35 research outputs found
Singlet-triplet decoherence due to nuclear spins in a double quantum dot
We have evaluated hyperfine-induced electron spin dynamics for two electrons
confined to a double quantum dot. Our quantum solution accounts for decay of a
singlet-triplet correlator even in the presence of a fully static nuclear spin
system, with no ensemble averaging over initial conditions. In contrast to an
earlier semiclassical calculation, which neglects the exchange interaction, we
find that the singlet-triplet correlator shows a long-time saturation value
that differs from 1/2, even in the presence of a strong magnetic field.
Furthermore, we find that the form of the long-time decay undergoes a
transition from a rapid Gaussian to a slow power law () when
the exchange interaction becomes nonzero and the singlet-triplet correlator
acquires a phase shift given by a universal (parameter independent) value of
at long times. The oscillation frequency and time-dependent phase
shift of the singlet-triplet correlator can be used to perform a precision
measurement of the exchange interaction and Overhauser field fluctuations in an
experimentally accessible system. We also address the effect of orbital
dephasing on singlet-triplet decoherence, and find that there is an optimal
operating point where orbital dephasing becomes negligible.Comment: 12 pages, 4 figure
Quantum versus classical hyperfine-induced dynamics in a quantum dot
In this article we analyze spin dynamics for electrons confined to
semiconductor quantum dots due to the contact hyperfine interaction. We compare
mean-field (classical) evolution of an electron spin in the presence of a
nuclear field with the exact quantum evolution for the special case of uniform
hyperfine coupling constants. We find that (in this special case) the
zero-magnetic-field dynamics due to the mean-field approximation and quantum
evolution are similar. However, in a finite magnetic field, the quantum and
classical solutions agree only up to a certain time scale t<\tau_c, after which
they differ markedly.Comment: 6 pages, 1 figure, accepted for publication in the Journal of Applied
Physics (ICPS06 conference proceedings); v2: updated references, final
published versio
Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
We have performed a systematic calculation for the non-Markovian dynamics of
a localized electron spin interacting with an environment of nuclear spins via
the Fermi contact hyperfine interaction. This work applies to an electron in
the s -type orbital ground state of a quantum dot or bound to a donor impurity,
and is valid for arbitrary polarization p of the nuclear spin system, and
arbitrary nuclear spin I in high magnetic fields. In the limit of p=1 and
I=1/2, the Born approximation of our perturbative theory recovers the exact
electron spin dynamics. We have found the form of the generalized master
equation (GME) for the longitudinal and transverse components of the electron
spin to all orders in the electron spin--nuclear spin flip-flop terms. Our
perturbative expansion is regular, unlike standard time-dependent perturbation
theory, and can be carried-out to higher orders. We show this explicitly with a
fourth-order calculation of the longitudinal spin dynamics. In zero magnetic
field, the fraction of the electron spin that decays is bounded by the
smallness parameter \delta=1/p^{2}N, where N is the number of nuclear spins
within the extent of the electron wave function. However, the form of the decay
can only be determined in a high magnetic field, much larger than the maximum
Overhauser field. In general the electron spin shows rich dynamics, described
by a sum of contributions with non-exponential decay, exponential decay, and
undamped oscillations. There is an abrupt crossover in the electron spin
asymptotics at a critical dimensionality and shape of the electron envelope
wave function. We propose a scheme that could be used to measure the
non-Markovian dynamics using a standard spin-echo technique, even when the
fraction that undergoes non-Markovian dynamics is small.Comment: 22 pages, 8 figure
Nuclear spin dynamics and Zeno effect in quantum dots and defect centers
We analyze nuclear spin dynamics in quantum dots and defect centers with a
bound electron under electron-mediated coupling between nuclear spins due to
the hyperfine interaction ("J-coupling" in NMR). Our analysis shows that the
Overhauser field generated by the nuclei at the position of the electron has
short-time dynamics quadratic in time for an initial nuclear spin state without
transverse coherence. The quadratic short-time behavior allows for an extension
of the Overhauser field lifetime through a sequence of projective measurements
(quantum Zeno effect). We analyze the requirements on the repetition rate of
measurements and the measurement accuracy to achieve such an effect. Further,
we calculate the long-time behavior of the Overhauser field for effective
electron Zeeman splittings larger than the hyperfine coupling strength and
