We introduce a quantum cloning bound which we apply to a straightforward and relatively direct security proof of the prepare-and-measure Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol against collective attacks. The approach we propose is able to handle the practical problem of source and detector alignment imprecisions in a simple way. Specifically, we derive a key-rate bound for a BB84 implementation in which Alice's source emits four given but arbitrary pure states, where the usual equivalence between prepare-and-measure and entanglement-based QKD no longer applies. Our result is similar to a key rate derived by  Marøy et al. [Phys. Rev. A 82, 032337 (2010)] and generally an improvement over the key rate derivable from the entropic uncertainty relation in situations where it applies. We also provide a stronger result for a source emitting arbitrary qubit states, and a further improved result if the detector is additionally assumed two dimensional.

A many-electron–multicenter classical-trajectory Monte Carlo model is developed and tested in charge-exchange studies involving projectiles with charges from $+$3 to $+$10 and the CO molecule. The present model is contrasted against simpler single-center and independent-atom approaches. Total and state-selective charge-exchange cross sections are presented and are compared to recent data from the Jet Propulsion Laboratory where available.

For energetic atomic beams grazingly incident at the surface along the low index directions, fast motion parallel to the surface and slow motion perpendicular to the surface lead to the quantum diffraction pattern in the scattered beam. In this experimental and theoretical joint study we show that when the incident beam is misaligned with respect to an axial channel, the characteristic deformation of the diffraction pattern reflects an overall deflection of the scattered beam from the specular direction. The deflection is maximum for the azimuthal misalignment angles close to the rainbow angle and we show how this effect can be explained with the detailed balance principle relating diffraction of misaligned and perfectly aligned beams. We also demonstrate that using the detailed balance principle the diffraction charts for the incident beams aligned along the axial channel can be reconstructed from the azimuthal incidence angle dependence of the data obtained with misaligned beams.

We study vortex lattices in three-component Bose-Einstein condensates (BECs) under rotation, where three kinds of fractional vortices winding one of three components are present. Unlike the cases of two-component BECs where the phases of square and triangular lattices are present depending on the intercomponent coupling constant and the rotation speed, we find triangular ordered “colorful” vortex lattices where three kinds of fractional vortices are placed in order without defects, in all parameter regions where the intercomponent coupling $g^{\prime }$ is less than the intracomponent coupling $g$. When $g>g^{\prime }$ on the other hand, we find the phase separation: In a region where one component is present, the other two components must vanish, where we find ghost vortices in these two components whose positions are separated. In the boundary $g=g^{\prime }$, the accidental U(3) symmetry is present, in which case two vortices in different components are close to each other in some regions.

The study of dynamical tunneling in a periodically driven anharmonic potential probes the quantum-classical transition via the experimental control of the effective Planck's constant for the system. In this paper we consider the prospects for observing dynamical tunneling with ultracold atoms in magnetic microtraps on atom chips. We outline the driven anharmonic potentials that are possible using standard magnetic traps and find the Floquet spectrum for one of these as a function of the potential strength, modulation, and effective Planck's constant. We develop an integrable approximation to the nonintegrable Hamiltonian and find that it can explain the behavior of the tunneling rate as a function of the effective Planck's constant in the regular region of parameter space. In the chaotic region we compare our results with the predictions of models that describe chaos-assisted tunneling. Finally, we examine the practicality of performing these experiments in the laboratory with Bose-Einstein condensates.

We study the population dynamics of a ring-shaped optical lattice with a high number of particles per site and a low (less than ten) number of wells. Using a localized on-site basis defined in terms of stationary states, we were able to construct a multiple-mode model depending on relevant hopping and on-site energy parameters. We show that in the case of two wells, our model corresponds exactly to a recent improvement of the two-mode model. We derive a formula for the self-trapping period, which turns out to be chiefly ruled by the on-site interaction energy parameter. By comparing to time-dependent Gross-Pitaevskii simulations, we show that the multimode model results can be enhanced in a remarkable way over all the regimes by only renormalizing such a parameter. Finally, using a different approach which involves only the ground-state density, we derive an effective interaction energy parameter that turns out to be in accordance with the renormalized one.

