Luận án: Quantum Repeaters, Coherent Control & Spin-Photon Entanglement trong InAs Quantum Dots

Springer Theses Recognizing Outstanding Ph. Research Kristiaan De Greve Towards Solid-State Quantum Repeaters Ultrafast, Coherent Optical Control and Spin-Photon Entanglement in Charged InAs Quantum Dots Springer Theses Recognizing Outstanding Ph. Research For further volumes: http://www.com/series/8790 www.com Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph. theses from around the world and across the physical sciences.

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• They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the significance of its content. • The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field.com Kristiaan De Greve Towards Solid-State Quantum Repeaters Ultrafast, Coherent Optical Control and Spin-Photon Entanglement in Charged InAs Quantum Dots Doctoral Thesis accepted by Stanford University, USA 123 www.com Kristiaan De Greve Supervisor Department of Physics Yoshihisa Yamamoto Harvard University Edward L. Ginzton Laboratory Cambridge, MA Stanford University USA Stanford, CA USA ISSN 2190-5053 ISSN 2190-5061 (electronic) ISBN 978-3-319-00073-2 ISBN 978-3-319-00074-9 (eBook) DOI 10.1007/978-3-319-00074-9 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013934550 © Springer International Publishing Switzerland 2013 This work is subject to copyright.

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The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.com Supervisor’s Foreword At the time of writing of this dissertation, the future of quantum information processing research, and in particular that of currently proposed quantum computing machines, is still elusive. The following is the summary of the current majority opinions in the scientific community (end of 2012). Any physical qubit has still a too short decoherence time compared to expected/required computational times for meaningful tasks, such as factoring of 1,024-bit integer numbers or quantum entan- glement distribution over 1,000 km distance.

Any current physical gate operation is faulty, and leads to computational errors, that need to be accounted for. The only existing solution for circumventing these two problems is the use of quantum error correcting codes, and fault-tolerant quantum computing architectures. A recent theoretical study on a layered quantum computing architecture with a topological surface code (N. Jones et al., Physical Review X, 2, 031007 (2012)) uncovers the prospective system size of such fault-tolerant quantum computers.

The required gate fidelity still exceeds 99.9 %, and the number of physical qubits is 108 –109, with an overall computational time as long as 1–10 days for factoring a relatively small (1,024-bit) integer number, or for quantum simulating a relatively small molecule with only 60 electrons and nuclei. How to physically implement such a huge quantum computer with numerous qubits? One is tempted to propose a distributed quantum information processing system connected by entangled memory qubits and quantum teleportation protocols. However, if we evaluate the resources required for high-fidelity entanglement distribution over non-local memory qubits, we can easily convince ourselves that a distributed quantum information processing network is not a practical solution. The overall computational time would be many years for factoring a 1,024-bit integer number instead of around 1 day.

We must integrate 108 –109 physical qubits into one chip in order to avoid this serious communication bottleneck and construct a useful quantum computer. Advanced molecular beam epitaxy and nanolithography techniques for optical semiconductors now allow us to grow InAs quantum dots (QDs) in GaAs host matrices or even in GaAs/AlAs microcavities in a square lattice geometry with v www.com vi Supervisor’s Foreword regular spacing of 100–1,000 nm (C. Schneider et al., Applied Physics Letters 92, 183101 (2008)). This means that 108 –109 QDs can be readily integrated into a reasonable 1 cm2 chip.

Such an optically active semiconductor QD can trap a single electron or hole as a matter (spin) qubit (M. Bayer et al., Physical Review B 65, 041308 (2002)), and simultaneously emit a single photon as a communication qubit (P. Michler et al. This particular system of an InAs QD embedded in a GaAs/AlAs microcavity is the platform on which Kristiaan De Greve has conducted various experiments in my research group while working toward his PhD thesis at Stanford University.

Before Kristiaan started his PhD thesis work in my group, we had accumulated some knowledge and techniques in this field. A Fourier-transform-limited single photon wavepacket, which is a quantum mechanically indistinguishable particle and an indispensible resource for quantum teleportation and quantum repeater systems, was generated from a single InAs QD in a micropost-microcavity (C. Santori et al. An entangled photon-pair can be produced by the collision of these two sequentially generated single photons at a 50–50 beam splitter, for which we demonstrated the violation of a Bell’s inequality.

