An efficient multimode quantum memory is a crucial resource for long-distance quantum communication based on quantum repeaters. We propose a quantum memory based on spectral shaping of an inhomogeneously broadened optical transition into an atomic frequency comb (AFC). The spectral width of the AFC allows efficient storage of multiple temporal modes without the need to increase the absorption depth of the storage material, in contrast to previously known quantum memories. Efficient readout is possible thanks to rephasing of the atomic dipoles due to the AFC structure. Long-time storage and on-demand readout is achieved by use of spin states in a lambda-type configuration. We show that an AFC quantum memory realized in solids doped with rare-earth-metal ions could store hundreds of modes or more with close to unit efficiency, for material parameters achievable today.

We propose two schemes for deterministically generating three-partite Greenberger-Horne-Zeilinger (GHZ) and $W$ states of distant atoms based on the selective photon emission and absorption processes. In our schemes, it is found that the effects of atomic spontaneous decay and photon leakage out of fiber are suppressed effectively due to the presences of dispersive atom-field interaction and strong cavity-fiber coupling intensity. To check the experimental feasibility of our schemes, we also numerically simulated the effects of photon leakage out of the cavities, and the numerical simulation shows that our proposal is good enough to demonstrate the generation of three-partite GHZ and $W$ states of distant atoms with high fidelity. In addition, the present schemes can also be generalized to prepare N-partite $W$ state of distant atoms.

Differential cross sections (DCSs) for elastic scattering of electrons from pyrimidine $\left({\text{C}}_4{\text{H}}_4{\text{N}}_2\right)$ are presented for incident energies from 50 to 300 eV. The measurements were performed using a cross beam technique, for scattering angles from $20°$ to $110°$. The relative DCSs were measured as a function of both the angle and incident energy and the absolute DCSs were determined using the relative flow method. The calculations of electron interaction cross sections are based on a corrected form of the independent-atom method, known as the screen corrected additivity rule procedure and using an improved quasifree absorption model. Calculated results agree very well with the experiment.

We develop a strong-coupling perturbation theory for the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on $\left(d>1\right)$-dimensional hypercubic lattices. Analytical expressions for the ground-state phase boundaries between the incompressible (Mott or charge-density-wave insulators) and the compressible (superfluid or supersolid) phases are derived up to third order in the hopping $t$. We also briefly discuss possible implications of our results in the context of ultracold dipolar Bose gases with dipole-dipole interactions loaded into optical lattices.

Perfect single-crystal neutron interferometers are adversely sensitive to environmental disturbances, particularly mechanical vibrations. The sensitivity to vibrations results from the slow velocity of thermal neutrons and the long measurement time that are encountered in a typical experiment. Consequently, to achieve a good interference solutions for reducing vibration other than those normally used in optical experiments must be explored. Here we introduce a geometry for a neutron interferometer that is less sensitive to low-frequency vibrations. This design may be compared with both dynamical decoupling methods and decoherence-free subspaces that are described in quantum information processing. By removing the need for bulky vibration isolation setups, this design will make it easier to adopt neutron interferometry to a wide range of applications and increase its sensitivity.

We examine the modal, spectral, and polarization entanglement properties of photon pairs generated in a nonlinear periodically poled two-mode waveguide (one-dimensional planar or two-dimensional circular) via nondegenerate spontaneous parametric down-conversion. Any of the possible degrees of freedom—mode number, frequency, or polarization—can be used to distinguish the down-converted photons while the others serve as attributes of entanglement. Distinguishing the down-converted photons based on their mode numbers enables us to efficiently generate spectral or polarization entanglement that is either narrowband or broadband. On the other hand, when the generated photons are distinguished by their frequencies in a type-0 process, modal entanglement turns out to be an efficient alternative to polarization entanglement. Moreover, modal entanglement in type-II down-conversion may be used to generate a doubly entangled state in frequency and polarization.

We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [M. Tsang et al., Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal phase with quantum-limited accuracy. We show that postprocessing can further improve the estimation performance if delay is allowed in the estimation. We also investigate the fundamental uncertainties in the simultaneous estimation of harmonic-oscillator position and momentum via continuous optical phase measurements from the classical estimation theory perspective. In the case of delayed estimation, we find that the inferred uncertainty product can drop below that allowed by the Heisenberg uncertainty relation. Although this result seems counterintuitive, we argue that it does not violate any basic principle of quantum mechanics.

In an arbitrated quantum signature scheme, the signatory signs the message and the receiver verifies the signature’s validity with the assistance of the arbitrator. We present an arbitrated quantum signature scheme using two-particle entangled Bell states similar to the previous scheme using three-particle entangled Greenberger-Horne-Zeilinger states [G. H. Zeng and C. H. Keitel, Phys. Rev. A 65, 042312 (2002)]. The proposed scheme can preserve the merits in the original scheme while providing a higher efficiency in transmission and reducing the complexity of implementation.

It is shown that entanglement, which is a quantum correlation property of at least two subsystems, is imprinted in the mode structure of a single photon. The photon, which is emitted by two coupled cavities, carries the information on the concurrence of the two intracavity fields. This can be useful for recording the entanglement dynamics of two cavity fields and for entanglement transfer.

