Search

The emerging edge computing has promoted immense interests in compacting a neural network without sacrificing much accuracy. In this regard, low-rank tensor decomposition constitutes a powerful tool to compress convolutional neural networks (CNNs) by decomposing the 4-way kernel tensor into multi-stage smaller ones. Building on top of Tucker-2 decomposition, we propose a generalized Higher Order Tucker Articulated Kernels (HOTCAKE) scheme comprising four steps: input channel decomposition, guided Tucker rank selection, higher order Tucker decomposition and fine-tuning. By subjecting each CONV layer to HOTCAKE, a highly compressed CNN model with graceful accuracy trade-off is obtained. Experiments show HOTCAKE can compress even pre-compressed models and produce state-of-the-art lightweight networks., Comment: 6 pages, 5 figures

This work investigates the distributed constrained optimization problem under inter-agent communication delays from the perspective of passivity. First, we propose a continuous-time algorithm for distributed constrained optimization with general convex objective functions. The asymptotic stability under general convexity is guaranteed by the phase lead compensation. The inequality constraints are handled by adopting a projection-free generalized Lagrangian, whose primal-dual gradient dynamics preserves passivity and smoothness, enabling the application of the LaSalle's invariance principle in the presence of delays. Then, we incorporate the scattering transformation into the proposed algorithm to enhance the robustness against unknown and heterogeneous communication delays. Finally, a numerical example of a matching problem is provided to illustrate the results., Comment: 6 pages, 3 figures

We study the phase diagram of the interacting two-dimensional electron gas (2DEG) with equal Rashba and Dresselhaus spin-orbit coupling, which for weak coupling gives rise to the well-known persistent spin-helix phase. We construct the full Hartree-Fock phase diagram using a classical Monte-Carlo method analogous to that used in Phys.Rev.B 96, 235425 (2017). For the 2DEG with only Rashba spin-orbit coupling, it was found that at intermediate values of the Wigner-Seitz radius rs the system is characterized by a single Fermi surface with an out-of-plane spin polarization, while at slightly larger values of rs it undergoes a transition to a state with a shifted Fermi surface and an in-plane spin polarization. The various phase transitions are first-order, and this shows up in discontinuities in the conductivity and the appearance of anisotropic resistance in the in-plane polarized phase. In this work, we show that the out-of-plane spin-polarized region shrinks as the strength of the Dresselhaus spin-orbit interaction increases, and entirely vanishes when the Rashba and Dresselhaus spin-orbit coupling strengths are equal. At this point, the system can be mapped onto a 2DEG without spin-orbit coupling, and this transformation reveals the existence of an in-plane spin-polarized phase with a single, displaced Fermi surface beyond rs > 2.01. This is confirmed by classical Monte-Carlo simulations. We discuss experimental observation and useful applications of the novel phase, as well as caveats of using the classical Monte-Carlo method., Comment: 9 pages, 7 figures, 2 tables

We investigate superradiant-like dynamics of the nuclear-spin bath in a single-electron quantum dot, by considering electrons cyclically shuttling on/off an isotopically enriched `nuclear-spin island'. Assuming a uniform hyperfine interaction, we discuss in detail the nuclear spin evolution under shuttling and its relation to superradiance. We derive the minimum shuttling time which allows to escape the adiabatic spin evolution. Furthermore, we discuss slow/fast shuttling under the inhomogeneous field of a nearby micromagnet. Finally, by comparing our scheme to a model with stationary quantum dot, we stress the important role played by non-adiabatic shuttling in lifting the Coulomb blockade and thus establishing the superradiant-like behavior., Comment: 14 pages, 12 figures

