In this thesis the entanglement properties of atom-atom, atom-photon, and photon-photon are investigated. The recent developments of quantum computation as well as quantum information and communication have attracted much interest in the generation of these entanglements in the laboratory. To generate atom-photon entanglement, I discuss a model system in the cavity QED setup. By using a four-level atom and two resonant cavity modes, we can generate atom-photon entanglement almost deterministically. An extension of the above model to a six-level atom and again two resonant cavity modes can generate entangled photon pairs by appropriately adjusting system parameters. I then investigate the atom-atom entanglement in a 1D harmonic trap. I show the dependence of the pair entanglement on the scattering length and temperature, as well as the particle symmetry requirement (bosons or fermions). Among many peculiar properties in a 1D system, we briefly discuss the Fermi-Bose duality". While the entanglement properties of a single-channel model have recently been obtained for 1D and 3D systems, I thus study the entanglement of a multi-channel process in a cylindrical harmonic trap. I discuss the dependence of entanglement on the trap geometry. Finally I present detailed studies of the spin mixing between two Rb87 atoms in a single lattice site. The topic is emphasized on various motional state approximations and dipolar effect. Various motional state approximations can cause up to 20% error to experimental data. I also find that the dipolar interaction can lead to an experimentally observable frequency shift in a cylindrical harmonic trap with very large aspect ratio. The spin mixing of spin-2 manifold has also been discussed.
In this thesis the entanglement properties of atom-atom, atom-photon, and photon-photon are investigated. The recent developments of quantum computation as well as quantum information and communication have attracted much interest in the generation of these entanglements in the laboratory. To generate atom-photon entanglement, I discuss a model system in the cavity QED setup. By using a four-level atom and two resonant cavity modes, we can generate atom-photon entanglement almost deterministically. An extension of the above model to a six-level atom and again two resonant cavity modes can generate entangled photon pairs by appropriately adjusting system parameters. I then investigate the atom-atom entanglement in a 1D harmonic trap. I show the dependence of the pair entanglement on the scattering length and temperature, as well as the particle symmetry requirement (bosons or fermions). Among many peculiar properties in a 1D system, we briefly discuss the Fermi-Bose duality". While the entanglement properties of a single-channel model have recently been obtained for 1D and 3D systems, I thus study the entanglement of a multi-channel process in a cylindrical harmonic trap. I discuss the dependence of entanglement on the trap geometry. Finally I present detailed studies of the spin mixing between two Rb87 atoms in a single lattice site. The topic is emphasized on various motional state approximations and dipolar effect. Various motional state approximations can cause up to 20% error to experimental data. I also find that the dipolar interaction can lead to an experimentally observable frequency shift in a cylindrical harmonic trap with very large aspect ratio. The spin mixing of spin-2 manifold has also been discussed.
The generation of entanglement in atomic systems plays a central topic in the fields of quantum information storage and processing. Moreover, a special category of entangled states of multi-atom ensembles, spin squeezed states, have been proven to lead to considerable improvement in the sensitivity of precision measurements compared to systems involving uncorrelated atoms. A treatment of entanglement in open systems is, however, incomplete without a precise description of the process of decoherence which necessarily accompanies it. The theory of entanglement and decoherence are the two main topics of this thesis. Methods are described for the generation of strong correlations in large atomic ensembles using either cavity quantum electrodynamics or measurement outcome conditioned quantum dynamics. Moreover, the description of loss of entanglement resulting from the coupling to a noise reservoir (electromagnetic vacuum) is explored. A spin squeezing parameter is used throughout this thesis as both a measure of entanglement strength and as an indication of the sensitivity improvement above the so-called standard quantum limit (sensitivity obtained with uncorrelated particles) in metrology. The first scheme considered consists of a single mode cavity field interacting with a collection of atoms for which spin squeezing is produced in both resonant and off-resonant regimes. In the resonant case, transfer of squeezing from a field state to the atoms is analyzed, while in the off-resonant regime squeezing is produced via an effective nonlinear interaction (one-axis twisting Hamiltonian). A second, more experimentally realistic case, is one involving the interaction of free space atoms with laser pulses; a projective measurement of a source field originating from atomic fluctuations provides a means of preparing atomic collective states such as spin squeezed and Schrodinger cat states. A new unravelling is proposed, that employs the detection of photon number in a single output channel and is capable of producing mesoscopic Schrodinger cat states in a single step. As a first step to understanding the role of cooperative decoherence, of importance in the case of dense pencil-shaped atomic ensembles, the collective spin decoherence of a two multilevel atom system is derived. This calculation is also relevant to entanglement loss for two qubits manipulated using with reading/writing pulses. Finally, a scheme is proposed in which arbitrarily strong entanglement can be produced in a four-wave mixing setup, where the preparation of the atoms in a dark state limits the decoherence to negligible values.