We analyze the detection of itinerant photons using a quantum nondemolition measurement. An important example is the dispersive detection of microwave photons in circuit quantum electrodynamics, which can be realized via the nonlinear interaction between photons inside a superconducting transmission line resonator. We show that the back action due to the continuous measurement imposes a limit on the detector efficiency in such a scheme. We illustrate this using a setup where signal photons have to enter a cavity in order to be detected dispersively. In this approach, the measurement signal is the phase shift imparted to an intense beam passing through a second cavity mode. The restrictions on the fidelity are a consequence of the quantum Zeno effect, and we discuss both analytical results and quantum trajectory simulations of the measurement process.

It is shown that the Hilbert-Schmidt (HS) norm and distance, unlike the trace norm and distance, are generally not contractive for open quantum systems under Lindblad dynamics. Necessary and sufficient conditions for contractivity of the HS norm and distance are given, and explicit criteria in terms of the Lindblad operators are derived. It is also shown that the requirements for contractivity of the HS distance are strictly weaker than those for the HS norm, although simulations suggest that noncontractivity is a typical case, i.e., that systems for which the HS distance between quantum states is monotonically decreasing are exceptional for $N>2$, in contrast to the $N=2$ case where it is always monotonically decreasing.

We present a detailed analysis of all the algebraic conditions an arbitrary $4\times 4$ symmetric matrix must satisfy in order to represent the correlation matrix of a two-mode bosonic system. Then, we completely clarify when this arbitrary matrix can represent the correlation matrix of a separable or entangled Gaussian state. In this analysis, we introduce alternative sets of conditions, which are expressed in terms of local symplectic invariants.

Entangled multiqubit states may be generated through a dispersive collective quantum nondemolition measurement of superconducting qubits coupled to a microwave transmission line resonator. Using the quantum trajectory approach, we analyze the stochastic measurement traces that would be observed in experiments. We illustrate the synthesis of three-qubit $W$ and Greenberger-Horne-Zeilinger states, and we analyze how the fidelity and the entanglement evolve in time during the measurement. We discuss the influence of decoherence and relaxation, as well as of imperfect control over experimental parameters. We show that the desired states can be generated on time scales much faster than the qubit decoherence rates.

Using the relativistic coupled-cluster method, we have calculated ionization potentials, electric dipole transition amplitudes, and dipole polarizabilities of many low-lying states of ${\text{Ca}}^{+}$. Contributions from the Breit interaction are given explicitly for these properties. Polarizabilities of the ground and the first excited $d$ states are determined by evaluating the wave functions that are perturbed to first order by the electric dipole operator and the black-body radiation shifts are estimated from these results. We also report the results of branching ratios and lifetimes of the first excited $p$ states using both the calculated and experimental wavelengths and compare them with their measured values.

A strong-coupling expansion for the Green’s functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to the dynamics of dissociation of a molecular Bose-Einstein condensate into correlated bosonic atom pairs. We also perform the same simulation using two stochastic phase-space techniques for quantum dynamics—the positive-$P$ representation method and the truncated Wigner method. By comparing the results of our calculations we are able to assess the relative strengths of these theoretical techniques in describing molecular dissociation in one spatial dimension. An important aspect of our analysis is the inclusion of atom-atom interactions, which can be problematic for the positive-$P$ method. We find that the truncated Wigner method mostly agrees with the positive-$P$ simulations, but can be simulated for significantly longer times. The pairing mean-field theory results diverge from the quantum dynamical methods after relatively short times.

We use functional-integral methods for an estimate of the three-body loss in a three-component ${}^6\text{L}\text{i}$ ultracold atom gas. We advocate a simple picture where the loss proceeds by the formation of a three-atom bound trimer state, the trion. In turn, the effective amplitude for the trion formation from three atoms is estimated from a simple effective boson exchange process. The energy gap of the trion and other key quantities for the loss coefficient are computed in a functional renormalization-group framework.

We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers. In the distributed model (complex cubic-quintic Ginzburg-Landau equation) we observe a discrete family of soliton pairs with equidistantly increasing peak separation. This family was identified by two alternative numerical schemes and the bound state instability was disclosed by a linear stability analysis. Moreover, similar families of unstable bound state solutions have been found in a more realistic lumped laser model with an idealized saturable absorber (instantaneous response). We show that a stabilization of these bound states can be achieved when the finite relaxation time of the saturable absorber is taken into account. The domain of stability can be controlled by varying this relaxation time.

I explore the entanglement evolution of a four-qubit cluster state in a dephasing environment concentrating on the phenomenon of entanglement sudden death (ESD). Specifically, I ask whether the onset of ESD has an effect on the utilization of this cluster state as a means of implementing a single-qubit rotation in the measurement-based cluster state model of quantum computation. To do this, I compare the evolution of the entanglement to the fidelity, a measure of how accurately the desired state (after the measurement-based operations) is achieved. I find that ESD does not cause a change in behavior or discontinuity in the fidelity but may indicate for certain states when the fidelity goes to 0.5.