The phase diagram of ultracold bosons in realistic optical superlattices is addressed via second-order cell strong coupling perturbative expansions for the Bose-Hubbard model describing the system. Taking advantage of the cell partition inherent in the complex periodic modulation of a superlattice, this technique allows for the description of the unusual loophole-shaped insulator domains that may occur in the phase diagram of the system, unlike the standard perturbative approach. Furthermore, comparisons with quantum Monte Carlo simulations show that our approach provides quantitatively satisfactory results at a significantly lower computational cost than brute force numerical methods. We explicitly consider the phase diagrams for two realistic 3-periodic optical superlattices. These show that many insulator domains exhibit an unusual reentrant character, which we discuss, and suggest that the quantum phase transition relevant to the loophole-shaped insulating domains does not require extreme experimental condition in order to be observed.

Quantum process tomography is used to fully characterize the evolution of the quantum vibrational state of atoms. Rubidium atoms are trapped in a shallow optical lattice supporting only two vibrational states, which we characterize by reconstructing the $2\times 2$ density matrix. Repeating this reconstruction for a complete set of inputs allows us to completely characterize both the system’s intrinsic decoherence and resonant coupling.

We propose a scheme for subwavelength localization of an atom conditioned upon the absorption of a weak probe field at a particular frequency. Manipulating atom-field interaction on a certain transition by applying drive fields on nearby coupled transitions leads to interesting effects in the absorption spectrum of the weak probe field. We exploit this fact and employ a four-level system with three driving fields and a weak probe field, where one of the drive fields is a standing-wave field of a cavity. We show that the position of an atom along this standing wave is determined when probe-field absorption is measured. We find that absorption of the weak probe field at a certain frequency leads to subwavelength localization of the atom in either of the two half-wavelength regions of the cavity field by appropriate choice of the system parameters. We term this result as sub-half-wavelength localization to contrast it with the usual atom localization result of four peaks spread over one wavelength of the standing wave. We observe two localization peaks in either of the two half-wavelength regions along the cavity axis.

We have employed ab initio molecular dynamics to investigate the equilibrium geometries, energetics, and the nature of bonding in mixed Li-Sn clusters. Our studies reveal that a small percentage of Sn in Li-rich clusters introduces significant changes in the equilibrium geometries. It is also seen that the geometries of Sn-rich clusters are influenced by the ${\mathrm{Sn}}_{10}$ motif. Analysis of the nature of bonding shows that there are two competing interactions in the clusters: the polar bond between Li-Sn in the mixed clusters and Sn-Sn interaction leading to covalent bond in Sn-rich clusters.

The consistency of the quantum adiabatic theorem has been doubted recently. It is shown in the present paper that the difference between the adiabatic solution and the exact solution to the Schrödinger equation with a slowly changing driving Hamiltonian is small; while the difference between their time derivatives is not small. This explains why substituting the adiabatic solution back into the Schrödinger equation leads to “inconsistency” of the adiabatic theorem. Physics is determined completely by the state vector, and not by its time derivative. Therefore the quantum adiabatic theorem is physically correct.

In this paper we present an approach to quantum cloning with unmodulated spin networks. The cloner is realized by a proper design of the network and a choice of the coupling between the qubits. We show that in the case of phase covariant cloner the $XY$ coupling gives the best results. In the $1\to 2$ cloning we find that the value for the fidelity of the optimal cloner is achieved, and values comparable to the optimal ones in the general $N\to M$ case can be attained. If a suitable set of network symmetries are satisfied, the output fidelity of the clones does not depend on the specific choice of the graph. We show that spin network cloning is robust against the presence of static imperfections. Moreover, in the presence of noise, it outperforms the conventional approach. In this case the fidelity exceeds the corresponding value obtained by quantum gates even for a very small amount of noise. Furthermore, we show how to use this method to clone qutrits and qudits. By means of the Heisenberg coupling it is also possible to implement the universal cloner although in this case the fidelity is 10% off that of the optimal cloner.

We explore the possibility of performing superdense coding with nonmaximally entangled states as a resource. Using this we find that one can send two classical bits in a probabilistic manner by sending a qubit. We generalize our scheme to higher dimensions and show that one can communicate $2{\log }_{2}d$ classical bits by sending a $d$-dimensional quantum state with a certain probability of success. The success probability in superdense coding is related to the success probability of distinguishing nonorthogonal states. The optimal average success probabilities are explicitly calculated. We consider the possibility of sending $2{\log }_{2}d$ classical bits with a shared resource of a higher dimensional entangled state $(D\times D,D>d)$. It is found that more entanglement does not necessarily lead to higher success probability. This also answers the question as to why we need ${\log }_{2}d$ ebits to send $2{\log }_{2}d$ classical bits in a deterministic fashion.

The entanglement of general asymmetric pure Gaussian two-mode states is examined in terms of the coefficients of the quadrature components of the wave function. The entanglement criterion and the entanglement of formation are directly evaluated as a function of these coefficients, without the need for local unitary transformations. These reproduce results for the special case of symmetric pure states which employ a relation between squeezed states and Einstein-Podolsky-Rosen correlations. The modification of the quadrature coefficients and the corresponding entanglement due to application of various optical elements is also derived.

The three-spin chain with a Heisenberg $XY$ interaction is simulated in a three-qubit nuclear magnetic resonance quantum computer. The evolution caused by the $XY$ interaction is decomposed into a series of single-spin rotations and the $J$-coupling evolutions between the neighboring spins. The perfect state transfer algorithm proposed by Christandl et al.[Phys. Rev. Lett. 92, 187902 (2004)] is realized in the $XY$ chain.

