We study the capacity of $d$-dimensional quantum channels with memory modeled by correlated noise. We show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of mutual information than product states. Moreover, a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension is found. We conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states saturate the channel capacity.

We propose a decoherence-free subspace (DFS) scheme to realize scalable quantum computation with trapped ions. The spin-dependent laser-ion coupling is exploited in the presence of Coulomb interactions. A universal set of unconventional geometric quantum gates is achieved in encoded subspaces that are immune from decoherence by collective dephasing. The scalability of the scheme for an ion-array system is demonstrated, either by adiabatically switching on and off the interactions, or by a fast gate scheme with DFS encoding and noise-decoupling techniques.

We suggest a fast two-qubit quantum logic gates for trapped ions in thermal motion via geometric phase shifts. In the scheme, several vibrational modes are simultaneously displaced by driving the ions with a single off-resonant standing-wave laser. Under certain conditions, all the vibrational modes simultaneously return to the original points in the phase spaces along corresponding closed paths depending on the electronic states, producing a geometric phase gate. During the gate operation, the ions undergo no electronic transitions and the gate time might be shorter than the period of the center-of-mass vibration.

In this work, we investigate the problem of a secretly broadcasting of a three-qubit entangled state between two distant partners. The interesting feature of this problem is that starting from two-particle entangle states shared between two distant partners we find that the action of a local cloner on the qubits and the measurement on the machine state vector generates three-qubit entanglement between them. The broadcasting of entanglement is made secret by sending the measurement result secretly using cryptographic scheme based on orthogonal states. Further we show that this idea can be extended to generate three-particle entangled states between three distant partners.

Recently Yeo and Chua [Phys. Rev. Lett. 96, 060502 (2006)] presented an explicit protocol for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entanglement channel. Here we generalize completely their results to teleporting an arbitrary $N$-qubit state via genuine $N$-qubit entanglement channels. And we present the general form of the genuine multipartite entanglement channels, namely, the sufficient and necessary condition the genuine $N$-qubit entanglement channels must satisfy to teleport an arbitrary $N$-qubit state.

We first propose an experimental scheme to implement a two-qubit conditional $z$ gate with atoms trapped in a high-$Q$ optical cavity. The scheme is based on a combination of resonant interaction and quantum interference. Further, we show that the scheme can be directly generalized to implement an $N$-qubit conditional $z$ gate, and the interaction time required to implement scheme does not change with increasing the number of qubits. This might lead to more efficient construction of quantum circuits and quantum algorithms.

The degree of dynamic alignment (the excess alignment beyond that due to geometric alignment) induced by linearly polarized, $100\mathrm{fs}$ pulses in the ${10}^{15}\mathrm{W}∕{\mathrm{cm}}^2$ intensity range, has been investigated. Exploiting circular polarization to turn off dynamic alignment and 4$\pi$ angular collection to capture all ejected ions, a quantitative measure of the excess alignment was extracted from the relative atomic ion yields subsequent to Coulomb explosion in linearly and circularly polarized fields for several linear molecules (${\mathrm{H}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{CO}}_2$). The degree of dynamic alignment was measured to be about 0.90 $\left({\mathrm{H}}_2\right)$, 0.16 (${\mathrm{N}}_2$ and ${\mathrm{O}}_2$), and 0.29 $\left({\mathrm{CO}}_2\right)$. The anomalously large value of ${\mathrm{CO}}_2$ implies a torque enhancement that we show is consistent with ${\mathrm{CO}}_2$ interacting with the field longer than ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ prior to enhanced ionization.

