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Precision measurements with ultracold atoms and molecules are primed to probe beyond-the-Standard Model physics. Isotopologues of homonuclear molecules are a natural testbed for new Yukawa-type mass-dependent forces at nanometer scales, complementing existing mesoscopic-body and neutron scattering experiments. Here we propose using isotopic shift measurements in molecular lattice clocks to constrain these new interactions from new massive scalar particles in keV$/c^2$ range: the new interaction would impart an extra isotopic shift to molecular levels on top of one predicted by the Standard Model. For the strontium dimer, a Hz-level agreement between experiment and theory could constrain the coupling of the new particles to hadrons by up to an order-of-magnitude over the most stringent existing experiments., Comment: 7 pages, 4 figures, submitted

Molecular lattice clocks enable the search for new physics, such as fifth forces or temporal variations of fundamental constants, in a manner complementary to atomic clocks. Blackbody radiation (BBR) is a major contributor to the systematic error budget of conventional atomic clocks and is notoriously difficult to characterize and control. Here, we combine infrared Stark-shift spectroscopy in a molecular lattice clock and modern quantum chemistry methods to characterize the polarizabilities of the Sr$_2$ molecule from dc to infrared. Using this description, we determine the static and dynamic blackbody radiation shifts for all possible vibrational clock transitions to the $10^{-16}$ level. This constitutes an important step towards mHz-level molecular spectroscopy in Sr$_2$, and provides a framework for evaluating BBR shifts in other homonuclear molecules., Comment: 7 pages, 4 figures, added supplemental with 3 extra figures

Neutral quantum absorbers in optical lattices have emerged as a leading platform for achieving clocks with exquisite spectroscopic resolution. However, the studies of these clocks and their systematic shifts have so far been limited to atoms. Here, we extend this architecture to an ensemble of diatomic molecules and experimentally realize an accurate lattice clock based on pure molecular vibration. We evaluate the leading systematics, including the characterization of nonlinear trap-induced light shifts, achieving a total systematic uncertainty of $4.6\times10^{-14}$. The absolute frequency of the vibrational splitting is measured to be 31 825 183 207 592.8(5.1) Hz, enabling the dissociation energy of our molecule to be determined with record accuracy. Our results represent an important milestone in molecular spectroscopy and THz-frequency standards, and may be generalized to other neutral molecular species with applications for fundamental physics, including tests of molecular quantum electrodynamics and the search for new interactions., Comment: 17 pages, 8 figures

The extraordinary success in laser cooling, trapping, and coherent manipulation of atoms has energized the efforts in extending this exquisite control to molecules. Not only are molecules ubiquitous in nature, but the control of their quantum states offers unparalleled access to fundamental constants and possible physics beyond the Standard Model. Quantum state manipulation of molecules can enable high-precision measurements including tests of fundamental symmetries and searches for new particles and fields. At the same time, their complex internal structure presents experimental challenges to overcome in order to gain sensitivity to new physics. In this Perspective, we review recent developments in this thriving new field. Moreover, throughout the text we discuss many current and future research directions that have the potential to place molecules at the forefront of fundamental science., Comment: Perspective article

The last decade has seen unprecedented effort in dark matter model building at all mass scales coupled with the design of numerous new detection strategies. Transformative advances in quantum technologies have led to a plethora of new high-precision quantum sensors and dark matter detection strategies for ultralight ($<10\,$eV) bosonic dark matter that can be described by an oscillating classical, largely coherent field. This white paper focuses on searches for wavelike scalar and vector dark matter candidates., Comment: Snowmass 2021 White Paper

We demonstrate optical cycling and sub-Doppler laser cooling of a cryogenic buffer-gas beam of calcium monohydride (CaH) molecules. We measure vibrational branching ratios for laser cooling transitions for both excited electronic states A and B. We measure further that repeated photon scattering via the $A\leftarrow X$ transition is achievable at a rate of $\sim$ $1.6\times10^6$ photons/s and demonstrate the interaction-time limited scattering of $\sim$ $200$ photons by repumping the largest vibrational decay channel. We also demonstrate the ability to sub-Doppler cool a molecular beam of CaH through the magnetically assisted Sisyphus effect. Using a standing wave of light, we lower the molecular beam's transverse temperature from $12.2(1.2)$ mK to $5.7(1.1)$ mK. We compare these results to sub-Doppler forces modeled using optical Bloch equations and Monte Carlo simulations of the molecular beam trajectories. This work establishes a clear pathway for creating a magneto-optical trap (MOT) of CaH molecules. Such a MOT could serve as a starting point for production of ultracold hydrogen gas via dissociation of a trapped CaH cloud., Comment: 11 pages, 4 figures, 3 tables

