Towards direct frequency comb spectroscopy using quantum logic

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Precision spectroscopy by photon-recoil signal amplification

Precision spectroscopy of atomic and molecular ions offers a window to new physics, but is typically limited to species with a cycling transition for laser cooling and detection. Quantum logic spectroscopy has overcome this limitation for species with long-lived excited states. Here, we extend quantum logic spectroscopy to fast, dipole-allowed transitions and apply it to perform an absolute frequency measurement. We detect the absorption of photons by the spectroscopically investigated ion through the photon recoil imparted on a co-trapped ion of a different species, on which we can perform efficient quantum logic detection techniques. This amplifies the recoil signal from a few absorbed photons to thousands of fluorescence photons. We resolve the line center of a dipole-allowed transition in 40Ca+ to 1/300 of its observed linewidth, rendering this measurement one of the most accurate of a broad transition. The simplicity and versatility of this approach enables spectroscopy of many previously inaccessible species.Comment: 25 pages, 6 figures, 1 table, updated supplementary information, fixed typo

Noise Thermometry with Two Weakly Coupled Bose-Einstein Condensates

Here we report on the experimental investigation of thermally induced fluctuations of the relative phase between two Bose-Einstein condensates which are coupled via tunneling. The experimental control over the coupling strength and the temperature of the thermal background allows for the quantitative analysis of the phase fluctuations. Furthermore, we demonstrate the application of these measurements for thermometry in a regime where standard methods fail. With this we confirm that the heat capacity of an ideal Bose gas deviates from that of a classical gas as predicted by the third law of thermodynamics.Comment: 4 pages, 4 figure

Algebraic synthesis of time-optimal unitaries in SU(2) with alternating controls

We present an algebraic framework to study the time-optimal synthesis of arbitrary unitaries in SU(2), when the control set is restricted to rotations around two non-parallel axes in the Bloch sphere. Our method bypasses commonly used control-theoretical techniques and easily imposes necessary conditions on time-optimal sequences. In a straightforward fashion, we prove that time-optimal sequences are solely parametrized by three rotation angles and derive general bounds on those angles as a function of the relative rotation speed of each control and the angle between the axes. Results are substantially different whether both clockwise and counterclockwise rotations about the given axes are allowed, or only clockwise rotations. In the first case, we prove that any finite time-optimal sequence is composed at most of five control concatenations, while for the more restrictive case, we present scaling laws on the maximum length of any finite time-optimal sequence. The bounds we find for both cases are stricter than previously published ones and severely constrain the structure of time-optimal sequences, allowing for an efficient numerical search of the time-optimal solution. Our results can be used to find the time-optimal evolution of qubit systems under the action of the considered control set and thus potentially increase the number of realizable unitaries before decoherence

Erratum to: Algebraic synthesis of time-optimal unitaries in SU(2) with alternating controls

Unfortunately, the co-author Xiaoting Wang’s name has been misspelled in the original article. The correct name is ‘Xiaoting Wang’

QUEST (Centre for Quantum Engineering and Space-Time Research) at the PTB

1.: Ertmer, Wolfgang and Ernst O. Göbel: Preface 2.: Pfalz, Stefan: Science in QUEST: The Quest of Science 3.: Riehle, Fritz: QUEST at the PTB 4.: Peik, Ekkehard and Andreas Bauch: More Accurate Clocks – What are They Needed for? 5.: Peik, Ekkehard and Uwe Sterr: The Development of Accurate Optical Clocks 6.: Piester, Dirk and Harald Schnatz: Novel Techniques for Remote Time and Frequency Comparisons 7.: Lisdat, Christian and Christian Tamm: Super-Stable Lasers 8.: Schmidt, Piet O., Börge Hemmerling, Birgit Brandstätter and Daniel Nigg: Quantum Logic for Precision Spectroscopy 9.: Sterr, Uwe and Fritz Riehle: Atom Interferometr