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It is widely accepted that the dynamic of entanglement in presence of a generic circuit can be predicted by the knowledge of the statistical properties of the entanglement spectrum. We tested this assumption by applying a Metropolis-like entanglement cooling algorithm generated by different sets of local gates, on states sharing the same statistic. We employ the ground states of a unique model, namely the one-dimensional Ising chain with a transverse field, but belonging to different macroscopic phases such as the paramagnetic, the magnetically ordered, and the topological frustrated ones. Quite surprisingly, we observe that the entanglement dynamics are strongly dependent not just on the different sets of gates but also on the phase, indicating that different phases can possess different types of entanglement (which we characterize as purely local, GHZ-like, and W-state-like) with different degree of resilience against the cooling process. Our work highlights the fact that the knowledge of the entanglement spectrum alone is not sufficient to determine its dynamics, thereby demonstrating its incompleteness as a characterization tool. Moreover, it shows a subtle interplay between locality and non-local constraints., Comment: 14 pages, 11 figures, 1 table

We introduce a highly sensitive and relatively simple technique to observe magnetization motion in single Ni nanoparticles, based on charge sensing by electron tunneling at millikelvin temperature. Sequential electron tunneling via the nanoparticle drives nonequilibrium magnetization dynamics, which induces an effective charge noise that we measure in real time. In the free spin diffusion regime, where the electrons and magnetization are in detailed balance, we observe that magnetic damping time exhibits a peak with the magnetic field, with a record long damping time of $\simeq 10$~ms., Comment: 5 pages 4 figures

In this article we study magnetotransport in single nanoparticles of Ni, Py=Ni$_{0.8}$Fe$_{0.2}$, Co, and Fe, with volumes $15\pm 6$nm$^3$, using sequential electron tunneling at 4.2K temperature. We measure current versus magnetic field in the ensembles of nominally the same samples, and obtain the abundances of magnetic hysteresis. The hysteresis abundance varies among the metals as Ni:Py:Co:Fe=4\,:50\,:100\,:100(\%), in good correlation with the magnetostatic and magnetocrystalline anisotropy. The abrupt change in the hysteresis abundance among these metals suggests a concept of minimum magnetic anisotropy required for magnetic hysteresis, which is found to be $\approx 13$meV. The minimum anisotropy is explained in terms of the residual magnetization noise arising from the spin-orbit torques generated by sequential electron tunneling. The magnetic hysteresis abundances are weakly dependent on the tunneling current through the nanoparticle, which we attribute to current dependent damping., Comment: 15 pages, 5 figures

This letter presents studies of spin-transfer efficiency in electron transport via discrete electron-in- a-box levels in individual nanometer-scale Ni particles at 0.06K temperature. In a strong magnetic field, the spin-transfer rates are estimated by measuring the amplitudes of the Zeeman splitting of the levels. We find that the spin- and the charge-transfer rates are comparable, demonstrating significant enhancement of the spin-transfer efficiency compared to that in larger magnets. In a low magnetic field, we find an additional energy splitting as evidence that the spin-transfer rate is far higher than the charge-transfer rate. The effect is explained in terms of the strong mesoscopic spin- orbit torques, which are exerted on the magnetization in response to sequential electron tunneling., Comment: 4 pages, 4 figures, submitted

We discuss a spin-transfer torque device, where the role of the soft ferromagnetic layer is played by a magnetic particle or a magnetic molecule, in weak tunnel contact with two spin polarized leads. We investigate if the magnetization of the particle can be manipulated electronically, in the regime where the critical current for magnetization switching is negligibly weak, which could be due to the reduced particle dimensions. Using master equation simulations to evaluate the effects of spin-orbit anisotropy energy fluctuations on spin-transfer, we obtain reliable reading and writing of the magnetization state of such magnetic particle, and find that the device relies on a critical voltage rather than a critical current. The critical voltage is governed by the spin-orbit energy shifts of discrete levels in the particle. This finding opens a possibility to significantly reduce the power dissipation involved in spin-transfer torque switching, by using very small magnetic particles or molecules.

