The security proofs of continuous-variable quantum key distribution are based on the assumptions that the eavesdropper can neither act on the local oscillator nor control Bob's beam splitter. These assumptions may be invalid in practice due to potential imperfections in the implementations of such protocols. In this paper, we consider the problem of transmitting the local oscillator in a public channel and propose a wavelength attack which allows the eavesdropper to control the intensity transmission of Bob's beam splitter by switching the wavelength of the input light. Specifically we target continuous-variable quantum key distribution systems that use the heterodyne detection protocol using either direct or reverse reconciliation. Our attack is proved to be feasible and renders all of the final keys shared between the legitimate parties insecure, even if they have monitored the intensity of the local oscillator. To prevent our attack on commercial systems, a simple wavelength filter should be randomly added before performing monitoring detection.

Decoy-state protocols provide a way to defeat photon-number-splitting attacks in quantum cryptography implemented with weak coherent pulses. We point out that previous security analyses of such protocols relied on assumptions about eavesdropping attacks that considered treating each pulse equally and independently. We give an example to demonstrate that, without such assumptions, the security parameters of previous decoy-state implementations could be worse than the ones claimed. Next we consider more general photon-number-splitting attacks, which correlate different pulses, and give an estimation procedure for the number of single-photon signals with rigorous security statements. The impact of our result is that previous analyses of the number of times a decoy-state quantum cryptographic system can be reused before it makes a weak key must be revised.

Any experiment attempting to verify the presence of entanglement in a physical system can only generate a finite amount of data. The statement that entanglement was present in the system can thus never be issued with certainty, requiring instead a statistical analysis of the data. Because entanglement plays a central role in the performance of quantum devices, it is crucial to make statistical claims in entanglement verification experiments that are reliable and have a clear interpretation. In this work, we apply recent results by Christandl and Renner [Phys. Rev. Lett. 109, 120403 (2012)] to construct a reliable entanglement verification procedure based on the concept of confidence regions. The statements made do not require the specification of a prior distribution, the assumption of independent measurements, or the assumption of an independent and identically distributed source of states. Moreover, we develop numerical tools that are necessary to employ this approach in practice, rendering the procedure ready to be applied to current experiments. We demonstrate this technique by analyzing the data of a photonic experiment generating two-photon states whose entanglement is verified with the use of an accessible nonlinear witness.

We consider a quantum key expansion (QKE) protocol based on entanglement-assisted quantum error-correcting codes (EAQECCs). In these protocols, a seed of a previously shared secret key is used in the postprocessing stage of a standard quantum key distribution protocol like the Bennett-Brassard 1984 protocol, in order to produce a larger secret key. This protocol was proposed by Luo and Devetak, but codes leading to good performance have not been investigated. We look into a family of EAQECCs generated by classical finite geometry (FG) low-density parity-check (LDPC) codes, for which very efficient iterative decoders exist. A critical observation is that almost all errors in the resulting secret key result from uncorrectable block errors that can be detected by an additional syndrome check and an additional sampling step. Bad blocks can then be discarded. We make some changes to the original protocol to avoid the consumption of the preshared key when the protocol fails. This allows us to greatly reduce the bit error rate of the key at the cost of a minor reduction in the key production rate, but without increasing the consumption rate of the preshared key. We present numerical simulations for the family of FG LDPC codes, and show that this improved QKE protocol has a good net key production rate even at relatively high error rates, for appropriate choices of these codes.

A theoretical study of the electronic and nuclear flux densities of a vibrating ${{\mathrm{H}}_2}^{+}$ molecular ion is presented. The time-dependent wave function is represented in the basis of vibronic eigenstates which are numerically obtained from the complete nonrelativistic Hamiltonian without the clamped-nuclei approximation. A one-center expansion in terms of $B$-splines and Legendre polynomials is employed to solve the corresponding eigenvalue equation. The electronic and nuclear flux densities are then calculated from the total wave function through their quantum-mechanical definition. Analysis of the flux densities close to the turning points shows that the nuclear wave packet takes longer time (1.4 fs) to change its direction compared to the electronic one (1 fs).

In recent years it was demonstrated that the negative hydrogen molecular ions H${}_2{}^{-}$ and D${}_2{}^{-}$ exist in long-lived states with lifetimes exceeding 1 $\mu$s (H${}_2{}^{-}$) and 1 ms (D${}_2{}^{-}$). These metastable ions exhibit very large internuclear distances and possess high angular momenta, which stabilizes them against autodetachment. Here we present the results of a foil-induced Coulomb explosion imaging experiment that allows for the measurement of the rovibrational wave functions of the metastable D${}_2{}^{-}$ ions. We compare our results to previous predictions from a nonlocal resonance theory. Our measurements do not confirm the discrepancy between experiment and theory that was inferred from previous photofragmentation studies. In fact, we find good agreement between the experiment and calculated wave functions for the most long-lived states with rotational quantum numbers $J=37$ and 38.

