spin is therefore usually referred to as a two-level system. Due to this property, the spin of electrons which are localized in semiconductor quantum dots has recently attracted significant attention regarding the implementation of quantum information processing: Electron spins can be used as carriers of quantum information. One can define that the spin pointing "up" corresponds to the logical value "0" and the spin pointing "down" corresponds to "1". Moreover, because the electron spin is a quantum mechanical property one can form arbitrary coherent superpositions of "up" and "down" with a single spin. Moreover, because the electron spin is a quantum mechanical property one can form arbitrary coherent superpositions of "up" and "down" with a single spin. A system with this property is called a quantum bit (qubit). The additional possibilities due to quantum superpositions of qubits are exploited, e.g., in the algorithms introduced by Shor and Grover to solve certain tasks much more efficiently than with a classical computer (i.e., the prime factorization of large numbers for Shor's algorithm and the search within an unstructured database for Grover's algorithm). While quantum computation has presently only been achieved in prototypical experiments with few qubits, the implementation of efficient largescale quantum computation with many qubits still remains an extremely demanding task. Yet, other quantum mechanical properties of qubits, such as entanglement, have already been exploited experimentally with photons in quantum communication schemes, for example, quantum teleportation and quantum data compression. In this thesis, we investigate the interaction of electrons and photons in semiconductor quantum dots. Optical transitions in quantum dots enable a direct link between electron spins and photon polarizations due to conservation laws. We show that entanglement can be transferred from electron spin qubits to qubits defined by the photon polarization, enabling the measurement of entangled spin states via photons. The mechanism under study can also be used for the production of entangled photons, for instance for the implementation of quantum communication protocols. In contrast to the presently used sources of entangled photons, the photon source we propose here is deterministic, providing entangled photons on demand. It has been demonstrated in several recent experiments that the most obvious way to achieve such a transfer of entanglement - using the recombination of biexcitons in a single quantum dot - fails in the presently available quantum dot structures. We have analyzed the problems of this approach. As a solution, we propose schemes based on charged excitons in single or coupled quantum dots. We discuss the generation of entangled two- and four-photon states. In addition to the transfer of quantum states, photons can also be used to probe electron spin states. We investigate in detail different methods to optically measure the decoherence time of a single electron spin in a quantum dot. The decoherence time of a spin establishes the time scale during which coherent manipulation is possible. Measurements of the electron spin decoherence time are therefore highly desirable in view of the implementation of spin-based quantum information processing. We show that the schemes we propose can be implemented with current experimental techniques. We then study the magneto-optical effect called Faraday rotation. Using the technique of time-resolved Faraday rotation, a recent experiment has demonstrated the coherent transfer of spin between quantum dots coupled by molecules. We calculate the Faraday rotation signal for a coupled dot system and show that a two-site Hamiltonian with a transfer term captures the essential features observed in this experiment. We also present results for a system of two coupled dots doped with a single electron. We finally show that the coupled states of two qubits can be detected via the optical interaction with a cavity in the dispersive regime. We present a Schrieffer-Wolff transformation which removes the coupling of the two qubits to the cavity in leading order. The different two-qubit states lead to a different spectral shift of the cavity line. For a sufficiently low cavity linewidth, this enables the direct readout of a two-qubit system

Spins in optically active quantum dots

Filling a gap in the literature, this up-to-date introduction to the field provides an overview of current experimental techniques, basic theoretical concepts, and sample fabrication methods. Following an introduction, this monograph deals with optically active quantum dots and their integration into electro-optical devices, before looking at the theory of quantum confined states and quantum dots interacting with the radiation field. Final chapters cover spin-spin interaction in quantum dots as well as spin and charge states, showing how to use single spins for break-through quantum compu

Spins in Optically Active Quantum Dots

Filling a gap in the literature, this up-to-date introduction to the field provides an overview of current experimental techniques, basic theoretical concepts, and sample fabrication methods. Following an introduction, this monograph deals with optically active quantum dots and their integration into electro-optical devices, before looking at the theory of quantum confined states and quantum dots interacting with the radiation field. Final chapters cover spin-spin interaction in quantum dots as well as spin and charge states, showing how to use single spins for break-through quantum compu

Biexcitons in coupled quantum dots as a source of entangled photons

We study biexcitonic states in two tunnel-coupled semiconductor quantum dots and show that such systems provide the possibility to produce polarization-entangled photons or spin-entangled electrons that are spatially separated at production. We distinguish between the various spin configurations and calculate the low-energy biexciton spectrum using the Heitler-London approximation as a function of magnetic and electric fields. The oscillator strengths for the biexciton recombination involving the sequential emission of two photons are calculated. The entanglement of the photon polarizations resulting from the spin configuration in the biexciton states is quantified as a function of the photon emission angles