Lagrangian formulation of quantum mechanical Schr\"odinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein-Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schr\"odinger equation., Comment: To appear in Foundation of Physics

We point out the crucial difference between the relative and absolute phase observables treated in our contribution \cite{1} and in the Comment by Hall and Pegg \cite{HP} respectively. The main contribution of our work is to show that the quantum expectation of the relative phase is highly discontinuous function of the frequency and to point out interesting dependence of the phase on the number-theoretic nature of the frequencies., Comment: This is our replay to the comment by M. Hall and D. Pegg (arXiv:1206.4385; Phys. Rev. A 86 (2012) 056101) on our paper Phys.Rev.A, 85 044103 (2012)

We present transfer-length-method measurements of the contact resistance between Cu and graphene, and a method to significantly reduce the contact resistance by vacuum annealing. Even in samples with heavily contaminated contacts, the contacts display very low contact resistance post annealing. Due to the common use of Cu, and it's low chemical reactivity with graphene, thermal annealing will be important for future graphene devices requiring non-perturbing contacts with low contact resistance., Comment: 8 pages, 3 figures

We present transport measurements of tunnel junctions made between Cu and graphene in a magnetic field. We observe a transition to a Landau level like structure at high fields, as well as a set of sharp features in the tunneling spectra that shift with gate and tunnel probe voltage along the lines of constant charge density. We explain the sharp features with the formation of degeneracy split localized Landau levels, and addition of electrons to those levels one by one. A large capacitive coupling to the tunnel probe also increases the gate voltage spacing between the Landau levels., Comment: 12 pages, 3 figures

The effects of Au grains on graphene conduction and doping are investigated in this report. To obtain a clean Au-graphene contact, Au grains are deposited over graphene at elevated temperature and in high vacuum, before any chemical processing. The bulk and the effective contact resistance versus gate voltage demonstrate that Au grains cause p-doping in graphene. The Fermi level shift is in agreement with first principles calculations, but the equilibrium separation we find between the graphene and the top-most Au layer is larger than predicted. Nonequilibrium electron transport displays giant-phonon thresholds observed in graphene tunnel junctions, demonstrating the tunneling nature of the contact, even though there are no dielectrics involved., Comment: 11 pages, 4 figures

Measurements of magnetic hysteresis loops in single Co nanoparticles at dilution refrigerator temperatures are presented. The nanoparticles are in electric contact with bulk Al leads via tunnel junctions. The tunnel current versus magnetic field displays a magnetic hysteresis loop. The magnetic switching field is reduced by current, and the magnetization of the nanoparticle can be switched by applying a voltage pulse, demonstrating that the magnetic stability of the nanoparticle is diminished by electron transport. Additional transitions and random switches of magnetization can be driven by large currents., Comment: This paper has been withdrawn due to the poor theoretical explanation provided in the paper

We study electron tunneling through Co nanoparticles in the presence of repeated microwave pulses at 4.2K. While individual pulses are too weak to affect the magnetic switching field, repeated microwave pulses start to reduce the magnetic switching field at 10{\mu}s spacing. We use I-V curve as a thermometer to show that the microwave pulses do not heat the sample, showing that magnetization in Co nanoparticles is directly excited by microwave pulses, and the relaxation time of the excitation energy is in the range of microsecond., Comment: 10 pages, 5 figures

We present a technique to fabricate tunnel junctions between graphene and Al and Cu, with a Si back gate, as well as a simple theory of tunneling between a metal and graphene. We map the differential conductance of our junctions versus probe and back gate voltage, and observe fluctuations in the conductance that are directly related to the graphene density of states. The conventional strong-suppression of the conductance at the graphene Dirac point can not be clearly demonstrated, but a more robust signature of the Dirac point is found: the inflection in the conductance map caused by the electrostatic gating of graphene by the tunnel probe. We present numerical simulations of our conductance maps, confirming the measurement results. In addition, Al causes strong n-doping of graphene, Cu causes a moderate p-doping, and in high resistance junctions, phonon resonances are observed, as in STM studies., Comment: 22 pages, 5 figures

