The decoherence of two initially entangled qubits in non-Markovian reservoirs has been investigated exactly without Born-Markovian approximation or rotating-wave approximation (RWA). The nonperturbative quantum master equation is derived and its exact solution is obtained. The decoherence behavior of two qubits, initially entangled in Bell states, has been investigated in the weak coupling regime and strong coupling regime. The results show that the counter-rotating wave terms have obvious influence on the decoherence behavior in the non-Markovian regime.

The calculation of the radial matrix elements of alkali metal Rydberg states is of interest with principal quantum number $n$ up to 70. Until now calculations of the radial matrix elements have mainly concerned the states with $n<30$. We use $B$-spline expansion technique and model potentials to calculate the radial matrix elements by numerical integration with 16 decimal digits precision. We are able to obtain the radial matrix elements of alkali metal Rydberg states with $n$ up to 145, with five significant digits. As a test example, we also compute the positions and widths of the anticrossings for highly excited Stark states of Na with principal quantum number $n$ up to 70.

We propose a method to measure the absolute photon absorption cross section of neutral molecules in a molecular beam. It is independent of our knowledge of the particle beam density, nor does it rely on photoinduced fragmentation or ionization. The method is based on resolving the recoil resulting from photon absorption by means of near-field matter-wave interference, and it thus applies even to very dilute beams with low optical densities. Our discussion includes the possibility of internal state conversion as well as fluorescence. We assess the influence of various experimental uncertainties and show that the measurement of absolute absorption cross sections is conceivable with high precision and using existing technologies.

Using the angular spectrum representation of fields and the first Born approximation we develop a theory of scattering of scalar waves with any spectral composition and any correlation properties from collections of particles which have either deterministic or random distributions of the index of refraction and locations. An example illustrating the far-field intensity and the far-field spectral degree of coherence produced on scattering of a model field from collections of several particles with Gaussian potentials is considered.

We investigate the evolution of the atomic coherence between Zeeman sublevels with $\Delta m_F=2$ in the region between pump and probe laser beams, in a Rb vapor cell using the Hanle configuration. The transmission of the probe beam, placed inside the hollow pump beam, shows the narrowing of the Hanle resonance (at external magnetic field $B=0$) by Ramsey fringes whose separation from the central peak depends on the distance between the beams. The temporal evolution of the pump induced alignment is evident from the changes of the probe transmission spectra with increasing the angle between linear polarizations of each beam. Experimental results are in agreement with the results of the model which calculates probe fluorescence by solving time-dependent optical Bloch equations, from the time when atom enters the pump beam to the time when it leaves the probe beam. The results for total excited state populations were averaged over atomic velocities distribution.

The mathematical theory of quantum feedback networks has recently been developed [J. Gough and M. R. James, e-print arXiv:0804.3442v2] for general open quantum dynamical systems interacting with bosonic input fields. In this article we show, for the special case of linear dynamical Markovian systems with instantaneous feedback connections, that the transfer functions can be deduced and agree with the algebraic rules obtained in the nonlinear case. Using these rules, we derive the transfer functions for linear quantum systems in series, in cascade, and in feedback arrangements mediated by beam splitter devices.

Structural approximations to positive, but not completely positive maps are approximate physical realizations of these nonphysical maps. They find applications in the design of direct entanglement-detection methods. We show that many of these approximations, in the relevant case of optimal positive maps, define an entanglement breaking channel and, consequently, can be implemented via a measurement and state-preparation protocol. We also show how our findings can be useful for the design of better and simpler direct entanglement detection methods.