Understanding (and controlling) hyperfine interactions in semiconductor nanostructures is important for fundamental studies of material properties as well as for quantum information processing with electron, hole, and nuclear-spin states. Through a combination of first-principles density-functional theory (DFT) and $\mathbf{k}\cdot\mathbf{p}$ theory, we have calculated hyperfine tensors for electrons and holes in GaAs and crystalline silicon. Accounting for relativistic effects near the nuclear core, we find contact hyperfine interactions for electrons in GaAs that are consistent with Knight-shift measurements performed on GaAs quantum wells and are roughly consistent with prior estimates extrapolated from measurements on InSb. We find that a combination of DFT and $\mathbf{k}\cdot\mathbf{p}$ theory is necessary to accurately determine the contact hyperfine interaction for electrons at a conduction-band minimum in silicon that is consistent with bulk Knight-shift measurements. For hole spins in GaAs, the overall magnitude of the hyperfine couplings we find from DFT is consistent with previous theory based on free-atom properties, and with heavy-hole Overhauser shifts measured in GaAs (and InGaAs) quantum dots. In addition, we theoretically predict that the heavy-hole hyperfine coupling to the As nuclear spins is stronger and almost purely Ising-like, while the (weaker) coupling to the Ga nuclear spins has significant non-Ising corrections. In the case of hole spins in silicon, we find (surprisingly) that the strength of the hyperfine interaction in the valence band is comparable to that in the conduction band and that the hyperfine tensors are highly anisotropic (Ising-like) in the heavy-hole subspace. These results suggest that the hyperfine coupling cannot be ruled out as a limiting mechanism for coherence ($T_2^{\ast}$) times recently measured for heavy holes in silicon quantum dots., Comment: v1: 17 pages, 3 figures; v2: minor revisions/clarifications to address referee comments

Complex applications and workflows needs are often exclusively expressed in terms of computational resources on HPC systems. In many cases, other resources like storage or network are not allocatable and are shared across the entire HPC system. By looking at the storage resource in particular, any workflow or application should be able to select both its preferred data manager and its required storage capability or capacity. To achieve such a goal, new mechanisms should be introduced. In this work, we introduce such a mechanism for dynamically provision a data management system on top of storage devices. We particularly focus our effort on deploying a BeeGFS instance across multiple DataWarp nodes on a Cray XC50 system. However, we also demonstrate that the same mechanism can be used to deploy BeeGFS on non-Cray system.

This technical note investigates the minimum average transmit power required for mean-square stabilization of a discrete-time linear process across a time-varying additive white Gaussian noise (AWGN) fading channel that is presented between the sensor and the controller. We assume channel state information at both the transmitter and the receiver, and allow the transmit power to vary with the channel state to obtain the minimum required average transmit power via optimal power adaptation. We consider both the case of independent and identically distributed fading and fading subject to a Markov chain. Based on the proposed necessary and sufficient conditions for mean-square stabilization, we show that the minimum average transmit power to ensure stabilizability can be obtained by solving a geometric program., Comment: 6 pages, 2 figures

This work is concerned with the problem of distributed resource allocation in continuous-time setting but with discrete-time communication over infinitely jointly connected and balanced digraphs. We provide a passivity-based perspective for the continuous-time algorithm, based on which an intermittent communication scheme is developed. Particularly, a periodic communication scheme is first derived through analyzing the passivity degradation over output sampling of the distributed dynamics at each node. Then, an asynchronous distributed event-triggered scheme is further developed. The sampled-based event-triggered communication scheme is exempt from Zeno behavior as the minimum inter-event time is lower bounded by the sampling period. The parameters in the proposed algorithm rely only on local information of each individual nodes, which can be designed in a truly distributed fashion, Comment: 12 pages, 7 figures

