This paper explores the sensitivity gains afforded by spin-squeezed states in atom interferometry, in particular using Bragg diffraction. We introduce a generalised input-output formalism that accurately describes realistic, non-unitary interferometers, including losses due to velocity selectivity and scattering into undesired momentum states. This formalism is applied to evaluate the performance of one-axis twisted spin-squeezed states in improving phase sensitivity. Our results show that by carefully optimising the parameters of the Bragg beam splitters and controlling the degree of squeezing, it is possible to improve the sensitivity of the interferometer by several dB with respect to the standard quantum limit despite realistic levels of losses in light pulse operations. However, the analysis also highlights the challenges associated with achieving these improvements in practice, most notably the impact of finite temperature on the benefits of entanglement. The results suggest ways of optimising interferometric setups to exploit quantum entanglement under realistic conditions, thereby contributing to advances in precision metrology with atom interferometers.
This paper explores the sensitivity gains afforded by spin-squeezed states in atom interferometry, in particular using Bragg diffraction. We introduce a generalised input-output formalism that accurately describes realistic, non-unitary interferometers, including losses due to velocity selectivity and scattering into undesired momentum states. This formalism is applied to evaluate the performance of one-axis twisted spin-squeezed states in improving phase sensitivity. Our results show that by carefully optimising the parameters of the Bragg beam splitters and controlling the degree of squeezing, it is possible to improve the sensitivity of the interferometer by several dB with respect to the standard quantum limit despite realistic levels of losses in light pulse operations. However, the analysis also highlights the challenges associated with achieving these improvements in practice, most notably the impact of finite temperature on the benefits of entanglement. The results suggest ways of optimising interferometric setups to exploit quantum entanglement under realistic conditions, thereby contributing to advances in precision metrology with atom interferometers.
Spin squeezing in atomic ensembles enables atom interferometry with sensitivities below the shot-noise limit, but the associated entanglement is highly susceptible to loss, making imperfections in atom optics a central limitation. Bragg diffraction is an established technique for driving transitions between atomic momentum states and enables large-momentum transfer through higher-order diffraction while preserving the internal state. However, it is intrinsically limited by two competing mechanisms: Short light pulses induce parasitic diffraction into off-resonant orders beyond an effective two-level description, while long pulses face velocity selectivity. We derive analytical expressions in a second-quantized framework for the atom optics and phase uncertainty of a Mach-Zehnder interferometer including these effects. We demonstrate that sub-shot-noise scaling is achieved only in a regime of intermediate pulse duration. Furthermore, we show that deleterious effects of higher-order diffraction are partially mitigated by optimizing the input quantum state.
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.
Bragg diffraction of matter waves is an established technique used in the most accurate quantum sensors. It is also the method of choice to operate large-momentum-transfer, high-sensitivity atom interferometers. It suffers, however, from an intrinsic multi-path character. Optimal control theory (OCT) has recently led to an improved robustness of atom interferometers to a range of challenging environmental effects such as vibrations or platform accelerations. In this theoretical work, we apply OCT protocols to control the Bragg diffraction phase shifts, thereby enhancing the metrological accuracy of the interferometer. We show a minimization of the diffraction phase for realistic conditions of finite temperature of the incoming wavepacket in a multi-path, high-order Bragg interferometer in a Mach–Zehnder configuration. We study input states with different momentum widths and find that our approach mitigates diffraction phases below the microradian level in the case of 1% of the photon recoil, thereby eliminating one of the leading systematic effects in atom interferometry.
Free-fall atom interferometers offer a powerful platform for accurate, absolute gravitational sensing. Szigeti et al. [Phys. Rev. Lett. 125, 100402 (2020)] recently proposed a quantum-enhanced scheme that uses a spin-squeezed Bose-Einstein condensate as an input state to improve the phase sensitivity of the interferometer. The spin squeezing, generated via one-axis twisting interactions, was limited by condensate expansion. Here we present an improved state preparation in which a sudden trapping potential -- a delta kick -- is initially applied to focus the condensate. The resulting increase in density enhances the one-axis-twisting interactions and produces greater spin squeezing. Using multimode truncated-Wigner simulations, we quantify the performance of the interferometer and find that, for an optimal kick strength, the phase sensitivity surpasses the standard quantum limit by a factor of ∼20. This represents a fourfold improvement over the original scheme without the delta kick and is well captured by a two-mode approximation.
Quantum Sensors, like atom interferometers (AI), can be employed for high-precision measurements of inertial forces, including their application as gravimeters, gradiometers, accelerometers, and gyroscopes. Their measurement principle relies on ultracold atoms that are prepared in quantum-mechanical superposition states in external degrees of freedom. These states can be prepared by a momentum transfer of a Raman laser. Then the superposition state senses the effect of an inertial force, which induce a corresponding relative phase. The phase is read out by a final coupling which converts the interferometric phase into a atom number difference between the two states. The difference provides an estimate of the interferometric phase and the corresponding quantity of interest. The quantum mechanical noise of the atomic ensemble cause a fundamental uncertainty of this estimation, which I analyze for generic AIs. For small atomic densities, the quantum phase noise of the ensemble limits the interferometric sensitivity. For large densities, quantum number fluctuations generate density fluctuations, which generates phase noise. I show that these two competing effects result in an optimal atom number with a maximal interferometer resolution. Squeezed atomic samples allow for a reduction of the quantum noise of one quantity at the expense of an increased noise along of a conjugate quantity. Phase and number are such quantities which obey to a variant of Heisenberg’s uncertainty principle. Neither phase nor number squeezing can improve the maximal interferometer resolution. As one main result of this thesis, I show how an optimal squeezing in between number and phase squeezing, allows for a fundamental improvement. I evaluate possible experimental paths to implement the proposed protocol. Concepts for a squeezing-enhanced operation of external-degree AIs have not yet been demonstrated. I propose and implement an atomic gravimeter, which is designed to accept spin-squeezed atomic states as input states. The interferometer is designed such that the interferometer couplings are performed in spin space, while the phase accumulation is performed in momentum states. For this interferometer, the squeezed input can be directly obtained from spin dynamics in spinor Bose-Einstein condensates. The main noise contributions in the experiment are analyzed, which results in a factor of 84 above the relevant quantum limit, preventing a squeezing enhancement so far. I outline a suppression of the main noise source, uncontrolled AC Stark shift on the squeezed mode and propose future important applications, including test of spontaneous collapse theories and an improvement of large-scale, high-precision gradiometers.
Quantum entanglement offers considerable advantages in how the sensitivity of interferometric precision scales with the resources available. However, when using entangled states it is important that a balance is found between the phase sensitivity of the state and its robustness to particle loss. Recent work (Dorner et al 2009 Phys. Rev. Lett. 102 040403) has optimized this balance and found the ideal initial state for any given loss rate in a two-path interferometer. Here we describe a route towards achieving precisions close to that of the theoretical optimum by using beam splitters with variable reflectivity. We also discuss how adopting a multipath approach may prove to be important in future metrology schemes that aim to surpass the standard quantum limit.