H. R. Sadeghpour

We compute the Rydberg spectrum of a single Ca$^+$ ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in Ca$^+$, charge (electron and ionic core) coupling to the radio frequency and static fields, ion-electron coupling in the Paul trap, and ion center-of-mass coupling. The electronic Rydberg states are precisely described by a one-electron model potential for e$^-$+Ca$^{2+}$, and accurate eigenenergies, quantum defect parameters, and static and tensor polarizabilities for a number of excited Rydberg states are obtained. The time-periodic rf Hamiltonian is expanded in the Floquet basis, and the trapping-field-broadened Rydberg lines are compared with recent observations of Ca$^+(23P)$ and Ca$^+(52F)$ Rydberg lines.

We investigate the work function (WF) variation of different Au crystallographic surface orientations with carbon atom adsorption. Ab-initio calculations within density-functional theory are performed on carbon deposited (100), (110), and (111) gold surfaces. The WF behavior with carbon coverage for the different surface orientations is explained by the resultant electron charge density distributions. The dynamics of carbon adsorption at sub-to-one-monolayer (ML) coverage depends on the landscape of the potential energy surfaces. At higher ML coverage, because of adsorption saturation, the WF will have weak surface orientation dependence. This systematic study has consequential bearing on studies of electric-field noise emanating from polycrystalline gold ion-trap electrodes that have been largely employed in microfabricated electrodes.

The decoherence of trapped-ion quantum gates due to heating of their motional modes is a fundamental science and engineering problem. This heating is attributed to electric-field noise arising from the trap-electrode surfaces. In this work, we investigate the source of this noise by focusing on the diffusion of carbon-containing adsorbates on the surface of Au(110). We show by density functional theory, based on detailed scanning probe microscopy, how the carbon adatom diffusion on the gold surface changes the energy landscape, and how the adatom dipole moment varies with the diffusive motion. A simple model for the diffusion noise, which varies quadratically with the variation of the dipole moment, qualitatively reproduces the measured noise spectrum, and the estimate of the noise spectral density is in accord with measured values.

Van der Pol oscillators are prototypical self-sustaining oscillators which have been used to model nonlinear processes in biological and other classical processes. In this work, we investigate how quantum fluctuations affect phase-locking in one or many van der Pol oscillators. We find that phase-locking is much more robust in the quantum model than in the equivalent classical model. Trapped-ion experiments are ideally suited to simulate van der Pol oscillators in the quantum regime via sideband heating and cooling of motional modes. We provide realistic experimental parameters for ${}^{171}\text{Yb}^+$ achievable with current technology.

Electric field noise is a hinderance to the assembly of large scale quantum computers based on entangled trapped ions. Apart from ubiquitous technical noise sources, experimental studies of trapped ion heating have revealed additional limiting contributions to this noise, originating from atomic processes on the electrode surfaces. In a recent work [A. Safavi-Naini et al., Phys. Rev. A 84, 023412 (2011)] we described a microscopic model for this excess electric field noise, which points a way towards a more systematic understanding of surface adsorbates as progenitors of electric field jitter noise. Here, we address the impact of surface monolayer contamination on adsorbate induced noise processes. By using exact numerical calculations for H and N atomic monolayers on an Au(111) surface representing opposite extremes of physisorption and chemisorption, we show that an additional monolayer can significantly affect the noise power spectrum and either enhance or suppress the resulting heating rates.

Motional heating of ions in micro-fabricated traps is a challenge hindering experimental realization of large-scale quantum processing devices. Recently a series of measurements of the heating rates in surface-electrode ion traps characterized their frequency, distance, and temperature dependencies, but our understanding of the microscopic origin of this noise is still vague. In this work we develop a theoretical model for the electric field noise which is associated with a random distribution of adsorbed atoms on the trap electrode surface. By using first principle calculations of the fluctuating dipole moments of the adsorbed atoms we evaluate the distance, frequency and temperature dependence of the resulting electric field fluctuation spectrum.Our theory calculates the noise spectrum beyond the standard scenario of two-level fluctuators, by incorporating all the relevant vibrational states. The $1/f$ noise is shown to commence at roughly the frequency of the fundamental phonon transition rate and the $d^{-4}$ dependence with distance of the ion from the electrode surface is established.