We include the dynamics of the angular straggling process in the angular distributions of Mott scattering of heavy ions. We model the passage of an incoming nucleus through a target as a diffusion process. It is then possible to derive a simple and physically transparent expression for the angular dispersion due to the straggling. The angular dispersion should be folded with the theoretical Mott cross section to see its effect on the amplitude of the Mott oscillations. Our results agree very well with data of ${}^{208}$Pb + ${}^{208}$Pb scattering. We define the “classical” limit as the limit when the angular dispersion due to straggling becomes comparable with the Mott oscillation period and get the disappearance of quantum interference occurring at the limit $0.050\sqrt{\xi }\frac{Z^4}{E^{3/2}}\ge 1$, where $\xi$ stands for the target thickness, $Z$ is the system's charge, and $E$ is the center-of-mass energy. The experiments on lead are very close to this limit. We show that the kinematical correlations due to the identity of the particles is maintained, as it should be, and the action of the environment is to reduce the fringe visibility.

We present a theoretical study for multiphoton double excitation of He atoms exposed to an intense ultrashort extreme-ultraviolet (EUV) pulse, where the photon energy coincides with the transition energy from the ground state to a Rydberg state, by solving the time-dependent Schrödinger equation in the hyperspherical coordinates. Photoelectron spectra under the conditions comparable with a recent experiment [Hishikawa et al., Phys. Rev. Lett. 107, 243003 (2011)] are calculated and analyzed. We identify the mechanism of the enhanced three-photon absorption probability which is more than one order of magnitude larger than that for the two-photon process in accordance with the experiment. The enhancement is attributed to a propensity rule for double excitation in a two-step mechanism, in which a one-photon absorption by one electron to a Rydberg state is followed by a two-photon absorption by the other electron to an excited orbital, while the first electron remains at nearly the same principle quantum number. Based on the time-dependent perturbation theory, the three-photon absorption probability exhibits peculiar cubic dependence on the pulse duration due to the propensity rule, in contrast to the linear dependence of the two-photon absorption probability. Thus a crossover between the two- and three-photon absorption probabilities takes place for sufficiently intense and long pulses. We also study the time evolution of a doubly excited two-electron wave packet created by an intense ultrashort EUV pulse efficiently using the same enhancement scheme, opening up the possibility of visualizing the correlated motion of two electrons in the time domain.

We have studied the ground-state Hanle effect (GSHE) excited by linearly polarized laser light on the $D$${}_1$ line of cesium atoms. We have solved algebraically the Liouville equation using the irreducible tensor formalism, and derive an analytical expression for the resonance line shapes in a magnetic field of arbitrary direction. The model predictions are in excellent agreement with experimental observations in various field geometries. Our model is valid for arbitrary $F\to F^{\prime }$ transitions in the low-power limit. We discuss the relation between the GSHE and electromagnetically induced transparency or absorption. Our approach allows a full understanding of the mechanism of the GSHE and provides tools for quantifying the resonance contrast, a crucial parameter for metrological applications of level crossing resonances.

We report continuous direct photoassociative formation of ultracold KRb molecules in the lowest vibrational levels $(v^{\prime \prime }=0-10)$ of the electronic ground state $\left(X{}^1{\Sigma }^{+}\right)$, starting from ${}^{39}$K and ${}^{85}$Rb atoms in a magneto-optical trap. The process exploits a new-found resonant coupling between the $2\left(1\right),v^{\prime }=165$ and $4\left(1\right),v^{\prime }=61$ levels, which exhibit an almost equal admixture of the uncoupled eigenstates. The production rate of the $X^1{\Sigma }^{+}$ $(v^{\prime \prime }=0)$ level is estimated to be $5\times {10}^3$ molecules/s.

Ultrafast UV excitation can prepare a nonstationary coherent superposition of molecular electronic states. The purely electronic dynamics before the onset of nuclear motion can be probed by a sudden XUV ionization of the electronic wave packet. Dynamical computations at the many-electron level on the LiH and 1-azabicyclo[3.3.3]undecane (C${}_{10}$H${}_{19}$N) molecules show that molecular frame photoelectron angular distributions reflect the spatial localization and undulations of the electronic coherent superposition accessed by the initial ultrafast UV excitation. The sudden ionization is sensitive to interference effects.

We analytically determine the properties of three interacting fermions in a harmonic trap subject to an external rotation. Many-body thermodynamic quantities such as the entropy and energy are calculated from the third-order quantum virial expansion. As the external rotation is increased, the regime over which the virial expansion is valid is extended to lower temperatures. By parameterizing the solutions in the rotating frame we find that the energy and entropy are universal for all rotations in the strongly interacting regime. Additionally, we find that rotation suppresses the onset of itinerant ferromagnetism in strongly interacting repulsive three-body systems.