Hole spins in semiconductor quantum dots or bound to acceptor impurities show promise as potential qubits, partly because of their weak and anisotropic hyperfine couplings to proximal nuclear spins. Since the hyperfine coupling is weak, it can be difficult to measure. However, an anisotropic hyperfine coupling can give rise to a substantial spin-echo envelope modulation that can be Fourier-analyzed to accurately reveal the hyperfine tensor. Here, we give a general theoretical analysis for hole-spin-echo envelope modulation (HSEEM), and apply this analysis to the specific case of a boron-acceptor hole spin in silicon. For boron acceptor spins in unstrained silicon, both the hyperfine and Zeeman Hamiltonians are approximately isotropic leading to negligible envelope modulations. In contrast, in strained silicon, where light-hole spin qubits can be energetically isolated, we find the hyperfine Hamiltonian and $g$-tensor are sufficiently anisotropic to give spin-echo-envelope modulations. We show that there is an optimal magnetic-field orientation that maximizes the visibility of envelope modulations in this case. Based on microscopic estimates of the hyperfine coupling, we find that the maximum modulation depth can be substantial, reaching $\sim 10\%$, at a moderate laboratory magnetic field, $B\lesssim 200\,\mathrm{mT}$., Comment: 10 pages, 1 figure; v2: minor revisions/clarifications to address referee comments

A cognitively plausible parsing algorithm should perform like the human parser in critical contexts. Here I propose an adaptation of Earley's parsing algorithm, suitable for Phase-based Minimalist Grammars (PMG, Chesi 2012), that is able to predict complexity effects in performance. Focusing on self-paced reading experiments of object clefts sentences (Warren & Gibson 2005) I will associate to parsing a complexity metric based on cued features to be retrieved at the verb segment (Feature Retrieval & Encoding Cost, FREC). FREC is crucially based on the usage of memory predicted by the discussed parsing algorithm and it correctly fits with the reading time revealed.

In this paper, a distributed optimization problem is investigated via input feedforward passivity. First, an input-feedforward-passivity-based continuous-time distributed algorithm is proposed. It is shown that the error system of the proposed algorithm can be decomposed into a group of individual input feedforward passive (IFP) systems that interact with each other using output feedback information. Based on this IFP framework, convergence conditions of a suitable coupling gain are derived over weight-balanced and uniformly jointly strongly connected (UJSC) topologies. It is also shown that the IFP-based algorithm converges exponentially when the topology is strongly connected. Second, a novel distributed derivative feedback algorithm is proposed based on the passivation of IFP systems. While most works on directed topologies require knowledge of eigenvalues of the graph Laplacian, the derivative feedback algorithm is fully distributed, namely, it is robust against randomly changing weight-balanced digraphs with any positive coupling gain and without knowing any global information. Finally, numerical examples are presented to illustrate the proposed distributed algorithms., Comment: 15 pages, 9 figures, accepted by IEEE Transactions on Automatic Control

The calculation of autocorrelation functions represents a routinely used tool to characterise quantum states of light. In this paper, we evaluate the $g^{(2)}$ function for detected photons in the case of mesoscopic multi-mode twin-beam states in order to fully investigate their statistical properties starting from measurable quantities. Moreover, we show that the second-order autocorrelation function is also useful to estimate the spurious effects affecting the employed Silicon-photomultiplier detectors., Comment: 8 pages, 6 figures

Silicon Photomultipliers are potentially ideal detectors for Quantum Optics and Quantum Information studies based on mesoscopic states of light. However, their non-idealities hampered their use so far. An optimal mode of operation has been developed and it is presented here, proving that this class of sensors can actually be exploited for the characterization of both classical and quantum properties of light., Comment: 15 pages, 14 figures

We study how strong mechanical squeezing (beyond 3 dB) can be achieved through reservoir engineering in an optomechanical system which is far from the resolved-sideband regime. In our proposed setup, the effect of unwanted counter-rotating terms is suppressed by quantum interference from two auxiliary cavities. In the weak coupling regime we develop an analytical treatment based on the effective master equation approach, which allows us to obtain explicitly the condition of maximum squeezing.

Detector stochastic deviations from an ideal response can hamper the measurement of quantum properties of light especially in the mesoscopic regime where photon-number resolution is required. We demonstrate that, by a proper analysis of the output signal, nonclassicality of twin-beam states can be detected and exploited with commercial and cost effective silicon-based photon-number-resolving detectors.

