Fine Structure in Energy Spectra of Ultrasmall Au Nanoparticles

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 fil

On Wheeler's delayed-choice Gedankenexperiment and its laboratory realization

Here, we present an analysis and interpretation of the experiment performed by Jacques et al. (2007 Science 315, 966), which represents a realization of Wheeler's delayed-choice Gedankenexperiment. Our analysis is based on the evolution of the photon state, since the photon enters into the Mach-Zehnder interferometer with a removable beam-splitter until it exits. Given the same incident photon state onto the output beam-splitter, BS_output, the photon's state at the exit will be very different depending on whether BS_output is on or off. Hence, the statistics of photon counts collected by the two detectors, positioned along orthogonal directions at the exit of the interferometer, is also going to be very different in either case. Therefore, it is not that the choice of inserting (on) or removing (off) a beam-splitter leads to a delayed influence on the photon behavior before arriving at the beam-splitter, but that such a choice influences the photon state at and after BS_output, i.e., after it has exited from the Mach-Zehnder interferometer. The random on/off choice at BS_output has no delayed effect on the photon to behave as a wave or a corpuscle at the entrance and inside the interferometer, but influences the subsequent evolution of the photon state incident onto BS_output.Comment: 7 pages, 4 figure

Modelling Electron Spin Accumulation in a Metallic Nanoparticle

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 figure

Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier

We consider the system of N two-level atoms, of which N0 atoms are unexcited and N1 are excited. This system of N two-level atoms, which forms a linear quantum amplifier, interacts with a single-mode electromagnetic field. The problem of amplification of the L-photon states using such an amplifier is studied. The evolution of the electromagnetic field density matrix is described by the master equation for the field under amplification. The dynamics of this process is such that it can be described as the transformation of the scale of the phase space. The exact solution of the master equation is expressed using the transformed Husimi function of the L-quantum state of the harmonic oscillator. The properties of this function are studied and using it the average photon number and its fluctuations in the amplified state are found. © 2021, Editura Academiei Romane. All rights reserved

Coherence loss and revivals in atomic interferometry: A quantum-recoil analysis

The coherence effects induced by external photons coupled to matter waves inside a MachZehnder three-grating interferometer are analyzed. Alternatively to atomphoton entanglement scenarios, the model considered here only relies on the atomic wavefunction and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. Good quantitative agreement is found when comparing the results obtained from our model with the experimental data. © 2012 IOP Publishing Ltd.MD, MB and DA acknowledge support from the Ministry of Science of Serbia under Projects OI171005, OI171028 and III45016. ASS acknowledges support from the Ministerio de Econom´ıa y Competitividad (Spain) under Projects FIS2010-22082 and FIS2010-29596-C02-01, as well as for a “Ram´on y Cajal” Research Fellowship.Peer Reviewe

Spectroscopy, Interactions and Level Splittings in Au Nanoparticles

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

Suppression of Spin-Orbit Scattering in Strong-Disordered Gold Nanojunctions

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 figure

Spin-Polarized Electron Transport through Nanometer-Scale Al Grains

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 figure

Magnetic-field dependence of energy levels in ultrasmall metal grains

We present a theory of mesoscopic fluctuations of g tensors and avoided crossing energies in a small metal grain. The model, based on random matrix theory, contains both the orbital and spin contributions to the g tensor. The two contributions can be experimentally separated for weak spin-orbit coupling while they merge in the strong coupling limit. For intermediate coupling, substantial correlations are found between g factors of neighboring levels.Comment: 9 pages, 5 figure

Coherence loss and revivals in atomic interferometry: A quantum-recoil analysis

The coherence effects induced by external photons coupled to matter waves inside a Mach-Zehnder three-grating interferometer are analyzed. Alternatively to atom-photon entanglement scenarios, the model considered here only relies on the atomic wave function and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. A good quantitative agreement is found when comparing the results obtained from our model with the experimental data.Comment: 18 pages, 4 figure