Second-order Tunneling Research Articles

Barrier height study of two-well resonant-phonon terahertz quantum cascade lasers. I. The third-order tunneling current theory

The third-order tunneling current model, reflecting the effect of carrier leakage from bound to continuum states, is modeled based on the second-order tunneling current and semi-classical leakage current theories and is incorporated in a simulation based on the rate equation. GaAs/AlGaAs-based two-well resonant-phonon terahertz quantum cascade lasers, published in the past, are theoretically examined by this method. Based on the latest recorded device, the influence of barrier height is investigated by changing the Al-composition from 12.5% to 45% with a fixed-layer thickness. As a result, there are carrier dynamics that diminish the carrier density of lasing subbands in both high and low barrier conditions. On the one hand, carrier leakage into continuum states increases drastically below 25% Al-composition. On the other hand, in high barrier conditions, substantial carriers accumulate in the ground state due to a strong confinement effect in addition to oscillator strength lowering.

Higher order curvature corrections to the field emission current density

A simple expression for the Gamow factor is obtained using a second-order curvature-corrected tunneling potential. Our results show that it approximates accurately the “exact-WKB” transmission coefficient obtained by numerically integrating over the tunneling region to obtain the Gamow factor. The average difference in current density using the respective transmission coefficients is about 1.5%, across a range of work functions ϕ∈[3−5.5] eV, Fermi energy EF∈[5−10] eV, local electric fields El∈[3−9] V/nm, and radius of curvature R≥5 nm. An easy-to-use correction factor λP is also provided to approximately map the “exact-WKB” current density to the “exact” current density in terms of EF/ϕ. The average error on using λP is found to be around 3.5%. This is a vast improvement over the average error of 15% when λP=1. Finally, an analytical expression for the curvature-corrected current density is obtained using the Gamow factor. It is found to compare well with the “exact-WKB” current density even at small values of local electric field and the radius of curvature.

Controlling directed atomic motion and second-order tunneling of a spin-orbit-coupled atom in optical lattices

We theoretically explore the tunneling dynamics for the tight-binding (TB) model of a single spin-orbit-coupled atom trapped in an optical lattice subjected to lattice shaking and to time-periodic Zeeman field. By means of analytical and numerical methods, we demonstrate that the spin-orbit (SO) coupling adds some new results to the tunneling dynamics in both multiphoton resonance and far-off-resonance parameter regimes. When the driving frequency is resonant with the static Zeeman field (multi-photon resonances), we obtain an unexpected new dynamical localization (DL) phenomenon where the single SO-coupled atom is restricted to making perfect two-site Rabi oscillation accompanied by spin flipping.By using the unconventional DL phenomenon, we are able to generate a ratchetlike effect which enables directed atomic motion towards different directions and accompanies periodic spin-flipping under the action of SO coupling. For the far-off-resonance case, we show that by suppressing the usual inter-site tunneling alone, it is possible to realize a type of spin-conserving second-order tunneling between next-nearest-neighboring sites, which is not accessible in the conventional lattice system without SO coupling. We also show that simultaneous controls of the usual inter-site tunneling and the SO-coupling-related second-order-tunneling are necessary for quasienergies flatness (collapse) and completely frozen dynamics to exist. These results may be relevant to potential applications such as spin-based quantum information processing and design of novel spintronics devices.

Quantum tunneling from a Bardeen black hole

The tunneling probability of a Schwarzschild black hole is ill-defined, if the second-order WKB approximation is considered. In this letter, the second-order tunneling probability of a Bardeen black hole is carefully investigated, and it is found to be regularized by the magnetic charge q. When the black hole entropy is maintained to be non-negative and monotonic increasing, the magnetic charge is restricted by . The minimal probability refers to such a transition that the final state is a black hole remnant of Planck length.

