We address the phase diagram of the disordered Bose-Hubbard model that has been realized in several recent experiments in terms of optically trapped ultracold bosons. We show that a systematic description of all of the expected quantum phases can be obtained at both zero and finite temperature via a site-dependent decoupling mean-field approach. Also, we relate the boundaries of the Mott-insulating phase to an off-diagonal noninteracting Anderson model whose spectral features provide an avenue for determining the debated nature of the phase surrounding the Mott lobes. Our approach is simple yet effective, and scalable to systems with experimentally relevant sizes and features.

It is shown that a representation of the decaying wave function as a resonant sum plus a nonexponential integral term may be written as a purely discrete resonant sum by evaluating at long times the integral term by the steepest descents method, and then expanding the resulting expression in terms of resonant states. This leads to a representation that is valid along the exponential and the inverse power in time regimes. A model calculation using the $\delta$ potential allows us to make a comparison of the expansion with numerical integrations in terms of continuum wave functions and, in the long time regime, with an exact analytic expression of the integral term obtained using the steepest descents method. The results demonstrate that resonant states give a correct description of the long-time behavior of decay.

We demonstrate how using two-qubit composite rotations a high fidelity controlled-NOT (CNOT) gate can be constructed, even when the strength of the interaction between qubits is not accurately known. We focus on the exchange interaction oscillation in silicon based solid-state architectures with a Heisenberg Hamiltonian. This method easily applies to a general two-qubit Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity when a single application of the composite rotations is combined with a modest level of Hamiltonian characterization. Operating the robust CNOT gate in a suitably characterized system means concatenation of the composite pulse is unnecessary, hence reducing operation time, and ensuring the gate operates below the threshold required for fault-tolerant quantum computation.

Electron capture by protons following collisions with carbon monoxide, and the reverse process, is studied with a quantal molecular-orbital coupled-channel method utilizing the infinite order sudden approximation for collision energies between 0.5 and $1000\mathrm{eV}∕\mathrm{u}$. The potential surfaces and couplings, computed with the multireference single- and double-excitation method for a range of ${\mathrm{H}}^{+}\text{−}\mathrm{C}\mathrm{O}$ orientation angles and C-O separations, are adopted in the scattering calculations. Results including vibrationally resolved and orientation-angle-dependent cross sections are presented for a range of CO and $\mathrm{C}{\mathrm{O}}^{+}$ vibrational levels. Comparison with experiment is made where possible and the relevance of the reaction in astrophysics and atmospheric physics is discussed.

Using cold target recoil ion momentum spectroscopy (COLTRIMS) we have investigated the production of one free electron in slow ${\mathrm{He}}^{2+}+\mathrm{He}\left(1s^2\right)$ collisions. At projectile velocities between 0.6 and $1.06\text{a.u.}$ (9–$28\mathrm{keV}∕u$), the fully differential cross section was measured state selective with respect to the second electron, which is bound either at the target or the projectile. We provide a comprehensive data set comprising state selective total cross section, scattering angle dependent single differential cross sections, and fully differential cross section. We show that the momentum distribution of the electron in the continuum image the relevant molecular orbitals for the reaction channel under consideration. By choosing the bound electron final state at the target or projectile and the impact parameter we can select these orbitals and manipulate their relative phase.

We obtain the ground-state quantum phase diagram for a two-species Bose mixture in a one-dimensional optical lattice using the finite-size density-matrix renormalization group method. We discuss our results for different combinations of inter- and intraspecies interaction strengths with commensurate and incommensurate fillings of the bosons. The phases we have obtained are a superfluid and a Mott insulator, and a phase separation where the two different species reside in spatially separate regions. The spatially separated phase is further classified into phase-separated superfluid and Mott insulator. The phase separation appears for all the fillings we have considered, whenever the interspecies interaction is slightly larger than the intraspecies interactions.

Motivated by the recent realization of a ${}^{52}\mathrm{Cr}$ Bose-Einstein condensate, we consider the phase diagram of a general spin-three condensate as a function of its scattering lengths. We classify each phase according to its reciprocal spinor, using a method developed in a previous work. We show that such a classification can be naturally extended to describe the vortices for a spinor condensate by using the topological theory of defects. To illustrate, we systematically describe the types of vortex excitations for each phase of the spin-three condensate.