We present a theoretical study on the system of laser-driven strongly interacting Rydberg atoms trapped in a two-dimensional triangular lattice, in which the dipole-dipole interactions between Rydberg states result in exotic quantum phases. By using the mean-field theory, we investigate the steady state solutions and analyze their dynamical stabilities. We find that in the strong-interaction limit, the dynamics of the system is chaotic and exhibits random oscillations under appropriate laser detunings. The Lyapunov exponent criterion is introduced to confirm the existence of this chaotic behavior. In addition, we present a full quantum calculation based on a six-atom model, and find that the system exhibits some biantiferromagnetic properties in every triangular cell when the one-photon detuning is exactly resonant or blue shifted.

We present a fast scheme for arbitrary unitary control of interacting bosonic atoms in a double well. Assuming fixed interwell tunneling rate and intrawell interaction strength, we control the many-atom state by a discrete sequence of shifts of the single-well energies. For strong interactions, resonant tunneling transitions implement beam-splitter U(2) rotations among atom number eigenstates, which can be combined and, thus, permit full controllability. By numerically optimizing such sequences of couplings at avoided level crossings, we extend the realm of full controllability to a wide range of realistic interaction parameters, while we remain in the simple control space. We demonstrate the efficiency and the high achievable fidelity of our proposal with nonadiabatic population transfer, NOON-state creation, a cnot gate, and a transistorlike, conditional evolution of several atoms.

We analyze the effects of in- and out-of-plane Zeeman fields on the BCS–Bose-Einstein condensation (BEC) evolution of a Fermi gas with equal Rashba-Dresselhaus (ERD) spin-orbit coupling (SOC). We show that the ground state of the system involves gapless superfluid phases that can be distinguished with respect to the topology of the momentum-space regions with zero excitation energy. For the BCS-like uniform superfluid phases with zero center-of-mass momentum, the zeros may correspond to one or two doubly degenerate spheres, two or four spheres, two or four concave spheroids, or one or two doubly degenerate circles, depending on the combination of Zeeman fields and SOC. Such changes in the topology signal a quantum phase transition between distinct superfluid phases and leave their signatures on some thermodynamic quantities. We also analyze the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)–like nonuniform superfluid phases with finite center-of-mass momentum and obtain an even richer phase diagram.

We theoretically study the instability of helical shear flows, in which one fluid component flows along the vortex core of the other, in phase-separated two-component Bose-Einstein condensates at zero temperature. The helical shear flows are hydrodynamically classified into two regimes: (1) a helical vortex sheet, where the vorticity is localized on the cylindrical interface and the stability is described by an effective theory for ripple modes, and (2) a core-flow vortex with the vorticity distributed in the vicinity of the vortex core, where the instability phenomena are dominated only by the vortex-characteristic modes (Kelvin and varicose modes). The helical shear-flow instability shows remarkable competition among different types of instabilities in the crossover regime between the two regimes.

It is well-known that cold atoms near $s$-wave Feshbach resonances have universal properties that are insensitive to the short-range details of the interaction. What is less known is that atoms near higher partial-wave Feshbach resonances also have remarkable universal properties. We illustrate this with a single atom interacting resonantly with two fixed static centers. At a Feshbach resonance point with orbital angular momentum $L\ge 1$, we find $2L+1$ shallow bound states whose energies behave like $1/R^{2L+1}$ when the distance $R$ between the two centers is large. We then compute corrections to the binding energies due to other parameters in the effective range expansions. For completeness we also compute the binding energies near $s$-wave Feshbach resonances, taking into account the corrections. Afterwards we turn to the bound states at large but finite scattering volumes. For $p$-wave and higher partial-wave resonances we derive a simple formula for the energies in terms of a parameter called “proximity parameter.” These results are applicable to a free atom interacting resonantly with two atoms that are localized to two lattice sites of an optical lattice, and to one light atom interacting with two heavy ones in free space. Modifications of the low energy physics due to the long range van der Waals potential are also discussed.

We investigate the rotating spin-1 Bose-Einstein condensates with anisotropic spin-orbit coupling by using the damped projected Gross-Pitaevskii equation. The anisotropic spin-orbit coupling can cause some vortices to form the vortex chain, where the vortices link up with each other in a line. The formation of the vortex chain starts from very small rotation frequency and coexists with more remanent vortices with the increasing rotation frequency. By increasing the anisotropy of the spin-orbit coupling, the creation of the vortex chain is enhanced, accompanied by the emergence of several types of vortex chain and other vortex configurations. When the vortices of the $m_F=-1$ and $m_F=+1$ components are of synchronous phases, such vortex configurations do not cause any topological excitation in the spin texture.

