We analyze the realization of a quantum-walk search algorithm in a passive, linear optical network. The specific model enables us to consider the effect of realistic sources of noise and losses on the search efficiency. Photon loss uniform in all directions is shown to lead to the rescaling of search time. Deviation from directional uniformity leads to the enhancement of the search efficiency compared to uniform loss with the same average. In certain cases even increasing loss in some of the directions can improve search efficiency. We show that while we approach the classical limit of the general search algorithm by introducing random phase fluctuations, its utility for searching is lost. Using numerical methods, we found that for static phase errors the averaged search efficiency displays a damped oscillatory behavior that asymptotically tends to a nonzero value.

We propose a quantum-key-distribution protocol that enables three parties to agree at once on a shared common random bit string in the presence of an eavesdropper without use of entanglement. We prove its unconditional security and analyze the key rate.

We propose a protocol of remote implementations of quantum operations by hybridizing bidirectional quantum-state teleportation (BQST) [Huelga et al., Phys. Rev. A 63, 042303 (2001)] and the Wang protocol [Wang, Phys. Rev. A 74, 032317 (2006)]. The protocol is available for remote implementations of quantum operations in the restricted sets specified in the paper. We also give a proof of the protocol and point out its optimization. As an extension, this hybrid protocol can be reduced to the BQST and Wang protocols.

We analyze the Bures metric over the manifold of thermal density matrices for systems featuring a zero temperature quantum phase transition. We show that the quantum critical region can be characterized in terms of the temperature scaling behavior of the metric tensor itself. Furthermore, the analysis of the metric tensor when both temperature and an external field are varied, allows one to complement the understanding of the phase diagram including crossover regions which are not characterized by any singular behavior. These results provide a further extension of the scope of the metric approach to quantum criticality.

Spin-dipole mediated interactions between tightly confined metastable helium atoms couple the spin-polarized quintet ${{}^5\sum }_g^{+}$ state to the singlet ${{}^1\sum }_g^{+}$ state from which autoionization is highly probable, resulting in finite lifetimes for the trap eigenstates. We extend our earlier study on spherically symmetric harmonic traps to the interesting cases of axially symmetric anisotropic harmonic traps and report results for the lowest 10 states in “cigarlike” and “pancakelike” traps with average frequencies of 100 kHz and 1 MHz. We find that there is a significant suppression of ionization, and subsequent increase in lifetimes, at trap aspect ratios $A=p/q$, where $p$ and $q$ are integers, for those states that are degenerate in the absence of collisions or spin-dipole interactions.

We analyze the evolution of a degenerate quantum gas (bosons and fermions) falling in Earth’s gravity during long times $\left(10\mathrm{s}\right)$ and over large distances $\left(100\mathrm{m}\right)$. This models an experiment that is currently performed by the QUANTUS Collaboration at ZARM drop tower in Bremen, Germany. Starting from the classical mechanics of the drop capsule and a single particle trapped within, we develop a quantum field theoretical description for this experimental situation in an inertial frame, the corotating frame of the Earth, as well as the comoving frame of the drop capsule. Suitable transformations eliminate noninertial forces, provided all external potentials (trap, gravity) can be approximated with a second-order Taylor expansion around the instantaneous trap center. This is an excellent assumption, and the harmonic potential theorem applies. As a first application, we study the quantum dynamics of a cigar-shaped Bose-Einstein condensate in the Gross-Pitaevskii mean-field approximation. Due to the instantaneous transformation to the rest frame of the superfluid wave packet, the long-distance drop can be studied easily on a numerical grid.

We extract the shear viscosity to entropy density ratio $\eta /s$ of cold fermionic atoms in the unitarity limit from experimental data on the damping of collective excitations. We find that near the critical temperature $\eta /s$ is roughly equal to 1/2 in units of $\hslash /k_B$. With the possible exception of the quark gluon plasma, this value is closer to the conjectured lower bound $1/\left(4\pi \right)$ than any other known liquid.

