In this work, three applications aimed at studying or exploiting various aspects of entanglement are considered. In the first project, the entanglement between two atoms inside a multimode resonator is investigated in the presence of retardation. Retardation is associated with the finite time required by a photon to propagate between atoms and cavity boundaries. It is found that retardation affects the atomic populations as well as the entanglement dynamics to a large degree. The second project is a study of entangled states of light to obtain an enhanced resolution. We have simulated optical centroid measurements for spatial resolution enhancement with various types of non-classical input states. By numerically simulating the measurement scheme, we optimize the detection parameters for an experimental implementation and also study the multiphoton absorption required for quantum lithography. The third project uses the scattered light from a resonantly driven correlated system to obtain information about the system. Techniques have been proposed using which in certain detection directions, n-atom correlations can be directly accessed in an experiment via light scattering with a significant count rate. Moreover, such detection of correlations is not limited to a particular spatial geometry but can be utilized for generalized geometries, too.
In this work, three applications aimed at studying or exploiting various aspects of entanglement are considered. In the first project, the entanglement between two atoms inside a multimode resonator is investigated in the presence of retardation. Retardation is associated with the finite time required by a photon to propagate between atoms and cavity boundaries. It is found that retardation affects the atomic populations as well as the entanglement dynamics to a large degree. The second project is a study of entangled states of light to obtain an enhanced resolution. We have simulated optical centroid measurements for spatial resolution enhancement with various types of non-classical input states. By numerically simulating the measurement scheme, we optimize the detection parameters for an experimental implementation and also study the multiphoton absorption required for quantum lithography. The third project uses the scattered light from a resonantly driven correlated system to obtain information about the system. Techniques have been proposed using which in certain detection directions, n-atom correlations can be directly accessed in an experiment via light scattering with a significant count rate. Moreover, such detection of correlations is not limited to a particular spatial geometry but can be utilized for generalized geometries, too.
In this thesis we will theoretically investigate three potentially useful physical systems, after first developing the theoretical framework necessary for studying them. First, we will study the multiphoton absorption properties of maximally path entangled number (N00N) states. This is directly relevant to quantum lithography, and beating the Rayleigh diffraction limit. Next, we will develop a new scheme for quantum interferometry: dubbed coherent-light boosted super-sensitive quantum interferometry, which has the potential to reach below the shot noise limit for high photon fluxes, and requires no esoteric detection protocol, or technological elements that have yet to be developed. Finally we propose a method to perform parity detection on the output modes of a Mach-Zehnder interferometer that has been fed with two-mode squeezed vacuum. This detection scheme relies on a double homodyning technique, that makes intensity correlation measurements at a series of chosen bias phases. Sub-Heisenberg sensitivity scaling is expected for this setup.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
This dissertation deals with theoretical and experimental research on nonclassical, or entangled, states of atoms and photons. In the first part, I describe two approaches to the preparation of entangled states of a large number of atoms. The first approach is based on the transfer of quantum correlations from non-classical light to the atomic spins. I consider three different situations: (a) the atoms are placed in a loss-free cavity and no relaxation of any kind is present; (b) the atoms are placed in a cavity with input and output for the electromagnetic field and the atoms spontaneously decay from the upper state; (c) there is no cavity around the atoms and spontaneous emission is present. I show that in all three situations with judicious choice of parameters, entangled samples of atoms can be produced. The second approach is based on quantum-nondemolition (QND) measurements of collective atomic operators. I describe experiments with pulsed and cw light as the probe, that result in squeezed spin states of atoms. When a rf magnetic field is applied to the atomic sample, sub- shot noise performance of an atomic spin interferometer is demonstrated. In the second part of the thesis I describe investigations of phase properties of two-photon and single-photon states. These experiments make use of spontaneous type-II down-conversion in a nonlinear crystal. First, interferometric measurement of a phase shift at the Heisenberg limit for a two-photon state is described. Next, a violation of Bell-type inequalities in phase space is demonstrated for the quantum optical version of the Einstein-Podolsky-Rosen state. Finally, some recent work directed toward homodyning a single photon against a strong local oscillator field is described.
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.
In the past decades, rapid advances in the experimental control of quantum systems have opened up unparalleled capabilities of engineering exotic quantum states. Nowadays, we may consider ourselves witnesses of a second quantum revolution as strongly correlated quantum matter is regularly created, on a daily basis, within the most diverse platforms, e.g. arrays of Rydberg atoms, ultra-cold atoms in optical lattices, superconducting qubits, trapped ions, and quantum dots. In this era, dubbed Noisy-Intermediate Scale Quantum (NISQ) era, the effort in pursuing research for realizing quantum technologies with practical purposes, such as quantum computing, simulations, communication and metrology, has greatly accelerated, and we are just starting to experience the immense progress that could be achieved. The remarkable breakthrough we are facing builds upon seminal theoretical and experimental advances in quantum physics. The key achievements in atomic, molecular, and optical (AMO) physics have opened up the possibility of controlling, trapping, and measuring single atoms, one by one, with high accuracy and reliability. In parallel, from a theoretical point of view, the study of quantum entanglement and correlations has bridged AMO physics and quantum information with crucial proposals for the realization of universal quantum computers. In this context, entanglement has emerged as one of the key tools to characterize and to exploit quantum many-body systems for quantum information purposes. We will study quantum entanglement in several scenarios to investigate and probe complex quantum many-body systems. We will consider examples ranging from generic mixed states in equilibrium to out-of-equilibrium dynamics, with and without dissipation, and topologically non-trivial systems. The leitmotif of this work will be how entanglement and correlations can be exploited to characterize the many-body quantum state describing a physical system and how entanglement can be detected in an experimentally efficient manner.