An array of high-$Q$ electromagnetic resonators coupled to qubits gives rise to the Jaynes-Cummings-Hubbard model describing a superfluid to Mott-insulator transition of lattice polaritons. From mean-field and strong-coupling expansions, the critical properties of the model are expected to be identical to the scalar Bose-Hubbard model. A recent Monte Carlo study of the superfluid density on the square lattice suggested that this does not hold for the fixed-density transition through the Mott lobe tip. Instead, mean-field behavior with a dynamical critical exponent $z=2$ was found. We perform large-scale quantum Monte Carlo simulations to investigate the critical behavior of the superfluid density and the compressibility. We find $z=1$ at the tip of the insulating lobe. Hence the transition falls in the three-dimensional $XY$ universality class, analogous to the Bose-Hubbard model.

When light waves propagate through disordered photonic lattices, they can eventually become localized due to multiple scattering effects. Here we show experimentally that while the evolution and localization of the photon density distribution is similar in the two cases of diagonal and off-diagonal disorder, the density-density correlation carries a distinct signature of the type of disorder. We show that these differences reflect a symmetry in the spectrum and eigenmodes that exists in off-diagonally disordered lattices but is absent in lattices with diagonal disorder.

We consider the influence of variation in the fine structure constant $\alpha$ on a promising experiment proposed by DeMille et al. to search for variation in the electron-to-proton mass ratio $\mu$ using diatomic molecules [DeMille et al., Phys. Rev. Lett. 100, 043202 (2008)]. The proposed experiment involves spectroscopically probing the splitting between two nearly degenerate vibrational levels supported by different electronic potentials. Here we demonstrate that this splitting may be equally or more sensitive to variation in $\alpha$ as to variation in $\mu$. For the anticipated experimental precision, this implies that the $\alpha$ variation may not be negligible, as previously assumed, and further suggests that the method could serve as a competitive means to search for $\alpha$ variation as well.

We consider a unified analytical approach for scattering and decay processes in one-dimensional resonant tunneling systems using the formalism of resonant states to address the issue of the differences and similarities in the time evolution of decay between the decay of an arbitrary state prepared initially within a system and the formation and subsequent decay of a quasistationary state in the scattering of a Gaussian wavepacket on that system. We find three distinctive regimes. A first regime, which refers only to the quasistationary state, that is characterized by a buildup time of the probability density at a given position within the internal region of the potential. Here we find that the buildup time has a dependence on position. A second regime, dominated by the exponentially decaying terms, where the decay of the quasistationary state proceeds in an almost identical fashion as for the initially prepared decaying state. And finally, a third regime that involves the transition to nonexponential decay at long times and its ulterior behavior as an inverse power of time. Here we find that the time scale of the transition occurs at different times, which implies a dependence on the parameters of the initial state.

Universal single-qubit gates are constructed from a basic Bloch rotation operator realized through nonadiabatic Abelian geometric phase. The driving Hamiltonian in a generic two-level model is parameterized using controllable physical variables. The fidelity of the basic geometric rotation operator is investigated in the presence of systematic error in control parameters, such as the driving pulse area and frequency detuning. Compared to a conventional dynamic rotation, the geometric rotation shows improved fidelity.

The secondary electron yields as a result of highly charged ions impinging on clean Au(111) and thin films of C${}_{60}$ on Au have been measured. This has been done for film thicknesses of one to five monolayers and several charge states of Ar and Xe ions. For all ions an increase of 35$\%$ in the secondary electron yield is observed when going from Au(111) to multiple C${}_{60}$ layers. The increase remains constant for a wide range (7–26) of charge states. Possible scenarios are given to explain the increase in electron yield.

We have designed a pump-probe experiment to excite I${}_2$ to the $B$ state and subsequently ionize the molecule with a two-color (800- and 400-nm) probe pulse. By varying the relative phase of the two colors we are able to probe the asymmetric dissociation of ${\mathrm{I}}_2{}^{2+}\to {\mathrm{I}}^{2+}+\mathrm{I}$ and we observe spatial asymmetries in the ion yield of this (2,0) channel. Because the durations (35 fs) of the pump and probe pulses are much shorter than the vibrational period of the $B$ state (700 fs) we can fully resolve the dynamics as a function of internuclear separation $R$. We find that the amplitude of the spatial asymmetry increases as a function of $R$ and that the relative phase of the two colors that produces the maximum asymmetry is independent of $R$. Both of these observations are consistent with ionization of I${}_2$ directly into the field-dressed potential curves of I${}_2{}^{2+}$, which we model with a two-electron one-dimensional double-well potential in an external field. Interestingly, we find a spatial asymmetry for dissociation channels with a charge difference $\Delta q=2$, [(2,0) and (3,1)], but not for $\Delta q=1$, [(1,0), (2,1), (3,2)]. Finally, substructure in the time-of-flight data shows two distinct states leading to the (2,0) dissociation limit, one of which may indicate a breakdown of the presented model.

