Atom interferometers measure the relative phase shifts between coherent matter-wave paths that arise from interactions with external fields or inertial forces. Due to their exceptional phase sensitivity, atom interferometers became an essential tool for precision measurements and fundamental physics experiments, finding applications in geodesy, gravimetry, and inertial navigation. However, their measurement precision is limited by quantum projection noise, which arises from the Heisenberg uncertainty principle, preventing the measurement of atomic states with absolute precision. The generation of entanglement between the atoms offers a path to surpass this so-called standard quantum limit, thereby enhancing the interferometer’s phase sensitivity beyond classical measurement bounds. This thesis reports on the development of an atom interferometer experiment designed to realize cavity-mediated, squeezed Mach-Zehnder-type interferometry with ultra-cold 87Rb atoms. The experiment combines cavity-aided spin-squeezing with cavity-mediated Mach-Zehnder interferometry to demonstrate entanglement-enhanced phase sensitivity. The experiment is centered on a triangular optical cavity that mediates all relevant atom-light interactions. The cavity provides optical trapping, spin-squeezing, and Raman beam-splitter operations, enabling to perform interferometry on a continuously trapped atomic ensemble. The thesis elaborates on the fundamental theoretical framework, the cavity design, and the full optical setup, including the detailed configuration of the developed laser stabilization methods. Experimentally, continuous loading methods were explored, resulting in an accumulation of up to 4 × 106 atoms in the dipole trap within a cycle time of 500 ms. The AC Stark shift compensation method developed for continuous loading was further applied for in-trap cooling to 10 µK, and optical pumping for efficient atomic state preparation. Coherent state control was verified via observation of microwave-driven Rabi oscillations, and used to characterize atom-cavity coupling. These presented results establish the experimental groundwork for the future development of cavity-mediated, entanglement-enhanced Mach-Zehnder-type atom interferometry.
Atom interferometers measure the relative phase shifts between coherent matter-wave paths that arise from interactions with external fields or inertial forces. Due to their exceptional phase sensitivity, atom interferometers became an essential tool for precision measurements and fundamental physics experiments, finding applications in geodesy, gravimetry, and inertial navigation. However, their measurement precision is limited by quantum projection noise, which arises from the Heisenberg uncertainty principle, preventing the measurement of atomic states with absolute precision. The generation of entanglement between the atoms offers a path to surpass this so-called standard quantum limit, thereby enhancing the interferometer’s phase sensitivity beyond classical measurement bounds. This thesis reports on the development of an atom interferometer experiment designed to realize cavity-mediated, squeezed Mach-Zehnder-type interferometry with ultra-cold 87Rb atoms. The experiment combines cavity-aided spin-squeezing with cavity-mediated Mach-Zehnder interferometry to demonstrate entanglement-enhanced phase sensitivity. The experiment is centered on a triangular optical cavity that mediates all relevant atom-light interactions. The cavity provides optical trapping, spin-squeezing, and Raman beam-splitter operations, enabling to perform interferometry on a continuously trapped atomic ensemble. The thesis elaborates on the fundamental theoretical framework, the cavity design, and the full optical setup, including the detailed configuration of the developed laser stabilization methods. Experimentally, continuous loading methods were explored, resulting in an accumulation of up to 4 × 106 atoms in the dipole trap within a cycle time of 500 ms. The AC Stark shift compensation method developed for continuous loading was further applied for in-trap cooling to 10 µK, and optical pumping for efficient atomic state preparation. Coherent state control was verified via observation of microwave-driven Rabi oscillations, and used to characterize atom-cavity coupling. These presented results establish the experimental groundwork for the future development of cavity-mediated, entanglement-enhanced Mach-Zehnder-type atom interferometry.
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.
Abstract An ensemble of atoms can operate as a quantum sensor by placing atoms in a superposition of two different states. Upon measurement of the sensor, each atom is individually projected into one of the two states. Creating quantum correlations between the atoms, that is entangling them, could lead to resolutions surpassing the standard quantum limit 1–3 set by projections of individual atoms. Large amounts of entanglement 4–6 involving the internal degrees of freedom of laser-cooled atomic ensembles 4–16 have been generated in collective cavity quantum-electrodynamics systems, in which many atoms simultaneously interact with a single optical cavity mode. Here we report a matter-wave interferometer in a cavity quantum-electrodynamics system of 700 atoms that are entangled in their external degrees of freedom. In our system, each individual atom falls freely under gravity and simultaneously traverses two paths through space while entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed sensitivity 3.4−0.9+1.1 3 . 4 − 0.9 + 1.1 dB and 2.5−0.6+0.6 2 . 5 − 0.6 + 0.6 dB below the standard quantum limit, respectively. We successfully inject an entangled state into a Mach–Zehnder light-pulse interferometer with directly observed sensitivity 1.7−0.5+0.5 1 . 7 − 0.5 + 0.5 dB below the standard quantum limit. The combination of particle delocalization and entanglement in our approach may influence developments of enhanced inertial sensors 17,18 , searches for new physics, particles and fields 19–23 , future advanced gravitational wave detectors 24,25 and accessing beyond mean-field quantum many-body physics 26–30 .