This thesis is devoted to the theoretical characterization and generation of strongly correlated many-body states from the perspective of quantum information theory.We first study the entanglement properties of general many-body states and define a new measure for multipartite entanglement, the "Localizable Entanglement (LE)".It quantifies the maximal entanglement that can be localized, on average, between two parties by performing local measurements on the other parties.This measure provides knowledge of the "entanglement length", which is of particular importance in the context of quantum repeaters for long-distance quantum communication.We prove upper and lower bounds on LE in terms of two-body correlation functions and develop a method for the numerical computation of LE in one-dimensional spin systems.We analyze the localizable entanglement in various spin systems and observe characteristic features for a quantum phase transition such as a diverging entanglement length.In the second part of the thesis we focus on a specific many-body system: ultra-cold atoms in an optical lattice.This system is a promising candidate for the first physical realization of a "quantum simulator", but the temperature in current experiments is still too high.We propose, analyze and compare several schemes to cool the atoms close to the ground state of the strong interaction regime.In particular, we devise an algorithmic cooling protocol that combines occupation number filtering with spin-dependent lattice shifts.In addition, we propose two different physical realizations of filtering and also design protocols that generate an ensemble of quantum registers for quantum computation.In the third part we propose how to create entanglement in small atomic clouds by deforming and rotating the harmonic trapping potential.The resulting states are entangled in their motional degrees of freedom and can be identified with strongly correlated fractional quantum Hall states.For the case of two, three and four atoms we show how to adiabatically transform the unentangled ground state into the desired entangled state.We further discuss characteristic features of these states and propose how to create and detect them experimentally using an optical lattice setup. A Proof of the lower bound on LEA.1 Theorem on connected correlation functions and local measurements . . . . . . . . .
The experiments discussed in this thesis focus on the interaction of a single trapped atom with the single mode of a high-finesse optical cavity, in the regime of strong coupling. Chapter 1 gives a brief introduction, after which Chapter 2 describes our recent measurements of the transmission spectrum of the atom-cavity system. The spectrum exhibits a clearly resolved vacuum-Rabi splitting, in good quantitative agreement with theoretical predictions. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements of this type that have required averaging over 10^3-10^5 atoms. Chapter 3 discusses our observations of photon blockade for the transmitted light in the presence of one trapped atom. Excitation of the atom-cavity system by a first photon blocks the transmission of a second one, thereby converting an incident Poissonian stream of photons into a sub-Poissonian, anti-bunched stream, as confirmed by measurements of the photon statistics of the transmitted field. The intensity correlations of the cavity transmission also reveal the energy distribution for oscillatory motion of the trapped atom. Chapter 4 details a set of simple but necessary measurements of relevant experimental parameters such as cavity geometry, linewidth, mirror properties, birefringence, and detection efficiency. The thesis concludes with Appendix A, describing the efficient laser setup we use for our magneto-optical traps.