In a recent Letter, Manschwetus et al. [Phys. Rev. Lett. 102, 113002 (2009)] reported evidence of electron recapture during strong-field fragmentation of H${}_2$—explained using a frustrated tunneling ionization model. Unusually, the signature of this process was detection of excited H${}^{*}$ atoms. We report here an extensive study of this process in D${}_2$. Our measurements encompass a study of the pulse duration, intensity, ellipticity, and angular distribution dependence of D${}^{*}$ formation. While we find that the mechanism suggested by Manschwetus et al. is consistent with our experimental data, our theoretical work shows that electron recollision excitation cannot be completely ruled out as an alternative mechanism for D${}^{*}$ production.

Above-threshold ionization of diatomic molecules by infrared carrier-envelope phase (CEP) stable few-cycle laser pulses is analyzed both experimentally and theoretically. The theoretical approach is based on the recently developed molecular improved strong-field approximation (ISFA), generalized to few-cycle pulses. Instead of using the first Born approximation, the rescattering matrix element in the ISFA is now calculated exactly. This modification leads to the appearance of characteristic minima in the differential cross section as a function of the scattering angle. Experimental angle-resolved photoelectron spectra of N${}_2$ and O${}_2$ molecules are obtained using the velocity map imaging technique. A relatively good agreement of experimental and simulated angle-resolved spectra, CEP-dependent asymmetry maps, and extracted electron-molecular ion elastic scattering differential cross sections is obtained.

Angle-resolved and internuclear-separation-resolved measurements of the single ionization rate of neutral I${}_2$ have been obtained. By launching a wave packet in the $B{}^3\Pi {{}_u}^{+}$ state ($B$ state) of I${}_2$ with a 50-fs tunable pump pulse we can measure the ionization rate as a function of internuclear separation as the wave packet evolves in the $B$ state. Moreover, since the ground to $B$-state optical transition dipole moment is parallel to the internuclear axis, the $B$-state subpopulation of the I${}_2$ thermal ensemble will have a high degree of alignment, allowing for angular measurements. The $B$ state shows the well-known effect of enhanced ionization at a critical separation, $R$${}_c$, with an enhancement factor of 22 when the ionizing field is polarized along the internuclear axis and the enhanced ionization decreases when the angle between the field and the axis increases from 0 ${}^{\circ }$ to 90 ${}^{\circ }$, finally disappearing at 90 ${}^{\circ }$. These results on the enhanced ionization of the $B$ state of I${}_2$ give the most precise determination of $R$${}_c$ for any molecule and agree extremely well with the prediction from a simple model of electron localization.

We propose various scenarios for molecular vibrational cooling combining the effects of two kinds of resonance states occurring during the photodissociation of Na${}_2$ taken as an illustrative example. Such resonances result from an appropriate sampling of laser parameters (wavelength and intensity): (a) For particular choices of intensity and wavelength, two resonance energies can be brought to complete coalescence, with their positions and widths becoming equal and leading to a so-called exceptional point (EP) in the parameter plane. Advantage can be taken from such points for very selective laser-controlled vibrational transfer strategies. (b) For specific intensities, far beyond the perturbation regime, some resonances can have a zero width (infinite lifetime). They are referred to as a zero-width resonance (ZWR) and may be used for vibrational purification purposes. We show how appropriately shaped, experimentally reachable laser pulses, encircling EPs or inducing ZWRs, may be used for a thorough and comprehensive control aiming at population transfer or purification schemes, which, starting from an initial field-free vibrational distribution, ends up in the ground vibrational level.

Two-color (800- and 400-nm) short (45-fs) linearly polarized pulses are used to ionize and dissociate CO and NO. The emission of C${}^q$${}^{+}$, N${}^q$${}^{+}$, and O${}^{+}$ fragments indicates that the higher ionization rate occurs when the peak electric field points from C to O in CO and from N to O in NO. This preferred direction is in agreement with that predicted by Stark-corrected strong-field-approximation calculations.

We experimentally demonstrate the manipulation of two orthogonal components of a spin wave in an atomic ensemble. Based on Raman two-photon transition and Larmor spin precession induced by magnetic field pulses, the coherent rotations between the two components of the spin wave are controllably achieved. Successively, the two manipulated spin-wave components are mapped into two orthogonal polarized optical emissions. By measuring Ramsey fringes of the retrieved optical signals, the π/2-pulse fidelity of ∼96% is obtained. The presented manipulation scheme can be used to build an arbitrary rotation for qubit operations in quantum information processing based on atomic ensembles.

