True tripartite entanglement of the state of a system of three qubits can be classified on the basis of stochastic local operations and classical communications. Such states can be classified into two categories: GHZ states and $W$ states. It is known that GHZ states can be used for teleportation and superdense coding, but the prototype $W$ state cannot be. However, we show that there is a class of $W$ states that can be used for perfect teleportation and superdense coding.

We present a theory of two-photon resonance fluorescence of an atom or molecule in which the excitation by an external electromagnetic field as well as fluorescence emission is mediated by two-photon processes. The treatment is based on first dressing the atom or molecule by the external field and then evaluating perturbatively the effect of the interaction with the vacuum or fluorescent field and so resonance fluorescence can be considered as spontaneous emission from the dressed atom. The introduction of the combined system of atom and external field via dressed states leads to simpler calculations and more transparent physics. The fluorescence spectrum derived by us has similarities as well as differences with that of one-photon resonance fluorescence and earlier theoretical predictions for the two-photon case.

We present a detailed study of the ground state of the Coulomb system $\left(\alpha \alpha ee\right)$ which corresponds to the ${\mathrm{He}}_2^{2+}$ molecular ion in a magnetic field $B=0-4.414\times {10}^{13}\mathrm{G}$ in parallel configuration (it is assumed that infinitely massive $\alpha$ particles are situated along a magnetic-field line). One uses a variational method, introducing a trial function which includes electronic correlation in the form $\exp \left(\gamma r_{12}\right)$, where $\gamma$ is a variational parameter. It is shown that the quantum numbers of the lowest total-energy state depend on the magnetic-field strength. This state evolves from the spin-singlet ${}^1{\Sigma }_g$ metastable state at $0\le B\lesssim 0.85\mathrm{a}.\mathrm{u}.$ to a repulsive spin-triplet ${}^3{\Sigma }_u$ state for $0.85\lesssim B\lesssim 1100\mathrm{a}.\mathrm{u}.$ and, finally, to a stable strongly bound spin-triplet ${}^3{\Pi }_u$ state at stronger fields $B\gtrsim 1100\mathrm{a}.\mathrm{u}.$ The lowest vibrational energy for the latter case is calculated.

Detailed numerical modeling of using the vibrational coherence of ${\mathrm{H}}_2$ for molecular modulation is presented. The focus of the calculation is on a strongly driven system aimed at producing many sidebands in the presence of Doppler broadening and the effects of collisions at room temperature. It is shown that Dicke narrowing that reduces the Doppler width plays a critical role in high order sideband generation in room temperature ${\mathrm{H}}_2$. In addition, the calculation shows that generation of many sidebands favors the phased state as has been reported in all gas phase experiments and is primarily a consequence of the Stark shifts that result from the applied high intensities. The influence of self-focusing in the gas medium that has been conjectured in previous studies is only secondary. The numerical results agree with experimental data obtained in our laboratory, where we have succeeded in generating collinearly propagating Raman sidebands with wavelengths that range from $2216\mathrm{nm}$ in the infrared to $133\mathrm{nm}$ in the vacuum ultraviolet. The frequencies covered by these sidebands span over four octaves for a total of more than $70600{\mathrm{cm}}^{-1}$ in the optical region of the spectrum.

The decay dynamics of the classical electromagnetic field in a leaky optical resonator supporting a single mode coupled to a structured continuum of modes (reservoir) is theoretically investigated, and the issue of threshold condition for lasing in presence of an inverted medium is comprehensively addressed. Specific analytical results are given for a single-mode microcavity resonantly coupled to a coupled resonator optical waveguide, which supports a band of continuous modes acting as decay channels. For weak coupling, the usual exponential Weisskopf-Wigner (Markovian) decay of the field in the bare resonator is found, and the threshold for lasing increases linearly with the coupling strength. As the coupling between the microcavity and the structured reservoir increases, the field decay in the passive cavity shows nonexponential features, and correspondingly the threshold for lasing ceases to increase, reaching a maximum and then starting to decrease as the coupling strength is further increased. A singular behavior for the “laser phase transition,” which is a clear signature of strong non-Markovian dynamics, is found at critical values of the coupling between the microcavity and the reservoir.

