We study analytically and numerically the behavior of the concurrence (a measure of the entanglement of formation) of a pair of qubits in a quantum computer operating an efficient algorithm for quantum chaos. Our results show that in an ideal algorithm the entanglement decays exponentially with the diffusive relaxation rate induced by classical chaos. This decay reaches a residual level which drops exponentially with increasing number of qubits $n_q.$ Decoherence destroys the residual entanglement with a rate exponential in $n_q.$

The decoherence mechanism of a single atom inside a high-Q cavity is studied, and the results are compared with experimental observations reported by M. Brune et al. [Phys. Rev. Lett. 76, 1800 (1996)]. Collision dephasing and cavity leakage are considered as the major sources giving rise to the decoherence effect. In particular, we show that the experimental data can be fitted very well by assuming suitable values of the collision Stark shifts and dark count rate in the detector.

The “locality hypothesis” in density-functional theory (DFT), implying that the functional derivative is equivalent to a multiplicative local function, forms the basis of models of Kohn-Sham type. This has been generally accepted by the community since the advent of the model, and has later been formally proved for a large class of functionals. The hypothesis has recently been questioned by Nesbet [Phys. Rev. A 58, R12 (1998) and Phys. Rev. A 65, 010502 (2001)], who claims that it fails for the kinetic-energy functional for a system with more than two noninteracting electrons with a nondegenerate ground state. This conclusion has been questioned by Gál [Phys. Rev. A 62, 044501 (2000)] and by Holas and March [Phys. Rev. A 64, 016501 (2001)]. We claim that the arguments of Nesbet are incorrect, since the orbital functional used for the kinetic energy is not a unique functional of the total density in the domain of unnormalized orbitals. We have demonstrated that with a proper definition of the kinetic energy, which is a unique density functional also in the unnormalized region, the derivative can be represented by a single local multiplicative function for all $v$-representable densities. Therefore, we consider the controversy connected with the issue raised by Nesbet as resolved. We believe that the proof of the differentiability given here can be extended to larger groups of DFT functionals, and works along these lines are in progress

Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel properties to gain an algorithmic speedup over classical algorithms. In this paper, we present a quantum search algorithm based on the quantum random-walk architecture that provides such a speedup. It will be shown that this algorithm performs an oracle search on a database of N items with $O\left(\sqrt{N}\right)$ calls to the oracle, yielding a speedup similar to other quantum search algorithms. It appears that the quantum random-walk formulation has considerable flexibility, presenting interesting opportunities for development of other, possibly novel quantum algorithms.

Wootters [Phys. Rev. Lett. $80,$ 2245 (1998)] has derived a closed formula for the entanglement of formation (EOF) of an arbitrary mixed state in a system of two qubits. There is no known closed-form expression for the EOF of an arbitrary mixed state in any system more complicated than two qubits. This paper, via a relatively straightforward generalization of Wootters’ original derivation, obtains a closed-form lower bound on the EOF of an arbitary mixed state of a system composed of a qubit and a qudit (a d-level quantum system, with $d>~3).$ The derivation of the lower bound is detailed for a system composed of a qubit and a qutrit $\mathrm{}(d=3\mathrm{});$ the generalization to $d>\mathrm{}3\mathrm{}$ then follows readily.

In this paper, we study the implementation of nonadiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding (manipulation) schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase, one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be, in principle, implemented.

A theory for ion-atom collisions at low energies based on the hyperspherical close-coupling (HSCC) method is presented. In hyperspherical coordinates the wave function is expanded in analogy to the Born-Oppenheimer approximation where the adiabatic channel functions are calculated with B-spline basis functions while the coupled hyperradial equations are solved by a combination of R-matrix propagation and the slow/smooth variable discretization method. The HSCC method is applied to calculate charge-transfer cross sections for ${\mathrm{He}}^{2+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{He}}^{+}\mathrm{}(n=2\mathrm{})+{\mathrm{H}}^{+}$ reactions at center-of-mass energies from 10 eV to 4 keV. The results are shown to be in general good agreement with calculations based on the molecular orbital (MO) expansion method where electron translation factors (ETF’s) or switching functions have been incorporated in each MO. However, discrepancies were found at very low energies. It is shown that the HSCC method can be used to study low-energy ion-atom collisions without the need to introduce the ad hoc ETF’s, and the results are free from ambiguities associated with the traditional MO expansion approach.

We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons, we find that as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location.

We present and solve a restricted Abelian hidden subgroup problem using the adiabatic quantum-computing paradigm. The time step complexity is shown to be a polynomial in the number of input qubits. This paper is a step towards looking at the Abelian hidden subgroup problem from a quantum adiabatic standpoint.

