Squeezing on momentum states for atom interferometry

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 figure

Neural signature kernels as infinite-width-depth-limits of controlled ResNets

Motivated by the paradigm of reservoir computing, we consider randomly initialized controlled ResNets defined as Euler-discretizations of neural controlled differential equations (Neural CDEs). We show that in the infinite-width-then-depth limit and under proper scaling, these architectures converge weakly to Gaussian processes indexed on some spaces of continuous paths and with kernels satisfying certain partial differential equations (PDEs) varying according to the choice of activation function. In the special case where the activation is the identity, we show that the equation reduces to a linear PDE and the limiting kernel agrees with the signature kernel of Salvi et al. (2021). In this setting, we also show that the width-depth limits commute. We name this new family of limiting kernels neural signature kernels. Finally, we show that in the infinite-depth regime, finite-width controlled ResNets converge in distribution to Neural CDEs with random vector fields which, depending on whether the weights are shared across layers, are either time-independent and Gaussian or behave like a matrix-valued Brownian motion

Bragg gravity-gradiometer using the 1^1S0_0-3^3P1_1 intercombination transition of 88^{88}Sr

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 figure

Canceling the cavity length induced phase noise in an optical ring cavity for phase shift measurement and spin squeezing

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 figure

Squeezed state metrology with Bragg interferometers operating in a cavity

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.Weshow 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

Novel Adaptive Fixturing for Precise Micro-positioning of Thin Walled Parts

Fixtures are used to locate and hold workpieces during machining. Because workpiece surface errors and fixture set-up errors (called source errors) always exist, the fixtured workpiece will consequently have position and/or orientation errors (called resultant errors) that will definitely affect the final machining accuracy. This paper illustrates a novel adaptive fixturing based on active clamping forces for smart micropositioning of thin walled precision parts. The aim of obtaining a modular unit, reusable and exploitable to different industrial applications has been pursued during the design phase. The proposed adaptive fixturing device can lead to the following advantages: - to perform an automatic errors-free workpiece clamping and then drastically reduce the overall fixturing set up time; - to recover unwanted strains induced on the workpiece, in order to limit the amplitude of elastic strain recovery; - to perform, if necessary, active vibration control (AVC) in order to limit vibration/chatter effects induced by the cutting tool