The codeword-stabilized (CWS) quantum code formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes [see A. Cross et al., e-print arXiv:0708.1021], but only for binary states. Here we generalize the CWS framework to the nonbinary case (of both prime and nonprime dimensions) and map the search for nonbinary quantum codes to a corresponding search problem for classical nonbinary codes with specific error patterns. We show that while the additivity properties of nonbinary CWS codes are similar to the binary case, the structural properties of the nonbinary codes differ substantially from the binary case, even for prime dimensions. In particular, we identify specific structure patterns of stabilizer groups, based on which efficient constructions might be possible for codes that encode more dimensions than any stabilizer codes of the same length and distance; similar methods cannot be applied in the binary case. Understanding of these structural properties can help prune the search space and facilitate the identification of good nonbinary CWS codes.

By encoding the digital input of a classical logic gate on the Hamiltonian of a quantum system and driving the logic operation by preparing it in the same nonstationary state whatever the input, NOR and NAND classical logic gates are designed with a minimum of three quantum states. The outputs of one gate are obtained either by measuring the distance between the $\rho \left(t\right)$ periodic quantum trajectory and the output target state ${\rho }_b$, or by measuring the secular frequency of the $\rho \left(t\right)$ almost periodic trajectory in the ${\rho }_b$ direction. A comparison of the stability to noise between the two approaches demonstrates that the frequency approach is more immune to random fluctuations in the Hamiltonian than a distance control approach, opening the way to determine the logic output using a tunneling current passing through the gate.

Inspired by Knill’s scheme for message passing error detection, here we develop a scheme for message passing error correction for the nine-qubit Bacon-Shor code. We show that for two levels of concatenated error correction, where classical information obtained at the first level is used to help interpret the syndrome at the second level, our scheme will correct all cases with four physical errors. This results in a reduction of the logical failure rate relative to conventional error correction by a factor proportional to the reciprocal of the physical error rate.

Calculations of recoil corrections to first order in $1∕M$, where $M$ is the mass of the nucleus, require an exact treatment of the electron propagator along with the evaluation of up to two transverse photon exchange diagrams. The real part of this effect was calculated in a previous paper, and in this paper we evaluate the imaginary part. Comparison with the known low-$Z$ recoil results is made, and the behavior of the effect at high $Z$ is studied.

Optical Feshbach resonances [Phys. Rev. Lett. 94, 193001 (2005)] and pump-dump photoassociation with short laser pulses [Phys. Rev. A 73, 033408 (2006)] have been proposed as means to coherently form stable ultracold-alkali-metal dimer molecules. In an optical Feshbach resonance, the intensity and possibly frequency of a cw laser are ramped up linearly followed by a sudden switch-off of the laser. This is applicable to tightly trapped atom pairs. In short-pulse photoassociation, the pump pulse forms a wave packet in an electronically excited state. The ensuing dynamics carries the wave packet to shorter internuclear distances where, after half a vibrational period, it can be deexcited to the electronic ground state by the dump pulse. Short-pulse photoassociation is suited for both shallow and tight traps. The applicability of these two means to produce ultracold molecules is investigated here for ${}^{88}\mathrm{Sr}$. Dipole-allowed transitions proceeding via the $B{}^1{\Sigma }_u^{+}$ excited state as well as transitions near the intercombination line are studied.

We consider a two-dimensional (2D) model of a rotating attractive Bose-Einstein condensate (BEC), trapped in an external potential. First, a harmonic potential with the critical strength is considered, which generates quasisolitons at the lowest Landau level (LLL). We describe a family of the LLL quasisolitons using both numerical method and a variational approximation (VA), which are in good agreement with each other. We demonstrate that kicking the LLL mode or applying a ramp potential sets it in the Larmor (cyclotron) motion that can also be accurately modeled by the VA. Collisions between two such moving modes may be elastic or inelastic depending on their total norm. If an additional confining potential is applied along with the ramp, it creates a stationary edge state. Applying a kick to the edge state in the direction of the ramp gives rise to a skipping motion in the perpendicular direction. These regimes may be interpreted as the Hall effect for the quasisolitons. Next, we consider the condensate trapped in an axisymmetric quartic potential. Three species of localized states and their stability regions are identified, viz., vortices with arbitrary topological charge $m$, “crescents” (mixed-vorticity states), and strongly localized center-of-mass (c.m.) states, alias quasisolitons, shifted off the rotation pivot. These results are similar to those reported before for the model with a combined quadratic-quartic trap. Stable pairs of c.m. states set at diametrically opposite points are found, too. We present a VA which provides for an accurate description of vortices with all values of $m$, and of the c.m. states. We also demonstrate that kicking them in the azimuthal direction sets the quasisolitons in epitrochoidal motion (which is also accurately predicted by the VA), collisions between them being elastic.