We report efficient all-optical creation of an ultracold gas of alkaline-earth-metal dimers, $^{88}\rm{Sr}_2$, in their absolute ground state. Starting with weakly bound singlet molecules formed by narrow-line photoassociation in an optical lattice, followed by stimulated Raman adiabatic passage (STIRAP) via a singlet-dominant channel in the $(1)0_u^+$ excited potential, we prepare pure samples of more than 5500 molecules in $X^1\Sigma_g^+(v=0,J=0)$. We observe two-body collisional loss rates close to the universal limit for both the least bound and most bound vibrational states in $X^1\Sigma_g^+$. We demonstrate the enhancement of STIRAP efficiency in a magic-wavelength optical lattice where thermal decoherence is eliminated. Our results pave the way for the use of alkaline-earth-metal dimers for high-precision spectroscopy, and indicate favorable prospects for robust quantum state preparation of ultracold molecules involving closed-shell atoms, as well as molecule assembly in deep optical traps tuned to a magic wavelength.

We discuss how molecule-based searches offer complementary probes to study the violation of fundamental symmetries. These experiments have the potential to probe not only the electron EDM, but also hadronic CPV phenomena. Future experimental developments will offer generic sensitivity to probe flavor neutral sources of both leptonic and hadronic CPV at scales of $\geq$ 100 TeV, and flavor changing CPV at scales of $\geq$ 1000 TeV.

Optical trapping of molecules with long coherence times is crucial for many protocols in quantum information and metrology. However, the factors that limit the lifetimes of the trapped molecules remain elusive and require improved understanding of the underlying molecular structure. Here we show that measurements of vibronic line strengths in weakly and deeply bound $^{88}$Sr$_2$ molecules, combined with \textit{ab initio} calculations, allow for unambiguous identification of vibrational quantum numbers. This, in turn, enables the construction of refined excited potential energy curves that inform the selection of magic wavelengths which facilitate long vibrational coherence. We demonstrate Rabi oscillations between far-separated vibrational states that persist for nearly 100 ms.

Vibrational branching ratios in the B$^2\Sigma^+$ -- X$^2\Sigma^+$ and A$^2\Pi$ -- X$^2\Sigma^+$ optical-cycling transitions of BaH molecules are investigated using measurements and {\it ab initio} calculations. The experimental values are determined using fluorescence and absorption detection. The observed branching ratios have a very sensitive dependence on the difference in the equilibrium bond length between the excited and ground state, $\Delta r_e$: a 1 pm (.5\%) displacement can have a 25\% effect on the branching ratios but only a 1\% effect on the lifetime. The measurements are combined with theoretical calculations to reveal a preference for a particular set of published spectroscopic values for the B$^2\Sigma^+$ state ($\Delta r_e^{B-X}$ = +5.733 pm), while a larger bond-length difference ($\Delta r_e^{B-X} = 6.3-6.7$ pm) would match the branching-ratio data even better. By contrast, the observed branching ratio for the A$^2\Pi_{3/2}$ -- X$^2\Sigma^+$ transition is in excellent agreement with both the {\it ab initio} result and the spectroscopically measured bond lengths. This shows that care must be taken when estimating branching ratios for molecular laser cooling candidates, as small errors in bond-length measurements can have outsize effects on the suitability for laser cooling. Additionally, our calculations agree more closely with experimental values of the B$^2\Sigma^+$ state lifetime and spin-rotation constant, and revise the predicted lifetime of the H$^2\Delta$ state to 9.5 $\mu$s.