By allowing a large ensemble of laser cooled and trapped 87Rb atoms to interact collectively with an optical cavity, I have explored two phenomena that may prove useful for enhancing precision measurements: superradiant lasing and spin squeezing.\nSuperradiant lasers have been proposed as future ultrastable optical frequency references, with predicted linewidths < 1 millihertz. These lasers operate in an unusual regime of laser physics where collective emission from an atomic ensemble maps the quantum phase stored in the atoms onto the optical cavity field. I will give an overview of my experimental work using a cold-atom, superradiant Raman laser as a model system to confirm a number of the key predictions concerning superradiant lasing, including the possibility of coherent emission with < 1 intracavity photon on average and greatly reduced sensitivity to cavity frequency noise.\nI also present work using cavity-aided, coherence-preserving measurements of the atomic state population to create entanglement between atoms. The entanglement enables more precise estimation of the quantum phase at the heart of nearly all precision measurements and sensors utilizing quantum objects. By utilizing a cycling transition for the quantum non-demolition probe, we have reduced by several orders of magnitude the measurement induced back-action caused by spontaneous Raman transitions. We directly observe, with no background subtraction, a spin squeezed state with sensitivity to measuring a quantum phase enhanced 10.5 times in variance (i.e. 10.2 dB) beyond the standard quantum limit for an unentangled state. This experimental breakthrough demonstrates that quantum-aided sensing techniques can realize large enough enhancements to have a substantial impact on precision measurements and may aid advances in technology as well as searches for new physics.
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.
Developments in the precise control of quantum systems have led to advances in both fundamental research and emerging technologies in areas including quantum sensing and computation. One particularly useful application is atom interferometry, which uses laser pulses to split, redirect, and recombine atomic wavepackets, enabling precision measurements of inertial effects. This thesis presents the construction and characterisation of a compact cold atom interferometer, to meet the longer-term aim of developing an atomic gyroscope. We detail the setup of a rubidium-85 Magneto-Optical Trap (MOT) and the development of a laser to perform Raman transitions across the hyperfine Rb-85 levels. We then demonstrate and characterise the coherent manipulation of the atomic state of the rubidium as well as atom-interferometric fringes, in a Doppler-insensitive configuration. Systematic errors can degrade the performance of laser pulse interactions with cold atoms by reducing the fidelity of the atom–light interactions. In this thesis, we investigate the implementation of composite pulses and optimal control pulses, which use pulses with varying phase sequences and durations to mitigate against experimental inhomogeneities. We also show that phase modulators can introduce distortions in both the applied laser phase and the Raman modulation amplitude, which can in turn degrade pulse performance. To address this, we develop a compensation protocol that corrects for these non-linearities and demonstrate that it leads to a further improvement in pulse fidelity, for the Waltz and Knill composite pulses. Applying this protocol to the rotary echo sequence led to Rabi oscillations that could last 4 times longer, compared to the uncalibrated IQ modulator. Although an optimal control inversion pulse showed more resilience to the IQ modulator distortions, the Mach-Zehnder interferometer sequence was more susceptible to them. It was demonstrated that compensating for IQ modulator non-linearities improved the optimised fringe signal-to-noise ratio, and reduced the phase-offset error by a factor of 2.4.
Abstract The coherent manipulation of a quantum wave is at the core of quantum sensing. For instance, atom interferometers require linear splitting and recombination processes to map the accumulated phase shift into a measurable population signal. Although Bose Einstein condensates (BECs) are the archetype of coherent matter waves, their manipulation between trapped spatial modes has been limited by the strong interparticle collisions. Here, we overcome this problem by using BECs with tunable interaction trapped in an innovative array of double-well potentials and exploiting quantum tunneling to realize linear beam splitting. We operate several Mach-Zehnder interferometers in parallel, canceling common-mode potential instabilities by a differential analysis, thus demonstrating a trapped-atom gradiometer. Furthermore, by applying a spin-echo protocol, we suppress additional decoherence sources and approach unprecedented coherence times of one second. Our interferometer will find applications in precision measurements of forces with a high spatial resolution and in linear manipulation of quantum entangled states for sensing with sub shot-noise sensitivity.