"Entanglement" is a nonclassical property of some states of quantum systems that are composed of parts: the "local" state describing the parts viewed individually looks "mixed," probabilistic, but the "global" state is "pure," as definite as a quantum state can be. The notion of entanglement is relative: it depends on a choice of "local" subalgebra. We generalize the notion of entanglement by considering as "generalized entangled" pure states that are mixed when viewed according to restrictions more general than "locality": restrictions to interaction and control of the system via a Lie subalgebra of the algebra of all of its operators. We discuss applications to quantum computation and condensed matter systems.

Ion traps are indispensable tools for studying quantum mechanical systems because they can tightly confine single ions almost indefinitely. We are using a linear Paul trap to test the statement the exact result of any arbitrary measurement of a quantum mechanical system should be unpredictable. The results of this test are important to interpreting the nature of information in a quantum mechanical system. Additionally, we are developing our system so that we may perform quantum logic operations in trapped ions.

We are attempting to harness the tight control over atoms provided by a Bose-Einstein condensate to build a waveguide atom interferometer. This device will be extremely sensitive to any interaction that affects the energies of atoms, such as electromagnetic fields, gravity and gravity gradients, and accelerations. The technology can also be miniaturized, ultimately down to the level of an integrated "atom chip" with dimensions of just a few millimeters, which would make possible a new generation of ultra-sensitive miniature sensors.

I will briefly overview our current quantum research, plans and ideas on modeling and simulations of quantum computation and quantum measurement. This will include: perturbation theory for scalable quantum computation, magnetic resonance force microscopy single-spin measurement, self-assembled quantum computation, type-II quantum computation.

Existing models of decoherence, applicable to quantum information theory or to fundamental questions in quantum dynamics, are based on integrable environments. In order to extend these models to chaotic environments, we have studied an analytic model involving an inverted harmonic oscillator. The results indicate that chaotic environments may produce decoherence much faster than integrable ones.

In this talk I will give a short overview of the research we are doing in T-QC in the fields of decoherence (including quantum-classical transition and quantum chaos) and quantum information (including quantum discord, mutual information and redundancy).

In this talk I will give a short overview of the research we are doing in T-QC in the fields of BEC optics (including quantum measurement of cold atoms and atom interferometry) and vacuum fluctuations physics (including static and dynamic Casimir forces).

The laser cooling of molecules to micro-Kelvin temperatures appears to be experimentally possible. We plan to demonstrate the first Doppler-cooling of molecules, targeting at first the alkaline-earth hydrides (e.g. BeH and CaH) which are paramagnetic and have electronic bands analogous to the S-P resonance transitions of the routinely-trapped alkali atoms. Once trapped and cooled, molecules will offer through their internal states a far richer range of inquiry than possible with atoms, including studies in the coherence of intramolecular modes and photodissociated fragments. We will highlight our strategy, the project’s status, and our future plans.

For the past decade molecular switches and selfassembly techniques have been developed that produce uniform planar molecular switch arrays (10**6 x 10**6). Optimal spin-containing molecules are being designed with DARPA support that maximally decouple from the environment and are being selfassembled by the same scientists who made the molecular switch arrays.
What will be gained when classical and quantum computers are combined to form hybrid computers? IBM plans to build a $5M/year research center to exploit the potential of hybrid computers. Arrays of quantum computers coupled by classical communication have been shown to solve partial differential equations efficiently. Applications of hybrid computers to problems of interest to LANL will be mentioned. Decoherence and fabrication limitations may restrict the size of quantum computers, yet much can be done with large arrays of these.

Computing and interpreting mixed state entanglement is a hard problem. We explore quantities that have a direct relationship to measureable quantities in quantum information science and may be easier to compute and interpret. One such quantity is the fully entangled fraction which is related to the fidelity of dense coding, teleportation, or entanglement swapping.

We are investigating process steps leading to a Kane architecture solid-state quantum computer (reference 1). We have performed hydrogen resist lithography, low-temperature silicon homoepitaxial growth and charge imaging in our ultra-high vacuum scanning tunneling microscope. These steps are necessary to create, activate and verify the phosphorus qubit array.
Holger Grube, Geoffrey W. Brown, Joshua M. Pomeroy, Marilyn E. Hawley (MST-8)
Reference 1: B. Kane, Nature 393, 133 (1998)

If a large quantum computer existed today, there are very few significant physical problems, quantum or classical, that could be solved on such a computer. I will summarize the work of our team to develop the necessary quantum algorithms (networks) to simulate quantum systems efficiently of a quantum computer. The results of the actual realization of one such algorithm for a toy problem on a liquid state NMR quantum computer will be shown.

We discuss natural geometric questions about entangled and separable states of bipartite quantum systems and linear maps on these systems, and investigations on the classical complexity of answering these questions.

Designing efficient high-level language compilers for quantum computers will require optimizing the mapping of application-source-level instructions into the logic of quantum entanglement (LQE, Zurek and Laflamme 1996; Julsgaard 2001). LQE can be represented as a system of propositions (Birkhoff and von Neumann 1936; Jauch 1968) that is isomorphic to an orthocomplemented, weakly modular lattice defined on the subspaces of an infinite-dimensional Hilbert space (Akhiezer and Glazman, 1961; Cohen 1989). Discovering efficient mappings from application-source to LQE will require identifying efficient derivations of quantum-logic theorems. Automated quantum-logic theorem-provers can significantly aid this discovery effort. I describe what I believe to be a novel and very brief proof generated by an automated backtracking (Dewar and Cleary 1990) theorem-prover, bvn, for Birkhoff-von Neumann quantum logic (Horner 2001).

