Abstract Currently planned and constructed terrestrial detectors for gravitational waves and dark matter based on differential light-pulse atom interferometry are designed around three primary strategies to enhance their sensitivity: (i) Resonant-mode enhancement using multiple diamonds, (ii) large-momentum-transfer (LMT) techniques to increase arm separation within the interferometer, and (iii) very-long baseline schemes that increase the distance between the two interferometers. Both resonant-mode enhancement and LMT techniques result in a greater number of light pulses, making high pulse fidelity during atom-light interactions imperative. At the same time, increasing the number of diamonds in vertical configurations leads to taller atomic fountains, which consequently reduces the available distance between interferometers. As a result, the number of diamonds, LMT pulses, and the fountain height are interdependent parameters that must be carefully balanced. In this work, we present optimal configurations for multi-diamond geometries in resonant mode, explicitly accounting for the spatial extent of a single interferometer, considering constraints imposed by the baseline dimensions and atomic losses due to imperfect pulses. For this optimization, we numerically scan the relevant parameters such as initial position and momentum of the atomic cloud, transferred momenta, and number of loops. For each parameter set, we verify whether the imposed conditions are met and evaluate the resulting sensitivities to identify optimal configurations. We provide practical analytical relations to estimate the optimal number of pulses that should be applied. Many proposals beyond demonstrator experiments require pulse numbers that demand efficiencies not yet demonstrated with state-of-the-art momentum transfer techniques. As a result, the observed sensitivity falls short of expectations—an effect caused by both arm separation and atom loss per pulse—highlighting the urgent need for research aimed at improving pulse fidelities.
Abstract Currently planned and constructed terrestrial detectors for gravitational waves and dark matter based on differential light-pulse atom interferometry are designed around three primary strategies to enhance their sensitivity: (i) Resonant-mode enhancement using multiple diamonds, (ii) large-momentum-transfer (LMT) techniques to increase arm separation within the interferometer, and (iii) very-long baseline schemes that increase the distance between the two interferometers. Both resonant-mode enhancement and LMT techniques result in a greater number of light pulses, making high pulse fidelity during atom-light interactions imperative. At the same time, increasing the number of diamonds in vertical configurations leads to taller atomic fountains, which consequently reduces the available distance between interferometers. As a result, the number of diamonds, LMT pulses, and the fountain height are interdependent parameters that must be carefully balanced. In this work, we present optimal configurations for multi-diamond geometries in resonant mode, explicitly accounting for the spatial extent of a single interferometer, considering constraints imposed by the baseline dimensions and atomic losses due to imperfect pulses. For this optimization, we numerically scan the relevant parameters such as initial position and momentum of the atomic cloud, transferred momenta, and number of loops. For each parameter set, we verify whether the imposed conditions are met and evaluate the resulting sensitivities to identify optimal configurations. We provide practical analytical relations to estimate the optimal number of pulses that should be applied. Many proposals beyond demonstrator experiments require pulse numbers that demand efficiencies not yet demonstrated with state-of-the-art momentum transfer techniques. As a result, the observed sensitivity falls short of expectations—an effect caused by both arm separation and atom loss per pulse—highlighting the urgent need for research aimed at improving pulse fidelities.
