This thesis is composed of two parts. In the first part we summarize our study on implementation of quantum information processing (QIP) in optical cavity QED systems, while in the second part we present our numerical investigations on strongly interacting Fermi systems using a powerful numerical algorithm developed from the perspective of quantum information theory. We explore various possible applications of cavity QED in the strong coupling regime to quantum information processing tasks theoretically, including efficient preparation of Schrodinger-cat states for traveling photon pulses, robust implemen- tation of conditional quantum gates on neutral atoms, as well as implementation of a hybrid controlled SWAP gate. We analyze the feasibility and performance of our schemes by solving corresponding physical models either numerically or analytically. We implement a novel numerical algorithm called Time Evolving Block Decimation (TEBD), which was proposed by Vidal from the perspective of quantum information science. With this algorithm, we numerically study the ground state properties of strongly interacting fermions in an anisotropic optical lattice across a wide Feshbach resonance. The interactions in this system can be described by a general Hubbard model with particle assisted tunneling. For systems with equal spin population, we find that the Luther-Emery phase, which has been known to exist only for attractive on-site interactions in the conventional Hubbard model, could also be found even in the case with repulsive on-site interactions in the general Hubbard model. Using the TEBD algorithm, we also study the effect of particle assisted tun- neling in spin-polarized systems. Fermi systems with unequal spin population and attractive interaction could allow the existence of exotic superfluidity, such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In the general Hubbard model, such exotic FFLO pairing of fermions could be suppressed by high particle assisted tunneling rates. However, at low particle assisted tunneling rates, the FFLO order could be enhanced. The effect of particle density inhomogeneity due to the presence of a harmonic trap potential is also discussed based on the local density approximation.
This thesis is composed of two parts. In the first part we summarize our study on implementation of quantum information processing (QIP) in optical cavity QED systems, while in the second part we present our numerical investigations on strongly interacting Fermi systems using a powerful numerical algorithm developed from the perspective of quantum information theory. We explore various possible applications of cavity QED in the strong coupling regime to quantum information processing tasks theoretically, including efficient preparation of Schrodinger-cat states for traveling photon pulses, robust implemen- tation of conditional quantum gates on neutral atoms, as well as implementation of a hybrid controlled SWAP gate. We analyze the feasibility and performance of our schemes by solving corresponding physical models either numerically or analytically. We implement a novel numerical algorithm called Time Evolving Block Decimation (TEBD), which was proposed by Vidal from the perspective of quantum information science. With this algorithm, we numerically study the ground state properties of strongly interacting fermions in an anisotropic optical lattice across a wide Feshbach resonance. The interactions in this system can be described by a general Hubbard model with particle assisted tunneling. For systems with equal spin population, we find that the Luther-Emery phase, which has been known to exist only for attractive on-site interactions in the conventional Hubbard model, could also be found even in the case with repulsive on-site interactions in the general Hubbard model. Using the TEBD algorithm, we also study the effect of particle assisted tun- neling in spin-polarized systems. Fermi systems with unequal spin population and attractive interaction could allow the existence of exotic superfluidity, such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In the general Hubbard model, such exotic FFLO pairing of fermions could be suppressed by high particle assisted tunneling rates. However, at low particle assisted tunneling rates, the FFLO order could be enhanced. The effect of particle density inhomogeneity due to the presence of a harmonic trap potential is also discussed based on the local density approximation.
Quantum information processing opens up completely new possibilities in communication and computation, that would be impossible in the realms of classical physics. While the benefits of quantum information processing are well understood in theory, it remains a formidable challenge to experimentally implement even simple quantum information processing tasks. Numerous physical architectures have been proposed for preparing and coherently manipulating quantum information. Amongst these, quantum optics has been identified as a particularly promising candidate. In particular this arises from the long decoherence times of single photon states, which can be used to encode logical qubits in a variety of ways. Nonetheless, there remain formidable challenges to implementing large scale quantum information processing using optical qubits. Most notably these include: the preparation of pure indistinguishable photons; efficient number-resolving photo-detection; mode-matching; photon loss; and the non-determinism of entangling gates. Any future large scale implementation of optical quantum information processing protocols will require significant advances on most, if not all these fronts. In this thesis we aim to present a comprehensive overview of the major requirements for optical quantum information processing, understand the effects they have, and how they can be modeled. From this we aim to understand what the realistic technological requirements are to achieve scalable optical quantum information processing, and, where possible, suggest means by which to help achieve these goals.
With a recently developed time-evolving block decimation algorithm, we numerically study the ground-state quantum phase diagram of Fermi mixtures with attractive interspecies interactions loaded in one-dimensional optical lattices. For our study, we adopt a general asymmetric Hubbard model with species-dependent tunneling rates to incorporate the possibility of mass imbalance in the mixtures. We find clear signatures for the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in this model in the presence of population imbalance. Our simulation also reveals that in the presence of mass imbalance, the parameter space for FFLO states shrinks or even completely vanishes depending on the strength of the attractive interaction and the degree of mass imbalance.
