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Atom interferometry on optical clock transitions is being pursued for numerous long-baseline experiments both terrestrially and for future space missions. Crucial to meeting these experiments' required sensitivities is the implementation of large momentum transfer ($>$10$^3\hbar k$). Here we show that to sequentially apply such a large momentum via $\pi$ pulses places stringent requirements on the frequency noise of the interferometry laser, finding that the linewidth is required to be considerably lower than has previously been suggested. This is due to imperfect pulse fidelity in the presence of noise and is apparent even for an atom at rest interacting with resonant light, making this a fundamental constraint on operational fidelity for a given laser and pulse sequence. Within this framework, we further present and analyse two high-power, frequency-stabilised laser sources designed to perform interferometry on the $^1$S$_0$ - $^3$P$_0$ clock transitions of cadmium and strontium, respectively operating at 332 nm and 698 nm., Comment: 9 pages, 5 figures

We summarize the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with ESA and national space and research funding agencies., Comment: Summary of the Community Workshop on Cold Atoms in Space and corresponding Road-map: https://indico.cern.ch/event/1064855/

High-power and narrow-linewidth laser light is a vital tool for atomic physics, being used for example in laser cooling and trapping and precision spectroscopy. Here we produce Watt-level laser radiation at 457.49 nm and 460.86 nm of respective relevance for the cooling transitions of cadmium and strontium atoms. This is achieved via the frequency doubling of a kHz-linewidth vertical-external-cavity surface-emitting laser (VECSEL), which is based on a novel gain chip design enabling lasing at > 2 W in the 915-928 nm region. Following an additional doubling stage, spectroscopy of the $^1S_0\to{}^1P_1$ cadmium transition at 228.89 nm is performed on an atomic beam, with all the transitions from all eight natural isotopes observed in a single continuous sweep of more than 4 GHz in the deep ultraviolet. The absolute value of the transition frequency of Cd-114 and the isotope shifts relative to this transition are determined, with values for some of these shifts provided for the first time, Comment: 14 pages, 5 figures, 2 tables

We demonstrate a new method of light phase shift measurement using a high-finesse optical ring cavity which exhibits reduced phase noise due to cavity length fluctuations. Two laser beams with a frequency difference of one cavity free spectral range are simultaneously resonant with the cavity, demonstrating noise correlations in the error signals due to the common-mode cavity length fluctuations. The differential error signal shows a 30 dB reduction in cavity noise down to the noise floor in a frequency range up to half the cavity linewidth ($\delta\nu/2 \simeq 30$ kHz). Various noise sources are analyzed and their contributions to the noise floor are evaluated. Additionally, we apply this noise-reduced phase shift measurement scheme in a simulated spin-squeezing experiment where we have achieved a factor of 40 improvement in phase sensitivity with a phase resolution of 0.7 mrad, which may remove one important barrier against attaining highly spin-squeezed states. The demonstrated method is the first reported measurement using an optical ring cavity and two independent beams, a flexible situation. This method can find direct application to non-destructive measurements in quantum systems, such as for the generation of spin-squeezed states in atom interferometers and atomic clocks., Comment: 9 pages, 5 figures

We characterize the performance of a gravimeter and a gravity gradiometer based on the $^{1}$S$_{0}$-$^3$P$_0$ clock transition of strontium atoms. We use this new quantum sensor to measure the gravitational acceleration with a relative sensitivity of $1.7\times10^{-5}$, representing the first realisation of an atomic interferometry gravimeter based on a single-photon transition. Various noise contributions to the gravimeter are measured and characterized, with the current primary limitation to sensitivity seen to be the intrinsic noise of the interferometry laser itself. In a gravity gradiometer configuration, a differential phase sensitivity of 1.53~rad/$\sqrt{Hz}$ was achieved at an artificially introduced differential phase of $\pi/2$~rad. We experimentally investigated the effects of the contrast and visibility based on various parameters and achieve a total interferometry time of 30~ms, which is longer than previously reported for such interferometers. The characterization and determined limitations of the present apparatus employing $^{88}$Sr atoms provides a guidance for the future development of large-scale clock-transition gravimeters and gravity gradiometers with alkali-earth and alkali-earth-like atoms (e.g., $^{87}$Sr, Ca, Yb)., Comment: 32 pages, 14 figures