Atomic lattice clocks have spurred numerous ideas for tests of fundamental physics, detection of general relativistic effects, and studies of interacting many-body systems. On the other hand, molecular structure and dynamics offer rich energy scales that are at the heart of new protocols in precision measurement and quantum information science. Here we demonstrate a fundamentally distinct type of lattice clock that is based on vibrations in diatomic molecules, and present coherent Rabi oscillations between weakly and deeply bound molecules that persist for 10's of milliseconds. This control is made possible by a state-insensitive magic lattice trap that weakly couples to molecular vibronic resonances and enhances the coherence time between molecules and light by several orders of magnitude. The achieved quality factor $Q=8\times10^{11}$ results from 30-Hz narrow resonances for a 25-THz clock transition in Sr$_2$. Our technique of extended coherent manipulation is applicable to long-term storage of quantum information in qubits based on ultracold polar molecules, while the vibrational clock enables precise probes of interatomic forces, tests of Newtonian gravitation at ultrashort range, and model-independent searches for electron-to-proton mass ratio variations.

At ultralow energies, atoms and molecules undergo collisions and reactions that are best described in terms of quantum mechanical wave functions. In contrast, at higher energies these processes can be understood quasiclassically. Here, we investigate the crossover from the quantum mechanical to the quasiclassical regime both experimentally and theoretically for photodissociation of ultracold diatomic strontium molecules. This basic reaction is carried out with a full control of quantum states for the molecules and their photofragments. The photofragment angular distributions are imaged, and calculated using a quantum mechanical model as well as the WKB and a semiclassical approximation that are explicitly compared across a range of photofragment energies. The reaction process is shown to converge to its high-energy (axial recoil) limit when the energy exceeds the height of any reaction barriers. This phenomenon is quantitatively investigated for two-channel photodissociation using intuitive parameters for the channel amplitude and phase. While the axial recoil limit is generally found to be well described by a commonly used quasiclassical model, we find that when the photofragments are identical particles, their bosonic or fermionic quantum statistics can cause this model to fail, requiring a quantum mechanical treatment even at high energies., Comment: 13 pages, 6 figures

Processes that break molecular bonds are typically observed with molecules occupying a mixture of quantum states and successfully described with quasiclassical models, while a few studies have explored the distinctly quantum mechanical low-energy regime. Here we use photodissociation of diatomic strontium molecules to demonstrate the crossover from the ultracold, quantum regime where the photofragment angular distributions strongly depend on the kinetic energy, to the energy-independent quasiclassical regime. Using time-of-flight velocity map imaging for photodissociation channels with millikelvin reaction barriers, we explore photofragment energies in the 0.1-300 mK range experimentally and up to 3 K theoretically, and discuss the energy scale at which the crossover occurs. Furthermore, we find that the effects of quantum statistics can unexpectedly persist to high photodissociation energies., Comment: 6 pages, 4 figures

Photodissociation of a molecule produces a spatial distribution of photofragments determined by the molecular structure and the characteristics of the dissociating light. Performing this basic chemical reaction at ultracold temperatures allows its quantum mechanical features to dominate. In this regime, weak applied fields can be used to control the reaction. Here, we photodissociate ultracold diatomic strontium in magnetic fields below 10 G and observe striking changes in photofragment angular distributions. The observations are in excellent qualitative agreement with a multichannel quantum chemistry model that includes nonadiabatic effects and predicts strong mixing of partial waves in the photofragment energy continuum. The experiment is enabled by precise quantum-state control of the molecules., Comment: 8 pages, 3 figures

Barium monohydride (BaH) is an attractive candidate for extending laser cooling and trapping techniques to diatomic hydrides. The apparatus and high-resolution optical spectroscopy presented here demonstrate progress toward this goal. A cryogenic buffer-gas-cooled molecular beam of BaH was constructed and characterized. Pulsed laser ablation into cryogenic helium buffer gas delivers $\sim1\times10^{10}$ molecules/sr/pulse in the X$^2\Sigma^+$ ($v''=0,N''=1$) state of primary interest. More than $1\times10^7$ of these molecules per pulse enter the downstream science region with forward velocities below 100 m/s and transverse temperature of 0.1 K. This molecular beam enabled high-resolution optical spectra of BaH in quantum states relevant to laser slowing and cooling. The reported measurements include hyperfine structure and magnetic $g$ factors in the X$^2\Sigma^+$, B$^2\Sigma^+$, and A$^2\Pi_{1/2}$ states., Comment: Improved velocity distributions