We obtain analytically close forms of benchmark quantum dynamics of the collapse and revival (CR), reduced density matrix, Von Neumann entropy, and fidelity for the XXZ central spin problem. These quantities characterize the quantum decoherence and entanglement of the system with few to many bath spins, and for a short to infinitely long time evolution. For the homogeneous central spin problem, the effective magnetic field $B$, coupling constant $A$ and longitudinal interaction $\Delta$ significantly influence the time scales of the quantum dynamics of the central spin and the bath, providing a tunable resource for quantum metrology. Under the resonance condition $B=\Delta=A$, the location of the $m$-th revival peak in time reaches a simple relation $t_{r} \simeq\frac{\pi N}{A} m$ for a large $N$. For $\Delta =0$, $N\to \infty$ and a small polarization in the initial spin coherent state, our analytical result for the CR recovers the known expression found in the Jaynes-Cummings model, thus building up an exact dynamical connection between the central spin problems and the light-matter interacting systems in quantum nonlinear optics. In addition, the CR dynamics is robust to a moderate inhomogeneity of the coupling amplitudes, while disappearing at strong inhomogeneity., Comment: added new result on inhomogeneous central spin problem and added new references and supplementary material, 6 pages + 15 pages; 4 figures + 14 figures

We study the current-carrying steady-state of a transverse field Ising chain coupled to magnetic thermal reservoirs and obtain the non-equilibrium phase diagram as a function of the magnetization potential of the reservoirs. Upon increasing the magnetization bias we observe a discontinuous jump of the magnetic order parameter that coincides with a divergence of the correlation length. For steady-states with a non-vanishing conductance, the entanglement entropy at zero temperature displays a bias dependent logarithmic correction that violates the area law and differs from the well-known equilibrium case. Our findings show that out-of-equilibrium conditions allow for novel critical phenomena not possible at equilibrium., Comment: 9 pages, 7 figures

With a perturbative treatment based on the Keldysh Green's function technique, we study the resonant enhancement of nonlinear interaction effects in a four-mode optomechanical ring. In such a system, we identify five distinct types of resonant scattering between unperturbed polariton modes, induced by the nonlinear optomechanical interaction. By computing the cavity density of states and optomechanical induced transparency signal, we find that the largest nonlinear effects are induced by a decay process involving the two phonon-like polaritons. In contrast to the conventional two-mode optomechanical system, our proposed system can exhibit prominent nonlinear features even in the regime when the single-photon coupling is much smaller than the cavity damping., Comment: 16 pages, 11 figures, 1 table

We address binary phase-shift-keyed communication channels based on Gaussian states and prove that squeezing improves state discrimination at fixed energy of the channel, also in the presence of phase diffusion. We then assess performances of homodyne detection against the ultimate quantum limits to discrimination, and show that homodyning achieves optimality in large noise regime. Finally, we consider noise in the preparation of the seed signal (before phase encoding) and show that also in this case squeezing may improve state discrimination in realistic conditions., Comment: 6 pages, 5 figures

We study the dynamic spin structure factor of the spin-$1/2$ square-lattice Heisenberg antiferromagnet and of the $J$-$Q$ model (with 4-spin interactions $Q$ and Heisenberg exchange $J$). Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with QMC simulations, we can treat the sharp ($\delta$-function) contribution from spinwaves (magnons) and a continuum at higher energy. The results for the Heisenberg model agree with neutron scattering experiments on Cu(DCOO)$_2$$\cdot$4D$_2$O, where a broad spectral-weight continuum at $q=(\pi,0)$ was interpreted as deconfined spinons. Our results at $(\pi,0)$ show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at $q=(\pi/2,\pi/2)$ (as also seen experimentally). Turning on $Q$, we observe a rapid reduction of the $(\pi,0)$ magnon weight to zero, well before the deconfined quantum phase transition into a spontaneously dimerized state. We re-interpret the picture of deconfined spinons at $(\pi,0)$ in the experiments as nearly deconfined spinons---a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile $(\pi,0)$-magnon in the Heisenberg model and its depletion in the $J$-$Q$ model, we introduce an effective model in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy with the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model reproduces the $(\pi,0)$ and $(\pi/2,\pi/2)$ features of the Heisenberg model. It can also account for the rapid loss of the $(\pi,0)$ magnon with increasing $Q$ and a remarkable persistence of a large magnon pole at $q=(\pi/2,\pi/2)$ even at the deconfined critical point., Comment: 25 pages, 24 figures, some additional discussion in version 3, to be appeared in PRX