It is now generally realized that the exploitation of fundamentally quantum mechanical phenomena can enable significant, and in some cases, tremendous, improvement for variety of tasks important to emergent technologies. Because of decades of successes in the experimental demonstration of such fundamental phenomena, quantum optics is playing a preeminent role in this endeavor; indeed, many of the objectives of quantum technologies are inherently suited to optics (e.g., communications, remote sensing), while others may have a strong optical component (e.g., distributed quantum computing, quantum repeaters). With our collaborators both within LANL and at other institutions worldwide, we are exploring various aspects of the development of photonics-based quantum technologies, in particular: entangled state preparation and characterization, high efficiency single photon detectors and Bell state analysis of photon pairs; optical based readouts for spin-based solid state quantum computers; optical probes for quantum phenomena in semiconductors; and the physics of cold trapped ions.

Colloidal synthesis allows the fabrication of almost monodisperse sub-10 nm semiconductor nanoparticles, known also as nanocrystal quantum dots (NQDs). Due to the extremely small, quantum-confined dimensions, NQDs exhibit discrete, atomic-like energy states that make them ideally suited for transferring the quantum-control approaches, well established for atoms and molecules, into the domain of condensed-matter systems. Similar to true atoms, NQDs offer well defined narrow resonances with potentially long dephasing times. In addition, they offer the advantage of tunability of electronic structures and electronic interactions via size/shape/structure control, not possible in actual atomic systems. Some potential applications of NQDs in quantum technologies include: NQDs as a single-photon source, NQD biexcitons as an entangled photon source, and NQD dimers for conditional logic operations.

We focus on the design and analysis of efficient quantum measurement techniques for individual quantum systems, mainly in condensed matter context. This includes electrical and mechanical detection and measurement of spins, and realistic displacement measurement schemes for mechanical objects, such as cantilevers. Applications that we have in mind include qubit design and read-out protocols, ultra-sensitive detection in atomic force microscopy and related experimental techniques, and molecular vibrational spectroscopy.

When laser radiation propagates in the atmosphere its photon statistics is modified because of the intensity scintillations caused by turbulence. We have found generally good agreement between the photon counting statistics measured at LANL and the generally accepted (but largely untested) theory that presumes a log-normal distribution for the scintillations. More generally we can in principle infer the distribution describing the intensity scintillations from the measured photon counting distribution.

The unique paring of photons of produced by parametric down conversion makes possible many new types of imaging and metrology. We will discuss some of the on-going developments in these two areas.

Quantum Key Distribution (QKD) is rapidly moving from experimental curiosity to practical applications. We have QKD projects ranging from all fiber network system development to free-space optical links to satellites. A brief overview of the work being performed in these areas will be given.

Characterizing and quantifying entanglement of quantum states in many-particle systems is at the core of a full understanding of the nature of quantum phase transitions in matter. Entanglement is a relative notion and, although many measures of entanglement have been defined in the literature, assessing the utility of those measures to characterize quantum phase transitions is still an open problem. Our aim is to introduce measures, based on a different concept of entanglement, which allows us to identify the transition and possibly classify quantum critical points.

My background is in the experimental study of the quantum dynamics of classically chaotic systems. My current interests build upon this background, and include the study (both theoretical and experimental) of feedback control of quantum systems, the quantum-classical transition, and nonlinear dynamics of Bose-Einstein condensates.

Coherent quantum control uses ultrafast optical pulse shaping techniques to selectively excite materials with the objective of preparing and manipulating specific electronic and photonic quantum states. Although coherent control has been implemented for atomic and molecular systems, its application to solid-state systems remains relatively untouched, yet the ability to coherently manipulate solids is of critical importance for building future quantum electronic and photonic devices. We will describe the development of the field of coherent control of solid-state systems using shaped ultrafast optical pulses for preparation, manipulation and interrogation of quantum wavepackets. We will explore a series of increasingly complex materials systems (nonlinear optical crystals, semiconductor quantum dots, and bulk materials) that will enable us to transfer quantum information processing and control approaches into the domain of condensed matter.

Multi-component Bose-Einstein condensates (BECs), atom optics and the use of optical lattice technology provide promising avenues for future BEC research. I will emphasize the remarkable prediction of dilute BECs with the liquid-like property of a self-determined density. I would also like to share some speculations on how such self-confined BECs could be helpful in realizing atom-laser applications.

Optical lattices provide a possible environment for the experimental realization of quantum computation. We have been exploring a promising scheme for the entanglement of trapped neutral atoms based on the magnetically controlled Feshbach resonances.

Using the isotopic selectivity and high sensitivity of the atomic trapping process, we have pioneered a coupled magneto-optical trap (MOT)—mass separator system for the isotopic ratio determination of ¹³⁵Cs/¹³⁷Cs. The system presently achieves an overall efficiency of 0.5%, an isotopic selectivity of >10¹², a sample detection limit of 10⁶ atoms, and an isotopic-ratio accuracy of 4% in the determination of ¹³⁷Cs/¹³⁵Cs. This new method has important applications to the areas of environmental science, nonproliferation, and homeland defense. We will briefly summarize this work and highlight future improvements/extensions of the method.

Recently, ultracold atoms have attracted quite some interests in quantum computing. At Los Alamos, we have been setting up an optical lattice experiment with the goal of studying spin entanglement and decoherence effects in optically trapped cold atoms. We have also successfully produced Bose-Einstein Condesate (BEC) in a separate experiment. We will present our latest ideas and progress towards the quantum entanglement of cold neutral atoms and BECs.