A method is suggested for the fabrication of three-dimensional photonic crystals operating in the visible by rolling patterned prestressed membranes. A variety of architectures accessible using this fabrication scheme, including $\langle 111\rangle$ and $\langle 100\rangle$ diamond structures, were theoretically examined and optimized using photonic-band and density-of-optical-states calculations. The influence that finite size and bending have on a band gap was explored using a finite-element analysis of a two-dimensional triangular lattice of air holes.

The ubiquitous decoherence phenomenon is responsible for the lack of quantum superpositions at the macroscopic scale. It is increasingly difficult to isolate a quantum system from its environment when its size increases. Making use of the weird quantum properties of mesoscopic quantum states thus requires efficient means to combat decoherence. One option is real-time quantum feedback. It features the components of a conventional feedback: measurement of the system's state (sensor), analysis (controller), and feedback action (actuator) aiming to the target state. The random back-action of the measurements by the sensor makes quantum feedback much more difficult than its classical counterpart. Mesoscopic photon number (Fock) states feature a decoherence rate proportional to the photon number. They are thus a simple example of a fragile quantum resource. We demonstrated recently two quantum feedback schemes continuously stabilizing Fock state of a microwave field in a high-quality cavity. Sensitive atoms, crossing the field one at a time, are used as quantum nondemolition (QND) probes of its photon number. The feedback actuator is either a classical source [Sayrin et al., Nature (London) 477, 73 (2011)] or individual resonant atoms emitting or absorbing one photon each [Zhou et al., Phys. Rev. Lett. 108, 243602 (2012)]. Both schemes detect the quantum jumps of the photon number and efficiently correct their adverse effects, preparing and preserving a fragile quantum resource. We present an in-depth analysis of our methods, which sheds light onto the fundamental difficulties encountered in quantum feedback, in particular concerning the state estimation algorithm, and onto the ways to circumvent them. These results open the way to informationally optimal QND measurements or to the stabilization of mesoscopic field state superpositions. More generally, they can be cast in a variety of contexts to loosen the tight constraints set by decoherence in quantum metrology and quantum information processing.

In this paper we examine the use of an adiabatic quantum data transfer protocol to build a universal quantum computer. Single-qubit gates are realized by using a bus protocol to transfer qubits of information down a spin chain with a unitary twist. This twist arises from altered couplings on the chain corresponding to unitary rotations performed on one region of the chain. We show how a controlled-not gate can be realized by using a control qubit with Ising-type coupling. The method discussed here can be extended to nonadiabatic quantum bus protocols. We also examine the potential of realizing such a quantum computer by using superconducting flux qubits.

Accurate variational quantum-mechanical calculations are performed for the nine lowest ${}^{2}S$ ($1s^{2}ns$), $n=2,\cdots ,10$ states of the lithium atom. The effect of the finite nuclear mass is explicitly included in the calculations allowing for the determination of the isotopic shifts of the energy levels. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions and their exponential parameters are variationally optimized with the aid of the analytical energy gradient determined with respect to those parameters. The experimental results for the lower states ($n=3,\cdots ,6$) and the calculated results for the higher states ($n=7,\cdots ,10$) fitted with quantum-defect-like formulas are used to predict the energies of ${}^{2}S$ $1s^{2}ns$ states for ${}^7$Li and ${}^6$Li with $n$ up to 30.

We consider the tunneling ionization of an electron, bound by a zero-range potential and a constant magnetic field, under the influence of a low-frequency monochromatic laser beam. An integral equation for the complex quasienergy is derived based upon the exact solution of the Schrödinger equation and the Green's function earlier obtained by  Rylyuk and Ortner [Phys. Rev. A 67, 013414 (2003)] for an electron moving in an arbitrary electromagnetic wave and a constant magnetic field. We show that accounting for an electron spin leads to drastic changes in ionization probability. For the case of a nonzero angle $\theta \ne 0$ between an electromagnetic wave direction and the magnetic field the ionization rate is shown to increase with the magnetic field when the electron spin is taken into account. The expressions for the level shift and width and for the diamagnetic and the paramagnetic susceptibilities of the electron in a zero-range force field and a constant magnetic field are found. In the case of ionization of neutral atoms and positive ions, we also take into consideration the Coulomb interaction of the emerging electron with the atomic or ionic core.