We investigate strong-coupling properties of a trapped two-dimensional normal Fermi gas. Within the framework of a combined $T$-matrix theory with the local density approximation, we calculate the local density of states, as well as the photoemission spectrum, to see how two-dimensional pairing fluctuations affect these single-particle quantities. In the BCS (Bardeen-Cooper-Schrieffer)–BEC (Bose-Einstein condensation) crossover region, we show that the local density of states exhibits a dip structure in the trap center, which is more remarkable than the three-dimensional case. This pseudogap phenomenon is found to naturally lead to a double-peak structure in the photoemission spectrum. The peak-to-peak energy of the spectrum at $p=0$ agrees well with a recent experiment on a two-dimensional ${}^{40}\mathrm{K}$ Fermi gas [Feld et al., Nature 480, 75 (2011)]. Since pairing fluctuations are sensitive to the dimensionality of a system, our results would be useful for the study of many-body physics in the BCS-BEC crossover regime of a two-dimensional Fermi gas.

We study the catastrophic stationary self-focusing (collapse) of a laser beam in nonlinear Kerr media. The width of self-similar solutions near the collapse distance $z=z_c$ obeys the ${(z_c-z)}^{1/2}$ scaling law with the well-known leading-order modification of loglog type $\propto \left(\ln \right|\ln (z_c-z){\left|\right)}^{-1/2}$. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution $\sim$${{10}^{10}}^{100}$, which is unrealistic to achieve in either physical experiments or numerical simulations. We derive an equation for the adiabatically slow parameter which determines the system self-focusing across a large range of solution amplitudes. Based on this equation we develop a perturbation theory for scaling modifications beyond the leading loglog. We show that, for the initial pulse with the optical power moderately above ($\lesssim$$1.2$) the critical power of self-focusing, the scaling agrees with numerical simulations beginning with amplitudes around only three times above the initial pulse.

A scheme for two-dimensional (2D) atom localization via probe absorption in a three-level $\Lambda$-type atomic system is suggested. The required atom-field configuration is obtained when the atom interacts with a weak probe field and two orthogonal standing-wave fields where each standing-wave field is obtained from the superposition of the two standing-wave fields along the corresponding directions. We study the effect of the probe field detuning and phase shifts associated with the standing-wave fields. Two equally probable position information of the single atom are observed in the conditional position probability distribution. However, a unique position of the single atom in the 2D $xy$ plane is observed for some arbitrary choices of the phases associated with standing-wave fields and by selecting slightly different wavelengths of standing-wave fields.

We investigate numerically the dynamics of optical vortex beams carrying different topological charges, launched in a dissipative three-level ladder-type nonlinear atomic vapor. We impose the electromagnetically induced transparency (EIT) condition on the medium. Linear, cubic, and quintic susceptibilities, considered simultaneously with the dressing effect, are included in the analysis. Generally, the beams slowly expand during propagation and new vortices are induced, commonly appearing in oppositely charged pairs. We demonstrate that not only the form and the topological charge of the incident beam but also its growing size in the medium greatly affect the formation and evolution of vortices. We formulate common rules for finding the number of induced vortices and the corresponding rotation directions, stemming from the initial conditions of various incident beams, as well as from the dynamical aspects of their propagation. The net topological charge of the vortex is conserved during propagation, as it should be, but the total number of charges is not necessarily the same as the initial number, because of the complex nature of the system. When the EIT condition is lifted, an enhancement region of beam dynamics is reached, in which the dynamics and the expansion of the beam greatly accelerate. In the end, we discuss the liquid-like behavior of light evolution in this dissipative system and propose a potential experimental scheme for observing such a behavior.

We extend our theory of Bloch oscillations of cold atoms inside an optical cavity [Venkatesh et al., Phys. Rev. A 80, 063834 (2009)] to include the effects of quantum noise arising from coupling to external modes. The noise acts as a form of quantum measurement backaction by perturbing the coupled dynamics of the atoms and the light. We take it into account by solving the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical mean fields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio, as well as heating effects. One of the hurdles we overcome in this paper is the proper treatment of fluctuations about time-dependent mean fields in the context of cold-atom cavity QED.