A model describing spin-polarized current via discrete energy levels of a metallic nanoparticle, which has strongly asymmetric tunnel contacts to two ferromagnetic leads, is presented. In absence of spin-relaxation, the model leads to a spin-accumulation in the nanoparticle, a difference ($\Delta\mu$) between the chemical potentials of spin-up and spin-down electrons, proportional to the current and the Julliere's tunnel magnetoresistance. Taking into account an energy dependent spin-relaxation rate $\Omega (\omega)$, $\Delta\mu$ as a function of bias voltage ($V$) exhibits a crossover from linear to a much weaker dependence, when $|e|\Omega (\Delta\mu)$ equals the spin-polarized current through the nanoparticle. Assuming that the spin-relaxation takes place via electron-phonon emission and Elliot-Yafet mechanism, the model leads to a crossover from linear to $V^{1/5}$ dependence. The crossover explains recent measurements of the saturation of the spin-polarized current with $V$ in Aluminum nanoparticles, and leads to the spin-relaxation rate of $\approx 1.6 MHz$ in an Aluminum nanoparticle of diameter $6nm$, for a transition with an energy difference of one level spacing., Comment: 37 pages, 7 figures

Spin-polarized current through an Al nanoparticle in tunnel contact with two ferromagnets is measured as a function of the direction of the applied magnetic field. The nanoparticle filters the spin of injected electrons along a direction specified by the magnetic field. The characteristic field scale for the filtering corresponds to a lower limit of $8ns$ for the spin-dephasing time. Spin polarized current versus applied voltage increases stepwise, confirming that the spin relaxation time is long only in the ground state and the low-lying excited states of the nanoparticle., Comment: 12 pages 4 figures

We describe measurements of spin-polarized tunnelling via discrete energy levels of single Aluminum grains. In high resistance samples ($\sim G\Omega$), the spin-polarized tunnelling current rapidly saturates as a function of the bias voltage. This indicates that spin-polarized current is carried only via the ground state and the few lowest in energy excited states of the grain. At the saturation voltage, the spin-relaxation rate $T_1^{-1}$ of the highest excited states is comparable to the electron tunnelling rate: $T_1^{-1}\approx 1.5\cdot 10^6 s^{-1}$ and $10^7s^{-1}$ in two samples. The ratio of $T_1^{-1}$ to the electron-phonon relaxation rate is in agreement with the Elliot-Yafet scaling, an evidence that spin-relaxation in Al grains is governed by the spin-orbit interaction., Comment: 5 pages, 4 figures

We present measurements of mesoscopic resistance fluctuations in cobalt nanoparticles and study how the fluctuations with bias voltage, bias fingerprints, respond to magnetization reversal processes. Bias fingerprints rearrange when domains are nucleated or annihilated. The domain-wall causes an electron wavefunction phase-shift of $\approx 5\pi$. The phase-shift is not caused by the Aharonov-Bohm effect; we explain how it arises from the mistracking effect, where electron spins lag in orientation with respect to the moments inside the domain-wall. Dephasing time in Co at $0.03K$ is short, $\tau_\phi\sim ps$, which we attribute to the strong magnetocrystalline anisotropy., Comment: 5 pages 3 figs colour

We investigate quantum interference effects with magnetic field (magnetofingerprints) in strongly disordered Au-nanobridges. The magnetofingerprints are unconventional because they are caused by the Zeeman effect, not by the Aharonov-Bohm effect. These spin-based magnetofingerprints are equivalent to the Ericson's fluctuations (the fluctuations in electron transmission probability with electron energy). We present a model based on the Landauer-Buttiker formalism that describes the data. We show that the dephasing time $\tau_\phi (E,T)$ of electrons at temperature $T$ and energy $E$ above the Fermi level can be obtained from the correlation magnetic field. In samples with localization length comparable to sample size, $h/\tau_\phi (E,T) \approx E$, for $E\gg k_B T$, which shows that the Fermi liquid description of electron transport breaks down at length scale comparable to the localization length., Comment: 10 pages, 8 figures

We investigate spin-polarized electron tunnelling through ensembles of nanometer scale Al grains embedded between two Co-reservoirs at 4.2K, and observe tunnelling-magnetoresistance (TMR) and effects from spin-precession in the perpendicular applied magnetic field (the Hanle effect). The spin-coherence time ($T_2^\star$) measured using the Hanle effect is of order $ns$. The dephasing is attributed to electron spin-precession in local magnetic fields. Dephasing process does not destroy $TMR$, which is strongly asymmetric with bias voltage. The asymmetric TMR is explained by spin relaxation in Al grains and asymmetric electron dwell times., Comment: 4 pages 4 figures

