We consider the Stark operator perturbed by a compactly supported potential (of a certain class) on the real line. We prove the following results: (a) upper and lower bounds on the number of resonances in complex discs with large radii, (b) the trace formula in terms of resonances only, (c) all resonances determine the potential uniquely.

Evgeny L. Korotyaev

We develop an efficient back gate for silicon-on-insulator (SOI) devices operating at cryogenic temperatures, and measure the quadratic hyperfine Stark shift parameter of arsenic donors in isotopically purified $^{28}$Si-SOI layers using such structures. The back gate is implemented using MeV ion implantation through the SOI layer forming a metallic electrode in the handle wafer, enabling large and uniform electric fields up to $\sim$ 2 V/$\mu$m to be applied across the SOI layer. Utilizing this structure we measure the Stark shift parameters of arsenic donors embedded in the $^{28}$Si SOI layer and find a contact hyperfine Stark parameter of $\eta_a=-1.9\pm0.2\times10^{-3} \mu$m$^2$/V$^2$. We also demonstrate electric-field driven dopant ionization in the SOI device layer, measured by electron spin resonance.

C. C. Lo S. Simmons R. Lo Nardo C. D. Weis A. M. Tyryshkin J. Meijer D. Rogalla S. A. Lyon J. Bokor T. Schenkel J. J. L. Morton

We will study the splitting in the energy spectrum of the hydrogen atom subjected to a uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases not degenerate ($n=1$) and degenerate ($n=2$), along with known results of corrections in these levels caused by the minimum length applied purely to the hydrogen atom, so that we may find and estimate the corrections of minimum length applied to the Stark effect.

H. L. C. Louzada H. Belich

The ability to monitor and control distinct states is at the heart of emerging quantum technologies. The valley pseudospin in transition metal dichalcogenide (TMDC) monolayers is a promising degree of freedom for such control, with the optical Stark effect allowing for valley-selective manipulation of energy levels in WS$_2$ and WSe$_2$ using ultrafast optical pulses. Despite these advances, understanding of valley-sensitive optical Stark shifts in TMDCs has been limited by reflectance-based detection methods where the signal is small and prone to background effects. More sensitive polarization-based spectroscopy is required to better probe ultrafast Stark shifts for all-optical manipulation of valley energy levels. Here, we show time-resolved Kerr rotation to be a more sensitive probe of the valley-selective optical Stark effect in monolayer TMDCs. Compared to the established time-resolved reflectance methods, Kerr rotation is less sensitive to background effects. Kerr rotation provides a five-fold improvement in the signal-to-noise ratio of the Stark effect optical signal and a more precise estimate of the energy shift. This increased sensitivity allows for observation of an optical Stark shift in monolayer MoS$_2$ that exhibits both valley- and energy-selectivity, demonstrating the promise of this method for investigating this effect in other layered materials and heterostructures.

Trevor LaMountain Hadallia Bergeron Itamar Balla Teodor K. Stanev Mark C. Hersam Nathaniel P. Stern

We demonstrate the absence of a DC Stark shift in an ytterbium optical lattice clock. Stray electric fields are suppressed through the introduction of an in-vacuum Faraday shield. Still, the effectiveness of the shielding must be experimentally assessed. Such diagnostics are accomplished by applying high voltage to six electrodes, which are grounded in normal operation to form part of the Faraday shield. Our measurements place a constraint on the DC Stark shift at the $10^{-20}$ level, in units of the clock frequency. Moreover, we discuss a potential source of error in strategies to precisely measure or cancel non-zero DC Stark shifts, attributed to field gradients coupled with the finite spatial extent of the lattice-trapped atoms. With this consideration, we find that Faraday shielding, complemented with experimental validation, provides both a practically appealing and effective solution to the problem of DC Stark shifts in optical lattice clocks.