Using the ray-optics approximation, we analyze the Casimir force in a two-dimensional domain formed by two metallic blocks adjacent to parallel metallic sidewalls, which are separated from the blocks by a finite distance $h$. For $h>0$, the ray-optics approach is not exact because diffraction effects are neglected. Nevertheless, we show that ray optics is able to qualitatively reproduce a surprising effect recently identified in an exact numerical calculation: the force between the blocks varies nonmonotonically with $h$. In this sense, the ray-optics approach captures an essential part of the physics of multibody interactions in this system, unlike simpler pairwise-interaction approximations such as proximity force approximations (PFA). Furthermore, by comparison to the exact numerical results, we are able to quantify the impact of diffraction on Casimir forces in this geometry.

We propose a generalization of quasi-phase-matching of quadratic nonlinear processes that we call angular quasi-phase-matching (AQPM). It corresponds to a propagation of three collinear interacting electromagnetic waves in a periodically poled nonlinear medium at any angle with respect to the grating vector. AQPM directions are analyzed using groups theory.

In this paper we report self-trapping of subnanojoule femtosecond near-infrared beams in photonic-grade undoped bulk lithium niobate under application of an external dc electric field. We show that the phenomenon occurs thanks to the photorefractive effect induced by a weak second-harmonic component generated under large velocity mismatch. It offers a way to extend lithium niobate’s photorefractive response to the near-infrared spectrum for peak intensity lower than $1\mathrm{GW}∕{\mathrm{cm}}^2$, which is three orders of magnitude lower than reported in the literature.

Optical near-field interactions are studied theoretically in the perspective of photon wave mechanics paying particular attention to the dynamics in the wave-vector time domain. A unitary transformation is used to replace the scalar and longitudinal photon variables by so-called near-field and gauge photon variables. Dynamical equations are established for these types of photon variables, and it is shown that these equations are invariant against gauge transformations within the Lorenz gauge. The near-field photon is absent in the free-field limit, and the gauge photon can be eliminated by a suitable gauge transformation. Implicit solutions for the near-field, gauge, and transverse photon variables are obtained and discussed. The general theory is applied to an investigation of transverse photon propagation in a uniform solid-state plasma dominated by the diamagnetic field-matter interaction. It is found that the diamagnetic response can be incorporated in a quantum mechanical wave equation for a massive transverse photon. The Compton wave number of the massive photon equals the plasma wave number of the electron system. A dynamical equation describing the emission of a massive transverse photon from a mesoscopic source embedded in the plasma is finally established.

We discuss the (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancilla under local operation and classical communication. Whereas any two orthogonal Greenberger-Horne-Zeilinger (GHZ) states taken from the canonical GHZ basis can be cloned with the help of a known GHZ state, surprisingly we find that no two $W$ states can be cloned by using any known three qubit (possibly entangled) state as a blank copy.

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs, which can only be constructed from dual-containing codes. Operator quantum error-correcting codes allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure. We combine these two extensions of standard quantum error correction into a unified entanglement-assisted quantum error-correction formalism. This new scheme, which we call entanglement-assisted operator quantum error correction (EAOQEC), is the most general and powerful quantum error-correcting technique known, retaining the advantages of both entanglement-assistance and passive correction. We present the formalism, show the considerable freedom in constructing EAOQECCs from classical codes, and demonstrate the construction with examples.

Research in nonorthogonal-state discrimination has given rise to two conventional optimal strategies: unambiguous discrimination (UD) and minimum error discrimination. We explore the experimentally relevant range of measurement strategies between the two, where the rate of inconclusive results is minimized for a bounded-error rate. We first provide some constraints on the problem that apply to generalized measurements [positive-operator-valued measurements (POVMs)]. We then provide the theory for the optimal projective measurement in this range. Through analytical and numerical results we investigate this family of projective, bounded-error strategies and compare it to the POVM family as well as to experimental implementation of UD using POVMs. We also discuss a possible application of these bounded-error strategies to quantum key distribution.

The inverse-scattering method within the $J$-matrix approach to the two-coupled-channel problem is discussed. We propose a generalization of the procedure to the case with different thresholds.