The light propagation of a probe field pulse in a four-level double-lambda type system driven by laser fields that form a closed interaction loop is studied. The finite frequency width of the probe pulse requires a time-dependent analysis beyond the multiphoton resonance assumption. We apply a Floquet decomposition to the equations of motion to solve this time-dependent problem and to identify the different scattering processes contributing to the medium response. We find that the response oscillating in phase with the probe field is phase-independent. The phase dependence arises from a scattering of the coupling fields into the probe field mode at a frequency which in general differs from the probe field frequency. In particular for short pulses with a large frequency width, inducing a closed loop interaction contour may lead to a distortion of the pulse shape via this phase-sensitive scattering. Finally, we demonstrate that both the closed loop and the nonclosed loop configuration allow for sub- and superluminal light propagation with small absorption or even gain, where one of the coupling field Rabi frequencies acts as a control parameter that enables one to switch between sub- and superluminal light propagation.

The emission spectrum of a single-emitter laser in a photonic crystal is presented. We consider a coherently pumped two-level emitter strongly coupled to a high-quality microcavity engineered within a photonic crystal. We show that the cavity spectrum consists of both elastic and inelastic components, for which we derive analytical expressions. Our study reveals enhanced, spectrally narrower emission resulting from the radiation reservoir of the photonic crystal. The cavity field spectral characteristics are fundamentally distinct from those of a corresponding microcavity in ordinary vacuum. At high pump intensities and for large discontinuities in the photon density of states between Mollow spectral components of atomic resonance fluorescence, the emitted intensity originating from the elastic spectral component increases with the intensity of the pump and the elastic component dominates the spectrum. In the case of a vanishing photon density of states in the spectral range surrounding the lower Mollow sideband and no dipolar dephasing, the cavity spectrum is elastic.

Quantum interference in a decaying three-level system of V type with degenerate upper levels driven by a single incoherent field is shown to lead to a coherent population-trapping state and more generally to a population-locked state. The latter is a state with half the population locked in two upper states regardless of the strength of incoherent pumping and decay rates. We reveal the mechanism by which half the population is pumped to the upper states no matter how weak is the incoherent pumping. Transient regimes of gain without inversion and inversion without gain are demonstrated. Quenching of spontaneous emission due to electron collisions is also discussed in support of the experiments and ideas of Suckewer and [Phys. Rev. Lett. 60, 1122 (1988)].

We consider a nonlinear sign gate implemented using a sequence of two beam splitters, and consider the use of further sequences of beam splitters to implement feed-forward so as to correct an error resulting from the first beam splitter. We obtain similar results to Scheel et al. [Phys. Rev. A 73, 034301 (2006)], in that we also find that our feed-forward procedure is only able to produce a very minor improvement in the success probability of the original gate.

We analyze some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to represent quantum states of systems with power-of-prime dimensional Hilbert spaces. We consider “cat” states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete Wigner function typically spread over the entire discrete phase space (including the regions where the two interfering states are localized). This is a generic property, which is in sharp contrast with the usual attributes of Wigner functions that make them useful candidates to display the existence of quantum coherence through oscillations. However, it is possible to find subsets of cat states with a natural phase-space representation, in which the oscillatory regions remain localized. We show that this can be done for interesting families of stabilizer states used in quantum error-correcting codes, and illustrate this by analyzing the phase-space representation of the five-qubit error-correcting code.

We discuss the effect of a single diagonal defect on both the static and dynamical properties of entanglement in a spin chain. We show that entanglement localizes at the defect and discuss its localization length, arguing that this can be used as a means to store entanglement. We also show that the impurity site can behave as an entanglement mirror and characterize the bouncing process in terms of reflection and transmission coefficients.

Quantum computers will be unique tools for understanding complex quantum systems. We report an experimental implementation of a sensitive, quantum coherence-dependent localization phenomenon on a quantum information processor (QIP). The localization effect was studied by emulating the dynamics of the quantum sawtooth map in the perturbative regime on a three-qubit QIP. Our results show that the width of the probability distribution in momentum space remained essentially unchanged with successive iterations of the sawtooth map, a result that is consistent with localization. The height of the peak relative to the baseline of the probability distribution did change, a result that is consistent with our QIP being an ensemble of quantum systems with a distribution of errors over the ensemble. We further show that the previously measured distributions of control errors correctly account for the observed changes in the probability distribution.

