Information science is entering into a new era in which certain subtleties of quantum mechanics enables large enhancements in computational efficiency and communication security. Naturally, precise control of quantum systems required for the implementation of quantum information processing protocols implies potential breakthoughs in other sciences and technologies. We discuss recent developments in quantum control in optical systems and their applications in metrology and imaging.

We show how quantum entanglement in the ground state of interacting quantum systems can arise from dynamical instabilities in the phase space of the corresponding classical system. Using the example of coupled giant spins we show that, when the fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state - the ground state - achieves its maximum amount of entanglement near the critical parameter.

We investigate the creation of squeezing via operations subject to noise and losses and ask for the optimal use of such devices when supplemented by noiseless passive operations. Both, single and repeated uses of the device are optimized and it is proven that in the latter case the squeezing converges exponentially fast to its asymptotic optimum, which we determine explicitly. For the case of multiple iterations we show that the optimum can be achieved with fixed intermediate passive operations. Finally, we relate the results to the generation of entanglement and derive the maximal two-mode entanglement achievable within the considered scenario.

We explore the entanglement between a single atom and a single, resonant field mode of a driven optical cavity, focusing on the strong driving regime. We show that, in the absence of spontaneous emission, there are special initial conditions that lead to approximately disentangled trajectories, whereas spontaneous emission results in coherent superpositions of such trajectories that may lead to (transient) near-maximally entangled atom-field states. We also discuss the possibility of using a special "asymmetric" field correlation function to track the time evolution of this entanglement.

In this paper, we discuss the theory of entanglement amplifiers. We first describe non-degenerate optical parametric oscillator as an entanglement amplifier and present an input-output calculation for the entanglement of the output fields. We show that two bright output entanglement beams can be produced from this system. We then show that a correlated spontaneous emission laser can be used to implement an entanglement amplifier.

The classical information capacity of channels that are subject to quantum Gaussian noise is studied. Recent work has established the capacity of the pure-loss channel, as well as bounds on and a conjecture for the capacity of the lossy channel with isotropic-Gaussian excess noise. This work is applied to the pure-loss free-space channel that uses multiple Hermite-Gaussian (HG) or Laguerre-Gaussian (LG) spatial modes to communicate between soft-aperture transmit and receive pupils, and to the lossy channel with anisotropic (colored) Gaussian noise.

We will describe keyed communication in quantum noise (KCQ) and how it can be used for either data encryption or key generation. Specifically, we will focus on the AlphaEta protocol for data encryption where the role of quantum noise will be discussed. Additionally, the potential of using classical noise to enhance security via deliberate signal randomization (DSR) will be investigated. We will also investigate the effect of unwanted impairments, such as nonlinearities in a wavelength-division-multiplexed fiber transmission system, and how they affect the ultimate allowable propagation distance. Our simulations and experiments suggest that AlphaEta-protocol based physical-layer encryption is compatible with long-haul optical transmission systems operating at Gb/s data rates.

Non-linear phenomena impact the quality of optical transmission along the dielectric fiber. The theoretical analysis of non-linear interaction of light and matter assumes that certain parameters are either positive or within a bounded range. However, these assumptions although pragmatic may overshadow other possible outcomes that lead to paradoxical consequences of interest. In this paper, we review the theory of optical propagation and particularly the non-linear interaction between adjacent optical channels that propagate in a dielectric medium such as fiber, and we challenge traditional mathematical assumptions. We describe under what conditions the mathematical relation of the dielectric constant e(w)is expressed in terms of tuning or detuning between two oscillators, and under what conditions it is e(w)>1, e(w)<1, and also under what conditions e(w) becomes negative. The latter is of particular importance because if such conditions are achievable, matter has negative dielectric constant, the refractive index is purely imaginary, the group velocity meaningless, and a new chapter in photonic technology opens.

The maximum rates for reliably transmitting classical information over Bosonic multiple-access channels (MACs) are derived when the transmitters are restricted to coherent-state encodings. Inner and outer bounds for the ultimate capacity region of the Bosonic MAC are also presented. It is shown that the sum-rate upper bound is achievable with a coherent-state encoding and that the entire region is asymptotically achievable in the limit of large mean input photon numbers.

We describe proof-of principle experiments demonstrating a novel approach for generating pulses of light with controllable photon numbers, propagation direction, timing, and pulse shapes. The approach is based on preparation of an atomic ensemble in a state with a desired number of atomic spin excitations, which is later converted into a photon pulse by exploiting long-lived coherent memory for photon states and electromagnetically induced transparency (EIT). We discuss our progress toward applying these techniques to transmit quantum states between atomic memory nodes connected by a photonic channel.

