Observation of the Kondo screening cloud.

When a magnetic impurity exists in a metal, conduction electrons form a spin cloud that screens the impurity spin. This basic phenomenon is called the Kondo effect1,2. Unlike electric-charge screening, the spin-screening cloud3-6 occurs quantum coherently, forming spin-singlet entanglement with the impurity. Although the spins interact locally around the impurity, the Kondo cloud can theoretically spread out over several micrometres. The cloud has not so far been detected, and so its physical existence-a fundamental aspect of the Kondo effect-remains controversial7,8. Here we present experimental evidence of a Kondo cloud extending over a length of micrometres, comparable to the theoretical length ξK. In our device, a Kondo impurity is formed in a quantum dot2,9-11, coupling on one side to a quasi-one-dimensional channel12 that houses a Fabry-Pérot interferometer of various gate-defined lengths L exceeding one micrometre. When we sweep a voltage on the interferometer end gate-separated by L from the quantum dot-to induce Fabry-Pérot oscillations in conductance we observe oscillations in the measured Kondo temperature TK, which is a signature of the Kondo cloud at distance L. When L is less than ξK the TK oscillation amplitude becomes larger as L becomes smaller, obeying a scaling function of a single parameter L/ξK, whereas when L is greater than ξK the oscillation is much weaker. Our results reveal that ξK is the only length parameter associated with the Kondo effect, and that the cloud lies mostly within a length of ξK. Our experimental method offers a way of detecting the spatial distribution of exotic non-Fermi liquids formed by multiple magnetic impurities or multiple screening channels13-16 and of studying spin-correlated systems.

Universal Thermal Entanglement of Multichannel Kondo Effects.

Quantum entanglement between an impurity and its environment is expected to be central in quantum impurity problems. We develop a method to compute the entanglement in spin-1/2 impurity problems, based on the entanglement negativity and the boundary conformal field theory (BCFT). Using the method, we study the thermal decay of the entanglement in the multichannel Kondo effects. At zero temperature, the entanglement has the maximal value independent of the number of the screening channels. At low temperature, the entanglement exhibits a power-law thermal decay. The power-law exponent equals two times of the scaling dimension of the BCFT boundary operator describing the impurity spin, and it is attributed to the energy-dependent scaling behavior of the entanglement in energy eigenstates. These agree with numerical renormalization group results, unveiling quantum coherence inside the Kondo screening length.

Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics.

When two identical fermions exchange their positions, their wave function gains a phase factor of -1. We show that this distance-independent effect can induce nonlocal entanglement in one-dimensional (1D) electron systems having Majorana fermions at the ends. It occurs in the system bulk and has a nontrivial temperature dependence. In a system having a single Majorana fermion at each end, the nonlocal entanglement has a Bell-state form at zero temperature and decays as the temperature increases, vanishing suddenly at a certain finite temperature. In a system having two Majorana fermions at each end, it is in a cluster-state form and its nonlocality is more noticeable at a finite temperature. By contrast, the thermal states of corresponding 1D spins do not have nonlocal entanglement.

Hierarchical entanglement shells of multichannel Kondo clouds.

Impurities or boundaries often impose nontrivial boundary conditions on a gapless bulk, resulting in distinct boundary universality classes for a given bulk, phase transitions, and non-Fermi liquids in diverse systems. The underlying boundary states however remain largely unexplored. This is related with a fundamental issue how a Kondo cloud spatially forms to screen a magnetic impurity in a metal. Here we predict the quantum-coherent spatial and energy structure of multichannel Kondo clouds, representative boundary states involving competing non-Fermi liquids, by studying quantum entanglement between the impurity and the channels. Entanglement shells of distinct non-Fermi liquids coexist in the structure, depending on the channels. As temperature increases, the shells become suppressed one by one from the outside, and the remaining outermost shell determines the thermal phase of each channel. Detection of the entanglement shells is experimentally feasible. Our findings suggest a guide to studying other boundary states and boundary-bulk entanglement.

Low myelin-related values in the fornix and thalamus of 7 Tesla MRI of major depressive disorder patients.