Spin-orbit coupling is a single-particle phenomenon known to generate topological order, and electron-electron interactions cause ordered many-body phases to exist. The rich interplay of these two mechanisms is present in a broad range of materials, and has been the subject of considerable ongoing research and controversy. Here we demonstrate that interacting two-dimensional electron systems with strong spin-orbit coupling exhibit a variety of time reversal symmetry breaking phases with unconventional spin alignment. We first prove that a Stoner-type criterion can be formulated for the spin polarization response to an electric field, which predicts that the spin polarization susceptibility diverges at a certain value of the electron-electron interaction strength. The divergence indicates the possibility of unconventional ferromagnetic phases even in the absence of any applied electric or magnetic field. This leads us, in the second part of this work, to study interacting Rashba spin-orbit coupled semiconductors in equilibrium in the Hartree-Fock approximation as a generic minimal model. Using classical Monte-Carlo simulations we construct the complete phase diagram of the system as a function of density and spin-orbit coupling strength. It includes both an out-of-plane spin polarized phase and in-plane spin-polarized phases with shifted Fermi surfaces and rich spin textures, reminiscent of the Pomeranchuk instability, as well as two different Fermi-liquid phases having one and two Fermi surfaces, respectively, which are separated by a Lifshitz transition. We discuss possibilities for experimental observation and useful application of these novel phases, especially in the context of electric-field-controlled macroscopic spin polarizations., Comment: 17 pages, 5 figures

We introduce a model of $2\pi$-flux loop semimetals which holds nodal loops described by a winding number $\nu=2$. By adding some extra terms, this model can be transformed into a recently discovered Hopf-link semimetal, and the symmetries distinguishing these two phases are studied. We also propose a simpler physical implementation of $2\pi$-flux loops and of the Hopf-link semimetals which only involves nearest-neighbor hoppings, although in the presence of spin-orbit interaction. Finally, we investigate the Floquet properties of the $2\pi$-flux loop, and find that such a loop may be driven into two separated $\pi$-flux loops or four Weyl points by light with circular polarization in certain directions., Comment: 5 pages, 5 figures

We investigate first- and second-order quantum phase transitions of the anisotropic quantum Rabi model, in which the rotating- and counter-rotating terms are allowed to have different coupling strength. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches we extract the phase diagram, scaling functions, and critical exponents, which allows us to establish that the universality class at finite? anisotropy is the same as the isotropic limit. We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are relevant in a variety of systems able to realize strong coupling between light and matter, such as circuit QED setups where a finite anisotropy appears quite naturally., Comment: 12 pages, 4 figures

Using a perturbative treatment, we quantify the influence of non-adiabatic leakage and system dissipation on the transfer fidelity of a stimulated Raman adiabatic passage (STIRAP) process. We find that, optimizing transfer time rather than coupling profiles, leads to a significant improvement of the transfer fidelity. The upper bound of the fidelity has been found as a simple analytical function of system cooperativities. We also provide a systematic approach to reach this upper bound efficiently., Comment: 10 pages, 3 figures

