884 research outputs found
Theory of dynamic nuclear polarization and feedback in quantum dots
An electron confined in a quantum dot interacts with its local nuclear spin
environment through the hyperfine contact interaction. This interaction
combined with external control and relaxation or measurement of the electron
spin allows for the generation of dynamic nuclear polarization. The quantum
nature of the nuclear bath, along with the interplay of coherent external
fields and incoherent dynamics in these systems renders a wealth of intriguing
phenomena seen in recent experiments such as electron Zeeman frequency
focusing, hysteresis, and line dragging. We develop in detail a fully quantum,
self-consistent theory that can be applied to such experiments and that
moreover has predictive power. Our theory uses the operator sum representation
formalism in order to incorporate the incoherent dynamics caused by the
additional, Markovian bath, which in self-assembled dots is the vacuum field
responsible for electron-hole optical recombination. The beauty of this
formalism is that it reduces the complexity of the problem by encoding the
joint dynamics of the external coherent and incoherent driving in an effective
dynamical map that only acts on the electron spin subspace. This together with
the separation of timescales in the problem allows for a tractable and
analytically solvable formalism. The key role of entanglement between the
electron spin and the nuclear spins in the formation of dynamic nuclear
polarization naturally follows from our solution. We demonstrate the theory in
detail for an optical pulsed experiment and present an in-depth discussion and
physical explanation of our results.Comment: 23 pages, 13 figures; published PRB versio
Holographic real-time non-relativistic correlators at zero and finite temperature
We compute a variety of two and three-point real-time correlation functions
for a strongly-coupled non-relativistic field theory. We focus on the theory
conjectured to be dual to the Schr\"{o}dinger-invariant gravitational spacetime
introduced by Balasubramanian, McGreevy, and Son, but our methods apply to a
large class of non-relativistic theories. At zero temperature, we obtain
time-ordered, retarded, and Wightman non-relativistic correlators for scalar
operators of arbitrary conformal dimension directly in field theory by applying
a certain lightlike Fourier transform to relativistic conformal correlators,
and we verify that non-relativistic AdS/CFT reproduces the results. We compute
thermal two and three-point real-time correlators for scalar operators dual to
scalar fields in the black hole background which is the finite temperature
generalization of the Schr\"{o}dinger spacetime. This is done by first
identifying thermal real-time bulk-to-boundary propagators, which combined with
Veltman's circling rules, yield two and three-point correlators. The two-point
correlators we obtain satisfy the Kallen-Lehmann relations. We also give
retarded and time-ordered three-point correlators.Comment: 55 pages; 5 appendices, 1 figure References added, PRD versio
Resource requirements for efficient quantum communication using all-photonic graph states generated from a few matter qubits
Quantum communication technologies show great promise for applications
ranging from the secure transmission of secret messages to distributed quantum
computing. Due to fiber losses, long-distance quantum communication requires
the use of quantum repeaters, for which there exist quantum memory-based
schemes and all-photonic schemes. While all-photonic approaches based on graph
states generated from linear optics avoid coherence time issues associated with
memories, they outperform repeater-less protocols only at the expense of a
prohibitively large overhead in resources. Here, we consider using matter
qubits to produce the photonic graph states and analyze in detail the trade-off
between resources and performance, as characterized by the achievable secret
key rate per matter qubit. We show that fast two-qubit entangling gates between
matter qubits and high photon collection and detection efficiencies are the
main ingredients needed for the all-photonic protocol to outperform both
repeater-less and memory-based schemes.Comment: 24 pages, 6 figure
Master equation approach to the central spin decoherence problem: the uniform coupling model and the role of projection operators
The generalized Master equation of the Nakajima-Zwanzig (NZ) type has been
used extensively to investigate the coherence dynamics of the central spin
model with the nuclear bath in a narrowed state characterized by a well defined
value of the Overhauser field. We revisit the perturbative NZ approach and
apply it to the exactly solvable case of a system with uniform hyperfine
couplings. This is motivated by the fact that the effective Hamiltonian-based
theory suggests that the dynamics of the realistic system at low magnetic
fields and short times can be mapped onto the uniform coupling model. We show
that the standard NZ approach fails to reproduce the exact solution of this
model beyond very short times, while the effective Hamiltonian calculation
agrees very well with the exact result on timescales during which most of the
coherence is lost. Our key finding is that in order to extend the timescale of
applicability of the NZ approach in this case, instead of using a single
projection operator one has to use a set of correlated projection operators
which properly reflect the symmetries of the problem and greatly improve the
convergence of the theory. This suggests that the correlated projection
operators are crucial for a proper description of narrowed state free induction
decay at short times and low magnetic fields. Our results thus provide
important insights toward the development of a more complete theory of central
spin decoherence applicable in a broader regime of timescales and magnetic
fields.Comment: 26 pages, 9 figure
Electromagnetic signatures of the chiral anomaly in Weyl semimetals
Weyl semimetals are predicted to realize the three-dimensional axial anomaly
first discussed in particle physics. The anomaly leads to unusual transport
phenomena such as the chiral magnetic effect in which an applied magnetic field
induces a current parallel to the field. Here we investigate diagnostics of the
axial anomaly based on the fundamental equations of axion electrodynamics. We
find that materials with Weyl nodes of opposite chirality and finite energy
separation immersed in a uniform magnetic field exhibit an anomaly-induced
oscillatory magnetic field with a period set by the chemical potential
difference of the nodes. In the case where a chemical potential imbalance is
created by applying parallel electric and magnetic fields, we find a
suppression of the magnetic field component parallel to the electric field
inside the material for rectangular samples, suggesting that the chiral
magnetic current opposes this imbalance. For cylindrical geometries, we instead
find an enhancement of this magnetic field component along with an
anomaly-induced azimuthal component. We propose experiments to detect such
magnetic signatures of the axial anomaly.Comment: 5 pages, 2 figure
Dynamic Nuclear Polarization from Topological Insulator Helical Edge States
Topological insulators are promising for spintronics and related technologies
due to their spin-momentum-locked edge states, which are protected by
time-reversal symmetry. In addition to the unique fundamental physics that
arises in these systems, the potential technological applications of these
protected states has also been driving TI research over the past decade.
