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Physical Review Letters

Density Matrix Tomography through Sequential Coherent Optical Rotations of an Exciton Qubit in a Single Quantum Dot

Yanwen Wu, Xiaoqin Li, Luming Duan, Duncan G. Steel, D. Gammon

Published Feb 28, 2006• 35 citations
Publisher

Abstract

We demonstrate single qubit density matrix tomography in a single semiconductor quantum dot system through consecutive phase sensitive rotations of the qubit via ultrafast coherent optical excitations. The result is important for quantifying gate operations in quantum information processing in the quantum dot systems as well as demonstrating consecutive arbitrary qubit rotations.

DOI
10.1103/physrevlett.96.087402

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We demonstrate single qubit density matrix tomography in a single semiconductor quantum dot system through consecutive phase sensitive rotations of the qubit via ultrafast coherent optical excitations. The result is important for quantifying gate operations in quantum information processing in the quantum dot systems as well as demonstrating consecutive arbitrary qubit rotations.
Coherent optically driven semiconductor quantum dot systems are proposed for the implementation of quantum information processing devices. Fundamental quantum computation units, the quantum bits (qubits), are realized and optically manipulated in the exciton and spin bases. In this thesis, consecutive phase-sensitive rotations of a single qubit and their importance in the measurement of the full physical density matrix have been demonstrated experimentally in the exciton system in neutral GaAs/Al0:3Ga0:7As interface fluctuation quantum dots. The experimental work done on the exciton system serves as a foundation for consequent work on the long coherence lifetime spin-based qubits in charged quantum dots. In the spin-based system in the charged GaAs/Al0:3Ga0:7As interface fluctuation quantum dots, we demonstrate the selective excitation from the two spin ground states to the charged exciton (trion) state through phase sensitive control of the spin coherence in an ensemble of three-level spin-trion Lambda systems. This controlled excitation utilized the optically coupled and decoupled states of the electron spin in the presence of coherent transient excitation of the spin ground states in singly charged quantum dots. This progress lays the ground work for achieving complete ultrafast spin rotations.
Potential application of elementary excitation in semiconductor quantum dot to quantum computation is discussed. Construction of scalable hardware and all optical implementation of logical gate that exploits discrete nature of electron-hole states and their well concentrated oscillator strenth for ultrafast gate operation are proposed. Rabi population oscillation of an excitonic two-level system in an isolated single InxGa1-xAs quantum dot is manifested by a quantum wave function interferometry in time domain, demonstrating a long lived coherence of zero-dimensional excitonic states and revealed the coherent population flopping under strong optical field. A phase-sensitive coherent gate operation on single-dot exciton qubit is demonstrated.
Single spins in semiconductor quantum dots form a promising platform for solid-state quantum information processing. The spin-up and spin-down states of a single electron or hole, trapped inside a quantum dot, can represent a single qubit with a reasonably long decoherence time. The spin qubit can be optically coupled to excited (charged exciton) states that are also trapped in the quantum dot, which provides a mechanism to quickly initialize, manipulate and measure the spin state with optical pulses, and to interface between a stationary matter qubit and a 'flying' photonic qubit for quantum communication and distributed quantum information processing. The interaction of the spin qubit with light may be enhanced by placing the quantum dot inside a monolithic microcavity. An entire system, consisting of a two-dimensional array of quantum dots and a planar microcavity, may plausibly be constructed by modern semiconductor nano-fabrication technology and could offer a path toward chip-sized scalable quantum repeaters and quantum computers. This article reviews the recent experimental developments in optical control of single quantum dot spins for quantum information processing. We highlight demonstrations of a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary SU(2) gate, and measurement. We review the decoherence and dephasing mechanisms due to hyperfine interaction with the nuclear-spin bath, and show how the single-qubit operations can be combined to perform spin echo sequences that extend the qubit decoherence from a few nanoseconds to several microseconds, more than 5 orders of magnitude longer than the single-qubit gate time. Two-qubit coupling is discussed, both within a single chip by means of exchange coupling of nearby spins and optically induced geometric phases, as well as over longer-distances. Long-distance spin-spin entanglement can be generated if each spin can emit a photon that is entangled with the spin, and these photons are then interfered. We review recent work demonstrating entanglement between a stationary spin qubit and a flying photonic qubit. These experiments utilize the polarization- and frequency-dependent spontaneous emission from the lowest charged exciton state to single spin Zeeman sublevels.
This paper discusses the potential application of elementary excitation in semiconductor quantum dots to quantum computation. We propose a scalable hardware design and all-optical implementation of logical gates that exploit the discrete nature of electron and hole states and their well-concentrated oscillator strength for ultrafast gate operations. We also propose a multiple-bit design based on the nearest neighbor dipole-dipole coupling. Rabi population oscillation of an excitonic two-level system in an isolated single In xGa1-xAs quantum dot is manifested by quantum wave function interferometry in the time domain, demonstrating a long lived coherence of zero-dimensional excitonic states and revealing the coherent population flopping under strong optical field. Phase-sensitive coherent gate operations on a single-dot exciton qubit are demonstrated.
Optically driven semiconductor quantum dots have many features similar to simpler atomic systems but with the potential for much easier development of large scale architectures for novel ideas in quantum optoelectronics. Of current interest is their potential for application to quantum information science. Here, we show the ability to perform arbitrary qubit rotation and conditional quantum logic operations in a single dot as well as showing the ability now to optically manipulate and control the electronic spin of a single electron.
The phase coherence of a physical qubit is essential for quantum information processing, motivating fast control methods to preserve that phase. Ultrafast optical techniques allow complete spin control to be performed on a much faster timescale than microwave or electrical control (ps vs. ns at best). Using our ultrafast control techniques, we demonstrate our experimental approach towards a spin echo sequence on the spin of a single electron confined in a semiconductor quantum dot (QD), increasing the observed decoherence time of a single QD electron spin from nanoseconds to several microseconds. The ratio of the observed decoherence time to the demonstrated single-qubit gate time exceeds 105, suggesting strong promise for future quantum information processors.