Chemical reactions at ultracold temperatures are expected to be dominated by quantum mechanical effects. Although progress towards ultracold chemistry has been made through atomic photoassociation, Feshbach resonances and bimolecular collisions, these approaches have been limited by imperfect quantum state selectivity. In particular, attaining complete control of the ground or excited continuum quantum states has remained a challenge. Here we achieve this control using photodissociation, an approach that encodes a wealth of information in the angular distribution of outgoing fragments. By photodissociating ultracold 88Sr2 molecules with full control of the low-energy continuum, we access the quantum regime of ultracold chemistry, observing resonant and nonresonant barrier tunneling, matter-wave interference of reaction products and forbidden reaction pathways. Our results illustrate the failure of the traditional quasiclassical model of photodissociation and instead are accurately described by a quantum mechanical model. The experimental ability to produce well-defined quantum continuum states at low energies will enable high-precision studies of long-range molecular potentials for which accurate quantum chemistry models are unavailable, and may serve as a source of entangled states and coherent matter waves for a wide range of experiments in quantum optics.

We describe a simple experimental apparatus for laser ablation of barium monohydride (BaH) molecules and the study of their rovibrational spectra that are relevant to direct laser cooling. We present a detailed analysis of the properties of ablation plumes that can improve the understanding of surface ablation and deposition technologies. A range of absorption spectroscopy and collisional thermalization regimes has been studied. We directly measured the Franck-Condon factor of the $\mathrm{B}^2\Sigma^+(v'=0)\leftarrow\mathrm{X}^2\Sigma^+(v"=1)$ transition. Prospects for production of a high luminosity cryogenic BaH beam are outlined. This molecule is a promising candidate for laser cooling and ultracold fragmentation, both of which are precursors to novel experiments in many-body physics and precision measurement., Comment: 11 pages, 10 figures

Optical frequency combs, coherent light sources that connect optical frequencies with microwave oscillations, have become the enabling tool for precision spectroscopy, optical clockwork and attosecond physics over the past decades. Current benchmark systems are self-referenced femtosecond mode-locked lasers, but four-wave-mixing in high-Q resonators have emerged as alternative platforms. Here we report the generation and full stabilization of CMOS-compatible optical frequency combs. The spiral microcomb's two degrees-of-freedom, one of the comb line and the native 18 GHz comb spacing, are first simultaneously phase-locked to known optical and microwave references. Second, with pump power control, active comb spacing stabilization improves the long-term stability by six orders-of-magnitude, reaching an instrument-limited 3.6 mHz/sqrt(t) residual instability. Third, referencing thirty-three of the nitride frequency comb lines against a fiber comb, we demonstrate the comb tooth-to-tooth frequency relative inaccuracy down to 53 mHz and 2.8x10-16, heralding unprecedented chip-scale applications in precision spectroscopy, coherent communications, and astronomical spectrography.

In weakly bound diatomic molecules, energy levels are closely spaced and thus more susceptible to mixing by magnetic fields than in the constituent atoms. We use this effect to control the strengths of forbidden optical transitions in $^{88}$Sr$_2$ over 5 orders of magnitude with modest fields by taking advantage of the intercombination-line threshold. The physics behind this remarkable tunability is accurately explained with both a simple model and quantum chemistry calculations, and suggests new possibilities for molecular clocks. We show how mixed quantization in an optical lattice can simplify molecular spectroscopy. Furthermore, our observation of formerly inaccessible $f$-parity excited states offers an avenue for improving theoretical models of divalent-atom dimers., Comment: 8 pages, 4 figures

The study of ultracold molecules tightly trapped in an optical lattice can expand the frontier of precision measurement and spectroscopy, and provide a deeper insight into molecular and fundamental physics. Here we create, probe, and image microkelvin $^{88}$Sr$_2$ molecules in a lattice, and demonstrate precise measurements of molecular parameters as well as coherent control of molecular quantum states using optical fields. We discuss the sensitivity of the system to dimensional effects, a new bound-to-continuum spectroscopy technique for highly accurate binding energy measurements, and prospects for new physics with this rich experimental system., Comment: 12 pages, 4 figures