Two color infrared–x-ray pump-probe spectroscopy of the NO molecule is studied theoretically and numerically in order to obtain a deeper insight of the underlying physics and of the potential of this suggested technology. From the theoretical investigation a number of conclusions could be drawn: It is found that the phase of the infrared field strongly influences the trajectory of the nuclear wave packet, and hence, the x-ray spectrum. The trajectory experiences fast oscillations with the vibrational frequency with a modulation due to the anharmonicity of the potential. The dependences of the x-ray spectra on the delay time, the duration, and the shape of the pulses are studied in detail. It is shown that the x-ray spectrum keep memory about the infrared phase after the pump field left the system. This memory effect is sensitive to the time of switching-off the pump field and the Rabi frequency. The phase effect takes maximum value when the duration of the x-ray pulse is one-fourth of the infrared field period, and can be enhanced by a proper control of the duration and intensity of the pump pulse. The manifestation of the phase is different for oriented and disordered molecules and depends strongly on the intensity of the pump radiation.

The generalized oscillator strengths for the valence-shell excitations to $2p^{5}3s$, $2p^{5}3p$, and $2p^{5}4s$ of neon were measured with an angle-resolved fast-electron energy-loss spectrometer at an incident electron energy of $2500\mathrm{eV}$. The transition multipolarities for these excitations were elucidated with the help of the calculated intermediate-coupling coefficients using the COWAN code. The generalized oscillator strength profiles for the electric monopole, electric dipole, and electric quadrupole excitations were analyzed and their positions of the extrema were obtained. Furthermore, the experimental generalized oscillator strength ratios between the excitations to $2p^{5}4s{[3∕2]}_1$ and $2p^{5}4s^{\prime }{[1∕2]}_1$ were determined and found to be in agreement with the calculated intermediate-coupling coefficient ratio.

General optimal coherent control of dissipative $N$-level systems in the Markovian time regime is formulated within Pointryagin’s principle and the Lindblad equation. In the present paper, we study feasibility and limitations of steering of dissipative two-, three-, and four-level systems from a given initial pure or mixed state into a desired final state under the influence of an external electric field. The time evolution of the system is computed within the Lindblad equation and a conjugate gradient method is used to identify optimal control fields. The influence of both field-independent population and polarization decay on achieving the objective is investigated in systematic fashion. It is shown that, for realistic dephasing times, optimum control fields can be identified which drive the system into the target state with very high success rate and in economical fashion, even when starting from a poor initial guess. Furthermore, the optimal fields obtained give insight into the system dynamics. However, if decay rates of the system cannot be subjected to electromagnetic control, the dissipative system cannot be maintained in a specific pure or mixed state, in general.

We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the pairing energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry: the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell phase, which is characterized by a nonvanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of ${}^6\mathrm{Li}$ atoms trapped in two different hyperfine states.

We present a mathematical framework for simulation of optical fields in complex gravitational-wave interferometers. The simulation framework uses the two-photon formalism for optical fields and includes radiation pressure effects, an important addition required for simulating signal and noise fields in next-generation interferometers with high circulating power. We present a comparison of results from the simulation with analytical calculation and show that accurate agreement is achieved.

The propagation of light through the system composed of two thin films with resonant nonlinearity has been considered. Conditions for the multistability and Hopf bifurcations have been found. Two kinds of self-sustained pulsations including Rabi oscillations have been distinguished. A possible experimental observation of the effects described using quantum-confined semiconductor structures as a resonant medium has been discussed.

We investigate duality relations between conjugate observables after measurements performed on a single realization of the system. The application of standard inference methods implies the existence of duality relations for single systems when using classical as well as quantum physics.

In a previous publication [Phys. Rev. A. 70, 062711 (2004)] we presented results for electron collisions with OCS molecules. We found a $\Pi$ shape resonance and discussed the existence of an $s$-wave virtual state through the analysis of the scattering length. The existence of the $\Pi$ shape resonance has been reported by other theoretical and experimental studies, and the existence of an $s$-wave virtual state has been suggested by an experimental study. In this Addendum we show that besides the $\Pi$ shape resonance and the $s$-wave virtual state, this molecule also presents a Ramsauer-Townsend minimum around 1 eV.

Considering as distance between two two-party correlations the minimum number of half local results one party must toggle in order to turn one correlation into the other, we show that the volume of the set of physically obtainable correlations in the Einstein-Podolsky-Rosen-Bell scenario is ${(3\pi ∕8)}^2\approx 1.388$ larger than the volume of the set of correlations obtainable in local deterministic or probabilistic hidden-variable theories, but is only $3{\pi }^2∕32\approx 0.925$ of the volume allowed by arbitrary causal (i.e., no-signaling) theories.

We propose a different implementation of discrete-time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of freedom that controls the displacement of the quantum walker, implemented as a spatially delocalized qubit, i.e., the coin is also encoded in position space. We analyze the dependence of the quantum walk on temperature and experimental imperfections such as shaking in the trap positions. Finally, combining a spatially delocalized qubit and a hyperfine qubit, we also give a scheme to realize a quantum walk on a two-dimensional square lattice with the possibility of implementing different coin operators.

We consider a two-component system of Fermi atoms and molecular bosons in the vicinity of a narrow Feshbach resonance. We derive an effective action for the system, which has a term describing coherent tunneling of the molecular bosons into Cooper pairs and vice versa. In the equilibrium regime, phase coherence between atom pairs and molecules may be destroyed by thermal or quantum phase fluctuations. In the nonequilibrium regime, the system may show an internal ac Josephson effect leading to real time oscillations in the number of molecular bosons.