We have analyzed effects of the hyperfine interaction on electric dipole spin resonance when the amplitude of the quantum-dot motion becomes comparable or larger than the quantum dot's size. Away from the well known small-drive regime, the important role played by transverse nuclear fluctuations leads to a gaussian decay with characteristic dependence on drive strength and detuning. A characterization of spin-flip gate fidelity, in the presence of such additional drive-dependent dephasing, shows that vanishingly small errors can still be achieved at sufficiently large amplitudes. Based on our theory, we analyze recent electric-dipole spin resonance experiments relying on spin-orbit interactions or the slanting field of a micromagnet. We find that such experiments are already in a regime with significant effects of transverse nuclear fluctuations and the form of decay of the Rabi oscillations can be reproduced well by our theory., Comment: 6 pages, 4 figures

We have theoretically analyzed coherent nuclear-spin dynamics induced by electron transport through a quantum-dot spin valve. The hyperfine interaction between electron and nuclear spins in a quantum dot allows for the transfer of angular momentum from spin-polarized electrons injected from ferromagnetic or half-metal leads to the nuclear spin system under a finite voltage bias. Accounting for a local nuclear-spin dephasing process prevents the system from becoming stuck in collective dark states, allowing a large nuclear polarization to be built up in the long-time limit. After reaching a steady state, reversing the voltage bias induces a transient current response as the nuclear polarization is reversed. Long-range nuclear-spin coherence leads to a strong enhancement of spin-flip transition rates (by an amount proportional to the number of nuclear spins) and is revealed by an intense current burst, analogous to superradiant light emission. The crossover to a regime with incoherent spin flips occurs on a relatively long time scale, on the order of the single-nuclear-spin dephasing time, which can be much longer than the time scale for the superradiant current burst. This conclusion is confirmed through a general master equation. For the two limiting regimes (coherent/incoherent spin flips) the general master equation recovers our simpler treatment based on rate equations, but is also applicable at intermediate dephasing. Throughout this work we assume uniform hyperfine couplings, which yield the strongest coherent enhancement. We propose realistic strategies, based on isotopic modulation and wavefunction engineering in core-shell nanowires, to realize this analytically solvable "box-model" of hyperfine couplings., Comment: 18 pages, 10 figures

We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a superposition of non-interacting eigenstates. For a model relevant to decoherence of a heavy-hole spin qubit in a quantum dot or for a singlet-triplet qubit for two electrons in a double quantum dot, we show that preparation of the qubit in its non-interacting ground state can actually be the worst choice to maximize purity. We further give analytical results for spin-echo envelope modulations of arbitrary spin components of a hole spin in a quantum dot, going beyond a standard secular approximation. We account for general dynamics in the presence of a pure-dephasing process and identify a crossover timescale at which it is again advantageous to initialize the qubit in the non-interacting ground state. Finally, we consider a general two-axis dynamical decoupling sequence and determine initial conditions that maximize purity, minimizing leakage to the environment., Comment: v1: 15 pages, 9 figures; v2: 19 pages, 14 figures, new sections on Born-Markov limit and dynamical decoupling

We provide analytic insight into the generation of stationary itinerant photon entanglement in a 3-mode optomechanical system. We identify the parameter regime of maximal entanglement, and show that strong entanglement is possible even for weak many-photon optomechanical couplings. We also show that strong tripartite entanglement is generated between the photonic and phononic output fields; unlike the bipartite photon-photon entanglement, this tripartite entanglement diverges as one approaches the boundary of system stability., Comment: 5 pages, 3 figures (main text); 8 pages, 4 figures (supplemental materials)

The manipulation of single spins in double quantum dots by making use of the exchange interaction and a highly inhomogeneous magnetic field was discussed in [W. A. Coish and D. Loss, Phys. Rev. B 75, 161302 (2007)]. However, such large inhomogeneity is difficult to achieve through the slanting field of a micromagnet in current designs of lateral double dots. Therefore, we examine an analogous spin manipulation scheme directly applicable to realistic GaAs double dot setups. We estimate that typical gate times, realized at the singlet-triplet anticrossing induced by the inhomogeneous micromagnet field, can be a few nanoseconds. We discuss the optimization of initialization, read-out, and single-spin gates through suitable choices of detuning pulses and an improved geometry. We also examine the effect of nuclear dephasing and charge noise. The latter induces fluctuations of both detuning and tunneling amplitude. Our results suggest that this scheme is a promising approach for the realization of fast single-spin operations., Comment: 13 pages, 11 figures