However, most known topological insulator materials naturally contain spinful
nuclei, and their hyperfine coupling to helical edge states intrinsically
breaks time-reversal symmetry, removing the topological protection and enabling
the buildup of dynamic nuclear spin polarization through hyperfine-assisted
backscattering. Here, we calculate scattering probabilities and nuclear
polarization for edge channels containing up to nuclear spins using a
numerically exact analysis that exploits the symmetries of the problem to
drastically reduce the computational complexity. We then show the emergence of
universal scaling properties that allow us to extrapolate our findings to
vastly larger and experimentally relevant system sizes. We find that
significant nuclear polarization can result from relatively weak helical edge
currents, suggesting that it may be an important factor affecting spin
transport in topological insulator devices
Robust quantum control using smooth pulses and topological winding
The greatest challenge in achieving the high level of control needed for
future technologies based on coherent quantum systems is the decoherence
induced by the environment. Here, we present an analytical approach that yields
explicit constraints on the driving field which are necessary and sufficient to
ensure that the leading-order noise-induced errors in a qubit's evolution
cancel exactly. We derive constraints for two of the most common types of noise
that arise in qubits: slow fluctuations of the qubit energy splitting and
fluctuations in the driving field itself. By theoretically recasting a phase in
the qubit's wavefunction as a topological winding number, we can satisfy the
noise-cancelation conditions by adjusting driving field parameters without
altering the target state or quantum evolution. We demonstrate our method by
constructing robust quantum gates for two types of spin qubit: phosphorous
donors in silicon and nitrogen-vacancy centers in diamond.Comment: 21 pages, 3 figures, v3: published versio
Exact Classification of Landau-Majorana-St\"uckelberg-Zener Resonances By Floquet Determinants
Recent experiments have shown that Landau-Majorana-Stuckelberg-Zener (LMSZ)
interferometry is a powerful tool for demonstrating and exploiting quantum
coherence not only in atomic systems but also in a variety of solid state
quantum systems such as spins in quantum dots, superconducting qubits, and
nitrogen vacancy centers in diamond. In this work, we propose and develop a
general (and, in principle, exact) theoretical formalism to identify and
characterize the interference resonances that are the hallmark of LMSZ
interferometry. Unlike earlier approaches, our scheme does not require any
approximations, allowing us to uncover important and previously unknown
features of the resonance structure. We also discuss the experimental
observability of our results.Comment: 5 pages+2 page supplementary material (published version
Nonperturbative master equation solution of central spin dephasing dynamics
We solve the long-standing central spin problem for a general set of
inhomogeneous bath couplings and a large class of initial bath states. We
compute the time evolution of the coherence of a central spin coupled to a spin
bath by resumming all orders of the time-convolutionless master equation, thus
avoiding the need to assume weak coupling to the bath. The fully quantum,
non-Markovian solution is obtained in the large-bath limit and is valid up to a
timescale set by the largest coupling constant. Our result captures the full
decoherence of an electron spin qubit coupled to a nuclear spin bath in a GaAs
quantum dot for experimentally relevant parameters. In addition, our solution
is quite compact and can readily be used to make quantitative predictions for
the decoherence process and to guide the design of nuclear state preparation
protocols.Comment: 5 pages, 3 figures, v2: new 4-page supplement added, PRL versio
Teaching quantum information science to high-school and early undergraduate students
We present a simple, accessible, yet rigorous outreach/educational program
focused on quantum information science and technology for high-school and early
undergraduate students. This program allows students to perform meaningful
hands-on calculations with quantum circuits and algorithms, without requiring
knowledge of advanced mathematics. A combination of pen-and-paper exercises and
IBM Q simulations helps students understand the structure of quantum gates and
circuits, as well as the principles of superposition, entanglement, and
measurement in quantum mechanics.Comment: 14 pages, 14 figures. (v2: Typos were corrected in Figs. 13 and 14.
v3: Figures updated to match current IBM Q Experience style. Expanded
discussion of formalism and limitations.
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