Dynamics of spin–orbit-coupled cold atomic gases in a Floquet lattice with an impurity

In this work, we have studied the quantum tunneling of a single spin–orbit-coupled atom held in a periodically modulated optical lattice with an impurity. As a result we find that the dynamical localization takes place globally at the collapse points of quasienergy spectrum, even when the impurity potential is far off-resonant with the driving field. Meanwhile, two types of local second-order tunneling processes appear beyond expectation between the two nearest-neighbor sites of the impurity, with the spin unchanged and with the impurity site population negligible. Though tunneling behaviors of the two types seem to be the same, they are believed to involve two distinct mechanisms: one is related to spin-independent process, while the other is to spin-dependent tunneling process. The two types of second-order processes can be identified by means of resonant tunneling with or without spin flipping by tuning the impurity potential to be in resonance with the driving field. In the Floquet picture, the system with the localized impurity develops a fine structure of avoided crossings of quasienergies near the collapse point, which is crucial to understand the so-called second-order tunneling dynamics. These results are confirmed analytically on the basis of effective three-site model and multiple-time-scale asymptotic perturbative method, and may be exploited for engineering the spin-dependent quantum transport in realistic experiments.

Second-order tunneling under the dynamic localization condition of two particles in driven one-dimensional lattices with an impurity

We investigate the effect of the interplay between the interatomic interaction and impurity on dynamic localization for two interacting bosons held in driven one-dimensional lattices with an impurity. We find that the interplay of the interatomic interaction and impurity can induce second-order tunneling under the dynamic localization condition. In the resonant regime, where the impurity potential is equal to a multiple of the driving frequency, two bosons form a stable bound pair and the dominant tunneling of the doublon in the paired state is a second-order process. In the non-resonant regime, the tunneling dynamics of the single boson in the unpaired state can also be a second-order process between the two nearest-neighbor sites of the impurity with the negligible impurity site population, and the other boson is localized in the initial site all the time. Our results provide a promising approach for controlling transport of realistic systems.

Magnetoconductivity of the La1–<italic>x</italic>Sr<italic>x</italic>MnO3@TiO2 Nanocomposite

This paper deals with tunneling magnetoresistance in a composite system of the so-called 0–3 connectivity, in which ferromagnetic (FM) metallic nanoparticles La1–xSrxMnO3 (0-D objects) are embedded in the (3-D) insulating matrix of TiO2. The sample fabrication included the sol–gel preparation of manganite particles of the x = 0.35 composition and 25 nm mean crystallite size, their coating by TiO2, and compacting the products by spark plasma sintering (SPS). A comparative nanogranular sample was prepared by SPS of bare manganite particles. The resistivities of the composite and comparative samples are 100 000 and 100 times higher compared to those of bulk metallic La1–xSrxMnO3. Otherwise, the temperature dependence observed in the nanogranular La1–xSrxMnO3 sample is similar to single crystal data, and marked localization is absent also in the La1–xSrxMnO3@TiO2 nanocomposite. The data taken in applied fields up to 4 T reveal effects typical for grain-boundary tunneling in manganites, namely, the coexistence of the low-field magnetoconductance (LFMC), reflecting the field-induced alignment of FM cores, and high-field linear magnetoconductance (HFMC) that is generally ascribed to the effect of spin canting at localized Mn4+ sites in the interface. This is considered as a signature for resonant tunneling of spin-polarized carriers, theoretically treated by Lee et al [1] . The present results show that the total extent of LFMC makes 45% in the La1–xSrxMnO3@TiO2 nanocomposite and 21% in the La1–xSrxMnO3 nanogranular sample. The slope of HFMC has been determined to 5.4% and 4.9% per Tesla, respectively. The large LFMC effect observed in the nanocomposite exceeds the theoretical prediction of 33% for the second-order tunneling, which might suggest for higher order tunneling via resonant states.

Higher-order spin and charge dynamics in a quantum dot-lead hybrid system

Understanding the dynamics of open quantum systems is important and challenging in basic physics and applications for quantum devices and quantum computing. Semiconductor quantum dots offer a good platform to explore the physics of open quantum systems because we can tune parameters including the coupling to the environment or leads. Here, we apply the fast single-shot measurement techniques from spin qubit experiments to explore the spin and charge dynamics due to tunnel coupling to a lead in a quantum dot-lead hybrid system. We experimentally observe both spin and charge time evolution via first- and second-order tunneling processes, and reveal the dynamics of the spin-flip through the intermediate state. These results enable and stimulate the exploration of spin dynamics in dot-lead hybrid systems, and may offer useful resources for spin manipulation and simulation of open quantum systems.

