We theoretically investigate supercurrents of ultracold atoms in angularly ac-shaken ring lattices subjected to external rotation. Our results demonstrate how these supercurrents can be harnessed for the development of high-precision atomtronic angular accelerometers. Using both analytical and numerical approaches within the Bose-Hubbard model framework, we demonstrate that a significant net atomic current arises when the lattice driving frequency is tuned to an integer fraction of the Bloch frequency, while the current averages to nearly zero away from such a resonance. In the single-particle regime, the resonance width scales inversely with the averaging time, thereby setting a fundamental Fourier-limited bound on the measurement's sensitivity. Strikingly, our numerical simulations demonstrate that this Fourier limit - a fundamental barrier in the non-interacting system - can be surpassed by introducing weak interactions between atoms. In the interacting regime, the sensitivity surpasses the Fourier-limited scaling with the averaging time, achieving an improvement of at least two orders of magnitude over the single-particle scenario, and exceeding the performance of previously proposed ultracold-atom-based angular accelerometers. These findings pave the way for developing new atomic-current-based inertial sensors with interaction-enhanced sensitivity.
We theoretically investigate supercurrents of ultracold atoms in angularly ac-shaken ring lattices subjected to external rotation. Our results demonstrate how these supercurrents can be harnessed for the development of high-precision atomtronic angular accelerometers. Using both analytical and numerical approaches within the Bose-Hubbard model framework, we demonstrate that a significant net atomic current arises when the lattice driving frequency is tuned to an integer fraction of the Bloch frequency, while the current averages to nearly zero away from such a resonance. In the single-particle regime, the resonance width scales inversely with the averaging time, thereby setting a fundamental Fourier-limited bound on the measurement's sensitivity. Strikingly, our numerical simulations demonstrate that this Fourier limit - a fundamental barrier in the non-interacting system - can be surpassed by introducing weak interactions between atoms. In the interacting regime, the sensitivity surpasses the Fourier-limited scaling with the averaging time, achieving an improvement of at least two orders of magnitude over the single-particle scenario, and exceeding the performance of previously proposed ultracold-atom-based angular accelerometers. These findings pave the way for developing new atomic-current-based inertial sensors with interaction-enhanced sensitivity.
Atom interferometers provide exquisite measurements of the properties of noninertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing. Here we explore the role of interactions in an analogy between atomic gyroscopes and SQUIDs, motivated by recent experiments realizing ring-shaped traps for ultracold atoms. We explore the one-dimensional limit of these ring systems with a moving weak barrier, such as that provided by a blue-detuned laser beam. In this limit, we employ Luttinger liquid theory and find an analogy with the superconducting phase-slip qubit, in which the topological charge associated with persistent currents can be put into superposition. In particular, we find that strongly interacting atoms in such a system could be used for precision rotation sensing. We compare the performance of this new sensor to an equivalent noninteracting atom interferometer, and find improvements in sensitivity and bandwidth beyond the atomic shot-noise limit.
The ability to generate and tune quantized persistent supercurrents is crucial for building superconducting or atomtronic devices with novel functionalities. In ultracold atoms, previous methods for generating quantized supercurrents are generally based on dynamical processes to prepare atoms in metastable excited states. Here, we show that arbitrary quantized circulation states can be adiabatically prepared and tuned as the ground state of a ring-shaped Bose-Einstein condensate by utilizing spin--orbital-angular-momentum (SOAM) coupling and an external potential. There exists superfluid hysteresis for tuning supercurrents between different quantization values with nonlinear atomic interactions, which is explained by developing a nonlinear Landau-Zener theory. Our work will provide a powerful platform for studying SOAM-coupled ultracold atomic gases and building atomtronic circuits.
Atomtronic quantum sensors based on trapped superfluids offer a promising platform for high-precision inertial measurements where the dynamics of quantized vortices can serve as sensitive probes of external forces. We analytically investigate the persistent current oscillations between two density-coupled Bose-Einstein condensate rings of equal radius and show that the vortex dynamics is governed by low-energy acoustic excitations circulating through the condensate bulk. The oscillation frequency and damping rate are quantitatively predicted by a simplified hydrodynamic model, in agreement with Bogoliubov–de Gennes analysis and Gross-Pitaevskii simulations. We identify the critical dissipation separating persistent oscillations from overdamped vortex localization. Furthermore, we demonstrate that periodic modulation of the interring barrier at resonant frequencies enables controlled vortex transfer even when the condensates are well separated in density. These results clarify the role of collective hydrodynamic modes in circulation transfer and establish a framework for employing vortex dynamics in atomtronic quantum technologies.
Persistent currents–inviscid quantized flow around an atomic circuit–are a crucial building block of atomtronic devices. We investigate how acceleration influences the transfer of persistent currents between two density-connected, ring-shaped atomic Bose-Einstein condensates, joined by a tunable weak link that controls system topology. We find that the acceleration of this system modifies both the density and phase dynamics between the rings, leading to a bias in the periodic vortex oscillations studied in T. Bland et al., Phys. Rev. Research 4, 043171 (2022). Accounting for dissipation suppressing such vortex oscillations, the acceleration facilitates a unilateral vortex transfer to the leading ring. We analyze how this transfer depends on the weak-link amplitude, the initial persistent current configuration, and the acceleration strength and direction. Characterization of the sensitivity to these parameters paves the way for a new platform for acceleration measurements, for which we outline a proof-of-concept ultracold double-ring accelerometer.
