Unpolarized, incoherent repumping light for prevention of dark states in a trapped and laser-cooled single ion

Many ion species commonly used for laser-cooled ion trapping studies have a low-lying metastable 2D3/2 state that can become populated due to spontaneous emission from the 2P1/2 excited state. This requires a repumper laser to maintain the ion in the Doppler cooling cycle. Typically the 2D3/2 state, or some of its hyperfine components if the ion has nuclear spin, has a higher multiplicity than the upper state of the repumping transition. This can lead to dark states, which have to be destabilized by an external magnetic field or by modulating the polarization of the repumper laser. We propose using unpolarized, incoherent amplified spontaneous emission (ASE) to drive the repumping transition. An ASE source offers several advantages compared to a laser. It prevents the buildup of dark states without external polarization modulation even in zero magnetic field, it can drive multiple hyperfine transitions simultaneously, and it requires no frequency stabilization. These features make it very compact and robust, which is essential for the development of practical, transportable optical ion clocks. We construct a theoretical model for the ASE radiation, including the possibility of the source being partially polarized. Using 88Sr+ as an example, the performance of the ASE source compared to a single-mode laser is analyzed by numerically solving the eight-level density matrix equations for the involved energy levels. Finally a reduced three-level system is derived, yielding a simple formula for the excited state population and scattering rate, which can be used to optimize the experimental parameters. The required ASE power spectral density can be obtained with current technology

Dark-state suppression and optimization of laser cooling and fluorescence in a trapped alkaline-earth-metal single ion

We study the formation and destabilization of dark states in a single trapped 88Sr+ ion caused by the cooling and repumping laser fields required for Doppler cooling and fluorescence detection of the ion. By numerically solving the time-dependent density matrix equations for the eight-level system consisting of the sublevels of the 5s 2S1/2, 5p 2P1/2, and 4d 2D3/2 states, we analyze the different types of dark states and how to prevent them in order to maximize the scattering rate, which is crucial for both the cooling and the detection of the ion. The influence of the laser linewidths and ion motion on the scattering rate and the dark resonances is studied. The calculations are then compared with experimental results obtained with an endcap ion trap system located at the National Research Council of Canada and found to be in good agreement. The results are applicable also to other alkaline earth ions and isotopes without hyperfine structure

Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations

In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-"coupled"- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g. coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as em goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz algorithm's philosophy, where here events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach

Broadband lasers for photo-ionization and repumping of trapped ions

A frequency-stable, broadband laser is presented for experiments on trapped ions. Since the design is based on widely available semiconductor optical amplifier technology, similar lasers can be realized for virtually any wavelength in the near-infrared, and the coherence properties and output power allow for efficient second harmonic generation. No closed-loop frequency stabilization for addressing Doppler- or naturally-broadened, dipole-allowed transitions is needed, and the light source can be turned on and off during a measurement cycle with sub-microsecond response time. As a case study, a 921.7-nm laser with an output power of 20mW and a linewidth of 10GHz is realized, which is then frequency doubled to 460.9nm for excitation of strontium as the first step in photo-ionization. The excitation efficiency is compared to that achievable with a narrow-linewidth distributed Bragg reflector laser as well as to theory.Comment: JOSA B accepted manuscript (9 pages, 5 figures

Broadband, unpolarized repumping and clearout light sources for Sr+^+ single-ion clocks

Future transportable optical clocks require compact and reliable light sources. Here, broadband, unpolarized repumper and state clearout sources for Sr+ single-ion optical clocks are reported. These turn-key devices require no frequency stabilization nor external modulators. They are fiber based, inexpensive, and compact. Key characteristics for clock operation are presented, including optical spectra, induced light shifts and required extinction ratios. Tests with an operating single-ion standard show a clearout efficiency of 100%. Compared to a laser-based repumper, the achievable fluorescence rates for ion detection are a few tens of per cent lower. The resulting ion kinetic temperature is 1--1.5 mK, near the Doppler limit of the ion system. Similar repumper light sources could be made for Ca+ (866 nm) and Ba+ (650 nm) using semiconductor gain media.Comment: 4 pages, 6 figure

Trapping atoms on a transparent permanent-magnet atom chip

We describe experiments on trapping of atoms in microscopic magneto-optical traps on an optically transparent permanent-magnet atom chip. The chip is made of magnetically hard ferrite-garnet material deposited on a dielectric substrate. The confining magnetic fields are produced by miniature magnetized patterns recorded in the film by magneto-optical techniques. We trap Rb atoms on these structures by applying three crossed pairs of counter-propagating laser beams in the conventional magneto-optical trapping (MOT) geometry. We demonstrate the flexibility of the concept in creation and in-situ modification of the trapping geometries through several experiments.Comment: Modifications: A) Reference I. Barb et al., Eur. Phys. JD, 35, 75 (2005) added. B)Sentence rewritten: We routinely capture more than 10^6 atoms in a micro-MOT on a magnetized pattern. C) The magnetic field strengths are now given in Teslas. D) The second sentence in the fourth paragraph has been rewritten in order to more clearly describe the geometry and purpose of the compensation coils.E) In the seventh paragraph we have rewritten the sentence about the creation of the external magnetic field for the magnetic-domain patterning. F) In the ninth paragraph, we clarify the way to shift the trap center. G) Caption of Fig. 4 changed. H) We have modified paragraph 12 to improve the description on the guiding of the trap center along a toroidal pattern. I) The last two sentences of the manuscript have been rewritte

Relational reasoning via probabilistic coupling

Probabilistic coupling is a powerful tool for analyzing pairs of probabilistic processes. Roughly, coupling two processes requires finding an appropriate witness process that models both processes in the same probability space. Couplings are powerful tools proving properties about the relation between two processes, include reasoning about convergence of distributions and stochastic dominance---a probabilistic version of a monotonicity property. While the mathematical definition of coupling looks rather complex and cumbersome to manipulate, we show that the relational program logic pRHL---the logic underlying the EasyCrypt cryptographic proof assistant---already internalizes a generalization of probabilistic coupling. With this insight, constructing couplings is no harder than constructing logical proofs. We demonstrate how to express and verify classic examples of couplings in pRHL, and we mechanically verify several couplings in EasyCrypt

Letters

Sabersky, Corcoran, and DuBridge articl

Surface ruptures on cross-faults in the 24 November 1987 Superstition Hills, California, earthquake sequence

Left-lateral slip occurred on individual surface breaks along northeast-trending faults associated with the 24 November 1987 earthquake sequence in the Superstition Hills, Imperial Valley, California. This sequence included the M_s = 6.2 event on a left-lateral, northeast-trending “cross-fault” between the Superstition Hills fault (SHF) and Brawley seismic zone, which was spatially associated with the left-lateral surface breaks. Six distinct subparallel cross-faults broke at the surface, with rupture lengths ranging from about Formula to 10 km and maximum displacements ranging from 30 to 130 mm. About half a day after the M_s = 6.2 event, an M_s = 6.6 earthquake nucleated near the intersection of the cross-faults with the SHF, and rupture propagated southeast along the SHF. Whereas right-lateral slip on the SHF occurred dominantly on a single trace in a narrow zone, the cross-fault surface slip was distributed over several stands across a 10-km-wide zone. Also, whereas afterslip accounted for a large proportion of total slip on the SHF, there is no evidence for afterslip on the cross-faults. We present documentation of these surface ruptures. A simple mechanical model of faulting illustrates how the foreshock sequence may have triggered the main rupture. Displacement on other cross-faults could trigger an event on the southern San Andreas fault by a similar mechanism in the future