Off-resonant many-body quantum carpets in strongly tilted optical lattices

A unit filling Bose-Hubbard Hamiltonian embedded in a strong Stark field is studied in the off-resonant regime inhibiting single- and many-particle first-order tunneling resonances. We investigate the occurrence of coherent dipole wavelike propagation along an optical lattice by means of an effective Hamiltonian accounting for second-order tunneling processes. It is shown that dipole wave function evolution in the short-time limit is ballistic and that finite-size effects induce dynamical self-interference patterns known as quantum carpets. We also present the effects of the border right after the first reflection, showing that the wave function diffuses normally with the variance changing linearly in time. This work extends the rich physical phenomenology of tilted one-dimensional lattice systems in a scenario of many interacting quantum particles, the so-called many-body Wannier-Stark system.

Microscopic models for charge-noise-induced dephasing of solid-state qubits

Several experiments have shown qubit coherence decay of the form $exp[\ensuremath{-}{(t/{T}_{2})}^{\ensuremath{\alpha}}]$ due to environmental charge-noise fluctuations. We present a microscopic description for temperature dependencies of the parameters ${T}_{2}$ and $\ensuremath{\alpha}$. Our description is appropriate to qubits in semiconductors interacting with spurious two-level charge fluctuators coupled to a thermal bath. We find distinct power-law dependencies of ${T}_{2}$ and $\ensuremath{\alpha}$ on temperature depending on the nature of the interaction of the fluctuators with the associated bath. We consider fluctuator dynamics induced by first- and second-order tunneling with a continuum of delocalized electron states. We also study one- and two-phonon processes for fluctuators in either GaAs or Si. These results can be used to identify dominant charge-dephasing mechanisms and suppress them.

Two fermions in a double well: exploring a fundamental building block of the Hubbard model.

We have prepared two ultracold fermionic atoms in an isolated double-well potential and obtained full control over the quantum state of this system. In particular, we can independently control the interaction strength between the particles, their tunneling rate between the wells and the tilt of the potential. By introducing repulsive (attractive) interparticle interactions we have realized the two-particle analog of a Mott-insulating (charge-density-wave) state. We have also spectroscopically observed how second-order tunneling affects the energy of the system. This work realizes the first step of a bottom-up approach to deterministically create a single-site addressable realization of a ground-state Fermi-Hubbard system.

Cyclotron dynamics of a Kondo singlet in a spin-orbit-coupled alkaline-earth-metal atomic gas

We propose a scheme to investigate the interplay between Kondo-exchange interaction and quantum spin Hall effect with ultracold fermionic alkaline-earth atoms trapped in two-dimensional optical lattices using ultracold collision and laser-assisted tunneling. In the strong Kondo-coupling regime, though the loop trajectory of the mobile atom disappears, collective dynamics of an atom pair in two clock states can exhibit an unexpected spin-dependent cyclotron orbit in a plaquette, realizing the quantum spin Hall effect of the Kondo singlet. We demonstrate that the collective cyclotron dynamics of the spin-zero Kondo singlet is governed by an effective Harper-Hofstadter model in addition to second-order diagonal tunneling.

Observation of density-induced tunneling.

We study the dynamics of bosonic atoms in a tilted one-dimensional optical lattice and report on the first direct observation of density-induced tunneling. We show that the interaction affects the time evolution of the doublon oscillation via density-induced tunneling and pinpoint its density and interaction dependence. The experimental data for different lattice depths are in good agreement with our theoretical model. Furthermore, resonances caused by second-order tunneling processes are studied, where the density-induced tunneling breaks the symmetric behavior for attractive and repulsive interactions predicted by the Hubbard model.

Nonlinear Zeno dynamics due to atomic interactions in Bose–Einstein condensate

We show that nonlinear interactions induce both the Zeno and anti-Zeno effects in the generalized Bose–Josephson model (with the on-site interactions and the second-order tunneling) describing Bose–Einstein condensate in double-well trap subject to particle removal from one of the wells. We find that the on-site interactions induce only the Zeno effect, which appears at long evolution times, whereas the second-order tunneling leads to a strong decay of the atomic population at short evolution times, reminiscent of the anti-Zeno effect, and destroys the nonlinear Zeno effect due to the on-site interactions at long times.