We consider a quantum system of two nonorthogonal bipartite quantum states. We distribute the qubits between two parties, Alice and Bob. They each measure their qubits and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary for one of the qubits to be stored until the result of the measurement on the other is known. We consider the cases in which, should a failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability as would be obtained if the qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit and qudit states. Applications to quantum secret sharing are discussed.

In quantum information and quantum computing, the carrier of information is some quantum system and information is encoded in its state. After processing the state in the quantum processor, the information has to be read out. Clearly, this task is equivalent to determining the final state of the system. We begin by briefly reviewing various possible state discrimination strategies that are optimal with respect to some reasonable criteria and report on recent advances in the unambiguous discrimination of mixed quantum states. This strategy has been successfully applied to devise a class of novel probabilistic quantum algorithms and has been demonstrated experimentally, using a linear optical implementation via generalized interferometers. In the second part we present a scheme for communication via completely unknown quantum states. In this context we discuss programmable quantum state discriminators that are universal, i.e. perform optimally on average, independently of the actual states used for the communication scheme. We conclude with a discussion of possible experimental implementations of the proposed device.

The architecture proposed by Duan, Lukin, Cirac, and Zoller (DLCZ) for entangling distant atomic ensembles is addressed and analyzed. Its performance, in terms of fidelity and throughput, is compared to that of the quantum communication architecture using trapped rubidium-atom quantum memories that has been proposed by a team from the Massachusetts Institute of Technology and Northwestern University (MIT/NU). It is shown that the DLCZ protocol for entanglement distribution achieves a better throughput versus distance behavior than does the MIT/NU architecture, with both being capable of high entanglement fidelities. The DLCZ scheme also admits to a conditional teleportation scheme based on its entangled atomic ensembles, whereas the MIT/NU architecture affords unconditional teleportation based on its trapped-atom quantum memories. It is shown that achieving unity fidelity in DLCZ teleportation requires photon-number resolving detectors; the maximum teleportation fidelity that can be realized with non-resolving detectors is 1/2.

We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding the nature of the quantum/classical computational transition. We refine some previously known upper bounds using two different strategies. The first one involves the introduction of bi-entangling operations, a class of classically simulatable machines that can generate at most bipartite entanglement. Using this class we show that it is possible to sharpen previously obtained upper bounds in certain cases. As an example, we show that under depolarizing noise on the controlled-not gate, the previously known upper bound of 74% can be sharpened to around 67%. Another interesting consequence is that measurement based schemes cannot work using only 2-qubit non-degenerate projections. In the second strand of the work we utilize the Gottesman-Knill theorem on the classically efficient simulation of Clifford group operations. The bounds attained using this approach for the pi/8-gate can be as low as 15% for general single gate noise, and 30% for dephasing noise.

Quantum error correction is an essential ingredient for quantum computation. The standard descriptions of how to implement active error correction assume ideal resources such as projective measurements and instantaneous gate operations. Unfortunately in practice such resources are not realizable in most quantum computing architectures and it is not clear how such error correction implementations will perform under more realistic conditions. Motivated by this we examine schemes for implementing active error correction that use a more modest set of resources. This leads to new implementations of error correction that are continuous in time, and thus described by continuous dynamical maps. We evaluate the performance of such schemes using numerical simulations and comment on the applicability and effectiveness of continuous error correction for quantum computing.

Dynamical decoupling is a feed-back free scheme for quantum error correction against noise and decoherence errors. An efficiency analysis of dynamical decoupling is performed. Furthermore we provide the basic concepts of dynamical decoupling and quantum error correction codes, and give an example of a hybrid protection scheme. Some interesting extensions of dynamical decoupling are discussed at the end.

A quantum version of the Minority game for an arbitrary number of agents is studied. When the number of agents is odd, quantizing the game produces no advantage to the players, however, for an even number of agents new Nash equilibria appear that have no classical analogue. The new Nash equilibria provide far preferable expected payoffs to the players compared to the equivalent classical game. The effect on the Nash equilibrium payoff of reducing the degree of entanglement, or of introducing decoherence into the model, is indicated.

Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is constant equal to the inverse 1/√d, with d the dimension of the finite Hilbert space, are becoming more and more studied for applications such as quantum tomography and cryptography, and in relation to entangled states and to the Heisenberg-Weil group of quantum optics. Complete sets of MUBs of cardinality d+1 have been derived for prime power dimensions d=p^m using the tools of abstract algebra (Wootters in 1989, Klappenecker in 2003). Presumably, for non prime dimensions the cardinality is much less. The bases can be reinterpreted as quantum phase states, i.e. as eigenvectors of Hermitean phase operators generalizing those introduced by Pegg and Barnett in 1989. The MUB states are related to additive characters of Galois fields (in odd characteristic p) and of Galois rings (in characteristic 2). Quantum Fourier transforms of the components in vectors of the bases define a more general class of MUBs with multiplicative characters and additive ones altogether. We investigate the complementary properties of the above phase operator with respect to the number operator. We also study the phase probability distribution and variance for physical states and find them related to the Gauss sums, which are sums over all elements of the field (or of the ring) of the product of multiplicative and additive characters. Finally we relate the concepts of mutual unbiasedness and maximal entanglement. This allows to use well studied algebraic concepts as efficient tools in our quest of minimal uncertainty in quantum information primitives.

