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Journal of the Arkansas Academy of Science

Multiphoton Interaction in a System of Two Quantum Dots

Brian C. Sawyer, Reeta Vyas

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

As the size and proximity of components on modern computer chips approaches quantum mechanical limits, various novel solutions have been proposed to ensure further increases in processing speed and reliability. Of these, small semiconductor devices called quantum dots may constitute the logic gates of future quantum computers - processors taking advantage of phenomena such as entanglement and quantum teleportation to enable ultra-fast computation speeds. Quantum dots behave much like designer atoms in that their absorption/emission energies can be adjusted lo desired values. A quantum mechanical model of semiconductor quantum dots having equal size and interacting with a single-mode electric field tuned to some fraction of the transition frequency has been developed Due to the similarities between two-level atoms and quantum dots, techniques common in quantum optics have been employed to describe the time evolution of the resulting exciton-field system. it is assumed that the quantum dots are initially prepared in a Bell entangled state and that the field is in a coherent state. Collapse and revivals in the entanglement are found when the mean photon number of the coherent state is very large.

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As the size and proximity of components on modern computer chips approaches quantum mechanical limits, various novel solutions have been proposed to ensure further increases in processing speed and reliability. Of these, small semiconductor devices called quantum dots may constitute the logic gates of future quantum computers - processors taking advantage of phenomena such as entanglement and quantum teleportation to enable ultra-fast computation speeds. Quantum dots behave much like designer atoms in that their absorption/emission energies can be adjusted lo desired values. A quantum mechanical model of semiconductor quantum dots having equal size and interacting with a single-mode electric field tuned to some fraction of the transition frequency has been developed Due to the similarities between two-level atoms and quantum dots, techniques common in quantum optics have been employed to describe the time evolution of the resulting exciton-field system. it is assumed that the quantum dots are initially prepared in a Bell entangled state and that the field is in a coherent state. Collapse and revivals in the entanglement are found when the mean photon number of the coherent state is very large.
Semiconductor Quantum dots are potentially an attractive source of non-classical light. They can confine bound electron-hole pairs, excitons, in all three spatial dimensions giving them discrete optical emission energies, much like the electronic states in atomic systems. The semiconductor nature of the system allows quantum dots to be integrated into complicated device structures including optical cavities [1] and electrical injection [2]. The radiative exciton emission from a semiconductor quantum dot can provide the simplest form of quantum light, a single photon source [2]. The finite re-excitation time following the radiative decay of an exciton in a quantum dot prevents the dot from emitting more than one photon if excited with a short optical or electronic pulse. In a similar fashion excitation of the biexciton state, consisting of two electrons and holes, in the quantum dot results in the emission of a pair of photons at the energy of the biexciton and exciton transitions. The biexciton state was, in fact, proposed as a possible source of polarisation-entangled photons in 2000 by Benson et al. [3] as it consists of two polarisation-correlated decay paths which could potentially be indistinguishable. The condition of indistinguishability is fundamental to the generation of entangled photons and is, in general, not true of the two decay paths from the biexciton state in a quantum dot; physical anisotropy causes the intermediate exciton states to hybridise and separate in energy providing ‘which-path’ information about the route taken through the biexciton decay. We demonstrate how the splitting between the intermediate exciton states in a single InAs quantum dot can be controlled by growth [4], rapid thermal annealing [5] and the application of an external magnetic field [6]. Each of these three techniques can be used to make the intermediate exciton states degenerate allowing the biexciton decay to produce singe pairs of entangled photons triggered by short laser pulses [7,8]. Entangled photon pair sources are essential for applications such as entanglement based quantum key distribution, and optical quantum computing. For these applications it is important that no more than one entangled photon pair is generated in a cycle, a requirement met by our quantum dot source which is not possible with traditional methods for generating entangled pairs of photons. Entanglement also enables quantum interferometry and metrology, the basis of image resolution beyond that possible with equivalent classical light. Biphoton interferometry using entangled emission from the biexciton decay reveals fringes with half the period of classical light [9], and less that that of the laser. In addition, interferometry suggests that this type of entangled light source is not limited by decoherence, we fine the biphoton is surprising robust against dephasing, in stark contrast to the devastating effect of decoherence upon single photons emitted by similar structures.
Semiconductor quantum dots have emerged as promising candidates for studying quantum optical phenomena. Observation of photon antibunching and spontaneous emission limited coherence decay rates have demonstrated that quantum dots behave as artificial atoms. Cavity-quantum electrodynamics (QED) phenomena can be investigated using a single quantum dot embedded inside a photonic nanostructure, where both carriers and photons are confined within sub-micron length scales in all three dimensions. Since quantum dot location inside the cavity is fixed by the growth, this system is free of the stringent trapping requirements that limit its atomic counterpart. Possibility of fabricating photonic nanostructures with ultra-small optical-mode volumes and long photon lifetimes enhances the prospects for applications in quantum information processing. 1
The optically active nature of direct bandgap semiconductors makes them well suited for applications in quantum optics. Semiconductor quantum dots (QDs) are particularly promising, due to their discrete atom-like energy levels. In this thesis, transitions between these energy levels are used to investigate the effects of electric and magnetic fields on the energy structure of single QDs, with a view to developing applications in the field of quantum computing. In the work presented here a novel method of creating entangled photon pair emitters is presented, in which an electric field is used to tune the energy structure of single QDs to allow the fidelity of the emitted entangled state to be increased. In addition, a technique for the creation of energy-tunable entangled photon pairs is proposed and shown to be feasible with current technology. Furthermore, the potential of QDs to act as an interface between photonic and spin qubits is explored. Application of a time varying electric field is used to dynamically tune the QD energy levels, allowing the evolution of excitons confined within single QDs to be manipulated. Using this system a controlled phase rotation of the exciton spin state is implemented. Finally, indistinguishable single photons, emitted by the radiative decay of the exciton state, are used to generate the input state for an integrated photonic two-qubit quantum logic gate. This is the first demonstration of a two-qubit gate using on-demand single photons. It is also the first demonstration of such a gate with all components realised using semiconductor materials.
A single atom in a cavity is the model system of cavity quantum electrodynamics (CQED). The strong coupling regime between the atom and cavity-confined photon corresponds to the reversible exchange of energy between the two modes, and underpins a wide range of CQED phenomena with applications in quantum information science, including for example as quantum logic gates and as sources of entangled states. An important advance was achieved recently when strong coupling between excitons and cavity photons was reported for the first time for localized quantum dots (QDs) in micron-size solid state cavities. This has significance in terms of scalability and integration with other optical devices, and could lead to the emergence of "quantum optics on a chip" technology. However the results presented so far for quantum dots are in the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi splitting); they are not a true QED effect and can equally well be described by classical physics as the coupling between two oscillators. In this paper, we present evidence for a purely quantum phenomenon for the QD/cavity photon system, namely the increase in splitting of the levels when the mean number of photons in the cavity is increased. This corresponds to non-linearities on the single-photon scale: the presence of a single excitation in the cavity changes the level structure, affecting the emission energies for a second photon. Such results are a first step in demonstrating the promise of quantum dots for CQED applications.
We present a series of coherent nonlinear optical experiments that show semiconductor quantum dots have optical properties very similar to simple atomic systems but are surprisingly robust against decoherence and have large dipole moments. By combining advances in nano-optical probing methodologies with the power of coherent nonlinear optical spectroscopy techniques, the measurements have enabled us to extend concepts of coherent optical control and wave function engineering to a single quantum dot exciton.