find, both in a Dyson series expansion and a generalized master equation
approach, that for a nuclear spin system with a sufficiently smooth
polarization the electron-mediated interaction alone leads only to a partial
decay of the Overhauser field by an amount on the order of the inverse number
of nuclear spins interacting with the electron.Comment: 11 pages, 3 figure
Harnessing nuclear spin polarization fluctuations in a semiconductor nanowire
Soon after the first measurements of nuclear magnetic resonance (NMR) in a
condensed matter system, Bloch predicted the presence of statistical
fluctuations proportional to in the polarization of an ensemble of
spins. First observed by Sleator et al., so-called "spin noise" has
recently emerged as a critical ingredient in nanometer-scale magnetic resonance
imaging (nanoMRI). This prominence is a direct result of MRI resolution
improving to better than 100 nm^3, a size-scale in which statistical spin
fluctuations begin to dominate the polarization dynamics. We demonstrate a
technique that creates spin order in nanometer-scale ensembles of nuclear spins
by harnessing these fluctuations to produce polarizations both larger and
narrower than the natural thermal distribution. We focus on ensembles
containing ~10^6 phosphorus and hydrogen spins associated with single InP and
GaP nanowires (NWs) and their hydrogen-containing adsorbate layers. We monitor,
control, and capture fluctuations in the ensemble's spin polarization in
real-time and store them for extended periods. This selective capture of large
polarization fluctuations may provide a route for enhancing the weak magnetic
signals produced by nanometer-scale volumes of nuclear spins. The scheme may
also prove useful for initializing the nuclear hyperfine field of electron spin
qubits in the solid-state.Comment: 18 pages, 5 figure
A quantum spin transducer based on nano electro-mechancial resonator arrays
Implementation of quantum information processing faces the contradicting
requirements of combining excellent isolation to avoid decoherence with the
ability to control coherent interactions in a many-body quantum system. For
example, spin degrees of freedom of electrons and nuclei provide a good quantum
memory due to their weak magnetic interactions with the environment. However,
for the same reason it is difficult to achieve controlled entanglement of spins
over distances larger than tens of nanometers. Here we propose a universal
realization of a quantum data bus for electronic spin qubits where spins are
coupled to the motion of magnetized mechanical resonators via magnetic field
gradients. Provided that the mechanical system is charged, the magnetic moments
associated with spin qubits can be effectively amplified to enable a coherent
spin-spin coupling over long distances via Coulomb forces. Our approach is
applicable to a wide class of electronic spin qubits which can be localized
near the magnetized tips and can be used for the implementation of hybrid
quantum computing architectures
Recipes for spin-based quantum computing
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.Comment: 45 pages, 12 figures (low-res in preprint, high-res in journal)
tutorial review for Nanotechnology; v2: references added and updated, final
version to appear in journa
Semiconductor Spintronics
Spintronics refers commonly to phenomena in which the spin of electrons in a
solid state environment plays the determining role. In a more narrow sense
spintronics is an emerging research field of electronics: spintronics devices
are based on a spin control of electronics, or on an electrical and optical
control of spin or magnetism. This review presents selected themes of
semiconductor spintronics, introducing important concepts in spin transport,
spin injection, Silsbee-Johnson spin-charge coupling, and spindependent
tunneling, as well as spin relaxation and spin dynamics. The most fundamental
spin-dependent nteraction in nonmagnetic semiconductors is spin-orbit coupling.
Depending on the crystal symmetries of the material, as well as on the
structural properties of semiconductor based heterostructures, the spin-orbit
coupling takes on different functional forms, giving a nice playground of
effective spin-orbit Hamiltonians. The effective Hamiltonians for the most
relevant classes of materials and heterostructures are derived here from
realistic electronic band structure descriptions. Most semiconductor device
systems are still theoretical concepts, waiting for experimental
demonstrations. A review of selected proposed, and a few demonstrated devices
is presented, with detailed description of two important classes: magnetic
resonant tunnel structures and bipolar magnetic diodes and transistors. In most
cases the presentation is of tutorial style, introducing the essential
theoretical formalism at an accessible level, with case-study-like
illustrations of actual experimental results, as well as with brief reviews of
relevant recent achievements in the field.Comment: tutorial review; 342 pages, 132 figure