In ultracold gases many experiments use atom imaging as a basic observable. The resulting image is averaged over a number of realizations and mostly only this average is used. Only recently the noise has been measured to extract physical information. In the present paper we investigate the quantum noise arising in these gases at zero temperature. We restrict ourselves to the homogeneous situation and study the fluctuations in particle number found within a given volume in the gas, and more specifically inside a sphere of radius $R$. We show that zero-temperature fluctuations are not extensive and the leading term scales with sphere radius $R$ as $R^2\text{ln}R$ (or $\text{ln}R$) in three- (or one-) dimensional systems. We calculate systematically the next term beyond this leading order. We consider first the generic case of a compressible superfluid. Then we investigate the whole Bose-Einstein-condensation (BEC) –BCS crossover, and in particular the limiting cases of the weakly interacting Bose gas and of the free Fermi gas.

We consider an atom-field coupled system in which two pairs of four-level atoms are respectively driven by laser fields and trapped in two distant cavities that are connected by an optical fiber. First, we show that an effective squeezing reservoir can be engineered under appropriate conditions. Then, we show that a two-qubit geometric controlled-PHASE (CPHASE) gate between the atoms in the two cavities can be implemented through adiabatically manipulating the engineered reservoir along a closed loop. This scheme that combines an engineering environment with decoherence-free space and geometric phase quantum computation together has the following remarkable feature: a CPHASE gate with arbitrary phase shift is implemented by simply changing the strength and relative phase of the driving fields.

The electric quadrupole moment for the $5d{}^{2}D_{3∕2}$ state of ${}^{171}\mathrm{Yb}^{+}$, has been calculated using the relativistic coupled-cluster method. Earlier a similar calculation was performed for the $4d{}^{2}D_{5∕2}$ state of ${}^{88}\mathrm{Sr}^{+}$ which is the most accurate determination to date [Sur et al., Phys. Rev. Lett. 96, 193001 (2006)]. The present calculation of the electric quadrupole moment of ${}^{171}\mathrm{Yb}^{+}$ yielded a value $2.157e{a}_0^2$ where the experimental value is $2.08\left(11\right)e{a}_0^2$; $a_0$ is the Bohr radius and $e$ the elementary charge. We discuss in this paper our results for ${}^{171}\mathrm{Yb}^{+}$ in detail and highlight the dominant correlation effects present. We have presented the effect of inner core excitations and their contribution to the electric quadrupole moment, which is a property sensitive to regions away from the nucleus.

We demonstrate that the quantum-mechanical equations of the Nikitin exponential model can be exactly solved at the energies coinciding with the inverted spectrum of an infinite box. Assuming specific potential parameters, the $N$ matrix has been derived for the second level in closed form. The general solution in the Bessel representation has been found for the third and fourth levels. The results show a logarithmic anomaly in the amplitude behavior at the threshold of three-channel–two-channel transformation.

The impact-parameter dependence of electron capture by 20-MeV/u ${\mathrm{U}}^{91+}$ ions has been studied by means of channeling in a $11\text{−}\mathrm{\mu }\mathrm{m}$-thick silicon crystal. Such ions are far from their equilibrium charge state in matter, and channeling offers a unique opportunity to study electron capture in conditions going from the extreme case of a single capture event (for the best channeled ions) to the case of multiple charge exchange events leading to charge state equilibrium (for unchanneled ions). For each incident ion, the charge states at emergence, energy loss, electron emission-, and x-ray yields are measured. The correlations between these quantities are studied. The data are reproduced by simulations based on the ion flux distribution. We show that the mechanical electron capture dominates at impact parameters smaller than $0.5\mathrm{\AA }$, whereas radiative electron capture is the only process occurring beyond. Specific features associated with highly charged heavy ions at intermediate velocities are discussed, in particular the ionization following capture into highly excited states and the local electron density enhancement due to the electron gas polarization. The measured impact-parameter dependence of capture probabilities is compared to continuum-distorted-wave eikonal-initial-state calculations, extrapolated to $n>5$ final states.