We study through controlled numerical simulation the ground-state properties of spin-polarized strongly interacting Fermi gas in an anisotropic optical lattice, which is described by an effective one-dimensional general Hubbard model with particle-correlated hopping rate. We show that the Fulde-Ferrell-Larkin-Ovchinnikov type of state, while enhanced by a negative correlated hopping rate, can be completely suppressed by positive particle-correlated hopping, yielding an unusual magnetic phase even for particles with on-site attractive interaction We also find several different phase-separation patterns for these atoms in an inhomogeneous harmonic trap, depending on the correlated hopping rate.
This thesis is devoted to quantum information processing using strongly correlated many-body systems, and we have focused our interest on systems realized with ultracold atoms in optical lattices. We have proposed different protocols based either on the free dynamics followed by a particular initial state -out of the ground-state manifold-, or on the non-trivial quantum dynamics generated by the optimal modulation of optical lattices. Our protocols demonstrate the potential of strongly correlated systems to perform short-distance quantum communication. Protocols based on dynamical manipulations of the optical lattices have also been extended to two-dimensional lattices to prepare decoherence-free cluster states. We have also proposed a novel scheme combining free dynamics and continuous measurements, which lead to the Quantum Zeno effect, for quantum information processing in spin chains. Despite of the recent progress in using atoms trapped in optical lattices to prepare and manipulate strongly correlated systems, the precise detection and experimental characterization of such states is a major challenge in modem physics. We have exploited some of the proposed protocols to analyze strongly correlated systems from the quality of their performance when implementing a quantum information task. Our approach provides a new insight into the study of these complex and fascinating systems. Regarding the detection, we have also addressed the fundamental problem of inferring the state of a given quantum system. First, we have studied the optimal state estimation of the most fundamental quantum system, a two-level system or qubit. Second, we have also considered and proposed new methods to tackle the experimental challenge of detecting the many-body systems prepared with ultracold atoms in optical lattices. We have extended the applicability of the noise-correlation method to detect a mesoscopic Schrodinger cat many-body state. Despite the success of this method, it has the drawback that it demolishes the physical system. To overcome such limitation, we have proposed an . extension of the well-known Faraday effect at the quantum level, which yields a quantum non-demolition method to detect strongly correlated systems.
English: Since its genesis, quantum mechanics has proved to be a very accurate model for predicting the behavior of the world below the nanoscale. However, crucial breakthroughs in technology were needed in order to be able to effectively access and manipulate such small magnitudes. During the last twenty years, the field of quantum information processing has experienced a growing interest, in its many variants, both theoretically and practically. Despite being still at a very basic stage, expectations are high. The uniqueness of quantum phenomena (superposition of states, creation of entanglement, etc.) have no classical analogue and allow novelties such as another paradigm of computation, more secure communications, quantum teleportation, quantum dense coding, etc. which are presented and analyzed here. The aim of this Thesis is to present in a unified way the main mathematical methods used in quantum information processing, as well as the state of the art of their corresponding technological implementations. Our contributions are based in making a self-contained presentation; seeking completeness, that is, treating the most relevant fields of research involved, focusing on their relations; and picking the most relevant, insightful references, given the quantity of literature produced in this field. We also discuss some of the fundamental questions that remain still unanswered, and which are the current lines of research to shed light on them.
Ultracold atomic gases have emerged as an ideal laboratory system to emulate many-body physics in an unprecedentedly controllable manner. Numerous many-body quantum states and phases have been experimentally explored and characterized using the ultracold atomic gases, offering new insights into many exciting physics ranging from condensed matters to cosmology. In this thesis, we will present a systematic numerical study of a novel experimental system, population imbalanced two-component ultracold Fermi gases. We explore the phase diagram of this system in both 3D and 1D especially focusing on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by a spatially oscillating order parameter. In 3D, we solve for the stationary states of trapped imbalanced Fermi gases in a wide range of parameter space with a home-made parallel eigen-solver for Bogoliubov-de Gennes (BdG) equations. Our results show that there exists a metastable state with a FFLO type oscillating order parameter. In 1D, we simulate the dynamical expansion of the population imbalanced Fermi gases from the trap. A numerically quasi-exact scheme, time-evolving block decimation (TEBD), is introduced for the comparative studies with the solution of the time-dependent BdG equation. Our results predict that the existence of FFLO states will leave conspicuous signatures in the density profiles during the expansion. For further understanding of the interplay between the population imbalance and two-body pairing interaction between two spin components, we also study the spin transport properties through trapped ultracold Fermi gases. The preliminary results will be discussed.