We study the propagation of linearly coupled polarization waves in a medium containing a two-level molecular dopant having a resonant degenerate two-photon transition. A Thirring-type model is derived for small amplitudes of waves and a solitary wave solution is obtained. For a case of three-wave interaction we derive an asymptotic approximate solution describing quasi-self-similar dynamics of light pulses. Solutions demonstrate that by using a dopant one is able to control the polarization of propagated light.

The preparation of coherent states of the harmonic oscillator on a sphere is considered. Based on the nonlinear coherent states of the atomic center-of-mass motion of a trapped ion, one may control the laser-ion interaction in such a way that sphere coherent states are obtained as motional dark states of the system. The curvature can be controlled by the Rabi frequencies of the driving lasers. The nonclassical properties of the resulting quantum states are analyzed. By variation of the curvature of the sphere, the states can be tuned continuously between spin-squeezed states and motional Fock states.

We report the existence of dark polariton solitons and study their stability and symmetry breaking in semiconductor microcavities operating in the strong-coupling regime. These half-light half-matter solitons are potential candidates for applications in all-optical signal processing. Their excitation time and required pump powers are a few orders of magnitude less than those of their weakly coupled light-only counterparts.

The lowest bound state of a one-electron ion in a constant magnetic field $\mathbf{B}$ is calculated from the pseudorelativistic no-pair Brown-Ravenhall operator. The variational wave function is chosen as the product of a Landau function (in the transverse direction) and a hydrogenic state (in the longitudinal direction). The dependence of the ground-state energy on the nuclear charge $Z$ as well as on the magnetic field strength is investigated, and a scaling with $B∕Z^2$ is observed. Relativistic effects are shown to be important both for large $B$ and large $Z$. When $B\to \infty$, a decrease of the ground-state energy with $\sqrt{B}$ is found in contrast to the $\ln B$ behavior of the Pauli operator.

Given a composite quantum system in which the states of the subsystems are independently (but not necessarily identically) prepared, we construct separate measurements on the subsystems from any given joint measurement such that the former always give at least as much information as the latter. This construction offers insights into the understanding of measurements on this type of composite system. Moreover, this construction essentially proves the intuition that separate measurements on the subsystems are sufficient to extract the maximal information about the separately prepared subsystems, thus making a joint measurement unnecessary. Furthermore, our result implies that individual attacks are as powerful as collective attacks in obtaining information about the raw key in quantum key distribution.

We investigate when the quantum correlations of a bipartite system, under the influence of environments with memory, are not reproducible with certainty by a classical local hidden variable model. For this purpose, we compare the dynamics of a Bell inequality with that of entanglement, as measured by concurrence. We find time regions when the Bell inequality is not violated even in correspondence with high values of concurrence (up to $\approx 0.8$). We also suggest that these results may be observed by adopting a modification of a recent experimental optical setup. These findings indicate that even highly entangled systems cannot be exploited with certainty in contexts where the nonclassical reproducibility of quantum correlations is required.

The transfer of a quantum state between distant nodes in two-dimensional networks is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It is shown that perfect state transfer is achieved in a network of size $N$, whose structure is that of an $(N∕2)$-cross polytope graph, if $N$ is a multiple of $4$. The result is reminiscent of the Babinet principle of classical optics. A quantum Babinet principle is derived, which allows for the identification of complementary graphs leading to the same fidelity of state transfer, in analogy with complementary screens providing identical diffraction patterns.