Introduction: Abnormalities in myelin are believed to be one of the important causes of major depressive disorder, and it is becoming important to more accurately quantify myelin in in vivo magnetic resonance imaging of major depressive disorder patients. We aimed to investigate the difference in myelin concentration in the white matter and subcortical areas using new quantitative myelin-related maps of high-resolution 7 Tesla (7 T) magnetic resonance imaging between patients with major depressive disorder and healthy controls. Methods: Myelin-related comparisons of the white matter and nearby subcortical regions were conducted between healthy controls (n = 36) and patients with major depressive disorder (n = 34). Smoothed quantitative ratio (sq-Ratio) myelin-related maps were created using the multi-echo magnetization-prepared two rapid gradient echoes (ME-MP2RAGE) sequence of the T1 and T2* images of 7 T magnetic resonance imaging. Differences in the myelin-related values of the regions of interest between the two groups were analyzed using a two-sample t-test, and multiple comparison corrections were performed using the false discovery rate. Results: The average sq-Ratio myelin-related values were 2.62% higher in the white matter and 2.26% higher in the subcortical regions of the healthy controls group than in the major depressive disorder group. In the group analysis of the healthy control and major depressive disorder groups, the sq-Ratio myelin-related values were significantly different in the fornix area of the white matter (false discovery rate-corrected p = 0.012). In addition, significant differences were observed in both the left (false discovery rate-corrected p = 0.04) and right thalamus (false discovery rate-corrected p = 0.040) among the subcortical regions. Discussion: The average sq-ratio myelin-related value and sq-ratio myelin-related values in the fornix of the white matter and both thalami were higher in the healthy controls group than in the major depressive disorder group. We look forward to replicating our findings in other populations using larger sample sizes.

Coulomb-mediated antibunching of an electron pair surfing on sound.

Electron flying qubits are envisioned as potential information links within a quantum computer, but also promise-like photonic approaches-to serve as self-standing quantum processing units. In contrast to their photonic counterparts, electron-quantum-optics implementations are subject to Coulomb interactions, which provide a direct route to entangle the orbital or spin degree of freedom. However, controlled interaction of flying electrons at the single-particle level has not yet been established experimentally. Here we report antibunching of a pair of single electrons that is synchronously shuttled through a circuit of coupled quantum rails by means of a surface acoustic wave. The in-flight partitioning process exhibits a reciprocal gating effect which allows us to ascribe the observed repulsion predominantly to Coulomb interaction. Our single-shot experiment marks an important milestone on the route to realize a controlled-phase gate for in-flight quantum manipulations.

Quantitative myelin-related maps from R1 and T2* ratio images using a single ME-MP2RAGE sequence in 7T MRI.

Background: There still are limitations associated with quantifying myelin content using brain magnetic resonance imaging (MRI) despite several studies conducted on this subject. Therefore, this study aimed: (1) to propose a myelin-related mapping technique to obtain the quantitative R1/T2* (q-Ratio) that has the advantage of quick processing and less dependency on imaging parameters, (2) to validate this adapted q-Ratio method by comparing the quantitative myelin-related map with those acquired through an existing mapping method [T1-weighted/T2*-weighted (w-Ratio)], and (3) to determine the q-Ratio myelin-related values in the white and gray matter, and the relationship between the q-Ratio myelin-related value and cerebral volume size in regions of interest (ROIs) in a healthy population. Methods: The multi-echo magnetization-prepared 2 rapid gradient echoes (ME-MP2RAGE) sequence was used in a 7 Tesla (7T) MRI for the acquisition of data regarding myelin content in 10 healthy participants. A correlation analysis was performed between myelin-related values obtained through the q-Ratio and w-Ratio methods. Additionally, myelin distribution was analyzed and compared in the white and gray matter, and the correlation between cerebral volume size and q-Ratio myelin-related value was analyzed in ROIs in the brain. Results: The myelin-related maps acquired through the q-Ratio and w-Ratio methods were significantly correlated (p < 0.001), but the q-Ratio myelin-related map was much clearer. Additionally, the cerebral volume size in the gray matter was 399.40% larger than that in the white matter, but the q-Ratio myelin-related value in the gray matter was 80.83% lower than that of the white matter. Furthermore, volume size was positively correlated with q-Ratio myelin-related values in the white matter (r = 0.509, p = 0.006) but not in the gray matter (r = -0.133, p = 0.402). Conclusions: In this study, we validated using a q-Ratio myelin-related map that was acquired in one imaging sequence at 7T MRI. In addition, we found a significant correlation between ROI volume size and the q-Ratio myelin-related value in the white matter but not in the gray matter. It is expected that this technique could be applied to the study of various neuropsychiatric diseases related to demyelination in the future.