A scheme for the generation of nonclassical pairs of photons in atomic vapors is proposed. The scheme exploits the fact that the cross correlation of the emission of photons from the extreme transitions of a four-level cascade system shows antibunching, unlike the case of the three-level cascade emission, which shows bunching. The Cauchy-Schwarz inequality, which is the ratio of the cross-correlation to the autocorrelation function, in this case is estimated to be ${10}^3–{10}^6$ for controllable time delay, and is one to four orders of magnitude larger compared to previous experiments. The choice of Doppler-free geometry, in addition to the fact that at three-photon resonance the excitation and deexcitation processes occur in a very narrow frequency band, ensures cleaner signals.

The interference of degenerate four-wave mixing (FWM) in three-level systems is examined in both the classical and quantum regimes with a backward configuration. In classical FWM, we find that the phase difference between two indistinguishable FWM transition paths can be varied by different driving laser parameters, and leads to interference in the amplitude and polarization of the generated conjugate field. In the paired-photon generation case, the interference in the nonlinearity disappears because of the time ordering in biphoton generation. However, because of the slow group velocity at the degenerate frequency and polarization, the biphoton-amplitude interference between two Feynman paths can erase the time-ordering information at the detectors. For small group delay, the biphoton correlation, determined by the third-order nonlinearity, shows antibunching and damped Rabi oscillations. For large group delay, where the biphoton bandwidth is determined by phase matching, we show that the biphoton interference leads to a bunching effect. The feasibility of generating polarization entanglement is also discussed.

From the time dependence of states of one of them, the dynamics of two interacting qubits is determined to be one of two possibilities that differ only by a change of signs of parameters in the Hamiltonian. The only exception is a simple particular case where several parameters in the Hamiltonian are zero and one of the remaining nonzero parameters has no effect on the time dependence of the states of the one qubit. The mean values that describe the initial state of the other qubit and of the correlations between the two qubits also are generally determined to within a change of signs by the time dependence of the states of the one qubit, but with many more exceptions. An example demonstrates all the results. Feedback in the equations of motion that allows time dependence in a subsystem to determine the dynamics of the larger system can occur in both classical and quantum mechanics. The role of quantum mechanics here is just to identify qubits as the simplest objects to consider and specify the form that equations of motion for two interacting qubits can take.

We propose a scheme to control the level of entanglement between two fixed spin-$1∕2$ systems by interaction with a third particle. For specific designs, entanglement is shown to be “pumped” into the system from the surroundings even when the spin-spin interaction within the system is small or nonexistent. The effect of the external particle on the system is introduced by including a dynamic spinor in the Hamiltonian. Controlled amplification of the internal entanglement to its maximum value is demonstrated. The possibility of entangling noninteracting spins in a stationary state is also demonstrated by coupling each one of them to a flying qubit in a quantum wire.

Quantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Duan et al., Nature (London) 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per $3\min$ over $1280\mathrm{km}$ distance with fidelity $(F⩾78\%)$ sufficient to violate Bell’s inequality.

The oscillator strength distribution in the discrete and continuous regions of the spectrum of helium from the $2s{}^{1}S_0$ metastable state has been determined using a Nd: yttrium aluminum garnet (YAG) pumped dye laser system in conjunction with a low pressure rf glow discharge. The saturation technique has been employed to determine the photoionization cross section from the $2s{}^{1}S_0$ excited state at and above the first ionization threshold. The measured value of the photoionization cross section at the ionization threshold has been used to extract the $f$ values for the $2s{}^{1}S\to np{}^{1}P$ Rydberg series from $n=10$ to $n=52$. The $f$ values of the observed Rydberg series decrease smoothly with an increase of the principal quantum number. In the continuum region the oscillator strength densities have been estimated by measuring the photoionization cross sections from the $2s{}^{1}S_0$ excited state at five ionizing laser wavelengths above the first ionization threshold. The discrete $f$ values smoothly merge into the continuous oscillator strength densities across the ionization threshold.

