We have devised an optical scheme for the recently proposed protocol for encoding two qubits into one qutrit. In this protocol, Alice encodes an arbitrary pure product state of two qubits into a state of one qutrit. Bob can then restore either of the two encoded qubit states error-free but not both of them simultaneously. We have successfully realized this scheme experimentally using spatial-mode encoding. Each qubit (qutrit) was represented by a single photon that could propagate through two (three) separate fibers. We theoretically propose two generalizations of the original protocol. We have found a probabilistic operation that enables us to retrieve both qubits simultaneously with average fidelity above 90% and we have proposed an extension of the original encoding transformation to encode $N$ qubits into one $(N+1)$-dimensional system.

The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state ${\psi }_I$ may need so as to evolve into a state orthogonal to itself. Recently [V. Giovanetti, S. Lloyd, and L. Maccone, Phys. Rev. A 67, 052109 (2003)] this bound has been generalized to the case where ${\psi }_I$ does not necessarily evolve into an orthogonal state, but into any other ${\psi }_F$. It was pointed out that, for certain classes of states, quantum entanglement enhances the evolution “speed” of composite quantum systems. In this work we provide an exhaustive and systematic QSL study for pure and mixed states belonging to the whole 15-dimensional space of two qubits, with ${\psi }_F$ a not necessarily orthogonal state to ${\psi }_I$. We display convincing evidence for a clear correlation between concurrence, on the one hand, and the speed of quantum evolution determined by the action of a rather general local Hamiltonian, on the other one.

In this paper we report total cross sections (TCS), $Q_T$, total elastic cross sections, $Q_{\mathit{el}}$, and total ionization cross section, $Q_{\mathit{ion}}$ for electron impact on water, formaldehyde, formic acid, and the formyl radical from circa $15\mathrm{eV}\text{to}2\mathrm{KeV}$. The results are compared where possible, with previous theoretical and experimental results and, in general, are found to be in good agreement. The total and elastic cross sections for HCHO, HCOOH, and CHO radical are reported.

We study the thermal fluctuations of vortex positions in small vortex clusters in a harmonically trapped rotating Bose-Einstein condensate. It is shown that the order-disorder transition of two-shell clusters occurs via the decoupling of shells with respect to each other. The corresponding “melting” temperature depends strongly on the commensurability between numbers of vortices in shells. We show that melting can be achieved at experimentally attainable parameters and very low temperatures. Also studied is the effect of thermal fluctuations on vortices in an anisotropic trap with small quadrupole deformation. We show that thermal fluctuations lead to the decoupling of a vortex cluster from the pinning potential produced by this deformation. The decoupling temperatures are estimated and strong commensurability effects are revealed.

Here we present the coherent control of two-photon induced birefringence in polymeric films containing Disperse Red 13 (DR13) azoaromatic molecules. Such control is achieved by enhancing and reducing the azochromophor cis-trans photoisomerization rate, which leads to the molecular orientation, inducing the birefringence. The dependence on chirp and phase mask of the birefringence signal was studied and modeled.

We present calculations of potential curves for very high-$n$ $\left(89D\right)$ Cs Rydberg-atom pairs, including a background electric field. From these potentials, we show that energy transfer occurs at rates of $\sim 30–70\mathrm{MHz}$, background electric fields play an important role and dipole-dipole- and quadrupole-quadrupole-induced avoided curve crossings should lead to conversion of electronic to kinetic energy, $n$-changing collisions, and observable ultracold long-range Rydberg molecules.

Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a general phenomenon displayed in various subfields of quantum physics, the use of holonomies has lately been suggested as a robust technique to obtain quantum gates; the building blocks of quantum computers. Non-Abelian holonomies are usually associated with cyclic changes of quantum systems, but here we consider a generalization to noncyclic evolutions. We argue that this open-path holonomy can be used to construct quantum gates. We also show that a structure of partially defined holonomies emerges from the open-path holonomy. This structure has no counterpart in the Abelian setting. We illustrate the general ideas using an example that may be accessible to tests in various physical systems.

We study the pairwise entanglement close to separable ground states of a class of one-dimensional quantum spin models. At $T=0$ we find that such ground states separate regions, in the space of the Hamiltonian parameters, which are characterized by qualitatively different types of entanglement, namely parallel and antiparallel entanglement; we further demonstrate that the range of the concurrence diverges while approaching separable ground states, therefore evidencing that such states, with uncorrelated fluctuations, are reached by a long range reshuffling of the entanglement. We generalize our results to the analysis of quantum phase transitions occurring in bosonic and fermionic systems. Finally, the effects of finite temperature are considered: At $T>0$ we evidence the existence of a region where no pairwise entanglement survives, so that entanglement, if present, is genuinely multipartite.

We propose a simple physical implementation of the quantum Householder reflection (QHR) $\mathbf{M}\left(v\right)=\mathbf{I}-2\mid v⟩⟨v\mid$ in a quantum system of $N$ degenerate states (forming a qunit) coupled simultaneously to an ancillary (excited) state by $N$ resonant or nearly resonant pulsed external fields. We also introduce the generalized QHR $\mathbf{M}(v;\phi )=\mathbf{I}+(e^{i\phi }-1)\mid v⟩⟨v\mid$, which can be produced in the same $N$-pod system when the fields are appropriately detuned from resonance with the excited state. We use these two operators as building blocks in constructing arbitrary preselected unitary transformations. We show that the most general $\mathrm{U}\left(N\right)$ transformation can be factorized (and thereby produced) by either $N-1$ standard QHRs and an $N$-dimensional phase gate, or $N-1$ generalized QHRs and a one-dimensional phase gate. Viewed mathematically, these QHR factorizations provide parametrizations of the $\mathrm{U}\left(N\right)$ group. As an example, we propose a recipe for constructing the quantum Fourier transform (QFT) by at most $N$ interaction steps. For example, the QFT requires a single QHR for $N=2$, and only two QHRs for $N=3$ and 4.