We present transport experiments performed in high quality quantum point contacts embedded in a GaAs two-dimensional hole gas. The strong spin-orbit interaction results in peculiar transport phenomena, including the previously observed anisotropic Zeeman splitting and level-dependent effective g-factors. Here we find additional effects, namely the crossing and the anti-crossing of spin-split levels depending on subband index and magnetic field direction. Our experimental observations are reconciled in an heavy hole effective spin-orbit Hamiltonian where cubic- and quadratic-in-momentum terms appear. The spin-orbit components, being of great importance for quantum computing applications, are characterized in terms of magnitude and spin structure. In the light of our results, we explain the level dependent effective g-factor in an in-plane field. Through a tilted magnetic field analysis, we show that the QPC out-of-plane g-factor saturates around the predicted 7.2 bulk value.

Diabolical points, which originate from parameter-dependent accidental degeneracies of a system's energy levels, have played a fundamental role in the discovery of the Berry phase as well as in photonics (conical refraction), in chemical dynamics, and more recently in novel materials such as graphene, whose electronic band structure possess Dirac points. Here we discuss diabolical points in an optomechanical system formed by multiple scatterers in an optical cavity with periodic boundary conditions. Such configuration is close to experimental setups using micro-toroidal rings with indentations or near-field scatterers. We find that the optomechanical coupling is no longer an analytic function near the diabolical point and demonstrate the topological phase arising through the mechanical motion. Similar to a Fabry-Perot resonator, the optomechanical coupling can grow with the number of scatterers. We also introduce a minimal quantum model of a diabolical point, which establishes a connection to the motion of an arbitrary-spin particle in a 2D parabolic quantum dot with spin-orbit coupling., Comment: 10 pages, 3 figures

We investigate the role that vortex loops play in characterizing eigenstates of interacting Majoranas. We first give some general results, and then we focus on ladder Hamiltonian examples to test further ideas. Two methods yield exact results: i.) We utilize the mapping of spin Hamiltonians to quartic interactions of Majoranas and show under certain conditions the spectra of these two examples coincide. ii) In cases with reflection-symmetric Hamiltonians, we use reflection positivity for Majoranas to characterize vortices. Aside from these exact results, two additional methods suggest wider applicability of these results: iii.) Numerical evidence suggests similar behavior for certain systems without reflection symmetry. iv.) A perturbative analysis also suggests similar behavior without the assumption of reflection symmetry., Comment: 28 pages

We review recent theoretical results for hole spins influenced by spin-orbit coupling and Coulomb interaction in two-dimensional quantum wells as well as the decoherence of single hole spins in quantum dots due to hyperfine interaction with surrounding nuclear spins. After reviewing the different forms of spin-orbit coupling that are relevant for electrons and heavy holes in III-V semiconductor quantum wells, we illustrate the combined effect of spin-orbit coupling and Coulomb interactions for hole systems on spin-dependent quasiparticle group velocities. We further analyze spin-echo decay for a single hole spin in a nuclear-spin bath, demonstrating that this decoherence source can be controlled in these systems by entering a motional-averaging regime. Throughout this review, we emphasize physical effects that are unique to hole spins (rather than electrons) in nanoscale systems., Comment: Lecture notes for Course CLXXXIII "Quantum Spintronics and Related Phenomena" Int. School of Physics "Enrico Fermi", Varenna, June 2012, 25 pages, 6 figures