Bragg interferometers, operating using pseudospin-1/2 systems composed of two momentum states, have become a mature technology for precision measurements. State-of-the-art Bragg interferometers are rapidly surpassing technical limitations and are soon expected to operate near the projection noise limit set by uncorrelated atoms. Despite the use of large numbers of atoms, their operation is governed by single-atom physics. Motivated by recent proposals and demonstrations of Raman gravimeters in cavities, we propose a scheme to squeeze directly on momentum states for surpassing the projection noise limit in Bragg interferometers. In our modeling, we consider the unique issues that arise when a spin squeezing protocol is applied to momentum pseudospins. Specifically, we study the effects of the momentum width of the atomic cloud and the coupling to momentum states outside the pseudospin manifold, as these atoms interact via a mode of the cavity. We show that appreciable levels of spin squeezing can be demonstrated in suitable parameter regimes in spite of these complications. Using this setting, we show how beyond mean-field techniques developed for spin systems can be adapted to study the dynamics of momentum states of interacting atoms. Our scheme promises to be feasible using current technology and is experimentally attractive because it requires no additional setup beyond what will be required to operate Bragg interferometers in cavities., Comment: 35 pages (21 Main Text), 5 figures, includes appendices

Spin squeezing can improve atomic precision measurements beyond the standard quantum limit (SQL), and unitary spin squeezing is essential for improving atomic clocks. We report substantial and nearly unitary spin squeezing in $^{171}$Yb, an optical lattice clock atom. The collective nuclear spin of $\sim 10^3$ atoms is squeezed by cavity feedback, using light detuned from the system's resonances to attain unitarity. The observed precision gain over the SQL is limited by state readout to 6.5(4) dB, while the generated states offer a gain of 12.9(6) dB, limited by the curvature of the Bloch sphere. Using a squeezed state within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2). In the future, the squeezing can be simply transferred onto the optical clock transition of $^{171}$Yb., Comment: 5 pages, 4 figures

Optical cavities are widely used to enhance the interaction between atoms and light. Typical designs using a geometrically symmetric structure in the near-concentric regime face a tradeoff between mechanical stability and high single-atom cooperativity. To overcome this limitation, we design and implement a geometrically asymmetric standing-wave cavity. This structure, with mirrors of very different radii of curvature, allows strong atom-light coupling while exhibiting good stability against misalignment. We observe effective cooperativities ranging from $\eta_{\rm eff}=10$ to $\eta_{\rm eff}=0.2$ by shifting the location of the atoms in the cavity mode. By loading $^{171}$Yb atoms directly from a mirror magneto-optical trap into a one-dimensional optical lattice along the cavity mode, we produce atomic ensembles with collective cooperativities up to $N\eta=2\times 10^4$. This system opens a way to preparing spin squeezing for an optical lattice clock and to accessing a range of nonclassical collective states., Comment: 8 pages, 7 figures, published version

We present a gradiometer based on matter-wave interference of alkaline-earth-metal atoms, namely $^{88}$Sr. The coherent manipulation of the atomic external degrees of freedom is obtained by large-momentum-transfer Bragg diffraction, driven by laser fields detuned away from the narrow $^1$S$_0$-$^3$P$_1$ intercombination transition. We use a well-controlled artificial gradient, realized by changing the relative frequencies of the Bragg pulses during the interferometer sequence, in order to characterize the sensitivity of the gradiometer. The sensitivity reaches $1.5 \times 10^{-5}$ s$^{-2}$ for an interferometer time of 20 ms, limited only by geometrical constraints. We observed extremely low sensitivity of the gradiometric phase to magnetic field gradients, approaching a value 10$^{5}$ times lower than the sensitivity of alkali-atom based gradiometers. An efficient double-launch technique employing accelerated red vertical lattices from a single magneto-optical trap cloud is also demonstrated. These results highlight strontium as an ideal candidate for precision measurements of gravity gradients, with potential application in future precision tests of fundamental physics., Comment: 10 pages, 7 figures

We propose and analyse a method that allows for the production of squeezed states of the atomic center-of-mass motion that can be injected into an atom interferometer. Our scheme employs dispersive probing in a ring resonator on a narrow transition of strontium atoms in order to provide a collective measurement of the relative population of two momentum states. We show that this method is applicable to a Bragg diffraction-based atom interferometer with large diffraction orders. The applicability of this technique can be extended also to small diffraction orders and large atom numbers by inducing atomic transparency at the frequency of the probe field, reaching an interferometer phase resolution scaling $\Delta\phi\sim N^{-3/4}$, where $N$ is the atom number. We show that for realistic parameters it is possible to obtain a 20 dB gain in interferometer phase estimation compared to the Standard Quantum Limit., Comment: 5 pages, 4 figures

We report on the realization of a matter-wave interferometer based on single-photon interaction on the ultra-narrow optical clock transition of strontium atoms. We experimentally demonstrated its operation as a gravimeter and as a gravity gradiometer. No reduction of interferometric contrast was observed up to an interferometer time $2T=10$ ms, limited by geometric constraints of the apparatus. In the gradiometric configuration, the sensitivity approaches the shot noise limit. Single-photon interferometers represent a new class of high-precision sensors that could be used for the detection of gravitational waves in so far unexplored frequency ranges and to enlighten the boundary between Quantum Mechanics and General Relativity., Comment: 5 pages, 4 figures