It is shown that bremsstrahlung can give rise to a loss of coherence for quantum systems. Here a particular mechanism is analyzed, which makes use of the formal properties of the infrared radiation in QED. A charged particle goes through a scattering process into a superposition of two kinematically distinct states. The scattering also gives rise to the emission of a cloud of soft photons, and it is precisely this process that washes out the interference term between the two final states.

Compared to single-photon rates, multiphoton excitation rates of atoms and molecules are generally quite small, even at high laser intensities, at least in a 2-level system. Small multiphoton coupling strengths, large ac Stark shifts, and ionization all inhibit real population transfer between bound states. However, it has recently been shown that a 3-level system consisting of a ground state and a pair of nearly degenerate strongly coupled upper states greatly enhances the multiphoton coupling with the ground state, while also greatly reducing the ac Stark shift of the ground state. In this paper I will derive an analytic expression for the n-photon Rabi frequency, for this system, in the case of degenerate upper states, as well as an expression for the level shifts induced in the case of nondegenerate upper states. Numerical calculations based on the 3-level system are presented to verify the analytic results and to show that high-order π pulses can be driven at moderate field strengths. To demonstrate the feasibility of this process in a real physical system, I will present fully correlated 2-electron calculations in a model one-dimensional molecular potential, including ionization that show a 12-photon π pulse driven with near-infrared photons. In other words, a single excited state 18.6 eV above the ground state can be populated with over 90% efficiency with little ionization while the ground state is almost completely depopulated. Besides the possibility of producing an amplifying medium in the vacuum ultraviolet, this 3-level configuration may open the door to other strong field effects previously restricted to single-photon interactions, such as adiabatic passage and inner-shell ionization.

We implement experimentally a deterministic method to prepare and measure the so-called single-photon two-qubit entangled states or single-photon Bell states, in which the polarization and the spatial modes of a single photon each represent a quantum bit. All four single-photon Bell states can be easily prepared and measured deterministically using linear optical elements alone. We also discuss how this method can be used for the recently proposed single-photon two-qubit quantum cryptography scheme.

We study the quantum Zeno effect and the anti-Zeno effect in the case of “indirect” measurements, where a measuring apparatus does not act directly on an unstable system, for a realistic model with finite errors in the measurement. A general and simple formula for the decay rate of the unstable system under measurement is derived. In the case of a Lorentzian form factor, we calculate the full time evolutions of the decay rate, the response of the measuring apparatus, and the probability of errors in the measurement. It is shown that not only the response time but also the detection efficiency plays a crucial role. We present the prescription for observing the quantum Zeno and anti-Zeno effects, as well as the prescriptions for avoiding or calibrating these effects in general experiments.

We examine the violation of the majorization relations between the eigenvalues of the full and reduced density operators of entangled states of composite systems and its detection using generalized entropic forms based on arbitrary concave functions. It is shown that the violation of these relations may not always be detected by the conditional von Neumann and Tsallis entropies (for any $q>\mathrm{}0).\mathrm{}$ Families of smooth entropic forms which are always able to detect such violations are, however, provided. These features are then examined for particular sets of mixed states in a two-qudit system, which for $d>~3$ may exhibit different types of violation of the majorization relations. Comparison with the Peres criterion for separability is also shown.

We describe explicitly the algebra of polynomial functions on the Hilbert space of four-qubit states that are invariant under the group $\mathrm{SL}(2,C{)}^4$ of stochastic local quantum operations assisted by classical communication. From this description, we obtain a closed formula for the hyperdeterminant in terms of low degree invariants.

Under certain conditions it is possible to describe time evolution using different times for different particles. Use of multiple times is optional in the independent particle approximation, where interparticle interactions are removed, and the N-particle evolution operator factors into N single-particle evolution operators. In this limit one may use either a single time, with a single energy-time Fourier transform, or N different times with a different energy-time transform for each particle. The use of different times for different particles is fully justified when coherence between single-particle amplitudes is lost, e.g., if relatively strong randomly fluctuating residual fields influence each particle independently. However, when spatial correlation is present the use of multiple times is not feasible, even when the evolution of the particles is uncorrelated in time. Some calculations in simple atomic systems with and without spatial and temporal correlation between different electrons are included.