We have obtained fast loading of a rubidium magneto-optical trap and very high collection efficiency by capturing the atoms desorbed by a light flash from a polydimethylsiloxane film deposited on the internal surface of a cell. The atoms are trapped with an effective loading time of about 65 ms at a loading rate greater than $2\times {10}^8$ atoms per second. This rate is larger than the values reported in literature and is obtained by preserving a long lifetime of the trapped atoms. This lifetime exceeds the filling time by nearly two orders of magnitude. Trap loading by light-induced desorption from siloxane compounds can be very effectively applied to store and trap a large number of atoms in the case of very weak atomic flux or extremely low vapor density. It can be also effectively used for fast production of ultracold atoms.

We show that the quantum many-body state of Bose-Einstein condensates consistent with the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations is a generalized coherent state. At zero temperature, the noncondensate density and the anomalous noncondensate correlation are not independent, allowing us to eliminate one of the three variables in the TDHFB.

We have measured two-photon decay of single K vacancies in gold atoms following photoionization with synchrotron radiation. Our results for the $2\overrightarrow{s}1s$ and $3\overrightarrow{d}1s$ two-photon transitions determine the rates for two-photon decay when the photons share the transition energy equally and have opening angles near $\theta =\pi /2.\mathrm{}$ These results are compared with nonrelativistic calculations for H-like Au ions and with theoretical and experimental results on lighter atoms.

We consider the behavior of quantum states under stochastic local quantum operations and classical communication (SLOCC) for an arbitrary fixed number of qubits. We use a real (Lorentz) group to describe the action of SLOCC operations on n-qubit states. We discuss the natural quantum Lorentz-group group-invariant length for an arbitrary number of qubits. We relate this approach to that based on local operations and classical communication and provide an example of how the invariant length can be used to describe entanglement. We also note that this invariant length is the Minkowskian analog to the quantum state purity, which is the corresponding Euclidean length.

The objective of this paper is to identify the necessary and sufficient minimum information carried by Reduced Density Matrices (RDMs). This minimum of essential information determines a set of equivalent compact-form matrices that are devoid of the redundant information present in the original RDMs when the system possesses symmetry invariances. The basic properties and algebra operations of these compact-form matrices are obtained here. The use of these new mathematical objects renders far more economical the operations and storage of RDMs and will thus be of interest in the study of systems with symmetry invariances. In particular, it opens the possibility of using large basis for medium-sized systems when solving iteratively the contracted Schrödinger equation.

In the theory of molecular light scattering and nonlinear optics, excited state damping is a significant consideration at frequencies near to resonance. Despite attempts to resolve a long-standing controversy over the propriety of such methods, there remains a dispute over the correct sign for the damping of antiresonant terms. Most established theory of Raman and associated light scattering employs a constant-sign rule at odds with a variable sign commonly used in nonlinear optics. However, by focusing on the polarizability it is demonstrated that arguments for the constant-sign convention vindicate standard Raman theory; flaws in the counterpropositions undermine the case for variable signing. It is also shown that a polarizability sum rule is valid only with constant-sign damping.

We study the role of continuous measurement in the quantum to classical transition for a system with coupled internal (spin) and external (motional) degrees of freedom. Even when the measured motional degree of freedom can be treated classically, entanglement between spin and motion causes strong measurement back action on the quantum spin subsystem so that classical trajectories are not recovered in this mixed quantum-classical regime. The measurement can extract localized quantum trajectories that behave classically only when the internal action also becomes large relative to ħ.

The wavelength of the ${3s}_{1/2}-{3p}_{3/2}$ transition of Na-like ${\mathrm{U}}^{81+}$ was determined to be $9.49985\pm 0.00015\mathrm{\AA }$ $(1305.12\mathrm{}\pm 0.02\mathrm{eV}),$ using the EBIT-I electron beam ion trap. The measurement is many times more sensitive to the radiative contributions from quantum electrodynamics than earlier measurements for ${\mathrm{Pt}}^{67+}$ and ${\mathrm{Pb}}^{71+}.$ Our result strongly deviates from various predictions employing scaled hydrogenic quantum electrodynamic corrections and establishes a benchmark for multielectron QED calculations that agrees well with the trend established by ab initio calculations.

We investigate superfluidity in the interior-gap states proposed by Liu and Wilczek. At weak coupling, we find the gapless interior-gap state unstable in physically accessible regimes of the parameter space, where the superfluid density is shown to be always negative. We therefore conclude that the spatially uniform interior-gap phase is extremely unstable unless it is fully gapped; in this case, however, the state is rather similar to conventional BCS states.

In this work we construct two classes of exact solutions for the most general time-dependent Dirac Hamiltonian in $1+1$ dimensions. Some problems regarding some formal solutions in the literature are discussed. Finally the possibility of existence of a generalized Lewis-Riesenfeld invariant connected with such solutions is discussed.