Weakly bound molecules have physical properties without atomic analogues, even as the bond length approaches dissociation. In particular, the internal symmetries of homonuclear diatomic molecules result in formation of two-body superradiant and subradiant excited states. While superradiance has been demonstrated in a variety of systems, subradiance is more elusive due to the inherently weak interaction with the environment. Here we characterize the properties of deeply subradiant molecular states with intrinsic quality factors exceeding $10^{13}$ via precise optical spectroscopy with the longest molecule-light coherent interaction times to date. We find that two competing effects limit the lifetimes of the subradiant molecules, with different asymptotic behaviors. The first is radiative decay via weak magnetic-dipole and electric-quadrupole interactions. We prove that its rate increases quadratically with the bond length, confirming quantum mechanical predictions. The second is nonradiative decay through weak gyroscopic predissociation, with a rate proportional to the vibrational mode spacing and sensitive to short-range physics. This work bridges the gap between atomic and molecular metrology based on lattice-clock techniques, yielding new understanding of long-range interatomic interactions and placing ultracold molecules at the forefront of precision measurements., Comment: 12 pages, 6 figures

Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold $^{88}$Sr$_2$ molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite $f$-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art \textit{ab initio} model., Comment: 5 pages, 3 figures, 1 table

We have produced large samples of ultracold $^{88}$Sr$_2$ molecules in the electronic ground state in an optical lattice. The molecules are bound by 0.05 cm$^{-1}$ and are stable for several milliseconds. The fast, all-optical method of molecule creation via intercombination line photoassociation relies on a near-unity Franck-Condon factor. The detection uses a weakly bound vibrational level corresponding to a very large dimer. This is the first of two steps needed to create Sr$_2$ in the absolute ground quantum state. Lattice-trapped Sr$_2$ is of interest to frequency metrology and ultracold chemistry., Comment: 5 pages, 3 figures

We report on the implementation of a dynamically configurable, servomotor- controlled, permanent magnet Zeeman slower for quantum optics experiments with ultracold atoms and molecules. This atom slower allows for switching between magnetic field profiles that are designed for different atomic species. Additionally, through feedback on the atom trapping rate, we demonstrate that computer-controlled genetic optimization algorithms applied to the magnet positions can be used in situ to obtain field profiles that maximize the trapping rate for any given experimental conditions. The device is lightweight, remotely controlled, and consumes no power in steady state; it is a step toward automated control of quantum optics experiments., Comment: 10 pages, 5 figures; accepted to JOSA B

Precision measurements with ultracold molecules require development of robust and sensitive techniques to produce and interrogate the molecules. With this goal, we theoretically analyze factors that affect frequency measurements between rovibrational levels of the Sr$_2$ molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio. Sr$_2$ is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr \cite{Zelevinsky2008}. The analysis includes calculations of two-photon transition dipole moments between deeply and weakly bound vibrational levels, lifetimes of intermediate excited states, and Stark shifts of the vibrational levels by the optical lattice field, including possibilities of Stark-cancellation trapping., Comment: 8 pages, 10 figures

Optical atomic clocks promise timekeeping at the highest precision and accuracy, owing to their high operating frequencies. Rigorous evaluations of these clocks require direct comparisons between them. We have realized a high-performance remote comparison of optical clocks over km-scale urban distances, a key step for development, dissemination, and application of these optical standards. Through this remote comparison and a proper design of lattice-confined neutral atoms for clock operation, we evaluate the uncertainty of a strontium (Sr) optical lattice clock at the 1x10-16 fractional level, surpassing the best current evaluations of cesium (Cs) primary standards. We also report on the observation of density-dependent effects in the spin-polarized fermionic sample and discuss the current limiting effect of blackbody radiation-induced frequency shifts., Comment: To be published in Science, 2008

The $^1\mathrm{S}_0$-$^3\mathrm{P}_0$ clock transition frequency $\nu_\text{Sr}$ in neutral $^{87}$Sr has been measured relative to the Cs standard by three independent laboratories in Boulder, Paris, and Tokyo over the last three years. The agreement on the $1\times 10^{-15}$ level makes $\nu_\text{Sr}$ the best agreed-upon optical atomic frequency. We combine periodic variations in the $^{87}$Sr clock frequency with $^{199}$Hg$^+$ and H-maser data to test Local Position Invariance by obtaining the strongest limits to date on gravitational-coupling coefficients for the fine-structure constant $\alpha$, electron-proton mass ratio $\mu$ and light quark mass. Furthermore, after $^{199}$Hg$^+$, $^{171}$Yb$^+$ and H, we add $^{87}$Sr as the fourth optical atomic clock species to enhance constraints on yearly drifts of $\alpha$ and $\mu$., Comment: Published version. 4 pages, 4 figures