K. Beloy X. Zhang W. F. McGrew N. Hinkley T. H. Yoon D. Nicolodi R. J. Fasano S. A. Schäffer R. C. Brown A. D. Ludlow

An applied field can modulate optical signals by resonance shifting via the Stark effect. The optical Stark effect (OSE) uses ultrafast light in the transparency region of a material to shift resonances with speeds limited by the pulse duration or system coherence. In this Letter we investigate the OSE in resonant optical harmonic generation (OHG) using the ground state exciton transition of WS2 with a variety of morphologies. Multidimensional pump-harmonic-probe measurements, in which the probe is second- or third-harmonic emission, reveal not only large Stark shifts that are commensurate with the large optical susceptibilities common to WS2 excitons, but also behaviors more complex than simple OSE treatments predict. We show how a new manifestation of the Stark Effect, brought forth by coherent photon exchange between the pump and OHG fundamental fields, can strongly enhance or suppress OHG.

Darien J. Morrow Daniel D. Kohler Yuzhou Zhao Jason M. Scheeler Song Jin John C. Wright

The quantum-confined Stark effect in InAs/In(Ga)As quantum dots (QDs) using non-intentionally doped and p-doped QD barriers was investigated to compare their performance for use in optical modulators. The measurements indicate that the doped QD barriers lead to a better figure of merit $(FoM)$, defined as the ratio of the change in absorption $\Delta\alpha$ for a reverse bias voltage swing to the loss at $1 V$ $\alpha(1 V)$, $FoM=\Delta\alpha/\alpha (1 V)$. The improved performance is due to the absence of the ground-state absorption peak and an additional component to the Stark shift. Measurements indicate that p-doping the QD barriers can lead to more than a 3$\times$ increase in FoM modulator performance between temperatures of -73 $\deg$C to 100 $\deg$C when compared with the stack with NID QD barriers.

Joe Mahoney Mingchu Tang Huiyun Liu Nicolás Abadía

We present a new method for solving the Schrodinger equation using the Lossless Transmission Line Model (LTL). The LTL model although extensively used in fiber optics and optical fiber design, it has not yet found application in solid state problems. We develop the transformation theory mapping the wave equation to LTL and we apply the model to the case of a solid state periodic lattice. We extend the theory with an additional Wannier-Stark term and we show with results the flexibility and the strength of the technique. The advantages of the method for arbitrary potentials are also stressed.

C. D. Papageorgiou A. C. Boucouvalas T. E. Raptis

Demonstrating the quantum-confined Stark effect (QCSE) in silicon nanocrystals (NCs) embedded in oxide has been rather elusive, unlike the other materials. Here, the recent experimental data from ion-implanted Si NCs is unambiguously explained within the context of QCSE using an atomistic pseudopotential theory. This further reveals that the majority of the Stark shift comes from the valence states which undergo a level crossing that leads to a nonmonotonic radiative recombination behavior with respect to the applied field. The polarizability of embedded Si NCs including the excitonic effects is extracted over a diameter range of 2.5--6.5 nm, which displays a cubic scaling, $\alpha=c D^3$, with $c=2.436\times 10^{-11}$ C/(Vm), where $D$ is the NC diameter. Finally, based on intraband electroabsorption analysis, it is predicted that p-doped Si NCs will show substantial voltage tunability, whereas n-doped samples should be almost insensitive. Given the fact that bulk silicon lacks the linear electro-optic effect as being a centrosymmetric crystal, this may offer a viable alternative for electrical modulation using p-doped Si NCs.

Ceyhun Bulutay Mustafa Kulakci Raşit Turan

Stark deceleration has been utilized for slowing and trapping several species of neutral, ground-state polar molecules generated in a supersonic beam expansion. Due to the finite physical dimension of the electrode array and practical limitations of the applicable electric fields, only molecules within a specific range of velocities and positions can be efficiently slowed and trapped. These constraints result in a restricted phase space acceptance of the decelerator in directions both transverse and parallel to the molecular beam axis; hence, careful modeling is required for understanding and achieving efficient Stark decelerator operation. We present work on slowing of the hydroxyl radical (OH) elucidating the physics controlling the evolution of the molecular phase space packets both with experimental results and model calculations. From these results we deduce experimental conditions necessary for efficient operation of a Stark decelerator.

Eric R. Hudson J. R. Bochinski H. J. Lewandowski Brian C. Sawyer Jun Ye