Second-order tunneling of two interacting bosons in a driven triple well

In this study we have investigated the quantum tunneling of two repulsive bosons in a triple-well potential, subject to a high-frequency driving field. By means of the multiple-time-scale asymptotic analysis, we evidence a far-off-resonant strongly interacting regime in which the dominant tunneling of doublons (paired states) is a second-order process and the selected coherent destruction of tunneling occurs either between doublons or between unpaired states. Two Floquet quasienergy bands of both kinds of states are given analytically, where a fine structure up to the second-order corrections is displayed. The analytical results are confirmed numerically, based on the exact model, and may be particularly relevant to controlling correlated tunneling in experiments.

Validity of the Wiedemann-Franz law in small molecular wires

We report our investigations on the finite-size effects of the Lorenz number in a molecular wire. Using Landauer-B\"uttiker formalism, we find that for sufficiently long wires there are two validity regimes of the Wiedemann-Franz (WF) law, the cotunneling and the sequential tunneling regimes, while in small systems only the first regime survives. We compare our results with the standard Kubo formalism and explain its failure to detect the WF law in small systems. Furthermore, our studies on exponentially localized disordered wires show that the Lorenz number value L_0 predicted by the WF law is obtained only in the cotunneling regime. Also, the Lorenz number L exhibits a typical distribution at different temperatures corresponding to different tunneling process. In particular, first-order tunneling results in a low value of L whereas second-order tunneling recovers the universal value L_0.

Electron transport through a silicon-germanium double quantum dot at 40mK

Low-temperature electron transport measurements have been performed on a trench-isolated silicon-germanium (SiGe) double quantum dot. Transport through the quantum-dot structure was via Coulomb blockade, allowing the control of single electrons. As the drain-source bias across the double dot was increased, it was found that the Coulomb peak broadened and a second smaller peak developed in proportion to the source-drain voltage. The structure behaved predominately as a single dot but the confinement potential was not simply a single well. Additionally, two extra peaks appeared on the Coulomb blockade plots at a fixed charge configuration. The transport mechanisms assigned to the peaks were via single electron tunneling through excited states and second-order tunneling via a second smaller dot formed in series with the main dot.

Effect of high-pressure annealing on magnetoresistance in manganese perovskites

Through high-pressure (HP) annealing, a large enhancement of the magnetoresistance (MR) has been achieved for polycrystalline La0.7Sr0.3MnO3 samples over a wide range of temperature at low applied magnetic fields. Moreover, the HP-annealed samples exhibit much lower resistivity and higher metal-insulator transition temperatures. Interestingly, the low-field MR (LFMR*) values at 5K of such HP-annealed samples are found to reach as high as 45%, significantly exceeding a theoretical upper limit of 33% based on the second-order tunneling through interfacial spin sites for the polycrystalline manganese oxides. We attribute the enhanced LFMR* to the effect of HP annealing that makes the grain boundary thinner and thus allows a large fraction of eg electrons tunnel directly across the grain boundary rather than by a two-step hop process.

Second-order tunneling in half-metallic CrO 2 grain pellets

The magnetoresistance (MR) of cold-pressed powder pellets of the half-metallic ferromagnet CrO 2 was measured in wide ranges of temperature T and magnetic fields H up to μ 0 H=16 T. The MR increases from 2% at 300 K up to 64% at T=1.5 K and no saturation is observed up to 16 T. The low field resistivity depends logarithmically on temperature whereas the high-field MR shows a scaling behavior with H/T. The results favor second-order tunneling (paramagnetic assisted tunneling) at zero bias via localized magnetic moments at or within the barrier between the CrO 2 grains as the dominant resistivity mechanism for both the low- and high-field MR, respectively.

More evidence for a distribution of tunnel splittings in Mn12–acetate

In magnetic fields applied parallel to the anisotropy axis, the magnetization of Mn12 has been measured in response to a field that is swept back and forth across the resonances corresponding to steps N=4,5,…9. The fraction of molecules remaining in the metastable well after each sweep through the resonance is inconsistent with expectations for an ensemble of identical molecules. The data are consistent instead with the presence of a broad distribution of tunnel splittings. A very good fit is obtained for a Gaussian distribution of the second-order anisotropy tunneling parameter XE=−ln(|E|/2D). We show that dipolar shuffling is a small effect and is not responsible for the nonexponential relaxation.