We examine the medium time quantum dynamics and population equilibration of two-, three-, and four-well Bose-Hubbard models using stochastic integration in the truncated Wigner phase-space representation. We find that all three systems will enter at least a temporary state of equilibrium, with the details depending on both the classical initial conditions and the initial quantum statistics. We find that classical integrability is not necessarily a good guide as to whether equilibration will occur. We construct an effective single-particle reduced density matrix for each of the systems, using the expectation values of operator moments, and use this to calculate an effective entropy. Knowing the expected maximum values of this entropy for each system, we are able to quantify the different approaches to equilibrium.

The quantum phase transition of the Dicke model has been observed recently in a system formed by motional excitations of a laser-driven Bose-Einstein condensate coupled to an optical cavity [Baumann et al., Nature (London) 464, 1301 (2010)]. The cavity-based system is intrinsically open: photons leak out of the cavity where they are detected. Even at zero temperature, the continuous weak measurement of the photon number leads to an irreversible dynamics toward a steady state. In the framework of a generalized Bogoliubov theory, we show that the steady state exhibits a dynamical quantum phase transition. We find that the critical point and the mean field are only slightly modified with respect to the phase transition in the ground state. However, the critical exponents of the singular quantum correlations are significantly different in the two cases. There is also a drastic modification of the atom-field entanglement, since the divergence of the logarithmic negativity of the ground state at the critical point is suppressed and a finite entanglement is found in the steady state.

We develop a three-dimensional theory for quantum memories based on light storage in ensembles of $\Lambda$-type atoms, where two long-lived atomic ground states are employed. We consider light storage in an ensemble of finite spatial extent and we show that within the paraxial approximation the Fresnel number of the atomic ensemble and the optical depth are the only important physical parameters determining the quality of the quantum memory. We analyze the influence of these parameters on the storage of light followed by either forward or backward read-out from the quantum memory. We show that for small Fresnel numbers the forward memory provides higher efficiencies, whereas for large Fresnel numbers the backward memory is advantageous. The optimal light modes to store in the memory are presented together with the corresponding spin waves and outcoming light modes. We show that for high optical depths such $\Lambda$-type atomic ensembles allow for highly efficient backward and forward memories even for small Fresnel numbers $F\gtrsim 0.1$.

We study large-amplitude one-dimensional solitary waves in photonic crystals featuring competition between linear and nonlinear lattices, with minima of the linear potential coinciding with maxima of the nonlinear pseudopotential, and vice versa (inverted nonlinear photonic crystals, INPCs), in the case of the saturable self-focusing nonlinearity. Such crystals were recently fabricated using a mixture of SU-8 and Rhodamine-B optical materials. By means of numerical methods and analytical approximations, we find that large-amplitude solitons are broad sharply localized stable pulses (quasicompactons, QCs). With the increase of the total power, $P$, the QC's centroid performs multiple switchings between minima and maxima of the linear potential. Unlike cubic INPCs, the large-amplitude solitons are mobile in the medium with the saturable nonlinearity. The threshold value of the kick necessary to set the soliton in motion is found as a function of $P$. Collisions between moving QCs are considered too.

The behavior of two-dimensional (2D) atom localization is explored by monitoring the probe absorption in a microwave-driven four-level atomic medium under the action of two orthogonal standing-wave fields. Because of the position-dependent atom-field interaction, the information about the position of the atom can be obtained via the absorption measurement of the weak probe field. It is found that the localization behavior is significantly improved due to the joint quantum interference induced by the standing-wave and microwave-driven fields. Most importantly, the atom can be localized at a particular position and the maximal probability of finding the atom in one period of the standing-wave fields reaches unity by properly adjusting the system parameters. The proposed scheme may provide a promising way to achieve high-precision and high-resolution 2D atom localization.

The process of two input electromagnetic waves at different frequencies overlapping in a nonlinear medium is a typical phenomenon of nonlinear optics. The traditional method of dealing with such a problem is to use the coupled-wave equations. In this paper, sum- and difference-frequency generation of cylindrical electromagnetic waves in a nonlinear medium is investigated in a different way. We use exact solutions of Maxwell's equations to describe the propagation of cylindrical electromagnetic waves in a nonlinear medium and show that sum- and difference-frequency generation comes out quite naturally from such exact solutions. For comparison, the traditional method of utilizing the coupled-wave equations is also discussed, and we find that the results obtained from the two different approaches are consistent with each other.

Diffractionless propagation of optical beams through atomic vapors is investigated. The atoms in the vapor are operated in a three-level Raman configuration. A suitably chosen control beam couples to one of the transitions, and thereby creates a spatially varying index of refraction modulation in the warm atomic vapor for a probe beam that couples to the other transition in the atoms. We show that a Laguerre-Gaussian control beam allows the propagation of single Gaussian probe field modes as well as multi-Gaussian modes and non-Gaussian modes over macroscopic distances without diffraction. This opens perspectives for the propagation of arbitrary images through warm atomic vapors.