By means of diffusion Monte Carlo calculations, we investigated the quantum phase transition between a superfluid and a Mott insulator for a system of hard-sphere bosons in a quasi-one-dimensional optical lattice. For this continuous Hamiltonian, we studied how the stability limits of the Mott phase changed with the optical lattice depth and the transverse confinement width. A comparison of these results to those of a one-dimensional homogeneous Bose-Hubbard model indicates that this last model describes accurately the phase diagram only in the limit of deep lattices. For shallow ones, our results are comparable to those of the sine-Gordon model in its limit of application. We provide an estimate of the critical parameters when none of those models are realistic descriptions of a quasi-one-dimensional optical lattice.

We investigate multiple scattering of near-resonant light in a Doppler-broadened atomic vapor. We experimentally characterize the length distribution of the steps between successive scattering events. The obtained power law is characteristic of a superdiffusive behavior, where rare but very long steps (Lévy flights) dominate the transport properties.

A spectral singularity is a mathematical notion with an intriguing physical realization in terms of certain zero-width resonances. In optics it manifests as lasing at the threshold gain. We explore the recently developed nonlinear generalization of spectral singularities for a complex barrier potential and study the associated resonance effect for an infinite planar slab of gain medium. In particular, for a Kerr nonlinearity, we show that the first-order perturbative equation that determines the nonlinear spectral singularities provides an explicit expression for the intensity of the emitted waves from the slab. This is a mathematical derivation of the known linear relationship between the output intensity of the slab and its gain coefficient. We also discuss the implications of our results for the time-reversed system which acts as a coherent perfect absorber.

On the basis of our general theoretical results developed previously [I. M. Sokolov et al., J. Exp. Theor. Phys. 112, 246 (2011)], we calculate the spatial distribution of atoms excited in a dense and cold atomic cloud by weak monochromatic light. We also study the atomic distribution over different Zeeman sublevels of the excited state in different parts of the cloud. The dependence of this distribution of atomic excitation on the density of the atomic ensemble and the frequency of external emission is investigated. We show that in the boundary regions of the cloud, the orientation and alignment of atomic angular momentum takes place. Analysis of the spatial distribution of atomic excitation shows no noticeable signs of light localization effects, even in those parameter regimes where the Ioffe-Regel criterium of strong localization is satisfied. However, comparative calculations performed in the framework of the scalar approximation to the dipole-dipole interaction reveal explicit manifestation of strong localization under some conditions.

Second-harmonic generation in negative-index metamaterials is considered. Theoretical analysis of the corresponding model demonstrates a significant difference of this phenomenon in conventional and negative-index materials. For example, and in contrast to conventional materials, there is nonzero critical phase mismatch. The behavior of interacting waves is dramatically different when phase mismatch is smaller or greater than a critical value.

In light of the interest in the transport of single photons in arrays of waveguides, fiber couplers, photonic crystals, etc., we consider the quantum mechanical process of the tunneling of photons through evanescently or otherwise coupled structures. We specifically examine the issue of tunneling between two structures when one structure already contains few photons. We demonstrate the possibility of both photon-aided and photon-inhibited tunneling of photons. The bosonic nature of photons enhances the tunneling probability. We also show how the multiphoton tunneling probability can be either enhanced or inhibited due to the presence of photons. We find similar results for higher-order tunneling. Finally, we show that the presence of a squeezed field changes the nature of tunneling considerably.

We consider a model for a two-dimensional kagome lattice with defocusing nonlinearity, and show that families of localized discrete solitons may bifurcate from localized linear modes of the flat band with zero power threshold. Each family of such fundamental nonlinear modes corresponds to a unique configuration in the strong-nonlinearity limit. By choosing well-tuned dynamical perturbations, small-amplitude, strongly localized solutions from different families may be switched into each other, as well as moved between different lattice positions. In a window of small power, the lowest-energy state is a symmetry-broken localized state, which may appear spontaneously.

When you measure an observable, $A$, in quantum mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some noncommuting observable, $B$. The standard uncertainty relation puts a lower bound on the uncertainty of $B$ in the initial state. What is relevant for a subsequent measurement of $B$, however, is the uncertainty of $B$ in the postmeasurement state. We re-examine this problem, both in the case where $A$ has a pure point spectrum and in the case where $A$ has a continuous spectrum. In the latter case, the need to include a finite detector resolution, as part of what it means to measure such an observable, has dramatic implications for the result of successive measurements. Ozawa, [Phys. Rev. A 67, 042105 (2003)] proposed an inequality satisfied in the case of successive measurements. Among our results, we show that his inequality is ineffective (can never come close to being saturated). For the cases of interest, we compute a sharper lower bound.