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Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators., Comment: 21+12 pages, 6+7 figures

The oscillating magnetic field produced by unbalanced currents in radio-frequency ion traps induces transition frequency shifts and sideband transitions that can be harmful to precision spectroscopy experiments. Here, we describe a methodology, based on two-photon spectroscopy, for determining both the strength and direction of rf-induced magnetic fields without modifying any DC magnetic bias field or changing any trap RF power. The technique is readily applicable to any trapped-ion experiment featuring narrow linewidth transitions., Comment: 13 pages, 6 figures

In this work, we present a method for measuring the motional state of a two-level system coupled to a harmonic oscillator. Our technique uses ultra-narrowband composite pulses on the blue sideband transition to scan through the populations of the different motional states. Our approach does not assume any previous knowledge of the motional state distribution and is easily implemented. It is applicable both inside and outside of the Lamb-Dicke regime. For higher phonon numbers especially, the composite pulse sequence can be used as a filter for measuring phonon number ranges. We demonstrate this measurement technique using a single trapped ion and show good detection results with the numerically evaluated pulse sequence., Comment: 8 pages, 7 figures

We perform quantum logic spectroscopy with a $^{27}$Al$^{+}$/$^{40}$Ca$^{+}$ mixed ion crystal in a linear Paul trap for a measurement of the $(3s^{2})\,^{1}\mathrm{S}_{0} \leftrightarrow \, (3s3p)\,^{3}\mathrm{P}_{1}, F=7/2$ intercombination transition in $^{27}$Al$^{+}$. Towards this end, Ramsey spectroscopy is used for probing the transition in $^{27}$Al$^{+}$ and the $(4s^{2})\,\mathrm{S}_{1/2} \leftrightarrow \, (4s3d)\,\mathrm{D}_{5/2}$ clock transition in $^{40}$Ca$^{+}$ in interleaved measurements. By using the precisely measured frequency of the clock transition in $^{40}$Ca$^{+}$ as a frequency reference, we determine the frequency of the intercombination line to be $\nu_{^{1}\mathrm{S}_{0} \leftrightarrow \,^{3}\mathrm{P}_{1},F=7/2}$=1122 842 857 334 736(93) Hz and the Land\'e g-factor of the excited state to be $g_{^{3}\mathrm{P}_{1}, F=7/2}$=0.428132(2)., Comment: 18 pages, 8 figures

We propose an experimental method to fully characterize the energy exchange of particles during the physical vapor deposition process of thin surface layers. Our approach is based on the careful observation of perturbations of the oscillation frequency of a Quartz Crystal $\mu$-balance induced by the particles interaction. With this technique, it is possible to measure the momentum exchange of the atoms during the evaporation process and determine the ideal evaporation rate for an uniform energy distribution. We are able to follow the desorption dynamics of particles immediately after the first layers have been formed. These results are in close relation to the surface binding energy of the evaporated material, they offer a better control to obtain the desired properties of the thin surface layer. We applied our technique to investigate the physical vapor evaporation process for diverse elements, usually implemented in the development of film surface layers, such as Cu, W, Au, Gd and In, and confirm that our results are in agreement with measurements done previously with other techniques such as low-temperature photoluminescence.

We aim to carry out an assessment of the scientific value of Oppenheimer's research on black holes in order to determine and weigh possible factors to explain its neglect by the scientific community, and even by Oppenheimer himself. Dealing primarily with the science and looking closely at the scientific culture and the scientific conceptual belief system of the 1930s, the present article seeks to supplement the existent literature on the subject by enriching the explanations and possibly complicating the guiding questions. We suggest a rereading of Oppenheimer as a more intriguing, ahead-of-his-time figure., Comment: 19 pages, Phys. Perspect. (2017)

We report on an investigation of a method that applies simultaneously two different mathematical models in order to optimize the design of a Zeeman Slower towards the implementation of ultra cold atoms in solid state physics. We introduce the implementation of a finite element simulation that allows us to predict with great accuracy the magnetic field intensity profile generated by the proposed design. Through the prediction of the behavior of the Zeeman Slower a greater control is acquired, which allows the optimization of the different experimental variables. We applied the method in the design of a multilayer solenoidal "Spin-Flip" Zeeman Slower for strontium atoms. The magnetic intensity profile generated by the Zeeman Slower is in agreement with the magnetic field strength profile necessary for the atom cooling and tends to zero in both end sides. The latter terms are essential in order to optimize the amount of trapped and cooled atoms., Comment: 12 pages, 5 figures, in Spanish