In a recent paper we reported dark pulse emission of an all-normal-dispersion-fiber laser [Zhang, Tang, Zhao, and Wu, Phys. Rev. A 80, 045803 (2009)]. However, the formation mechanism of the dark pulse in the laser was unclear due to the limited temporal resolution of the measurement system. Using an improved detection system we have further investigated the phenomenon. We not only experimentally, unambiguously confirmed the existence of dark solitons in the fiber laser, but also identified that the dark pulses observed previously were bunches of the dark solitons. Moreover, we show that the dark soliton formation is a generic feature of the all-normal-dispersion-fiber lasers.

Two-dimensional localized edge modes in optical honeycomb lattices are found and analyzed analytically and computationally. Weak nonlinearity and transverse modulation are found to introduce self-phase modulation in the phase and create internal nonlinear interactions as the electromagnetic field propagates through the lattice. Even with relatively strong nonlinearity localization and persistence of modes along the edge are found.

By using the quantum-memory-assisted entropic uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to an arbitrary bipartite state. Detailed examples show that this upper bound is tighter than other known bounds in a wide regime. Furthermore, we show that for any tripartite pure state, the quantum-memory-assisted EUR imposes a constraint on the shareability of quantum correlations among the constituent parties. This conclusion amends the well-accepted result that quantum discord is not monogamous.

It is shown that the well-defined unbiased measurement or disturbance of a dynamical variable is not maintained for the precise measurement of the conjugate variable, independently of uncertainty relations. The conditionally valid uncertainty relations on the basis of those additional assumptions, which include most of the familiar Heisenberg-type relations, thus become singular for the precise measurement. We clarify some contradicting conclusions in the literature concerning those conditionally valid uncertainty relations: The failure of a naive Heisenberg-type error-disturbance relation and the modified Arthurs-Kelly relation in the recent spin measurement is attributed to this singular behavior. The naive Heisenberg-type error-disturbance relation is formally preserved in quantum estimation theory, which is shown to be based on the strict unbiased measurement and disturbance, but it leads to unbounded disturbance for bounded operators such as spin variables. In contrast, the Heisenberg-type error-error uncertainty relation and the Arthurs-Kelly relation, as conditionally valid uncertainty relations, are consistently maintained.

Nonlinear Compton scattering in ultrashort intense laser pulses is discussed with the focus on angular distributions of the emitted photon energy. This is an observable which is easily accessible experimentally. Asymmetries of the azimuthal distributions are predicted for both linear and circular polarization. We present a systematic survey of the influence of the laser intensity, the carrier envelope phase, and the laser polarization on the emission spectra for single-cycle and few-cycle laser pulses. For linear polarization, the dominant direction of the emission changes from a perpendicular pattern with respect to the laser polarization at low-intensity to a dominantly parallel emission for high-intensity laser pulses.

We propose a linear-optical scheme for an efficient amplification of a photonic qubit based on interaction of the signal mode with a pair of entangled ancillae. In contrast to a previous proposal for qubit amplifier by Gisin et al. [Phys Rev. Lett. 105, 070501 (2010)], the success probability of our device does not decrease asymptotically to zero with increasing gain. Moreover, we show how the device can be used to restore entanglement deteriorated by transmission over a lossy channel and calculate the secure key rate for device-independent quantum key distribution.

We propose two schemes for implementing graph states useful for fault-tolerant topological measurement-based quantum computation in two-dimensional (2D) optical lattices. We show that bilayer cluster and surface-code states can be created by global single-row and controlled-$Z$ operations. The schemes benefit from the accessibility of atom addressing on 2D optical lattices and the existence of an efficient verification protocol which allows us to ensure the experimental feasibility of measuring the fidelity of the system against the ideal graph state. The simulation results show potential for a physical realization toward fault-tolerant measurement-based quantum computation against dephasing and unitary phase errors in optical lattices.

We propose how to realize high-fidelity quantum storage using a hybrid quantum architecture including two coupled flux qubits and a nitrogen-vacancy center ensemble (NVE). One of the flux qubits is considered as the quantum-computing processor and the NVE serves as the quantum memory. By separating the computing and memory units, the influence of the quantum-computing process on the quantum memory can be effectively eliminated, and hence the quantum storage of an arbitrary quantum state of the computing qubit could be achieved with high fidelity. Furthermore, the present proposal is robust with respect to fluctuations of the system parameters, and it is experimentally feasible with currently available technology.