A wide variety of dissipative and fluctuation problems involving a quantum system in a heat bath can be described by the independent-oscillator (IO) model Hamiltonian. Using Heisenberg equations of motion, this leads to a generalized quantum Langevin equation (QLE) for the quantum system involving two quantities which encapsulate the properties of the heat bath. Applications include: atomic energy shifts in a blackbody radiation heat bath; solution of the problem of runaway solutions in QED; electrical circuits (resistively shunted Josephson barrier, microscopic tunnel junction, etc.); conductivity calculations (since the QLE gives a natural separation between dissipative and fluctuation forces); dissipative quantum tunneling; noise effects in gravitational wave detectors; anomalous diffusion; strongly driven quantum systems; decoherence phenomena; analysis of Unruh radiation and entropy for a dissipative system.

We discuss the emergence of the classical description from quantum mechanics for chaotic systems. We consider a specific model, which corresponds to an ion trapped in a harmonic potential and submitted to a sequence of laser pulses: the kicked harmonic oscillator, under conditions that lead to chaotic behavior for the classical system. We show that noise plays an essential role in the transition from quantum to classical behavior. This transition is described in terms of the separation between the classical phase space distribution and the Wigner function corresponding to the quantum system, obtained by integrating over the whole phase space the magnitude of the difference between the two distributions. It is shown that, in the semiclassical limit, this separation is governed by a single parameter, which depends on the diffusion coefficient, the Lamb-Dicke parameter, and the kick strength. The Lamb-Dicke parameter plays the role of a dimensioneless Planck constant. As this parameter goes to zero, we show that both distributions remain close together for all times.

We study the quantum to classical transition in bipartite entangled systems in which one system is continuously coupled to a measurement apparatus as in the von Neumann model of quantum measurement. As an example, we study the open system dynamics of a particle in a harmonic well whose motion in the well is coupled to the internal spin. This system provides a rich illustration of the quantum to classical transition in weakly measured coupled systems. We analyze and derive conditions for which the dual constraints of strong localization/small noise required for the quantum-classical transition are satisfied for both regular and chaotic dynamics. We also study the dynamics of bipartite entanglement in the regime where classical trajectories emerge in the measurement record. Our analysis shows the surprising result that bipartite entanglement can persist in the classical limit.

We discuss various aspects of the incoherent spontaneous emission in atomic few-level systems arising from the coupling of the atom to the surrounding vacuum. First, we consider systems where the decoherence due to spontaneous emission acts as a limiting factor. Here, we combine collective effects in larger samples of atoms with control mechanisms known from single-atom schemes, or modify the system dynamics by externally inducing multiphoton quantum interference effects. In the second part, we discuss ground-state laser cooling of trapped atoms and ions. Here, the momentum transfer in the spontaneous emission events is required to cool the particles, but needs to be controlled in order to achieve a low cooling limit. In our scheme, we make use of double electromagnetically induced transparency in order to design the absorption spectrum of the trapped particle. In the final part, we show that the incoherent part of the resonance fluorescence spectrum of a two-level system may serve as an interesting candidate for high-precision spectroscopy. For this, we discuss relativistic and radiative corrections to the resonance fluorescence spectra of laser-driven few-level systems.

We investigate the spontaneous emission of a two-level atom in one dimensional photonic crystals composed of left-hand material (LHM) and right-hand material (RHM). A complete set of mode functions is constructed for the quantization of the radiation field. It is found that the mode functions for the frequency with in the band gap decreases exponentially from the surface to the interior of the photonic crystal which results in a much weaker field than the vacuum in the free space. The depression of the field leads to weak interaction with the atom, which leads to the suppressed spontaneous emission. Due to the strong reflection, the field in the LHM-RHM structure is much weaker than that in the RHM-RHM structure, thus the spontaneous emission is more strongly suppressed.

Quantum systems may be used to transmit classical information. To do this the sender encodes information by preparing the system in one of an alphabet of possible states, and sends it to the receiver. The receiver then performs a measurement on the system in order to obtain information about which state was sent. Here we describe a general bound on the information which is accessible to the receiver in such a channel when the receivers measurement is noisy. In addition to extracting classical information, measurements also reduce the entropy of a quantum system. This is important, for example, in quantum feedback control. We discuss two corollaries of the information bound that involve this entropy reduction.