Stark effects in Rydberg states of xenon atoms were investigated both experimentally and theoretically. The experimental part consisted of laser-induced fluorescence-dip spectroscopy. Using a $(2+1)$-photon excitation scheme, xenon atoms were excited from the ground state to high-lying Rydberg $ns$ and $nd$ levels. Measurements were made in a controllable electric field environment, produced by applying a pulsed voltage to two parallel metal electrodes. For energy levels with principal quantum numbers ranging from 12 to 18, Stark shifts of up to $4.8{\mathrm{cm}}^{-1}$ were observed for electric fields ranging from $0\text{to}4000\mathrm{V}∕\mathrm{cm}$. Additionally, mixing of energy levels in high electric fields was measured for $nd$ levels. The experimental results were compared to a theoretical calculation based on solving the Schrödinger equation for a perturbed Hamiltonian. The calculation method proved to be very accurate for predicting Stark effects in Rydberg $nd$ levels, while for $ns$ levels the agreement was only moderate, probably due to deviations from the assumption of a hydrogenlike atom that is used in the calculation. Finally, the feasibility of using measurements of Stark shifts of Rydberg levels as a diagnostic for electric fields in low-pressure discharges was discussed.

We consider a Bose-Einstein condensate of polar molecules in a harmonic trap, where the effective dipole may be tuned by an external field. We demonstrate that taking into account the dependence of the scattering length on the dipole moment is essential to reproducing the correct energies and for predicting the stability of the condensate. We do this by comparing Gross-Pitaevskii calculations with diffusion Monte Carlo calculations. We find very good agreement between the results obtained by these two approaches once the dipole dependence of the scattering length is taken into account. We also examine the behavior of the condensate in nonisotropic traps.

A measurement process is constructed to project an arbitrary two-mode $N$-photon state to a maximally entangled $N$-photon state. The result of this projection measurement shows a typical interference fringe with an $N$-photon de Broglie wavelength. For an experimental demonstration, this measurement process is applied to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. Generalization to the projection measurement of an arbitrary $N$-photon state can be easily made and may have wide applications in quantum information. As an example, we formulate it for precision phase measurement.

We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection, and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of $n⩽4$, and conjecture that this can be generalized for an arbitrary $n$ Fock state. We describe our experimental demonstration of this scheme using coherent input states and measuring experimental fidelities that are only achievable using quantum resources.

We calculate ionization probabilities for the $\mathrm{H}_2{}^{+}$ molecule subject to a linearly polarized infrared laser field. The time-dependent Schrödinger equation is solved numerically for all electronic degrees of freedom while the nuclei are fixed at arbitrary separations and orientations with respect to the direction of the field. The ionization signal displays a strong dependence on the degree of alignment between the laser polarization and the internuclear vector. At perpendicularly aligned geometry the signal is suppressed due to a symmetry selection rule that excludes an important intermediate resonance.

We show the maximal violation of Bell inequalities for two $d$-dimensional systems by using the method of the Bell operator. The maximal violation corresponds to the maximal eigenvalue of the Bell operator matrix. The eigenvectors corresponding to these eigenvalues are described by asymmetric entangled states. We estimate the maximum value of the eigenvalue for large dimension. A family of elegant entangled states $\mid \Psi {⟩}_{\mathrm{app}}$ that violate Bell inequality more strongly than the maximally entangled state but are somewhat close to these eigenvectors is presented. These approximate states can potentially be useful for quantum cryptography as well as many other important fields of quantum information.

Spherical and parabolic partial cross sections and asymmetry parameters, defined in the ejected electron frame, are presented for photoionization excitation of the helium atom at $0.1\mathrm{eV}$ above its double ionization threshold. A quantitative law giving the dominant spherical partial wave $l_{\mathrm{dom}}$ for each excitation level $n$ is obtained. The parabolic partial cross sections are shown to satisfy the same approximate selection rules as the related Rydberg series of doubly excited states ${(K,T)}_n^A$. The analysis of radial and angular correlations reveals the close relationship between double excitation, ionization excitation, and double ionization. Opposite to a widespread belief, the observed value of the asymmetry parameter is shown to result from the interplay of radial correlations and symmetry constraints, irrespective of angular correlations. Finally, the measurement of parabolic partial cross sections is proposed as a challenge to experimentalists.