A system comprised of a small number of neutral atoms coupled to the mode of a high finesse optical resonator is a model system to study light-matter interaction at the quantum level and to explore fundamental effects like the influence of the measurement process on the atomic state. Promising proposals to generate entangled states in such systems are based on the simultaneous coupling of two atoms to one resonator mode. In chapter 1 of this thesis I shortly summarise the experimental tools to capture, trap, and transport single atoms using a magneto-optical trap and an optical conveyor belt. I discuss theoretical foundations to describe our system and present numerical simulations, the results of which enter the analysis of our experimental data. The average atom-cavity coupling strength is deduced from the measured cavity transmission and compared to a model taking atomic motion into account. The dynamics of the hyperfine spin state of one and two coupled atoms is the focus of chapter 2. I describe a nondestructive cavity-based state detection method, quantify the state detection fidelity, and identify optimum experimental parameters. This method is then used to record random telegraph signals, exhibiting quantum jumps on a timescale of milliseconds. Telegraph signals for two atoms are analysed employing Bayesian statistics, yielding additional information on the evolution of the hyperfine states. A good localisation of the atom is necessary to achieve stable coupling to the cavity mode. In chapter 3, I discuss two different aspects of how the motion of the atom can be controlled. Firstly an intracavity dipole trap is characterised and it is shown that it results in improved confinement of the atom. Secondly I examine the dependence of cavity-cooling forces on our experimental parameters and compare two different cooling regimes.
Strong coupling between light and matter has been demonstrated both in classical cavity quantum electrodynamics (QED) systems and in more recent circuit-QED experiments. This enables the generation of strong nonlinear photon-photon interactions at the single-photon level, which is of great interest for the observation of quantum nonlinear optical phenomena, the control of light quanta in quantum information protocols such as quantum networking, as well as the study of strongly correlated quantum many-body systems using light. Recently, strong coupling has also been realized in a variety of one-dimensional (1D) waveguide- QED experimental systems, which in turn makes them promising candidates for quantum information processing. Compared to cavity-QED systems, there are two new features in waveguide-QED: the existence of a continuum of states and the restricted 1D phase space, which together bring in new physical effects, such as the bound-state effects. This thesis consists of two parts: 1) understanding the fundamental interaction between local quantum objects, such as two-level systems and four-level systems, and photons confined in the waveguide; 2) exploring its implications in quantum information processing, in particular photonic quantum computation and quantum key distribution. First, we demonstrate that by coupling a two-level system (TLS) or three/fourlevel system to a 1D continuum, strongly-correlated photons can be generated inside the waveguide. Photon-photon bound states, which decay exponentially as a function of the relative coordinates of photons, appear in multiphoton scattering processes. As a result, photon bunching and antibunching can be observed in the photon-photon correlation function, and nonclassical light source can be generated on demand. In the case of an N-type four-level system, we show that the effective photon-photon interaction mediated by the four-level system, gives rise to a variety of nonlinear optical phenomena, including photon blockade, photon-induced tunneling, and creation of single-photon states and photon pairs with a high degree of spectral entanglement, all in the absence of a cavity. However, to enable greater quantum networking potential using waveguide- QED, it is important to study systems having more than just one TLS/qubit. We develop a numerical Green function method to study cooperative effects in a system of two qubits coupled to a 1D waveguide. Quantum beats emerge in photon-photon correlations, and persist to much longer time scales because of non-Markovian processes. In addition, this system can be used to generate a high-degree of long-distance entanglement when one of the two qubits is driven by an on-resonance laser, further paving the way toward waveguide-QED-based quantum networks. Furthermore, based on our study of light-matter interactions in waveguide- QED, we investigate its implications in quantum information processing. First, we study quantum key distribution using the sub-Possonian single photon source obtained by scattering a coherent state off a two-level system. The rate for key generation is found to be twice as large as for other sources. Second, we propose a new scheme for scalable quantum computation using flying qubits--propagating photons in a one-dimensional waveguide--interacting with matter qubits. Photonphoton interactions are mediated by the coupling to a three- or four-level system, based on which photon-photon -phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.
A neutral atom interacting with a single mode of a high finesse cavity provides an opportunity to study uncharted quantum mechanical systems and to explore the field of quantum computing and networking. Ranging from being a deterministic single photon source to a coherent storage unit for quantum information, a strong coupling cavity QED system has proven to be a powerful tool. In this thesis, single atoms are deterministically delivered over long distances and probed in an optical cavity. Once in the cavity, a single atom is stored and continuously observed for over 15 seconds. Progress towards using atoms in the cavity to produce entangled photon pairs is presented. Dual 1D optical lattices are implemented to create a foundation for advancements in two qubit quantum operations and entanglements.