We present a breeding protocol that distills pure copies of any stabilizer state from noisy copies and a pool of predistilled pure copies of the same state, by means of local Clifford operations, Pauli measurements, and classical communication.

The time-dependent-wave-packet method has been applied to calculate the kinetic energy distribution of ${\mathrm{H}}^{+}$ ion resulting from the recollision between the electron and its parent ion ${\mathrm{H}}_2^{+}\left(X^2{\sum }_g^{+}\right)$ within subfemtosecond time scale. The recollision probabilities between the electron and ${\mathrm{H}}_2^{+}$ as a function of time have also been obtained. Also, an accurate quantum dynamics method has been applied to describe the motion of both the electron and the nuclear wave packets with attosecond resolution. The calculated results are in good agreement with experimental ones.

We study the ground-state properties of spin-1/2 fermionic atoms confined in a one-dimensional optical superlattice with harmonic confinement by using the density-matrix renormalization group method. For this purpose, we consider an ionic Hubbard model that has superlattice potentials with two-site periodicity. We find that several different types of insulating regimes coexist even if the number of atoms at each site is not an integer, but its average within the unit cell is an integer or half integer. This is contrasted to the coexisting phase of the metallic and Mott-insulating regimes known for the ordinary Hubbard model in an optical lattice. The phase characteristics are elucidated by investigating the profiles of the atom density, the local density (spin) fluctuations, the double occupation probability, and the spin correlations in detail.

We study the splitting of a harmonically trapped atomic Bose-Einstein condensate when we continuously turn up an optical lattice (or a double-well) potential. As the lattice height is increased, quantum fluctuations of atoms are enhanced. The resulting nonequilibrium dynamics of the fragmentation process of the condensate, the loss of the phase coherence of atoms along the lattice, and the reduced atom number fluctuations in individual lattice sites are stochastically studied within the truncated Wigner approximation. We perform a detailed study of the effects of temperature and lattice height on atom dynamics, and investigate the validity of the classical Gross-Pitaevskii equation in optical lattices. We find the atom number squeezing to saturate in deep lattices due to nonadiabaticity in turning up of the lattice potential that is challenging to avoid in experiments when the occupation number of the lattice sites is large, making it difficult to produce strongly number squeezed (or the Mott insulator) states with large filling factors. We also investigate some general numerical properties of the truncated Wigner approximation.

Through detailed numerical and analytical studies, we establish that the significant enhancement of thermal emission via $Q$ matching, which has been possible in one-dimensional (1D) systems only, can be extended to two-dimensional (2D) systems by means of Fano resonances in the 2D system. In particular, we show the existence of essentially 1D behavior in a 2D system—a case of reduced dimensionality. Moreover, we show how properties of these spectra can be controlled by changing the geometrical parameters of the 2D system.

We perform precision microwave spectroscopy—aided by Stark deceleration—to reveal the low-magnetic-field behavior of OH in its ${}^2\Pi _{3∕2}$ rovibronic ground state, identifying two field-insensitive hyperfine transitions suitable as qubits and determining a differential Landé $g$ factor of $1.267\left(5\right)\times {10}^{-3}$ between opposite-parity components of the $\Lambda$ doublet. The data are successfully modeled with an effective hyperfine Zeeman Hamiltonian, which we use to make a tenfold improvement of the magnetically sensitive, astrophysically important $\Delta F=\pm 1$ satellite-line frequencies, yielding $1720529887\left(10\right)\mathrm{Hz}$ and $1612230825\left(15\right)\mathrm{Hz}$.

A magnetically trapped atom experiences an adiabatic geometric (Berry’s) phase due to changing field direction. We investigate theoretically such an Aharonov-Bohm-like geometric phase for atoms adiabatically moving inside a storage ring as demonstrated in several recent experiments. Our result shows that this phase shift is easily observable in a closed-loop interference experiment, and thus the shift has to be accounted for in the proposed inertial sensing applications. The spread in phase shift due to the atom transverse distribution is quantified through numerical simulations.