Pulsed Laser Chemical Vapor Deposition (PLCVD) has been used to fabricate single atoms doped nanoparticles of magnesium sulfide. These particles were dispersed in optically transparent Poly-methyl-methacrylate (PMMA) films for near field nano-microscopy such that each nanoparticle doped with a single europium atom falls in the focusing range of the near field microscope. By atomic tailoring, the concentration of the doubly ionized europium, Eu²⁺, has been maximized in these nanoparticles. The energy and the oscillator strength of the 4f⁷-4f⁶5d¹ electronic transition has been tailored to maximize its addressing by photons in single atom spectroscopy experiments. Results have been presented on the fabrication of these single atom doped nanoparticles and their spectroscopy by laser excited fluorescence technique. Studies of a single Eu²⁺ ion by confocal micro-spectroscopy are in progress.

Detection and manipulation of single electron spin states in solids has recently been given much attention for applications to quantum computing. In this architecture, the inter-atomic spacing of spins in a solid is an important parameter. One way to control the inter-atomic spacing is to implant spin impurities in pairs via ion implantation. Here, we discuss a proof-of-principle demonstration in synthetic diamond, wherein N₂ was implanted to create pairs of nitrogen-vacancy (NV) color centers.

Enhancement and suppression of spontaneous emission is vital to both quantum optics research and optoelectronics industry. Surface plasmon has been known to feature such characteristics. Waveguide-coupled-atom systems are studied for this goal. The enhancement is proportional to a field focusing factor and inverse to the group velocity along the waveguide. Comparison is made to the Purcell factor. A numerical example shows a promising structure with a grating-coupled plasmonic waveguide, projecting an emission enhancement by 51 times in spite of heat dissipation.

A critical limitation of slow light schemes is the limited time-bandwidth product. Recently we showed that this limitation can be overcome by making use of inhomogeneities. Here we analyze the effects of crosstalk noise that can be induced by these inhomogeneities in certain situations, and how to minimize such noise. The proof of principle experiment was done using three-wave mixing in a photorefractive crystal Ce:BaTiO₃ where Bragg selection is used to provide the inhomogeneity.

We report on an experiment to study the properties of nonlasing subthreshold sidemodes in a semiconductor laser operating in an external grating cavity configuration. We measure optical spectra consisting of the lasing mode and subthreshold nonlasing sidemodes, as well as radio frequency spectra at low frequency (0-100MHz) and at high frequency near the external grating cavity mode frequency. As the laser frequency is varied, the features of the rf spectra and the optical sidemode spectra all vary systematically. We present results on how these variations depend upon the external grating cavity mode frequency. Our results are compared with previous experiments and with theoretical predictions based upon four-wave mixing between the lasing mode and the adjacent sidemodes.

When imaging schemes such as Magnetic Resonance Imaging are applied to nano-scale samples, the practical resolution is often limited by noise due to the difficulty of detecting a signal from a small number of nuclear or electronic spins. In this paper we discuss the potential for improving resolution by using optically detected magnetic resonance imaging such as optical Raman excited ESR transitions. Comparisons will be made between magnetic field gradients vs ac Stark gradients and optical Raman vs. direct microwave spin excitations. To make the analysis more concrete we will use nitrogen-vacancy (NV) defect centers in diamond as a test system.

Associative memories that recognize a pattern based on partial input have numerous applications such as homeland security. Optical implementations of associative memories, for example using computer-generated holograms, have the inherent parallelism as an advantage over software realizations. The nonlinear thresholding operation is a key step in the optical associative memories. A major source error in these memories is the thresholding uncertainties caused by fluctuation, for example in the input illumination or varying degrees of partial obscuration. Here, we show a proof-of-principle demonstration of a new scheme to suppress such errors using real time thresholding and a modified Hopfield associative memory model.

Inhomogeneous broadening in optically addressed solids provides a convenient technique for individually addressing a large number of optically active defects in a crystal. Such a capability is important for quantum computer development. However, the random nature of inhomogeneous broadening can limit scalability. Here, techniques that can be used to suppress inhomogeneous broadening will be reviewed including a recently proposed VLSI quantum computer design based on nitrogen-vacancy (NV) color centers in diamond.

We first introduce a method called quantum path verification, where we search for a break in a quantum network. After explaining these capabilities, we address gate internal faults. We present new fault models to represent crosstalk and unwanted nearest neighbor entanglement. When witnessed, these errors are probabilistic, but there is a set of tests that has the highest probability of detecting a fault. We introduce a method of probabilistic set covering to identify this set of tests. A large part of our work consisted of writing a software package that allows us to compare various fault models and test strategies.

A brief overview is given of the research activities in the Quantum Optics Group at Caltech related to the new science of Quantum Information.