We investigate the dynamics of cavity cooling of a single ion beyond the Lamb-Dicke regime and demonstrate a cooling limit of approximately 50$\%$ of the Doppler temperature using a high finesse cavity. We also study the statistical properties of the ion-cavity emission and present a model that maps the phonon states to the photon states. With this model, we explain the super-Poissonian photon distribution observed in our experiments and propose a method to estimate the ion temperature in a real-time manner based on the statistical behavior of the photon emission from the cavity.

In this study, we perform a strong-coupling expansion up to third order of the hopping parameter $t$ for the spin-1 Bose-Hubbard model with antiferromagnetic interaction. As expected from previous studies, the Mott-insulator phase is considerably more stable against the superfluid phase when filling with an even number of bosons than when filling with an odd number of bosons. The phase-boundary curves are consistent with the perturbative mean-field theory in the limit of infinite dimensions. The critical value of the hopping parameter $t_{\mathrm{C}}$ at the peak of the Mott lobe depends on the antiferromagnetic interaction. This result indicates the reliability of the strong-coupling expansion when $U_2$ possesses large (intermediate) values for Mott lobe with an even (odd) number of bosons. Moreover, in order to improve our results, we apply a few extrapolation methods up to infinite order in $t$. The fitting results of the phase-boundary curves agree better with those of the perturbative mean-field approximation. In addition, the linear fit error of $t_{\mathrm{C}}$ is very small for the strong antiferromagnetic interaction.

Ultracold atoms with two hyperfine internal states in optical lattices are proposed to demonstrate a two-dimensional spin-$1/2$ model under a transverse effective staggered magnetic field. The transverse magnetic field is produced by a Raman process and can be modulated by the intensities of the additional light fields. This optical lattice protocol can investigate magnetic quantum phenomena induced by the effective staggered magnetic field in a wider parameter range with controllable interaction between the spins of the nearest-neighbor atoms.

We present a scheme for the amplification of Schrödinger cat states that collapses two smaller states onto their constructive interference via a homodyne projection. We analyze the performance of the amplification in terms of fidelity and success rate when the input consists of either exact coherent state superpositions or of photon-subtracted squeezed vacua. The impact of imprecise homodyne detection and of impure squeezing is quantified. We also assess the scalability of iterated amplifications.

We report the existence and properties of localized modes described by a nonlinear Schrödinger equation with a complex $\mathcal{PT}$-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one-dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters, although the corresponding linear Schrödinger eigenvalue problem possesses unbroken $\mathcal{PT}$ symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power-flow density associated with these localized modes has also been examined.

Relying only on first principles, we derive a master equation of Lindblad form generally applicable for adiabatically driven time-dependent systems. Our analysis shows that the much-debated secular approximation can be valid for slowly time-dependent Hamiltonians when performed in an appropriate basis. We apply our approach to the well-known Landau-Zener problem, where we find that adiabaticity is improved by coupling to a low-temperature environment.

We analyze the time-optimal control of spin-1/2 particles with bounded field amplitudes in the presence of dissipative and radiation damping effects. Using tools of geometric optimal control theory, we determine different optimal syntheses for specific values of the system parameters. We show the nontrivial role of the effective radiation damping effect on the optimal control law.

We introduce a high-fidelity technique for coherent control of three-state quantum systems, which combines two popular control tools—stimulated Raman adiabatic passage (STIRAP) and composite pulses. By using composite sequences of pairs of partly delayed pulses with appropriate phases, the nonadiabatic transitions, which prevent STIRAP from reaching unit fidelity, can be canceled to an arbitrary order by destructive interference, and therefore, the technique can be made arbitrarily accurate. The composite phases are given by simple analytic formulas, and they are universal for they do not depend on the specific pulse shapes, the pulse delay, and the pulse areas.

A non-Poisson regular quasienergy spectrum is found for the generalized kicked particle under quantum-resonance conditions at generic quasimomentum, a quantity most relevant in atom-optics experimental realizations of kicked-rotor systems. The regular spectrum has the structure of a staggered ladder, i.e., it is the superposition of a finite number of ladder subspectra all having the same spacing, which is independent of the nonintegrability of the system. This spectral structure is shown to have distinct quantum-dynamical manifestations: a suppression of quantum resonances and a dynamical localization characterized by unique features such as traveling-wave components in the time evolution. These phenomena are found to be robust under small variations of the quasimomentum and should therefore be experimentally observable using Bose-Einstein condensates with sufficiently small quasimomentum width.

