We study the spatial coherence of entangled photon pairs that are generated via type-I spontaneous parametric down-conversion (SPDC). By manipulating the spatial overlap between the two down-converted beams in a Hong-Ou-Mandel interferometer we observe the spatial interference of multiple transverse modes for an even and an odd number of mirrors in the interferometer. We demonstrate that the two-photon spatial coherence, which is quantified in terms of a transverse coherence length, differs completely for the two mirror geometries and support this result by a theoretical and experimental explanation in terms of photon labeling.

Mapping the system evolution of a two-state system allows the determination of the effective system Hamiltonian directly. We show how this can be achieved even if the system is decohering appreciably over the observation time. A method to include various decoherence models is given and the limits of this technique are explored. This technique is applicable both to the problem of calibrating a control Hamiltonian for quantum computing applications and for precision experiments in two-state quantum systems. The accuracy of the results obtained with this technique are ultimately limited by the validity of the decoherence model used.

We suggest an efficient method for generating matter-wave gap solitons in a repulsive Bose-Einstein condensate, when the gap soliton is formed from a condensate cloud in a harmonic trap after turning on a one-dimensional optical lattice. We demonstrate numerically that this approach does not require preparing the initial atomic wave packet in a specific state corresponding to the edge of the Brillouin zone of the spectrum, and losses that occur during the soliton generation process can be suppressed by an appropriate adiabatic switching of the optical lattice.

We compare two distinct models of evaporative cooling of a magnetically guided atomic beam: a continuous one, consisting in approximating the atomic distribution function by a truncated equilibrium distribution, and a discrete-step one, in which the evaporation process is described in terms of successive steps consisting in a truncation of the distribution followed by rethermalization. Calculations are performed for the semilinear potential relevant for experiments. We show that it is possible to map one model onto the other, allowing us to infer, for the discrete-step model, the rethermalization kinetics, which turns out to be strongly dependent upon the shape of the confining potential.

Two-dimentional systems of trapped samples of few cold bosonic atoms submitted to strong rotation around the perpendicular axis may be realized in optical lattices and microtraps. We investigate theoretically the evolution of ground state structures of such systems as the rotational frequency $\Omega$ increases. Various kinds of ordered structures are observed. In some cases, hidden interference patterns exhibit themselves only in the pair correlation function; in some other cases explicit broken-symmetry structures appear that modulate the density. For $N<10$ atoms, the standard scenario, valid for large sytems is absent, and is only gradually recovered as $N$ increases. On the one hand, the Laughlin state in the strong rotational regime contains ordered structures much more similar to a Wigner molecule than to a fermionic quantum liquid. On the other hand, in the weak rotational regime, the possibility to obtain equilibrium states, whose density reveals an array of vortices, is restricted to the vicinity of some critical values of the rotational frequency $\Omega$.

The approximate expression for the propagator of Herman and Kluk is systematically improved by application of semiclassical corrections for a double-well system. The results confirm the semiclassical nature of the Herman-Kluk approximation. The influence of caustics on the effectiveness of the corrections is discussed.

We have measured energy spectra of secondary electrons produced by fast-carbon-cluster $\mathrm{C}_n{}^{+}$ $(n=1–4)$ bombardment of thin carbon foils (3.2, 7.3, 11.9, and $20.3\mu \mathrm{g}∕{\mathrm{cm}}^2$). For clusters of identical velocity, the convoy-electron yield is enhanced with increasing cluster size $n$, while the yield of secondary electrons is reduced. The yield of convoy electrons normalized to the number of injected atoms increases proportionally with cluster size $n$. This proportionality suggests that there is only a weak vicinage effect on the number of primary electrons scattered by the projectile. The vicinage effect observed in low-energy secondary electrons must therefore arise from either transport or transmission through the surface.

The entanglement of assistance quantifies the entanglement that can be generated between two parties, Alice and Bob, given assistance from a third party, Charlie, when the three share a tripartite state and where the assistance consists of Charlie initially performing a measurement on his share and communicating the result to Alice and Bob through a one-way classical channel. We argue that if this quantity is to be considered an operational measure of entanglement, then it must be understood to be a tripartite rather than a bipartite measure. We compare it with a distinct tripartite measure that quantifies the entanglement that can be generated between Alice and Bob when they are allowed to make use of a two-way classical channel with Charlie. We show that the latter quantity, which we call the entanglement of collaboration, can be greater than the entanglement of assistance. This demonstrates that the entanglement of assistance (considered as a tripartite measure of entanglement), and its multipartite generalizations such as the localizable entanglement, are not entanglement monotones, thereby undermining their operational significance.

Brüschweiler’s database search in a spin Liouville space can be efficiently simulated on a conventional computer without error as long as the simulation cost of the internal circuit of an oracle function is polynomial, unlike the fact that in true NMR experiments, it suffers from an exponential decrease in the variation of a signal intensity. With the simulation method using the matrix-product-state proposed by Vidal [G. Vidal, Phys. Rev. Lett. 91, 147902 (2003)], we perform such a simulation. We also show the extensions of the algorithm without utilizing the $J$-coupling or $DD$-coupling splitting of frequency peaks in observation: searching can be completed with a single query in polynomial postoracle circuit complexities in an extension; multiple solutions of an oracle can be found in another extension whose query complexity is linear in the key length and in the number of solutions (this extension is to find all of marked keys). These extended algorithms are also simulated with the same simulation method.