Two-photon interferometric quantum photon lithography for light of wavelength λ is capable of beating the Rayleigh diffraction limit of resolution λ/4 to the level of λ/8. The required twin single-photon states $|1{〉}_a|1{〉}_b,$ which are converted into maximally entangled states by a 50:50 beam splitter, can be generated from a nondegenerate parametric amplifier initially in vacuum states and with a weak pump field. Increasing the pump strength can slightly increase the production rate of the desired state and it will also increase the production of the twin two-photon states $|2{〉}_a|2{〉}_b,$ which leads to an unwanted background term. In this paper we show that, assuming a weak pair coherent state as input to the amplifier, quantum interference can be used to quench the production of the $|2{〉}_a|2{〉}_b$ state and to enhance the production of the $|1{〉}_a|1{〉}_b$ state by almost sixfold.

The effect of unitary noise on the performance of Grover’s quantum search algorithm is studied. This type of noise may result from tiny fluctuations and drift in the parameters of the (quantum) components performing the computation. The resulting operations are still unitary, but not precisely those assumed in the design of the algorithm. Here we focus on the effect of such noise in the Hadamard gate W, which is an essential component in each iteration of the quantum search process. To this end W is replaced by a noisy Hadamard gate U. The parameters of U at each iteration are taken from an arbitrary probability distribution (e.g., a Gaussian distribution) and are characterized by their statistical moments around the parameters of W. For simplicity, we assume that the noise is unbiased and isotropic, namely, all noise variables in the parametrization we use have zero average and the same standard deviation $\epsilon .$ The noise terms at different calls to U are assumed to be uncorrelated. For a search space of size ${N=2\mathrm{}}^n$ (where n is the number of qubits used to span this space) it is found that as long as $\epsilon <{O(n}^{-1/2}{N}^{-1/4})$ the algorithm maintains significant efficiency, while above this noise level its operation is hampered completely. It is also found that below this noise threshold, when the search fails, it is likely to provide a state that differs from the marked state by only a few bits. This feature can be used to search for the marked state by a classical postprocessing, even if the quantum search has failed, thus improving the success rate of the search process.

When one performs a continuous measurement, whether on a classical or quantum system, the measurement provides a certain average rate at which one becomes certain about the state of the system. For a quantum system this is an average rate at which the system is projected onto a pure state. We show that for a standard kind of continuous measurement, for a qubit this rate may be increased by applying unitary operations during the measurement (that is, by using Hamiltonian feedback), in contrast to the equivalent measurement on a classical bit, where reversible operations cannot be used to enhance the rate of entropy reduction. We determine the optimal feedback algorithm and discuss the Hamiltonian resources required.

If a generalized measurement is performed on a quantum system and we do not know the outcome, are we able to retrodict it with a second measurement? We obtain a necessary and sufficient condition for perfect retrodiction of the outcome of a known generalized measurement, given the final state, for an arbitrary initial state. From this, we deduce that, when the input and output Hilbert spaces have equal (finite) dimension, it is impossible to perfectly retrodict the outcome of any fine-grained measurement [where each positive, operator-valued measure (POVM) element corresponds to a single Kraus operator] for all initial states unless the measurement is unitarily equivalent to a projective measurement. It also enables us to show that every POVM can be realized in such a way that perfect outcome retrodiction is possible for an arbitrary initial state when the number of outcomes does not exceed the output Hilbert space dimension. We then consider the situation where the initial state is not arbitrary, though it may be entangled, and describe the conditions under which unambiguous outcome retrodiction is possible for a fine-grained generalized measurement. We find that this is possible for some state if the Kraus operators are linearly independent. This condition is also necessary when the Kraus operators are nonsingular. From this, we deduce that every trace-preserving quantum operation is associated with a generalized measurement whose outcome is unambiguously retrodictable for some initial state, and also that a set of unitary operators can be unambiguously discriminated iff they are linearly independent. We then examine the issue of unambiguous outcome retrodiction without entanglement. This has important connections with the theory of locally linearly dependent and locally linearly independent operators.

A recently developed theory for eliminating decoherence and design constraints in quantum computers, “encoded recoupling and decoupling,” is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature (London) 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the Sørensen-Mølmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme directly to the encoded qubits, are capable of further reducing various other sources of qubit decoherence, such as due to differential dephasing and due to decohered vibrational modes. The feasibility of using the relatively slow SM pulses in a decoupling scheme quenching the latter source of decoherence follows from the observed $1/f$ spectrum of the vibrational bath.

