This dissertation consists of three sections. In the first section, we discuss the generation \nof arbitrary two-qubit entangled states and present three generation methods. \nThe first method is based on the interaction of an atom with classical and quantized \ncavity fields. The second method is based on the interaction of two coupled two-level \natoms with a laser field. In the last method, we use two spin-1/2 systems which \ninteract with a tuned radio frequency pulse. Using those methods we have generated \ntwo qubit arbitrary entangled states which is widely used in quantum computing and \nquantum information. In the second section, we discuss a possible experimental implementation \nof quantum walk which is based on the passage of an atom through a \nhigh-Q cavity. The chirality is determined by the atomic states and the displacement \nis characterized by the photon number inside the cavity. Our scheme makes quantum \nwalk possible in a cavity QED system and the results could be widely used on \nquantum computer. In the last section, we investigate the properties of teleporting \nan arbitrary superposition of entangled Dicke states of any number of atoms (qubits) \nbetween two distant cavities. We also studied teleporting continuous variables of an \noptical field. Teleportation of Dicke states relies on adiabatic passage using multiatom \ndark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate \nthe protocol of quantum teleportation of arbitrary input optical field states in \nthe density matrix form, and established the relation between the P-function of the \ninput and output states. We then present a condition involving squeeze parameter \nand detection efficiency under which the P-function of the output state becomes the \nQ function of the input state such that any nonclassical features in the input state \nwill be eliminated in the teleported state. Based on the research in this section we \nhave made it possible of arbitrary atomic Dicke states teleportation from one cavity \nto another, and this teleortation will play an essential role in quantum communication. \nSince quantum properties is so important in quantum communication, the \ncondition we give in this section to distinguish classical and quantum teleportation is \nalso important.
This dissertation consists of three sections. In the first section, we discuss the generation \nof arbitrary two-qubit entangled states and present three generation methods. \nThe first method is based on the interaction of an atom with classical and quantized \ncavity fields. The second method is based on the interaction of two coupled two-level \natoms with a laser field. In the last method, we use two spin-1/2 systems which \ninteract with a tuned radio frequency pulse. Using those methods we have generated \ntwo qubit arbitrary entangled states which is widely used in quantum computing and \nquantum information. In the second section, we discuss a possible experimental implementation \nof quantum walk which is based on the passage of an atom through a \nhigh-Q cavity. The chirality is determined by the atomic states and the displacement \nis characterized by the photon number inside the cavity. Our scheme makes quantum \nwalk possible in a cavity QED system and the results could be widely used on \nquantum computer. In the last section, we investigate the properties of teleporting \nan arbitrary superposition of entangled Dicke states of any number of atoms (qubits) \nbetween two distant cavities. We also studied teleporting continuous variables of an \noptical field. Teleportation of Dicke states relies on adiabatic passage using multiatom \ndark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate \nthe protocol of quantum teleportation of arbitrary input optical field states in \nthe density matrix form, and established the relation between the P-function of the \ninput and output states. We then present a condition involving squeeze parameter \nand detection efficiency under which the P-function of the output state becomes the \nQ function of the input state such that any nonclassical features in the input state \nwill be eliminated in the teleported state. Based on the research in this section we \nhave made it possible of arbitrary atomic Dicke states teleportation from one cavity \nto another, and this teleortation will play an essential role in quantum communication. \nSince quantum properties is so important in quantum communication, the \ncondition we give in this section to distinguish classical and quantum teleportation is \nalso important.
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 concerned with variations on, and improvements to, optical strategies of implementing quantum teleportation. In particular, I investigate four continuous variable teleportation schemes. Two schemes are based upon number-phase entanglement between two coupled harmonic oscillator modes. Joint measurements of number and phase on the coupled states are the basis for the protocols. The effects of phase decoherence on output quality are analysed and an equivalent classical protocol is introduced. The two remaining schemes improve and extend standard continuous variable teleportation. In one, coincidence measurements on the two-mode squeezed vacuum condition the entanglement resource, improving the efficacy of the protocol. In the other, the measurements made by the sender and displacements performed by the receiver are tailored to make more efficient use of the available information. In each case the protocol is described and relevant output
parameters derived. The trends in output quality with respect to input parameters are interpreted and discussed.