We develop a theory for the spin-echo dynamics of a heavy hole in a quantum dot, accounting for both hyperfine- and electric-field-induced fluctuations. We show that a moderate applied magnetic field can drive this system to a motional-averaging regime, making the hyperfine interaction ineffective as a decoherence source. Furthermore, we show that decay of the spin-echo envelope is highly sensitive to the geometry. In particular, we find a specific choice of initialization and {\pi}-pulse axes which can be used to study intrinsic hyperfine-induced hole-spin dynamics, even in systems with substantial electric-field-induced dephasing. These results point the way to designed hole-spin qubits as a robust and long-lived alternative to electron spins., Comment: 5 pages, 4 figures; v2: table added, discussion simplified, final published version

We propose an inhomogeneous open spin ladder, related to the Kitaev honeycomb model, which can be tuned between topological and nontopological phases. In extension of Lieb's theorem, we show numerically that the ground state of the spin ladder is either vortex free or vortex full. We study the robustness of Majorana end states (MES) which emerge at the boundary between sections in different topological phases and show that while the MES in the homogeneous ladder are destroyed by single-body perturbations, in the presence of inhomogeneities at least two-body perturbations are required to destabilize MES. Furthermore, we prove that x, y, or z inhomogeneous magnetic fields are not able to destroy the topological degeneracy. Finally, we present a trijunction setup where MES can be braided. A network of such spin ladders provides thus a promising platform for realization and manipulation of MES.

We study the influence of spin-orbit interactions on quasiparticle dispersions in two-dimensional electron and heavy-hole liquids in III-V semiconductors. To obtain closed-form analytical results, we restrict ourselves to spin-orbit interactions with isotropic spectrum and work within the screened Hartree-Fock approximation, valid in the high-density limit. For electrons having a linear-in-momentum Rashba (or, equivalently, Dresselhaus) spin-orbit interaction, we show that the screened Hartree-Fock approximation recovers known results based on the random-phase approximation and we extend those results to higher order in the spin-orbit coupling. While the well-studied case of electrons leads only to a weak modification of quasiparticle properties in the presence of the linear-in-momentum spin-orbit interaction, we find two important distinctions for hole systems (with a leading nonlinear-in-momentum spin-orbit interaction). First, the group velocities associated with the two hole-spin branches acquire a significant difference in the presence of spin-orbit interactions, allowing for the creation of spin-polarized wavepackets in zero magnetic field. Second, we find that the interplay of Coulomb and spin-orbit interactions is significantly more important for holes than for electrons and can be probed through the quasiparticle group velocities. These effects should be directly observable in magnetotransport, Raman scattering, and femtosecond-resolved Faraday rotation measurements. Our results are in agreement with a general argument on the velocities, which we formulate for an arbitrary choice of the spin-orbit coupling., Comment: 11 pages, 4 figures

We investigate the exact solution of the honeycomb model proposed by Kitaev and derive an explicit formula for the projector onto the physical subspace. The physical states are simply characterized by the parity of the total occupation of the fermionic eigenmodes. We consider a general lattice on a torus and show that the physical fermion parity depends in a nontrivial way on the vortex configuration and the choice of boundary conditions. In the vortex-free case with a constant gauge field we are able to obtain an analytical expression of the parity. For a general configuration of the gauge field the parity can be easily evaluated numerically, which allows the exact diagonalization of large spin models. We consider physically relevant quantities, as in particular the vortex energies, and show that their true value and associated states can be substantially different from the one calculated in the unprojected space, even in the thermodynamic limit.

Inspired by spin-electric couplings in molecular magnets, we introduce in the Kitaev honeycomb model a linear modification of the Ising interactions due to the presence of quantized cavity fields. This allows to control the properties of the low-energy toric code Hamiltonian, which can serve as a quantum memory, by tuning the physical parameters of the cavity modes, like frequencies, photon occupations, and coupling strengths. We study the properties of the model perturbatively by making use of the Schrieffer-Wolff transformation and show that, depending on the specific setup, the cavity modes can be useful in several ways. They allow to detect the presence of anyons through frequency shifts and to prolong the lifetime of the memory by enhancing the anyon excitation energy or mediating long-range anyon-anyon interactions with tunable sign. We consider both resonant and largely detuned cavity modes., Comment: 16 pages, 6 figures