An experimental study of ionization and fragmentation of ${\mathrm{C}}_{60}$ has been performed for $2\text{−}\mathrm{MeV}$ ${\mathrm{Si}}^{2+}$ incident ions under charge-changing conditions. Time-of-flight (TOF) spectra of product ions and number distributions of secondary electrons $\left(n_e\right)$ were measured in coincidence with charge-selected outgoing projectiles. TOF spectra from transiently formed highly charged $\mathrm{C}_{60}{}^{r+}$ ions are obtained for individual charge states $r$, and $n_e$ distributions correlated with size-fixed $\mathrm{C}_m{}^{+}$ ions are also obtained for $m<15$. It is found that mass spectra and $n_e$ distributions are both significantly different between loss and capture collisions, whereas a remarkable similarity in the partial $n_e$ distributions is observed almost independently of the different charge-changing conditions when compared at given $\mathrm{C}_m{}^{+}$ ions size. We find also that a number of secondary electrons as high as 20 are emitted in the production of small fragment ions. Furthermore, small fragment ions are produced predominantly in close collisions even at very low charge states of $r\simeq 3$ in comparison with distant collisions. This indicates that the energy partition rate between ionization and internal excitation might be considerably different in close and distant collisions.

A beam splitter is an important component of an atomic/optical Mach-Zehnder interferometer. Here we study a Bose-Einstein condensate beam splitter, realized with a double well potential of tunable height. We analyze how the sensitivity of a Mach-Zehnder interferometer is degraded by the nonlinear particle-particle interaction during the splitting dynamics. We distinguish three regimes, Rabi, Josephson and Fock, and associate to them a different scaling of the phase sensitivity with the total number of particles.

We present a full quantum theory for the dissipative dynamics of an optical cavity in the ultrastrong light-matter coupling regime, in which the vacuum Rabi frequency is a significant fraction of the active electronic transition frequency and the antiresonant terms of the light-matter coupling play an important role. In particular, our model can be applied to the case of intersubband transitions in doped semiconductor quantum wells embedded in a microcavity. The coupling of the intracavity photonic mode and of the electronic polarization to the external, frequency-dependent, dissipation baths is taken into account by means of quantum Langevin equations in the input-output formalism. In the case of a time-independent vacuum Rabi frequency, exact analytical expressions for the operators are obtained, which allows us to characterize the quantum dissipative response of the cavity to an arbitrary initial condition (vacuum, coherent field, thermal excitation). For a vacuum input in both the photonic and electronic polarization modes, the ground state of the cavity system is a two-mode squeezed vacuum state with a finite population in both photonic and electronic modes. These excitations are, however, virtual and cannot escape from the cavity: for a vacuum input, a vacuum output is found, without any trace of the intracavity squeezing. For a coherent photonic input the linear optical response spectra (reflectivity, absorption, transmission) have been studied, and signatures of the ultrastrong coupling have been identified in the asymmetric and peculiar anticrossing of the polaritonic eigenmodes. Finally, we have calculated the electroluminescence spectra in the case of an incoherent electronic input: the emission intensity in the ultrastrong coupling regime results in being significantly enhanced as compared to the case of an isolated quantum well without a surrounding cavity.

In this paper we demonstrate that optimal $1\to M$ phase-covariant cloning quantum cloning is available via free dynamical evolution of spin networks. By properly designing the network and the couplings between spins, we show that optimal $1\to M$ phase-covariant cloning can be achieved if the initial state is prepared as a specific symmetric state. Especially, when $M$ is an odd number, the optimal phase-covariant cloning can be achieved without ancillas. Moreover, we demonstrate that the same framework is capable for optimal $1\to 2$ universal cloning.

We have investigated the one-dimensional spin-1 boson Hubbard model with antiferromagnetic interactions using quantum Monte Carlo methods. We obtain the shapes of the two lowest Mott lobes and show that the ground state within the lowest Mott lobe is dimerized. The results presented here are relevant for optically trapped antiferromagnetic spin-1 bosons. An experimental signature of the dimerized ground state is modulated Bragg peaks in the noise distribution of the atomic cloud obtained after switching off the trap. These Bragg peaks are located at wave vectors corresponding to half-integer multiples of the reciprocal wave vector of the optical lattice.