We discovered that spin-orbit scattering in strong-disordered gold nanojunctions is strongly suppressed relative to that in weak-disordered gold thin films. This property is unusual because in weak-disordered films, spin-orbit scattering increases with disorder. Granularity and freezing of spin-orbit scattering inside the grains explains the suppression of spin-orbit scattering. We propose a generalized Elliot-Yafet relation that applies to strong-disordered granular regime., Comment: 4 pages 4 figures

Nano-junctions, containing atomic-scale gold contacts between strongly disordered leads, exhibit different transport properties at room temperature and at low temperature. At room temperature, the nano-junctions exhibit conductance quantization effects. At low temperatures, the contacts exhibit Coulomb-Blockade. We show that the differences between the room-temperature and low temperature properties arise from the localization of electronic states in the leads. The charging energy and capacitance of the nano-junctions exhibit strong fluctuations with applied magnetic field at low temperature, as predicted theoretically., Comment: 20 pages 8 figures

We describe a technique for connecting a nanometer-scale gold grain to leads by atomic-scale gold point contacts. These devices differ from previous metallic quantum dots in that the conducting channels are relatively well-transmitting. We investigate the dependence of the Coulomb blockade on contact resistance. The high-resistance devices display Coulomb blockade and the low-resistance devices display a zero-bias conductance dip, both in quantitative agreement with theory. We find that in the intermediate regime, where the sample resistance is close to $h/e^2$, the I-V curve displays a Coulomb staircase with symmetric contact capacitances., Comment: Submitted to Journal of Applied Physics

We discuss electron transport in individual nanometer-scale metallic grains at dilution refrigerator temperatures. In the weak coupling regime, the grains exhibit Coulomb blockade and discrete energy levels. Electron-electron interactions lead to clustering and broadening of quasiparticle states. Magnetic field dependences of tunneling resonances directly reveal Kramers degeneracy and Lande g-factors. In grains of Au, which have strong spin-orbit interaction, g-factors are strongly suppressed from the free electron value. We have recently studied grains in the strong coupling regime. Coulomb blockade persists in this regime. It leads to a suppression in sample conductance at zero bias voltage at low temperatures. The conductance fluctuates with the applied magnetic field near zero bias voltage. We present evidence that the fluctuations are induced by electron spin. This paper reviews the evolving progress in interpreting these observations., Comment: Since the original submission, we have gathered data in weak coupling regime, showing that our initial speculation - that the conductance dip is due to EE interactions in the Altshuler-Aronov sense - is not correct. Instead, it is caused by the Coulomb Blockade. Conference Proceedings, "Quantum Transport and Quantum Coherence" Localisation 2002, Sophia University, Tokyo, August 16-19, to be published in the supplement of the Journal of the Physical Society of Japan

We describe a method for creating atomic-scale electric contacts. A metal source is deposited on two insulating substrates separated by a 70 nm gap. Electric conductance across the gap is monitored, while protrusions from the bulk extend into the gap and reach corresponding protrusions on the other side of the gap. When the voltage across the gap is large, a pair of corresponding protrusions assembles into a point contact, via equilibrium between electrostatic attraction and a maximum sustained current. The current voltage characteristics of the point contact display crossover from weak link into tunneling junction when its conductance is near 2e2/h, indicating that the point contact is atomic-scale., Comment: submitted applied physics letters, 10/10/01

We have studied tunneling into individual Au nanoparticles of estimated diameters 2-5 nm, at dilution refrigerator temperatures. The I-V curves indicate resonant tunneling via discrete energy levels of the particle. Unlike previously studied normal metal particles of Au and Al, in these samples we find that the lowest energy tunneling resonances are split into clusters of 2-10 subresonances. Such effects appear to be increasingly important in smaller grains, as might be expected from the larger characteristic energies., Comment: 1 pdf file

We have measured the electronic energy spectra of nm-scale Au particles using a new tunneling spectroscopy configuration. The particle diameters ranged from 5nm to 9nm, and at low energies the spectrum is discrete, as expected by the electron-in-a-box model. The density of tunneling resonances increases rapidly with energy, and at higher energies the resonances overlap forming broad resonances. Near the Thouless energy, the broad resonances merge into a continuum. The tunneling resonances display Zeeman splitting in a magnetic field. Surprisingly, the g-factors (~0.3) of energy levels in Au nano-particles are much smaller than the g-factor (2.1) in bulk gold.

This papaer has been withdrawn, Comment: 4 pages, 4 figures