We analyze the phase diagram of superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of scattering parameter, population imbalance, and mass anisotropy. We identify regions corresponding to normal, or uniform or nonuniform superfluid phases, and discuss topological quantum phase transitions in the BCS, unitarity, and BEC limits. We derive the Ginzburg-Landau equation near the critical temperature, and show that it describes a dilute mixture of paired and unpaired fermions in the BEC limit. We also obtain the zero temperature low frequency and long wavelength collective excitation spectrum, and recover the Bogoliubov relation for weakly interacting dilute bosons in the BEC limit. Lastly, we discuss the effects of harmonic traps and the resulting density profiles in the BEC regime.

A system with Bose-Einstein condensate is considered in the frame of the self-consistent mean-field approximation, which is conserving, gapless, and applicable for arbitrary interaction strengths and temperatures. The main attention is paid to the thorough analysis of the condensate and superfluid fractions in the whole range of the interaction strength, between zero and infinity, and for all temperatures between zero and the critical point $T_c$. The normal and the anomalous averages are shown to be of the same order for almost all interactions and temperatures, except the close vicinity of $T_c$. But even in the vicinity of the critical temperature, the anomalous average cannot be neglected, since only in the presence of the latter the phase transition at $T_c$ becomes of second order, as it should be. Increasing temperature influences the condensate and superfluid fractions in a similar way, by diminishing them; but their behavior with respect to the interaction strength is very different. For all temperatures, the superfluid fraction is larger than the condensate fraction. These coincide only at $T_c$ or under zero interactions. For asymptotically strong interactions, the condensate is almost completely depleted, even at low temperatures, while the superfluid fraction can be close to one.

We study localized modes in binary mixtures of Bose-Einstein condensates embedded in one-dimensional optical lattices. We report a diversity of asymmetric modes and investigate their dynamics. We concentrate on the cases where one of the components is dominant, i.e., has a much larger number of atoms than the other one, and where both components have the numbers of atoms of the same order but different symmetries. In the first case we propose a method of systematically obtaining the modes, considering the “small” component as bifurcating from the continuum spectrum. A generalization of this approach combined with the use of the symmetry of the coupled Gross-Pitaevskii equations allows for obtaining breather modes, which are also presented.

We calculate the line shape and linewidths for electromagnetically induced transparency (EIT) in optically thick, Doppler broadened media (buffer gasses are also considered). In generalizing the definition of the EIT linewidth to optically thick media, we find two different linewidth definitions apply depending on whether the experiment is pulsed or continuous wave (cw). Using the cw definition for the EIT line shape we derive analytic expressions describing the linewidth as a function of optical depth. We also review the EIT line shapes in optically thin media and provide physical arguments for how the line shapes change as a function of various parameters.

The entanglement fidelity provides a measure of how well the entanglement between two subsystems is preserved in a quantum process. By using a simple model, we show that in some cases this quantity in its original definition fails in the measurement of entanglement preservation. On the contrary, the modified entanglement fidelity, obtained by using a proper local unitary transformation on a subsystem, is shown to exhibit behavior similar to that of the concurrence in quantum evolution.

The dynamics of a driven spin-boson model is studied by means of the perturbation approach based on a unitary transformation. Analytical expressions for the population difference and the coherence of the two state system are obtained. The results show that for weak driving, the population difference displays damping coherent oscillation and/or damping quantum beat, depending on the initial preparation. The coherence exhibits damped oscillation with Rabi frequency. When driving is strong enough, the population difference exhibits undamped large-amplitude coherent oscillation. In addition, our theory leads to correct results in two limiting cases: without dissipation and without driving field.

We present a random-matrix analysis of the entangling power of a unitary operator as a function of the number of times it is iterated. We consider unitaries belonging to the circular ensembles of random matrices [the circular unitary (CUE) or circular orthogonal ensemble] applied to random (real or complex) nonentangled states. We verify numerically that the average entangling power is a monotonically decreasing function of time. The same behavior is observed for the “operator entanglement”—an alternative measure of the entangling strength of a unitary operator. On the analytical side we calculate the CUE operator entanglement and asymptotic values for the entangling power. We also provide a theoretical explanation of the time dependence in the CUE cases.