We theoretically investigate above-threshold ionization of Mg by linearly and circularly polarized fs laser pulses. We find that the above-threshold ionization peaks are accompanied by small subpeaks for both linearly and circularly polarized pulses. We interpret the physical origin of the subpeaks as above-threshold ionization from the low-lying bound states which are far off-resonantly excited by the spectral wing of the pulse. This interpretation is confirmed by our comparative numerical studies. Furthermore, we provide a clear explanation of why this kind of subpeak in the photoelectron energy spectra has not been reported for smaller photon energies with Mg and other commonly used atoms such as H and rare gas atoms.

In order to understand what kind of information can be extracted from the vortex-core structure in superfluid fermion-atom gases we make a systematic study for the core structure of a singly quantized vortex in the range of broad Feshbach resonance, solving numerically the generalized Bogoliubov–de Gennes equation derived from the fermion-boson model. Numerical calculations reveal that the vortex core can be well characterized by three length scales from the spatial variation of the fermionic and bosonic gap functions. We also predict that the profile of matter depletion and the quasiparticle spectrum show distinctive differences between the BCS and Bose-Einstein Condensate regimes.

We study the finite temperature $T$ behavior of trapped Fermi gases as they undergo BCS–Bose-Einstein condensation (BEC) crossover, in the presence of a population imbalance. Our results, in qualitative agreement with recent experiments, show how the superfluid phase transition is directly reflected in the particle density profiles. We demonstrate that at $T\ne 0$ and in the near-BEC and unitary regimes, the polarization is excluded from the superfluid core. Importantly, a substantial polarization fraction is carried by a normal region of the trap having strong pair correlations, which we associate with noncondensed pairs or the “pseudogap phase.”

We discuss the generation of a macroscopic entangled state in a single atom cavity-QED system. The three-level atom in a cascade configuration interacts dispersively with two classical coherent fields inside a doubly resonant cavity. We show that a macroscopic entangled state between these two cavity modes can be generated under large detuning conditions. The entanglement persists even under the presence of cavity losses.

Third-order relativistic many-body perturbation theory (MBPT) is applied to obtain energies of ions with two valence electrons in the no virtual-pair approximation (NVPA). A total of 302 third-order Goldstone diagrams are organized into 12 one-body and 23 two-body terms. Only third-order two-body terms and diagrams are presented in this paper, owing to the fact that the one-body terms are identical to the previously studied third-order terms in monovalent ions. Dominant classes of diagrams are identified. The model potential is the Dirac-Hartree-Fock potential $V^{N-2}$, and $B$-spline basis functions in a cavity of finite radius are employed in the numerical calculations. The Breit interaction is taken into account through the second order of perturbation theory, and the lowest-order Lamb shift is also evaluated. Sample calculations are performed for berylliumlike ions with $Z=4–7$, and for the magnesiumlike ion $\mathrm{P}\mathrm{IV}$. The third-order excitation energies are in excellent agreement with measurement with an accuracy at 0.2% level for the cases considered. Comparisons are made with second-order MBPT results, and with other calculations. The third-order energy correction is shown to be significant, improving the previous second-order calculations by an order of magnitude.

The integral equation for the time-dependent optimized effective potential (TDOEP) in time-dependent density-functional theory is transformed into a set of partial-differential equations. These equations only involve occupied Kohn-Sham orbitals and orbital shifts resulting from the difference between the exchange-correlation potential and the orbital-dependent potential. Due to the success of an analog scheme in the static case, a scheme that propagates orbitals and orbital shifts in real time is a natural candidate for an exact solution of the TDOEP equation. We investigate the numerical stability of such a scheme. An approximation beyond the Krieger-Li-Iafrate approximation for the time-dependent exchange-correlation potential is analyzed.

We present measurements of polarization-gradient cooling in a Cs magneto-optic trap (MOT). The temperature in the MOT is found to vary linearly with the light shift. The slope gives a value of $C_{\sigma }=0.25\pm 0.05$ while the minimum temperature $T_0=3.8\pm 3.3\mu \mathrm{K}$, in agreement with measurements done in the absence of a magnetic field. The temperature is determined by using a nondestructive method which uses Rydberg time-of-flight velocity distributions of trapped atoms.

A theoretical model is presented for the study of the dynamics of a cold atomic cloud falling in the gravity field in the presence of two crossing dipole guides. The cloud is split between the two branches of this laser guide, and we compare experimental measurements of the splitting efficiency with semiclassical simulations. We then explore the possibilities of optimization of this beam splitter. Our numerical study also gives access to detailed information, such as the atom temperature after the splitting.

We discuss the detection of field quadrature fluctuations in conditional homodyne detection experiments and possible sources of error in such an experiment. We also present modifications to these experiments to help eliminate such errors and extend their range of applicability.

The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasiclassical (in fact, diffusive) in the long time limit. We present here a counterexample, in which a particle makes quantum transitions between the sites of a $d$-dimensional hypercubic lattice while strongly coupled to a bath of two-level systems that “record” the transitions. The long-time evolution of an initial wave packet is found to be most unusual: the mean square displacement of the particle density matrix shows long-range ballistic behavior, with $⟨n^2⟩\sim t^2$, but simultaneously a kind of weakly localized behavior near the origin. This result may have important implications for the design of quantum computing algorithms, since it describes a class of quantum walks.