The quantum many-body problem, and especially the study of dynamical properties of a multipartite quantum system, is one of the hardest problems of modern physics. There exist only a few analytical results and exact numerical simulations require an amount of resources that grow exponentially with the system size.In this thesis, we studied correlations and entanglement properties for systems composed of magnetic atoms on a lattice, for instance via the generation of spin squeezing. For this purpose we have developed new approximate numerical methods that allow us to study large system sizes. This enabled us to propose protocols to generate an amount of spin squeezing that scales with the system size. The advantage is twofold. Since spin squeezing is an entanglement witness, this would allow for entanglement detection in a system of magnetic atoms - which has yet to be realized experimentally. Moreover, spin squeezing offers an important metrological advantage, asspin-squeezed states can be used for extremely precise measurements of external magnetic fields, far beyond what one can achieve within dependent atoms.Finally, we studied the generation of other forms of entanglement, namely Dicke squeezing (of spin or momentum), in systems of Bose condensed atoms. This form of entanglement is well-known in spin-1 atomic condensates. Here, we propose a protocol to generalize it to the case of momentum modes, using a time-dependent Hamiltonian. The entangled states generated during the dynamics are potentially useful for the precision measurements of inertial forces.
The quantum many-body problem, and especially the study of dynamical properties of a multipartite quantum system, is one of the hardest problems of modern physics. There exist only a few analytical results and exact numerical simulations require an amount of resources that grow exponentially with the system size.In this thesis, we studied correlations and entanglement properties for systems composed of magnetic atoms on a lattice, for instance via the generation of spin squeezing. For this purpose we have developed new approximate numerical methods that allow us to study large system sizes. This enabled us to propose protocols to generate an amount of spin squeezing that scales with the system size. The advantage is twofold. Since spin squeezing is an entanglement witness, this would allow for entanglement detection in a system of magnetic atoms - which has yet to be realized experimentally. Moreover, spin squeezing offers an important metrological advantage, asspin-squeezed states can be used for extremely precise measurements of external magnetic fields, far beyond what one can achieve within dependent atoms.Finally, we studied the generation of other forms of entanglement, namely Dicke squeezing (of spin or momentum), in systems of Bose condensed atoms. This form of entanglement is well-known in spin-1 atomic condensates. Here, we propose a protocol to generalize it to the case of momentum modes, using a time-dependent Hamiltonian. The entangled states generated during the dynamics are potentially useful for the precision measurements of inertial forces.
Quantum simulation platforms such as cold atoms, superconducting circuits, and trapped ions enable the experimental investigation of quantum many-body systems, with important implications for quantum technologies. In this thesis, we investigate how entanglement and correlations develop in such systems and how they can be harnessed both for the theoretical study of models relevant to condensed matter physics and for practical applications in quantum metrology. We begin by focusing on the adiabatic preparation of quantum many-body ground states. In particular, we show that quantum simulators can probe the link between spectral degeneracy and Spontaneous Symmetry Breaking, as pioneered by P.W. Anderson. We prove that odd-sized spin-½ systems exhibiting time-reversal symmetry sustain a net magnetization even away from the thermodynamic limit, thanks to an exact spectral degeneracy. Moreover, the symmetry-broken state exhibits scalable spin squeezing, a key resource for quantum metrology. We then turn to a different paradigm of evolution: quench dynamics. In particular, we show that monitoring the real-time evolution of correlations allows for the experimental measurement of the dispersion relation of fundamental excitations. In the case of two-dimensional long-range ordered systems, such as the dipolar XY model, these excitations are spin waves, leading to sharp features in the evolution of two-point correlation functions. Conversely, in one-dimensional systems, fundamental excitations have a fermionic nature, and their detection requires the measurement of non-local correlation functions. The latter, while inaccessible in condensed matter, are instead well suited to quantum simulators with individually addressable degrees of freedom.
The production of large-scale entangled states is one of the main goals of next-generation quantum technologies, with an immediate potential for applications in the context of entanglement-assisted quantum sensing. A very promising platform to achieve this goal is offered by ultracold spinor gases, made of atoms with a large internal spin sensitive to magnetic fields. Here we show that the native spin-changing collisions in a spinor Bose-Einstein condensate, combined with an arbitrary quadratic Zeeman shift, can generate scalable spin squeezing in the collective spin of the ensemble, following the universal paradigm of the celebrated one-axis-twisting model. Squeezing dynamics is driven by the quadratic Zeeman shift when this shift is small; and by the spin-changing collisions for large shifts, in the form of stroboscopic squeezing. Turning off the Zeeman shift freezes out the collective-spin dynamics, so that the ensuing collective spin dynamics can be uniquely governed by an external field to be sensed. Our theoretical results pave the way for the use of spinor Bose gases with a large spin in fundamental studies of entanglement, as well as in advanced metrological applications.
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.
Spin squeezing inequalities (SSI) represent a major tool to probe quantum entanglement among a collection of few-level atoms, and are based on collective spin measurements and their fluctuations. Yet, for atomic ensembles of spin- j atoms and ultracold spinor gases, many experiments can image the populations in all Zeeman sublevels s=−j,−j+1,…,j , potentially revealing finer features of quantum entanglement not captured by SSI. Here we present a systematic approach which exploits Zeeman-sublevel population measurements in order to construct novel entanglement criteria, and illustrate our approach on ground states of spin-1 and spin-2 Bose-Einstein condensates. Beyond these specific examples, our approach allows one to infer, in a systematic manner, the optimal permutationally-invariant entanglement witness for any given set of collective measurements in an ensemble of d -level quantum systems.
The creation and manipulation of quantum entanglement is central to improving precision measurements. A principal method of generating entanglement for use in atom interferometry is the process of spin squeezing whereupon the states become more sensitive to SU(2) rotations. One possibility to generate this entanglement is provided by one-axis twisting (OAT), where a many-particle entangled state of one degree of freedom is generated by a nonlinear Hamiltonian. We introduce a method which goes beyond OAT to create squeezing and entanglement across two distinct degrees of freedom. We present our work in the specific physical context of a system consisting of collective atomic energy levels and discrete collective momentum states, but also consider other possible realizations. Our system uses a nonlinear Hamiltonian to generate dynamics in SU(4), thereby creating the opportunity for dynamics not possible in typical SU(2) one-axis twisting. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement. The states prepared in this system are potentially more versatile for use in multiparameter or auxiliary measurement schemes than those prepared by standard spin squeezing.
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.