This report presents the results of the 2012-2013 NASA Institute for Advanced Concepts (NIAC) Phase 1 Atom Interferometry for Detection of Gravitational Waves project. The origin of this GW (Gravitational Wave) detection concept using atoms can be traced to theoretical work that first appeared in 2008 and also to a satellite mission-focused followup study that was done in 2011. The goal of the current project was to explore both theoretical and technical issues surrounding the implementation of this idea, as well as to begin performing proof-of-concept experiments to validate critical aspects of the proposal.The top level trade space for the detector design is driven by the strategy employed to mitigate laser frequency noise, which, if uncontrolled, can mask GW signatures. One of the advantages of the atom interferometric approach is the possibility of single baseline detection (Fig. 1.1), even in the presence of laser noise. This is enabled by the differential measurement between the two ensembles of atoms, which can result in substantial laser noise suppression. The details of this suppression depend on the atomic physics techniques used to implement the atom interferometry. Specifically, we considered the effect on noise suppression that results from using traditional two-photon Raman transitions (with alkali atoms) and also single-photon transitions (with alkaline earth-like atoms).The interferometers shown in Fig 1.1(b) take advantage of single-photon transitions (as opposed to traditional Raman transitions) because using light pulses from one direction at a time allows for near perfect common-mode cancellation of laser phase noise, even for long baselines. This calls for the use of atomic transitions with an (ideally large) optical energy level difference with a long (greater than 1 second) lifetime, such as high-transitions routinely used for optical atomic clocks in species like Sr, Ca and Yb. Notably, large momentum transfer (LMT) atom optics - and the sensitivity enhancement they confer – can still be realized by simply adding additional pairs of alternating pulses to each beam splitter process. Section 3 reports on the theoretical work we performed to justify this GW detection protocol using single-photon transitions. This approach represents a new method for GW detection using atoms that is distinct from the original proposal from 2008. At the system level, we evaluated three architectures, each of which implements a different solution to the laser frequency noise issue. The first two designs are based on two-photon Raman transitions with Rb atoms. One of these is a three-satellite, multiple baseline design while the other is a two-satellite, single baseline design. The third proposal is a two-satellite, single baseline design that uses single-photon transitions with Sr atoms. These three architectures are described in more detail in Section 2. There are a number of known technical issues that we have started to address using ground-based experiments. These issues include atom technology development needs such as, for example, lower ensemble temperature requirements and large momentum transfer (LMT) atom optics. To this end, we have built a 10-meter scale atom drop tower, where we can perform proof-of-principle demonstrations of the proposed AGIS detector in an environment that permits more than 2.5 seconds of free-fall time. This facility allows for demonstration of atom interferometry with long interrogation time (seconds) and large atom wavepacket
Abstract Large-scale atom interferometers promise unrivaled strain sensitivity to mid-band gravitational waves, and will probe a new parameter space in the search for ultra-light scalar dark matter. These proposals require gradiometry with kilometer-scale baselines, a momentum separation above 104ℏk between interferometer arms, and optical transitions to long-lived clock states to reach the target sensitivities. Prohibitively high optical power and wavefront flatness requirements have thus far limited the maximum achievable momentum splitting. Here we propose a scheme for optical cavity enhanced atom interferometry, using circulating, spatially resolved pulses, and intracavity frequency modulation to meet these requirements. We present parameters for the realization of 20 kW circulating pulses in a 1 km interferometer enabling 104ℏk splitting on the 698 nm clock transition in 87Sr. This scheme addresses the presently insurmountable laser power requirements and is feasible in the context of a kilometer-scale atom interferometer facility.
Atom interferometers employing optical cavities to enhance the beam splitter pulses promise significant advances in science and technology, notably for future gravitational wave detectors. Long cavities, on the scale of hundreds of meters, have been proposed in experiments aiming to become demonstrators for gravitational wave detection at frequencies below 1 Hz, where laser interferometers, such as LIGO, have poor sensitivity. Our group at the Birmingham Institute of Gravitational Wave Astronomy has explored the fundamental limitations of two-mirror cavities for atomic beam splitting, and established upper bounds on the temperature of the atomic ensemble as a function of cavity length and three design parameters: the cavity g-factor, the bandwidth, and the optical suppression factor of the first and second order spatial modes. A lower bound to the cavity bandwidth which avoids elongation of the interaction time and maximizes power enhancement was found. An upper limit to cavity length is also found for symmetric two-mirror cavities. These key limitations impact the feasibility of long-baseline detectors, which suffer from a naturally larger bandwidth and worse optical suppression of higher order optical modes. Our findings will aid the design of current and future experiments using this technology, such as the MIGA experiment in Bordeaux. In the future we aim to fully model the effect that the imperfect optical wavefronts have on the atomic transitions.
Large momentum transfer (LMT) enhances the gravitational phase of a light-pulse atom interferometer by a factor n, while mirrorless operation with momentum-resolved detection can quadruple the phase-carrying quantum Fisher information. These gains compete in practice because the momentum-space fringe period scales as 1/n, making the fringe signal increasingly vulnerable to finite detector resolution. We analyze this trade-off in a solvable model with instantaneous lossless n-photon pulses, a Gaussian source, and Gaussian detection blur, allowing continuous interpolation between Kasevich--Chu and mirrorless geometries. Closed-form expressions for the blurred output distributions and classical Fisher information are obtained, with a fringe-phase averaging approximation whose error is exponentially suppressed and agrees with numerical simulations at the 10−8 level. We find that mirrorless operation surpasses a conventional interferometer with the same momentum transfer only when σp<0.91m/(nk0T). Fringe-based readout exhibits an optimal momentum transfer n∗≃0.93m/(σpk0T) and a resolution-limited sensitivity floor Δg≃4.4σp/(mTN), independent of photon momentum. When this criterion is not satisfied, partial mirror asymmetry can recover part of the enhancement, whereas population-based readout remains insensitive to detector blur and ultimately favors the conventional sequence at sufficiently large n. Estimates for 87Rb sensors show that the mirrorless advantage is primarily restricted to short-baseline instruments.