We investigate the pair condensation of a two-spin-component Fermi gas in the presence of both Rashba and Dresselhaus spin-orbit couplings. We calculate the condensate fraction in the BCS-BEC (Bardeen-Cooper-Schrieffer–Bose-Einstein condensate) crossover in both two and three dimensions by taking into account singlet and triplet pairings. These quantities are studied by varying the spin-orbit interaction from the case with the only-Rashba to the equal-Rashba-Dresselhaus one. We find that by mixing the two couplings, the singlet pairing decreases while the triplet pairing is suppressed in the BCS regime and increased in the BEC regime, both in two and three dimensions. At fixed spin-orbital strength, the greatest total condensate fraction is obtained when only one coupling (only Rashba or only Dresselhaus) is present.

We derive exact general relations between various observables for $N$ bosons with zero-range interactions, in two or three dimensions, in an arbitrary external potential. Some of our results are analogous to relations derived previously for two-component fermions and involve derivatives of the energy with respect to the two-body $s$-wave scattering length $a$. Moreover, in the three-dimensional case, where the Efimov effect takes place, the interactions are characterized not only by $a$, but also by a three-body parameter $R_t$. We then find additional relations which involve the derivative of the energy with respect to $R_t$. In short, this derivative gives the probability of finding three particles close to each other. Although it is evaluated for a totally lossless model, it also gives the three-body loss rate always present in experiments (due to three-body recombination to deeply bound diatomic molecules), at least in the limit where the so-called inelasticity parameter $\eta$ is small enough. As an application, we obtain, within the zero-range model and to first order in $\eta$, an analytic expression for the three-body loss rate constant for a nondegenerate Bose gas at thermal equilibrium with infinite scattering length. We also discuss the generalization to arbitrary mixtures of bosons and/or fermions.

We have achieved a full implementation of the stochastic projected Gross-Pitaevskii equation for a three-dimensional trapped Bose gas at finite temperature. Our work advances previous applications of this theory, which have only included growth processes, by implementing number-conserving scattering processes. We evaluate an analytic expression for the coefficient of the scattering term and compare it to that of the growth term in the experimental regime, showing that the two coefficients are comparable in size. We give an overview of the numerical implementation of the deterministic and stochastic terms for the scattering process, and use simulations of a condensate excited into a large amplitude breathing mode oscillation to characterize the importance of scattering and growth processes in an experimentally accessible regime. We find that in such nonequilibrium regimes the scattering can dominate over the growth, leading to qualitatively different system dynamics. In particular, the scattering causes the system to rapidly reach thermal equilibrium without greatly depleting the condensate, suggesting that it provides a highly coherent energy-transfer mechanism.

We report on frequency- and angle-multiplexed image storage by electromagnetically induced transparency (EIT) in a ${\mathrm{Pr}}^{3+}$:${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal. Frequency multiplexing by EIT relies on simultaneous storage of light pulses in atomic coherences, driven in different frequency ensembles of the inhomogeneously broadened solid medium. Angular multiplexing by EIT relies on phase matching of the driving laser beams, which permits simultaneous storage of light pulses propagating under different angles into the crystal. We apply the multiplexing techniques to increase the storage capacity of the EIT-driven optical memory, in particular to implement multiplexed storage of larger two-dimensional amounts of data (images). We demonstrate selective storage and readout of images by frequency-multiplexed EIT and angular-multiplexed EIT, as well as the potential to combine both multiplexing approaches towards further enhanced storage capacities.

Nonlinearity and entanglement are two important properties by which physical systems can be identified as nonclassical. We study the dynamics of the resonant interaction of up to $N=3$ two-level systems and a single mode of the electromagnetic field sharing a single excitation dynamically. We observe coherent vacuum Rabi oscillations and their nonlinear $\sqrt{N}$ speedup by tracking the populations of all qubits and the resonator in time. We use quantum state tomography to show explicitly that the dynamics generates maximally entangled states of the $W$ class in a time limited only by the collective interaction rate. We use an entanglement witness and the 3-tangle to characterize the state whose fidelity $F=78\%$ is limited in our experiments by crosstalk arising during the simultaneous qubit manipulations which is absent in a sequential approach with $F=91\%$.

We study ultranarrow $5s_{1/2}$-$4f_{5/2}$ transitions in Nd${}^{13+}$ and Sm${}^{15+}$ and demonstrate that they lie in the optical region. The transitions are insensitive to external perturbations. At the same time they are sensitive to the variation of the fine structure constant $\alpha$. The fractional accuracy of the frequency of the transitions can be smaller than ${10}^{-19}$, which may provide a basis for atomic clocks of superb accuracy. Sensitivity to the variation of $\alpha$ approaches ${10}^{-20}$ per year.