Matter-wave interferometers show great a potential for improving inertial sensing. The absence of drifts recommends them for a variety of applications in geodesy, navigation, or fundamental physics. Here, ultracold atomic ensembles, featuring a velocity distribution well below the photon recoil velocity, open up new perspectives. In contrast to standard laser cooling methods, they allow to reach better beam-splitting efficiencies and, hence, a higher contrast as well as to reduce systematic uncertainties and biases. Presently, Bose-Einstein condensates (BECs) provide the means to achieve the lowest expansion energies of few picokelvin. Indeed, the momentum distribution of a BEC can be further narrowed after reaching the regime of ballistic expansion, where all mean field energy is converted to kinetic energy, by the application of the delta-kick collimation technique. With such ensembles, Bragg processes can be driven with an efficiency of above 95% as well as Bloch oscillations performed without large atomic losses or dephasing. Both enable efficient large momentum transfer in interferometers to enhance their sensitivity for inertial effects. In a so-called twin-lattice atom interferometers more than thousand photon recoils are used to form compact but sensitive atom interferometers. These methods not only bring in reach extremely accurate gravimeters and accelerometers but also gyroscopes. Like the Sagnac effect in ring laser or fiber gyroscopes, the sensitivity of atom interferometers to rotations increases with the space-time area enclosed by the interferometer. In the case of light interferometers, the latter can be enlarged by forming multiple fiber loops. However, the equivalent for matter-wave interferometers remains an experimental challenge. An atom interferometer with scalable area may be formed in a twin lattice combined with a relaunch mechanism to obtain multi loops as well. Due to this scalability, it offers the perspective of reaching unprecedented sensitivities for rotations in comparably compact sensor head setups. Moreover, atom-chip technologies offer the possibility to generate a BEC and perform delta-kick collimation in a fast and reliable away, paving the way for field-deployable miniaturized atomic devices. Last but not least, the extremely low expansion energies of BECs open up to extend the time atoms spend in the interferometer to tens of seconds. This brings in reach unprecedented sensitivities in space-borne applications such as satellite geodesy.
Ultra-cold atoms are highly sensitive to both inertial effects and electromagnetic fields, making atom interferometers excellent candidates for a variety of precision sensing applications. Furthermore, highly tunable atomic interactions combined with well established experimental techniques for trapping, cooling and manipulating ensembles of ultra-cold atoms, make them well suited to quantum enhancement. For these reasons, ensembles of ultra-cold atoms are excellent candidates for quantum-enhanced measurement devices. Broadly, this thesis presents a number of theoretical results which share the aim of progressing the proof-of-principle regime of current experiments to genuinely useful, ultra-precise quantum enhanced sensors.In Chapter 4 we explore the challenge of devising a useful, quantum-enhanced inertial measurement - to date no such experiment has been performed. Specifically, we present a model of a spin-squeezed rotation sensor utilising the Sagnac effect in a spin-1 Bose-Einstein condensate in a ring trap. The two input states for the interferometer are seeded using Raman pulses with Laguerre-Gauss beams and are amplified by the bosonic enhancement of spin-exchange collisions, resulting in spin-squeezing and potential quantum enhancement in the interferometry. The ring geometry has an advantage over separated beam path atomic rotation sensors due to the uniform condensate density. We model the interferometer both analytically and numerically for realistic experimental parameters and find that significant quantum enhancement is possible. However, this enhancement is partially degraded when working in a regime with strong atomic interactions, indicating that perhaps interaction-based squeezing is not the best route to a quantum-enhanced inertial measurement.Continuing the theme of practical spin-squeezing with atomic interactions, in Chapter 5 we explore methods to combat detection noise, which is currently one of the most significant experimental limitations for quantum-enhanced atom interferometers. A useful quantum-enhanced interferometer requires nonclassical states with a high particle number and the (close to) optimal exploitation of the states' quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cram´er-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. “Interaction-based readout” protocols have been shown to allow optimal interferometry or to provide robustness against detection noise at the expense of optimality. We prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily-accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal and robust quantum metrology is achievable in current spin-squeezing experiments.Macroscopic superposition states (known as spin-cat states in atomic ensembles) achieve the ultimate quantum precision limit. In Chapters 6 and 7 we turn our attention to studying decoherence that arises in creating and manipulating these states. In its simplest form, decoherence occurs when a quantum state is entangled with a second state, but the results of measurements made on the second state are not accessible. As the second state has effectively ``measured the first, in Chapter 6 we argue that the quantum Fisher information is the relevant metric for predicting and quantifying this kind of decoherence. In particular we apply this analysis to studying decoherence imparted on spin-cat states via atom-light interactions, which are an essential process in atom interferometry. We find that, compared to classical atomic states, spin-cat states are highly susceptible to this kind of decoherence. We investigate the required optical field occupation, such that this decoherence is negligible.Finally, in Chapter 7 we explore the deleterious effects of spatial and phase dynamics during the creation of spin-cat states via one-axis twisting in a two-component Bose-Einstein condensate. We simulate the breathing dynamics in 1 spatial dimension, employing the method of Sinatra and Castin, whereby the state is expanded into the Fock basis, with each basis state evolving within the Hartree-Fock approximation. This method is able to capture both multi-mode effects and quantum correlations, which allows us to calculate the quantum Fisher information. We find that so long as the time taken for the condensate to reach a spin-cat state is an integer multiple of the breathing period, it is sometimes possible to realise something extremely close to a spin-cat state, despite significant dynamics. These results indicate that large non-linearities, and the associated speed-up in entangling dynamics, are not fundamentally incompatible with the production of fragile, highly entangled states such as spin-cat states.