Inconclusive photon subtraction (IPS) is a conditional measurement scheme to force nonlinear evolution of a given state. In IPS the input state is mixed with the vacuum in a beam splitter and then the reflected beam is revealed by on-off photodetection. When the detector clicks we have the (inconclusive) photon subtracted state. We show that IPS on both channels of an entangled twin beam of radiation improves the fidelity of coherent state teleportation if the energy of the incoming twin beam is below a certain threshold, which depends on the beam splitter transmissivity and the quantum efficiency of photodetectors. We show that the energy threshold diverges when the transmissivity and the efficiency approach unity and compare our results with that of previous works on conclusive photon subtraction.

We investigate the absorption mechanism in a four-level system proposed by Harris and Yamamoto [Phys. Rev. Lett. 81, 3611 (1998)] by using the quantum-jump approach. We show that the one-photon and three-photon absorption processes are both responsible for the whole absorption at the line center of the probe field. In particular, we show the important role of the one-photon absorption process.

Existence of self-similar, superposed pulse-train solutions of the nonlinear, coupled Maxwell-Schrödinger equations, with the frequencies controlled by the oscillator strengths of the transitions, is established. Some of these excitations are specific to the resonant media, with energy levels in the configurations of $\Lambda$ and N and arise because of the interference effects of cnoidal waves, as evidenced from some recently discovered identities involving the Jacobian elliptic functions. Interestingly, these excitations also admit a dual interpretation as single pulse trains, with widely different amplitudes, which can lead to substantially different field intensities and population densities in different atomic levels.

Time-resolved coherent x-ray Raman signals of molecules are computed by formulating the nonlinear response in terms of correlation functions of charge and current densities. Simulations performed on one-dimensional molecular chains demonstrate that Raman resonances provide a direct local probe for valence-excitation dynamics with high spatial and temporal resolutions.

Spontaneous decay behavior from an assembly of atoms (or molecules) in a dielectric slab sandwiched by two dielectric semi-infinite spaces with arbitrary refractive indices is investigated. We introduce a lifetime distribution function to describe decay kinetics. The zero-point fluctuations of the electromagnetic field are calculated as a function of the position of atom in the slab. They display a symmetric profile with respect to the central plane of the slab in symmetric structure sample and the contributions of the guided modes and the radiation modes components both exhibit cosinelike variation with a base but with a phase difference of π. With the increase of the thickness of the slab, the oscillations become dense. In contrast, for the asymmetric structure case, the related curves are asymmetric with respect to the middle plane of slab and exhibit considerably distorted cosinelike oscillations. The dependence of the spontaneous emission rate of atoms on the thickness of the slab and the refractive indices of substrate also is surveyed. Our calculations show that quite wide or narrow lifetime distribution can occur for different thicknesses of the slab. The coexistence of both accelerated and inhibited decay processes appears. The calculated results are in good agreement with experimental results.

Ensemble quantum algorithms are well suited to calculate estimates of the energy spectra for spin-lattice systems. Based on the phase estimation algorithm, these algorithms efficiently estimate discrete Fourier coefficients of the density of states. Their efficiency in calculating the free energy per spin of general spin lattices to bounded error is examined. We find that the number of Fourier components required to bound the error in the free energy due to the broadening of the density of states scales polynomially with the number of spins in the lattice. However, the precision with which the Fourier components must be calculated is found to be an exponential function of the system size.

The computable cross-norm (CCN) criterion is a powerful analytical and computable separability criterion for bipartite quantum states, which is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension $2\times 2.$ In higher dimensions, theorems connecting the fidelity of a quantum state with the CCN criterion are proved. We also analyze the behavior of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.

Excitation and ionization cross sections are calculated for $e-{\mathrm{He}}^{+}$ scattering at electron impact energies of 100, 200, and 300 eV, using a time-dependent close-coupling method that employs variable lattice spacings. The ${\mathrm{He}}^{+}$ ionization cross section is found to be in good agreement with previous converged close-coupling calculations and experimental measurements. Excitation cross sections for $1\overrightarrow{s}ns,np$ transitions in ${\mathrm{He}}^{+}$ are presented for high n values well beyond the reach of available experimental measurements and previous nonperturbative theories. The relative difference between the nonperturbative close-coupling and the perturbative distorted-wave results is found to grow larger as the principal quantum number n is increased. This difference has important implications in the collisional-radiative modeling of many astrophysical and laboratory plasmas that use perturbation theory.