Abstract Multi-photon Bragg diffraction is a powerful method for fast, coherent momentum transfer of atom waves. However, laser noise, Doppler detunings, and cloud expansion limit its efficiency in large momentum transfer (LMT) pulse sequences. We present simulation studies of robust Bragg pulses developed through numerical quantum optimal control. Optimized pulse performance under noise and cloud inhomogeneities is analyzed and compared to analogous Gaussian and adiabatic rapid passage pulses in simulated LMT Mach–Zehnder interferometry sequences. The optimized pulses maintain robust population transfer and phase response over a broader range of noise, resulting in superior contrast in LMT sequences with thermal atom clouds and intensity inhomogeneities. Large optimized LMT sequences use lower pulse area than Gaussian pulses, making them less susceptible to spontaneous emission loss. The optimized sequences maintain over five times better contrast with tens of ℏ k momentum separation and offer more improvement with greater LMT. Such pulses could allow operation of Bragg atom interferometers with unprecedented sensitivity, improved contrast, and hotter atom sources.
The present cumulative thesis (Publications (I)–(III) [1– 3]) explores three complementary directions: (i) tunneling-based gravimetry, (ii) phase contributions of tunneled Ramsey clocks, and (iii) resource optimization for very-long-baseline atom interferometers designed for the detection of gravitational waves and dark matter. The development of atom interferometers and atomic clocks seeks to steadily increase the measurement sensitivity, with the ultimate bound set by the Heisenberg limit. Enhancements can be achieved by exploiting quantum phenomena such as entanglement and squeezing, which allow sensitivities below the shot-noise limit. Another fundamental quantum effect, tunneling, remains less explored in the context of metrology, despite its inherent quantum nature. While entanglement and squeezing have already been demonstrated in atom interferometers, tunneling has not yet been widely investigated for gravimetric sensing applications. Publication (I) explores two configurations of tunneling-based gravimeters using a matter-wave Fabry–Pérot interferometer. (i) In the transmission setup, the wave packet is prepared in front of the cavity generated by optical potentials and transmitted. (ii) In the tunneling setup, the wave packet is prepared inside the cavity, representing a configuration without a classical analogue. Through our numerical simulations of the wave packet dynamics, including gravitational effects, we find that gravity primarily alters the motion of the packet by accelerating, decelerating, and deforming it, which modifies in particular its width at impact. While a single Gaussian barrier shows no resonances, the Fabry–Pérot configuration supports multiple resonances, defining tunable working points and acting as a velocity filter. In Publication (II), we turn to the phase accumulated during tunneling, investigated via a Ramsey clock. The Ramsey clock consists of a superposition of two internal states, accumulating a phase that is read out via a Ramsey sequence. Adopting an operational definition where time is what you read off a clock, we identify a tunneling time associated with the tunneling phase, alongside relativistic contributions accumulated by the tunneled clock. This approach naturally unifies several conventional definitions of tunneling time. Furthermore, the tunneling phase can be amplified experimentally by introducing state-dependent barrier heights through differential light shifts. In Publication (III), we study differential geometries of terrestrial very-long baseline atom interferometers, currently in development for gravitational-wave and dark-matter detection. We analyze three strategies for signal enhancement: (i) large-momentum-transfer pulses to increase atom–light interaction points, (ii) resonant-mode enhancement by matching the interrogation time to the target frequency, and (iii) extending baseline lengths. The achievable number of pulses is limited by atomic losses, distributed between large-momentum-transfer sequences and number of diamonds. Additionally, more diamonds require taller atomic fountains, constrained by the finite baseline. Thus, a trade-off emerges between the number of large-momentum-transfer pulses, the number of diamonds, and the baseline length. Considering this interplay, we derive an analytical relation for the optimal number of pulses under given loss rates. We explicitly optimize the allocation of the available resources and account for the finite spatial extent of individual interferometers, baseline constraints, and atom loss from imperfect pulses.