We study the effects of the spin orbit interaction (SOI) of light in an optical trap and show that the propagation of the tightly focused trapping beam in a stratified medium can lead to significantly enhanced SOI. For a plane polarized incident beam the SOI manifests itself by giving rise to a strong anisotropic linear diattenuation effect which produces polarization-dependent off-axis high-intensity side lobes near the focal plane of the trap. Single micron-sized asymmetric particles can be trapped in the side lobes and transported over circular paths by a rotation of the plane of input polarization. We demonstrate such controlled motion on peapod-shaped single soft oxometalate particles of dimension around $1\times 0.5$ $\mu$m over lengths up to $\sim$15 $\mu$m. The observed effects are supported by calculations of the intensity profiles based on a variation of the Debye-Wolf approach. The enhanced SOI could thus be used as a generic means of transporting mesoscopic asymmetric particles in an optical trap without the use of complex optical beams or changing the alignment of the beam into the trap.

We analyze the nonlinear optics of quasi-one-dimensional quantum graphs and manipulate their topology and geometry to generate nonlinearities in a simple system approaching the fundamental limits of the first and second hyperpolarizabilities. We explore a huge configuration space in order to determine whether the fundamental limits may be approached for specific topologies, independent of molecular details, when the geometry is manipulated to maximize the intrinsic response. Changes in geometry result in smooth variations of the nonlinearities. Topological changes between geometrically similar systems cause profound changes in the nonlinear susceptibilities that include a discontinuity due to abrupt changes in the boundary conditions. We demonstrate the same universal scaling behavior for quantum graphs that is predicted for general quantum nonlinear optical systems near their fundamental limits, indicating that our results for quantum graphs may reflect general structure-property relationships for globally optimized nonlinear optical systems.

We investigate the destructive influence of noise on the shape-invariant solitons in a three-dimensional model that includes the highly nonlocal nature of nematic liquid crystals. We first determine the fundamental shape-preserving solitons and then establish that any noise added to the medium or to the solitons induces them to breathe at short propagation distances and to disperse at long propagation distances. The characteristics of breathing solitons at short distances are well predicted by the variational calculation [Phys. Rev. A 85, 033826 (2012)]. At longer propagation distances soliton beams suddenly spread, almost without radiation losses. Their power remains almost conserved until they reach the transverse boundaries of the sample. The increase in the amount of noise accelerates beam spreading and soliton destruction. The influence of the correlation length of noise is more complex. An initial increase in the correlation length causes solitons to disperse at shorter propagation distances. However, further increase in the correlation length leads to a reversal—to prolonged stability and dispersal at longer propagation distances. We give theoretical explanation for such behavior in terms of mean-field evolution equations.

In their recent paper [N. B. Aleksić, M. S. Petrović, A. I. Strinić, and M. R. Belić, Phys. Rev. A 85, 033826 (2012)], Aleksić et al. numerically study the propagation of spatial solitary waves in nematic liquid crystals in the presence of noise. As expected, and reported earlier in their previous work on the same topic, the authors find that optical solitary waves in the presence of perturbations are no longer stationary, oscillate in amplitude and width as they propagate, and eventually decay to linear waves. Surprisingly, they conclude that spatial solitary waves are difficult to observe in nematic liquid crystals, in contrast to numerous experimental reports and the vast literature on the topic. We argue with such a conclusion in light of the behavior of wave-packet solutions of nonlinear Schrödinger-type equations.

We reply to the Comment by G. Assanto and N. F. Smyth [Phys. Rev. A 87, 047801 (2013)] regarding our paper [Phys. Rev. A 85, 033826 (2012)]. We show that most of the comments do not apply to our paper. We point out that the analysis of multidimensional nonlocal systems of partial differential equations in noisy media, which we considered, cannot be done using analogies with simplified one-dimensional systems without noise, advanced by the commentators.

We consider spin-relaxation dynamics in cold Fermi gases with a pure-gauge spin-orbit coupling corresponding to recent experiments. We show that such experiments can give direct access to the collisional spin drag rate, and establish conditions for the observation of spin drag effects. In recent experiments the dynamics is found to be mainly ballistic leading to new regimes of reversible spin-relaxation-like processes.