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arXiv:quant-ph/9911123 · Physical Review A

Quantum entanglement and information processing via excitons in optically driven quantum dots

John Henry Reina, Luis Quiroga, Neil F. Johnson

Published Jun 12, 2000• 120 citations
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Abstract

We show how optically driven coupled quantum dots can be used to prepare maximally entangled Bell and Greenberger-Horne-Zeilinger states. Manipulation of the strength and duration of the selective light pulses needed for producing these highly entangled states provides us with crucial elements for the processing of solid-state-based quantum information. Theoretical predictions suggest that several hundred single quantum bit rotations and controlled-NOT gates could be performed before decoherence of the excitonic states takes place.

DOI
10.1103/physreva.62.012305

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We show how optically driven coupled quantum dots can be used to prepare maximally entangled Bell and Greenberger-Horne-Zeilinger states. Manipulation of the strength and duration of the selective light pulses needed for producing these highly entangled states provides us with crucial elements for the processing of solid-state-based quantum information. Theoretical predictions suggest that several hundred single quantum bit rotations and controlled-NOT gates could be performed before decoherence of the excitonic states takes place.
We show that excitons in coupled quantum dots are ideal candidates for reliable preparation of entangled states in solid-state systems. An optically controlled exciton transfer process is shown to lead to the generation of Bell and Greenberger-Horne-Zeilinger states in systems comprising two and three coupled dots, respectively. The strength and duration of selective light pulses for producing maximally entangled states are identified by both analytic and full numerical solution of the quantum dynamical equations. Experimental requirements to build such entangled states are discussed.
Since information has been regarded as a physical entity, the field of quantum information theory has blossomed. This brings novel applications, such as quantum computation. This field has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineering, to the physical sciences. Thus, we now have an interdisciplinary field where great efforts are being made in order to build devices that should allow for the processing of information at a quantum level, and also in the understanding of the complex structure of some physical processes at a more basic level. This thesis is devoted to the theoretical study of structures at the nanometer-scale, "nanostructures," through physical processes that mainly involve the solid-state and quantum optics, in order to propose reliable schemes for the processing of quantum information. Initially, the main results of quantum information theory and quantum computation are briefly reviewed. Next, the state-of-the-art of quantum dots technology is described. In so doing, the theoretical background and the practicalities required for this thesis are introduced. A discussion of the current quantum hardware used for quantum information processing is given. In particular, the solid-state proposals to date are emphasised. A detailed prescription is given, using an optically-driven coupled quantum dot system, to reliably prepare and manipulate exciton maximally entangled Bell and Greenberger-Horne-Zeilinger (GHZ) states. Manipulation of the strength and duration of selective light-pulses needed for producing these highly entangled states provides us with crucial elements for the processing of solid-state based quantum information. The all-optical generation of states of the so-called Bell basis for a system of two quantum dots (QDs) is exploited for performing the quantum teleportation of the excitonic state of a dot in an array of three coupled QDs. Theoretical predictions suggest that several hundred single quantum bit rotations and controlled-NOT gates could be performed before decoherence of the excitonic states takes place. In addition, the exciton coherent dynamics of a coupled QD system confined within a semiconductor single mode microcavity is reported. It is shown that this system enables the control of exciton entanglement by varying the coupling strength between the optically-driven dot system and the microcavity. The exciton entanglement shows collapses and revivals for suitable amplitudes of the incident radiation field and dot-cavity coupling strengths. The results given here could offer a new approach for the control of decoherence mechanisms arising from entangled "artificial molecules." In addition to these ultrafast coherent optical control proposals, an approach for reliable implementation of quantum logic gates and long decoherence times in a QD system based on nuclear magnetic resonance (NMR) is given, where the nuclear resonance is controlled by the ground state "magic number" transitions of few-electron QDs in an external magnetic field. The dynamical evolution of quantum registers of arbitrary length in the presence of environmentally-induced decoherence effects is studied in detail. The cases of quantum bits (qubits) coupling individually to different environments ("independent decoherence"), and qubits interacting collectively with the same reservoir ("collective decoherence") are analysed in order to find explicit decoherence functions for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: this sensitivity is a characteristic of both types of coupling (collective and independent) and not only of the collective coupling, as has been reported previously. A non-trivial behaviour - "recoherence" - is found in the decay of the off-diagonal elements of the reduced density matrix in the specific situation of independent decoherence. The results lead to the identification of decoherence-free states in the collective decoherence limit. These states belong to subspaces of the system's Hilbert space that do not become entangled with the environment, making them ideal elements for the engineering of "noiseless" quantum codes. The relations between decoherence of the quantum register and computational complexity based on the new dynamical results obtained for the register density matrix are also discussed. This thesis concludes by summarising and pointing out future directions, and in particular, by discussing some biological resonant energy transfer processes that may be useful for the processing of information at a quantum level.
A major question for condensed matter physics is whether a solid-state quantum computer can ever be built. Here we discuss two different schemes for quantum information processing using semiconductor nanostructures. First, we show how optically driven coupled quantum dots can be used to prepare maximally entangled Bell and Greenberger-Horne-Zeilinger states by varying the strength and duration of selective light pulses. The setup allows us to perform an all-optical generation of the quantum teleportation of an excitonic state in an array of coupled quantum dots. Second, we give a proposal for reliable implementation of quantum logic gates and long decoherence times in a quantum dots system based on nuclear magnetic resonance (NMR), where the nuclear resonance is controlled by the ground state transitions of few-electron QDs in an external magnetic field. The dynamical evolution of these systems in the presence of environmentally-induced decoherence effects is also discussed.
We propose a practical solid-state system capable of demonstrating quantum teleportation. The setup exploits recent advances in the optical control of excitons in coupled quantum dots, in order to produce maximally entangled Bell and Greenberger-Horne-Zeilinger states. Only two unitary transformations are then required: a quantum controlled-NOT\mathrm{NOT}NOT gate and a Hadamard gate. The laser pulses necessary to generate the maximally entangled states, and the corresponding unitary transformations, are given explicitly.
Optically controlled exciton dynamics in coupled quantum dots is studied. We show that the maximally entangled Bell states and Greenberger-Horne-Zeilinger (GHZ) states can be robustly generated by manipulating the system parameters to be at the avoided crossings in the eigenenergy spectrum. The analysis of population transfer is systematically carried out by using a dressed-state picture. In addition to the quantum dot configuration that has been discussed by Quiroga and Johnson [Phys. Rev. Lett. 83, 2270 (1999)], we show that the GHZ states also may be produced in a ray of three quantum dots with a shorter generation time.
We report on exciton-acoustic-phonon coupling effects on the generation of exciton maximally entangled states in N = 2 and 3 quantum dot systems. In particular, we address the question of the combined effect of laser pulses, appropriate for generating Bell and Greenberger-Horne-Zeilinger entangled states, together with decoherence mechanisms as provided by a phonon reservoir. By solving numerically the master equation for the optically driven exciton–phonon kinetics, we show that the generation of maximally entangled exciton states is preserved over a reasonable parameter window.