We propose a precision measurement of time variations of the proton-electron mass ratio using ultracold molecules in an optical lattice. Vibrational energy intervals are sensitive to changes of the mass ratio. In contrast to measurements that use hyperfine-interval-based atomic clocks, the scheme discussed here is model-independent and does not require separation of time variations of different physical constants. The possibility of applying the zero-differential-Stark-shift optical lattice technique is explored to measure vibrational transitions at high accuracy., Comment: 4 pages, 4 figures

With ultracold $^{88}$Sr in a 1D magic wavelength optical lattice, we performed narrow line photoassociation spectroscopy near the $^1$S$_0 - ^3$P$_1$ intercombination transition. Nine least-bound vibrational molecular levels associated with the long-range $0_u$ and $1_u$ potential energy surfaces were measured and identified. A simple theoretical model accurately describes the level positions and treats the effects of the lattice confinement on the line shapes. The measured resonance strengths show that optical tuning of the ground state scattering length should be possible without significant atom loss., Comment: 4 pages, 4 figures

With ultracold $^{87}$Sr confined in a magic wavelength optical lattice, we present the most precise study (2.8 Hz statistical uncertainty) to-date of the $^1S_0$ - $^3P_0$ optical clock transition with a detailed analysis of systematic shifts (20 Hz uncertainty) in the absolute frequency measurement of 429 228 004 229 867 Hz. The high resolution permits an investigation of the optical lattice motional sideband structure. The local oscillator for this optical atomic clock is a stable diode laser with its Hz-level linewidth characterized across the optical spectrum using a femtosecond frequency comb., Comment: 4 pages, 4 figures, 1 table

This paper has been temporarily withdrawn. Highly nonlinear dependences of 4He 2^3S - 2^3P lines on pressure were observed in vapor cell saturation spectroscopy. Line shifts agree with those expected from light-pressure-induced perturbation of atomic velocity distribution. In the lin-perp-lin pump and probe polarization configuration, multilevel atomic structure must be taken into account. For a two-level atom, the shift magnitude is determined by the collisional time constant, but when the system has dark states there is an additional time constant due to optical pumping. The collisional and optical time constants compete, and become equal at a certain pressure p_0. Saturation signal vanishes at p_0 whereas signal due to light pressure remains. This leads to a dependence of line centers on pressure that exhibits apparently singular behavior at p_0. The 2S - 2P(J=1) line shift reaches the natural half width. Vapor cells may be more suitable for investigation of this effect than atomic beams since the shifts vanish at sufficiently high pressures. Two ways of controlling the shifts for the helium 2P fine structure measurement are discussed., Comment: This paper has been temporarily withdrawn

This paper has been temporarily withdrawn by the authors. In the process of 4He 2P fine structure measurement in a vapor cell, highly nonlinear dependences of 2S_1 - 2P_J intervals on helium density are observed and attributed to light pressure. If total angular momentum of the excited state is not greater than that of the ground state, there are large polarization dependences and variations of shifts with helium pressure that exhibit apparent singularities. A pressure-variable cell may be a better system for control of this effect than an atomic beam. A method of avoiding the shifts for the fine structure measurement is suggested., Comment: This paper has been temporarily withdrawn

We have shown via explicit analysis as well as numerical simulation the design of two large angle interferometers employing two-photon pulses. The first one uses the technique of adiabatic following in a dark state to produce a large splitting angle atomic interferometer that is capable of producing one dimensional gratings with spacings as small as 2 nm. Unlike other large angle interferometers, this technique is not sensitive to errors in optical pulse area and decoherence from excited state decay. This may lead to a nearly two orders of magnitude improvement in the sensitivity of devices such as atomic gyroscopes, which are already as good as the best laser gyroscopes. The second interferometer uses the technique of Raman pulses to produce a two-dimensional interferometer, with independent choice of grating spacings in each direction, each being as small as 2 nm. This scheme may enable one to produce uniform arrays of quantum dots with dimensions of only a few nm on each side. In addition, it may be possible to generalize this process to produce arbitrary patterns with the same type of resolution., Comment: 16 pages, 7 figures