In this thesis, we investigate the uses of entanglement and its verification in quantum communication. Typically, it is the presence of entanglement which allows quantum communication protocols to outperform their classical counterparts, or to achieve tasks which are infeasible with classical physics. Therefore, the verification of entanglement can provide fundamental tests to certify that experimental implementations of such protocols operate quantum mechanically. The main object here is to develop a verification procedure which is adaptable to a wide range of applications, and whose implementation has low requirements on experimental resources. We present such a procedure in the form of the Expectation Value Matrix. The structure of this thesis is as follows: Chapters 1 and 2 give a short introduction and background information on quantum theory and the quantum states of light. In particular, we discuss the basic postulates of quantum mechanics, quantum state discrimination, the description of quantum light and the homodyne detector. Chapter 3 gives a brief introduction to quantum information and in particular to entanglement, and we discuss the basics of quantum key distribution and teleportation. The general framework of the Expectation Value Matrix is introduced. The main matter of this thesis is contained in the subsequent three chapters, which describe different quantum communication protocols and the corresponding adaptation of the entanglement verification method. The subject of Chapter 4 is quantum key distribution, where the detection of entanglement is a means of excluding intercept-resend attacks, and the presence of quantum correlations in the raw data is a necessary precondition for the generation of secret key. We investigate a continuous-variable version of the two-state protocol and develop the Expectation Value Matrix method for such qubit-mode systems. Furthermore, we analyse the role of the phase reference with respect to the security of the protocol and raise awareness of a corresponding security threat. For this, we adapt the verification method to different settings of Stokes operator measurements. In Chapter 5, we investigate quantum memory channels and propose a fundamental bench- mark for these based on the verification of entanglement. After describing some physical effects which can be used for the coherent storage of light, we focus on the storage of squeezed light. This situation requires an extension of our verification procedure to sources of mixed input states. We propose such an extension, and give a detailed analysis of its application to squeezed thermal states, displaced thermal states and mixed qubit states. This is supplemented by finding the optimal entanglement-breaking channels for each of these situations, which provides us with an indication of the strength of the extension to our entanglement criterion. The subject of Chapter 6 is also the benchmarking of quantum memory or teleportation experiments. Considering a number of recently published benchmark criteria, we investigate the question which one is most useful to actual experiments. For this, a criterion must be both strong, i.e., easy to overcome, and it must be implementable with a reasonable amount of experimental resources. We first compare the different criteria for typical settings and sort them according to their resilience to excess noise. Then, we introduce a further improvement to the Expectation Value Matrix method, which results in the desired optimal benchmark criterion. Finally, we investigate naturally occurring phase fluctuations and find them to further simplify the implementation of our criterion. Thus, we formulate the first truly useful way of validating experiments for the quantum storage or transmission of light.
Summary form only given. In the quantum optics group at Caltech, we are attempting to lay the foundations for quantum information science by way of advances on several fronts in optical physics. Within the setting of cavity QED, single atoms are strongly coupled to the field of a high finesse optical cavity at the single photon level, with current work directed toward trapping and localization of atoms inside the cavity. Although there are daunting technical problems to overcome, a principal scientific objective is the creation of quantum networks to implement fundamental quantum communication protocols and for distributed quantum computation. Beyond quantum information processing with internal atomic states and photons serving as qubits, we are also investigating algorithms for continuous quantum variables. A recent example is our realization of quantum teleportation for the quadrature amplitudes of a beam of light. The experiment utilizes squeezed-state entanglement to achieve unconditional quantum teleportation.
In this thesis we have focused on the study of various systems which are presently widely studied in different areas of quantum optics and quantum information sciences. These, for example, include the coupled system of photonic waveguides which are known to be highly efficient in manipulating the flow of light. The Hamiltonian describing the evolution of field mode in coupled waveguides is effectively identical to the well-known tight binding Hamiltonian used in solid state physics. The advantage of waveguide system is the possibility to control various interactions by design and their low decoherence rate. The excellent stability offered by coupled waveguides has led to the observation of many key coherent effects such as quantum walk, Bloch oscillation, and discrete Talbot effect. For example, Bloch oscillations have been investigated in coupled waveguides using coherent beam of light. We wanted to inquire whether coherent phenomena such as Bloch oscillations can be possible with incoherent single photon sources. We discovered that Bloch oscillations are indeed possible with single photons provided we prepare single photons in a W state. Moreover, coupled waveguides also find applications in the field of quantum information processing. Since entanglement plays a prominent role in all these applications, it is important to understand the entanglement dynamics in these structures. We considered the case of squeezed input in one of the waveguide and showed that one can generate entanglement between the waveguide modes. We further continued our work on the entanglement generation in coupled waveguides by incorporating the effect of loss in the waveguide structure for the squeezed and photon number input states. We considered relevant experimental parameters and showed that waveguide structures are reasonably robust against the effect of loss. Another system which has attracted a great deal of interest is the optomechanical system. We consider an optomechanical system where an optical cavity mode is coupled to the square of the position of a mechanical oscillator. The optomechanical system can then be regarded as a quantum optical spring, i.e., a spring whose spring constant depends on the quantum state of another system. In particular, we consider the situation where the field inside the cavity is in a coherent state and the oscillator is prepared in its ground state. The quantized nature of the field produces new features in the optomechanical system.
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.