We present the results of a set of quantum and semiclassical simulations of the response of $\mathrm{H}_2{}^{+}$ molecular ions, when submitted to a strong and ultrashort (femtosecond) infrared laser pulse. Going beyond the framework of the fixed nuclei (Born-Oppenheimer) approximation, we have addressed several questions related to the competition between excitation, dissociation, and ionization. In this context, it is shown that semiclassical simulations can provide valuable informations about the dynamics of the processes considered.

We investigate the properties of the vortex-antivortex superposed state for a Bose-Einstein condensate confined in a harmonic potential. The density distribution of the vortex-antivortex superposed state has a petal structure which is determined by the quantum circulations and proportion of the vortex and antivortex. Based on the Gross-Pitaevskii equation, we show that this vortex-antivortex superposed state can be stable through both analytical derivation and numerical calculations. Furthermore, we propose a feasible scheme to generate a coherently superposed vortex-antivortex state with arbitrary proportion by compressing and rehabilitating the harmonic trap with specific time order, which is proven by numerical simulations.

We present a theoretical framework for the analysis of the statistical properties of thermal fluctuations on a lossy transmission line. A quantization scheme of the electrical signals in the transmission line is formulated. We discuss two applications in detail. Noise spectra at finite temperature for voltage and current are shown to deviate significantly from the Johnson-Nyquist limit, and they depend on the position on the transmission line. We analyze the spontaneous emission, at low temperature, of a Rydberg atom and its resonant enhancement due to vacuum fluctuations in a capacitively coupled transmission line. The theory can also be applied to study the performance of microscale and nanoscale devices, including high-resolution sensors and quantum information processors.

Experimental cross sections for charge exchange between a negative ion ($\mathrm{TCNQ}\mathrm{F}_4{}^{-}$, perfluorinated tetracyanoquinodimethane anion) and a xenon atom to produce a dianion ($\mathrm{TCNQ}\mathrm{F}_4{}^{2-}$) exhibit a delayed threshold and pronounced oscillations as a function of collision energy. These features are explained by a post-collision-interaction theory which includes phase interferences between the two final state surfaces involving the two ${\mathrm{Xe}}^{+}$ fine structure levels. In support of this interpretation, charge-exchange cross sections between $\mathrm{TCNQ}\mathrm{F}_4{}^{-}$ and sodium are found to smoothly decline as a function of energy from $5\text{to}100\mathrm{keV}$.

We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric, and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors a rich set of features which find their interpretation in the unusual and interesting properties of the classical motion of the electrons: For instance, the number of interfering trajectories can be adjusted in this system, and the turning surfaces of classical motion contain a complex array of singularities. We perform a comprehensive analysis of the semiclassical approximation and compare it to the quantum solution, and we make predictions that should serve as a guide for future photodetachment experiments.

We present a variational Monte Carlo formulation for the universal equations of state at the van der Waals length scale [B. Gao, J. Phys. B 37, L227 (2004)] for $N$ Bose atoms in a trap. The theory illustrates both how such equations of state can be computed exactly, and the existence and the importance of long-range atom-atom correlation under strong confinement. Explicit numerical results are presented for $N=3$ and 5, and used to provide a quantitative understanding of the shape-dependent confinement correction that is important for few atoms under strong confinement.

Efficient high-order harmonic generation was obtained in helium below $10\mathrm{nm}$ using a linearly polarized two-color field consisting of a Ti:sapphire laser pulse $\left(\omega \right)$ with a 40-fs duration and its second harmonic $\left(2\omega \right)$ with a 24-fs duration. The intensity of the two-color harmonics was enhanced more than that of the $\omega$ or $2\omega$ field alone by more than one order of magnitude along with the extension of the cutoff order and the generation of efficient even-order harmonics. This observation was explained by the contribution of the lower branch rather than the upper branch of the cutoff energy, which are split in the $\omega \text{−}2\omega$ field. The supercontinuum around $10\mathrm{nm}$ provides the bandwidth capable of attosecond pulse generation.

We have previously [Phys. Rev. A 65, 043803 (2002)] analyzed adaptive measurements for estimating the continuously varying phase of a coherent beam, and a broadband squeezed beam. A real squeezed beam must have finite photon flux $\mathcal{N}$ and hence can be significantly squeezed only over a limited frequency range. In this paper we analyze adaptive phase measurements of this type for a realistic model of a squeezed beam. We show that, provided it is possible to suitably choose the parameters of the beam, a mean-square phase uncertainty scaling as ${(\mathcal{N}∕\kappa )}^{-5∕8}$ is possible, where $\kappa$ is the linewidth of the beam resulting from the fluctuating phase. This is an improvement over the ${(\mathcal{N}∕\kappa )}^{-1∕2}$ scaling found previously for coherent beams. In the experimentally realistic case where there is a limit on the maximum squeezing possible, the variance will be reduced below that for coherent beams, though the scaling is unchanged.

We propose a potentially practical scheme to implement a three-qubit Toffoli gate by a single resonant interaction in cavity QED. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the phase gate can be implemented by only a single resonant interaction of the atoms with the cavity mode. Both the situations with and without cavity decay are considered. We discuss the advantages and the experimental feasibility of our scheme.

We consider a family of chaotic Bose-Hubbard Hamiltonians parametrized by the coupling strength $k$ between neighboring sites. As $k$ increases the eigenstates undergo changes, reflected in the structure of the local density of states. We analyze these changes, both numerically and analytically, using perturbative and semiclassical methods. Although our focus is on the quantum trimer, the presented methodology is applicable for the analysis of longer lattices as well.

We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of nonunit quantum efficiency and unbalanced mode mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and the number of thermal photons being only partially known.