Address: | Department of Physics
Broida Hall University of California Santa Barbara, CA 93106-9530 USA |

e-mail: | gywat@physics.ucsb.edu |

phone (office): | ++1-805-893-5010 |

fax: | ++1-805-893-6132 |

Wiley-VCH (2009) (ISBN: 978-3-527-62899-5)

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 computation. A conclusion and outlook round off the volume. The result is a primer providing the essential basic knowledge necessary for young researchers entering the field, as well as semiconductor and theoretical physicists, PhD students in physics and material sciences, electrical engineers and materials scientists.

Science 320, 352 (2008) ; published online 13 March 2008 (Science DOI: 10.1126/science.1155400)

Phase coherence is a fundamental concept in quantum mechanics. Understanding the loss of coherence is paramount for future quantum information processing. We studied the coherent dynamics of a single central spin (a nitrogen-vacancy center) coupled to a bath of spins (nitrogen impurities) in diamond. Our experiments show that both the internal interactions of the bath and the coupling between the central spin and the bath can be tuned in situ, allowing access to regimes with surprisingly different behavior. The observed dynamics are well explained by analytics and numerical simulations, leading to valuable insight into the loss of coherence in spin systems. These measurements demonstrate that spins in diamond provide an excellent test bed for models and protocols in quantum information.

Nature Physics 2, 831 (2006); published online 12 November 2006 (doi:10.1038/nphys458).

In the field of quantum information science,
semiconductor quantum dots are of significant interest for their ability to confine a single
electron for use as a qubit. However, to realize the potential offered by quantum information
processing, it is necessary to couple two or more qubits. In contrast to coupling individual quantum
dots, we demonstrate the integration of two coupled electronic states within a single quantum dot
heterostructure. These chemically-synthesized nanocrystals, known as quantum dot quantum wells
(QDQWs), are comprised of concentric layers of different semiconducting materials.
We investigate carrier and spin dynamics in these structures using transient absorption and
time-resolved Faraday rotation measurements. By tuning the excitation and probe energies,
we find that we can selectively initialize and read out spins in different coupled states within
the QDQW. These results open a pathway for engineering coupled qubits within a single
nanostructure.

Science 314, 1916 (2006) ; published online 9 November 2006 (10.1126/science.1133862).

Kerr rotation measurements on a single electron spin confined
in a charge-tunable semiconductor quantum dot demonstrate a means to directly probe the spin
off-resonance, thus minimally disturbing the system. Energy-resolved magneto-optical spectra reveal
information about the optically-oriented spin polarization and the transverse spin lifetime of the
electron as a function of the charging of the dot. These results represent progress towards the
manipulation and coupling of single spins and photons for quantum information processing.

Phys. Rev. B

We report on room-temperature coherent manipulation of the spin of a single nitrogen-vacancy center in diamond and a study of its coherence as a function of magnetic field. We use magnetic resonance to induce Rabi nutations, and apply a Hahn spin echo to remove the effect of low-frequency dephasing. A sharp rise in the decoherence rate is observed at magnetic fields where the nitrogen-vacancy center spin couples resonantly to substitutional nitrogen spins via the magnetic dipolar coupling. Finally, we find evidence that away from these energy resonances spin flips of nitrogen electrons are the main source of decoherence.

Phys. Rev. B

We study a model for a pair of qubits which interact with a single off-resonant cavity mode and, in addition, exhibit a direct inter-qubit coupling. Possible realizations for such a system include coupled superconducting qubits in a line resonator as well as exciton states or electron spin states of quantum dots in a cavity. The emergent dynamical phenomena are strongly dependent on the relative energy scales of the inter-qubit coupling strength, the coupling strength between qubits and cavity mode, and the cavity mode detuning. We show that the cavity mode dispersion enables a measurement of the state of the coupled-qubit system in the perturbative regime. We discuss the effect of the direct inter-qubit interaction on a cavity-mediated two-qubit gate. Further, we show that for asymmetric coupling of the two qubits to the cavity, the direct inter-qubit coupling can be controlled optically via the ac Stark effect.

PhD thesis, University of Basel (2005) html pdf

Nanotechnology 16, R27 (2005), see also cond-mat/0412028.

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.

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.

Phys. Rev. B

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.

J. Superconductivity 18, 175 (2005); see also cond-mat/0408451.

We propose to use optical detection of magnetic resonance (ODMR) to measure the decoherence time T_{2} of a single electron spin in a semiconductor quantum dot. The electron is in one of the spin 1/2 states and a circularly polarized laser can only create an optical excitation for one of the electron spin states due to Pauli blocking. An applied electron spin resonance (ESR) field leads to Rabi spin flips and thus to a modulation of the photoluminescence or, alternatively, of the photocurrent. This allows one to measure the ESR linewidth and the coherent Rabi oscillations, from which the electron spin decoherence can be determined. We study different possible schemes for such an ODMR setup, including cw or pulsed laser excitation.

Phys. Rev. B

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%.

Phys. Rev. B

We propose a method based on optically detected magnetic resonance (ODMR) to measure the decoherence time T_{2} of a single electron spin in a semiconductor quantum dot. The electron spin resonance (ESR) of a single excess electron on a quantum dot is probed by circularly polarized laser excitation. The photoluminescence is modulated due to the ESR which enables the measurement of electron spin decoherence. We study different possible schemes for such an ODMR setup.

Superlattices and Microstructures 31, 127 (2002). Special issue on quantum dots for quantum computing.

We review recent theoretical progress on the use of
electron spins as qubits in coupled semiconductor quantum dots for
quantum information processing. We discuss the spin exchange
mechanism and its microscopic origin in both laterally and
vertically tunnel-coupled quantum dots and explain how it can be
used to implement the quantum XOR gate which, in combination with
single spin rotations, allows to perform arbitrary quantum
computations. In addition to their functionality as a quantum
gate, coupled quantum dots can act as a source for photon pairs in
entangled polarization states which are useful for quantum
communication. We describe a mechanism for the production of such
entangled photon pairs via a biexciton state in tunnel-coupled
quantum dots.

Phys. Rev. B

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.

Kavli Institute of Theoretical Physics, University of California at Santa Barbara, March 13, 2006 - June 23, 2006.

Centro Stefano Franscini, Monte Verità, Ascona, Switzerland, September 5 - 10, 2004.

Low-dimensional systems. Mauterndorf, Province of Salzburg, Austria, February 15 - 20, 2004.

Center for Spintronics and Quantum Computation, University of California, Santa Barbara. June 27 - July 9, 2003 and November 1 - 12, 2004.

ISQCI 2002, Instituto Superior Técnico, Lisbon, Portugal, September 2 - 7, 2002.