We study the hard-core bosons in one-dimensional (1D) interacting topological bands at different filling factors using exact diagonalization. At the filling factor $\nu =1$ and in the presence of the on-site Hubbard interaction, we find no sign of the existence of the bosonic topological phase, which is in contrast to the fermionic case. Instead by studying the momentum distribution and the condensate fraction we find a superfluid to Mott-insulator transition driven by the Hubbard interaction. At the filling factor $\nu =1/3$ and in the presence of longer-ranged interactions, we identify the bosonic fractional topological phase whose ground states are characterized by a threefold degeneracy and a quantized total Berry phase, which is very similar to the fermionic case. Finally we discuss the reason for the different behaviors of hard-core bosons at different filling factors by mapping them to spinless fermions. Our results can be realized in cold-atom experiments.

The Stark shift of the ytterbium (Yb) optical clock transition due to room-temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. However, room-temperature realization of the clock at ${10}^{-18}$ uncertainty requires a dynamic contribution to this static approximation. This dynamic term largely depends on a single electric dipole matrix element for which theoretically and experimentally derived values disagree significantly. We determine this important matrix element by two independent methods, which yield consistent values. Along with precise radiative lifetimes of $6s6p{}^3{P}_1^{}$ and $5d6s{}^3{D}_1^{}$, we report the clock shift due to an ideal 300 K blackbody environment to 0.05$\%$ precision.

We numerically investigate low-energy stationary states of pseudospin-1 Bose-Einstein condensates in the presence of Rashba-Dresselhaus-type spin-orbit coupling. We show that for experimentally feasible parameters and strong spin-orbit coupling, the ground state is a square vortex lattice irrespective of the nature of the spin-dependent interactions. For weak spin-orbit coupling, the lowest-energy state may host a single vortex. Furthermore, we analytically derive constraints that explain why certain stationary states do not emerge as ground states. Importantly, we show that the distinct stationary states can be observed experimentally by standard time-of-flight spin-independent absorption imaging.

With an easily applicable criterion based on permutation symmetries of (identically prepared) replicas of quantum states we identify distinct entanglement classes in high-dimensional multipartite systems. The different symmetry properties of inequivalent states provide a rather intuitive picture of the otherwise very abstract classification of many-body entangled states.

We analyze the entanglement change, as seen by different relativistic observers, for a system consisting of two spin-1 particles, considering different partitions of the Hilbert space, which has spin and momentum degrees of freedom. We show that there exists a complete set of states of the spin subspace in which the entanglement change of any state in the set is zero for all partitions and all values of the Wigner angle. Moreover, these states only change by a global phase factor under the Lorentz boost. Within this basis, maximally entangled invariant states, interesting for quantum information purposes, are explicitly obtained. On the other hand, the entanglement in the particle-particle partition $is$ Lorentz invariant, thus protecting the consistency of quantum correlations and teleportation results. We show how our results may be generalized to arbitrary spin.

Here we propose a feasible experimental setup for implementing optimal probabilistic cloning of two arbitrary nonorthogonal qubit states. This proposal is based on linear optics together with a pair of entangled twin photons generated via spontaneous parametric down-conversion. The states to be cloned are encoded in the polarization degree of freedom of one of the photons while two perfect clones are generated and encoded in the polarization and the spatial degree of freedom of the resting photon. Therefore, the clones are produced nonlocally. The proposed implementation requires the application of recovery unitary operations onto the photon hosting the clones which are conditional on measurements performed on the other photon in a process akin to quantum teleportation.

We propose a quantum-cryptography network based on a continuous-variable graph state along with its corresponding quantum key distribution (QKD) protocol. It allows two arbitrary parties in the graph state to share a secret Gaussian key (any-to-any QKD). A mathematical model is established to determine an arbitrary graph state’¡¯s properties, including the possibility of QKD and the relevant criteria. The general entangling cloner attack strategy is analyzed in detail employing Shannon information theory. Results show that the proposed network is secure against such attack if the graph state meets certain criteria.

In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular max-cut. The cost functions associated with these two clause-based optimization problems are similar as they are both defined on 3-regular hypergraphs. For 3-regular 3-XORSAT the clauses contain three variables and for 3-regular max-cut the clauses contain two variables. The quantum adiabatic algorithms we study for these two problems use interpolating Hamiltonians which are amenable to sign-problem free quantum Monte Carlo and quantum cavity methods. Using these techniques we find that the quantum adiabatic algorithm fails to solve either of these problems efficiently, although for different reasons.