Indistinguishable single photons can also be generated by two independent emitters using another optically active compound semiconductor, ZnSe. We had managed to manipulate a single electron spin in an InAs QD by off- resonant stimulated Raman scattering using single picosecond optical pulses, by which a general SU(2) operation for an electron spin can be implemented within tens of picoseconds (D. Press et al. Using Ramsey-interometry, the dephasing time (T2∗ ) of a donor bound electron had also been measured to be a few ns.

By virtue of a Hahn-spin-echo protocol, this noise source could be decoupled, resulting in a decoherence time (T2 ) of a few microcseconds. This is where Kristiaan’s research adventure started: with a project to implement an optical refocusing pulse technique to increase the decoherence time of a single quantum dot electron spin (D. De Greve et al. He then moved on to second project, in line with the former one, to demonstrate a quantum dot hole spin qubit which enjoys a suppressed hyperfine interaction with In and As nuclear spins (K.

De Greve et al., Nature Physics 7, 872 (2011)), to end with a third major project: a system-level experiment to generate and demonstrate an entangled state of a single photon and a single spin (K. De Greve et al. Stanford, CA, USA Yoshihisa Yamamoto www.com Summary of the Dissertation Single spins in optically active semiconductor host materials have emerged as leading candidates for quantum information processing (QIP). The quantum nature of the spin degree of freedom allows for encoding of stationary, memory quantum bits (qubits), and their relatively weak interaction with the host material preserves the coherence between the spin states that is at the very heart of QIP.

On the other hand, the optically active host material permits direct interfacing with light, which can be used both for all-optical manipulation of the quantum bits, and for efficiently mapping the matter qubits into flying, photonic qubits that are suited for long-distance communication. In particular, and over the past two decades or so, advances in materials science and processing technology have brought self-assembled, GaAs-embedded InAs quantum dots to the forefront, in view of their strong light-matter interaction, and good isolation from the environment. In addition, advanced and established microfabrication techniques allow for enhancing the light-matter interaction in photonic microstructures, and for scaling up to large- size systems. One of the (as of yet) most successful applications of QIP resides in the distribution of cryptographic keys, for use in one-time-pad cryptographic systems.

Here, the bizarre laws of quantum mechanics allow for clever schemes, where it is in principle impossible to copy or obtain the key (as opposed to practically, computationally hard schemes used in current, ‘classical’ schemes). Proof-of- principle schemes were demonstrated using transmission of single photons, though unavoidable photon losses and limited efficiency of the detectors used limit their use to distances of several hundred kilometers at most. Longer-range systems will need to rely on massively parallel, pre-established links consisting of quantum mechanically entangled memory qubits, with the information transfer occurring through quantum teleportation: the so-called quantum repeater. The establishment of such entangled qubit pairs relies on the possibility to efficiently map quantum information from memory qubits to flying, photonic qubits – the realm of charged, InAs quantum dots.

This work elaborates on previously established all-optical coherent control techniques of individual InAs quantum dot electron spins, and demonstrates vii www.com viii Summary of the Dissertation proof-of-principle experiments that should allow the utilization of such quantum dots for future, large-scale quantum repeaters. First, we show how more elaborate, multi-pulse spin control sequences can markedly increase the fidelity of the individual spin control operations, thereby allowing many more such operations to be concatenated before decoherence destroys the quantum memory. Furthermore, we implemented an ultrafast, gated version of a different type of control operation, the so-called geometric phase gate, which is at the basis of many proposals for scalable, multi-qubit gate operations. Next, we realized a new type of quantum memory, based on the optical control of a single hole (pseudo-)spin, that was shown to overcome some of the detrimental effects of nuclear spin hyperfine interactions, which are assumed to be the predominant sources of decoherence in electron spin- based quantum memories – at the expense, however, of a larger sensitivity to electric field-related noise sources.

Finally, we discuss a system-level experiment where the quantum dot electron spin is shown to be entangled with the polarization of a spontaneously emitted pho- ton after ultrafast, time-resolved (few picoseconds) downconversion to a wavelength (1,560 nm) that is compatible with low-loss optical fiber technology.