We present results of a theoretical study of para-${\mathrm{H}}_2$ $\left(p\text{−}{\mathrm{H}}_2\right)$ and ortho-${\mathrm{D}}_2$ $\left(o\text{−}{\mathrm{D}}_2\right)$ clusters at low temperature $(0.5\mathrm{K}⩽T⩽3.5\mathrm{K})$ based on path integral Monte Carlo simulations. Clusters of $N⩽21$ $p\text{−}{\mathrm{H}}_2$ molecules are nearly entirely superfluid at $T⩽1\mathrm{K}$. For $22⩽N⩽30$, the superfluid response displays strong variations with $N$, reflecting structural changes that occur on adding or removing even a single molecule. Some clusters in this size range display quantum melting, going from solidlike to liquidlike as $T\to 0$. Melting is caused by quantum exchanges of molecules. The largest $p\text{−}{\mathrm{H}}_2$ cluster for which a significant superfluid response is observed comprises $N=27\text{molecules}$. Evidence of a finite superfluid response is presented for $o\text{−}{\mathrm{D}}_2$ clusters of size up to $N=14$. Magic numbers are observed, at which both types of clusters feature pronounced stability.

The lifetime of the $3s^{2}3p{}^{2}P_{3∕2}^o$ first excited energy level of $\mathrm{Fe}\mathrm{XIV}$ (Al like) was measured at the Heidelberg electron beam ion trap by monitoring its optical decay to the ground state by a magnetic dipole $\left(M1\right)$ forbidden transition at $\lambda =530.29\mathrm{nm}$ (green coronal line), a well-known line in stellar spectra. A new trapping scheme has been applied. Possible systematic effects were investigated by studying the dependence of the decay curves on various trapping conditions with high statistical significance. The result of ${16.726}_{-0.010}^{+0.020}\mathrm{ms}$ shows an unexplained discrepancy in the average value of existing theoretical predictions. The inclusion of the electron anomalous magnetic moment within the theoretical calculations increases this disagreement, thus pointing at other possible origins of this discrepancy.

Variational principles for three-body reaction amplitudes are derived which allow for colliding systems that are charged and composite and are applicable for energies lying below the threshold for breakup into four subsystems. The starting point of the analysis is a formulation of the collision dynamics based on coupled integral equations of the Faddeev type that are applicable in the presence of long-range Coulomb interactions. A variational identity (which becomes a variational approximation with the introduction of trial functions) for the amplitude for the breakup of a bound pair by a third particle is derived within the integral equation formulation. The expression is then converted to a differential form of the Kohn type involving wave functions in configuration space. Knowledge of the asymptotic form of the wave function representing the time-reversed final state, in which three unbound particles are incident, is not required in performing this derivation. The variational principle is enhanced by the existence of a subsidiary minimum principle satisfied by that component of the wave function describing virtual excitations of one or more of the three clusters that make up the scattering system.

We present a detailed analysis of Feshbach resonances in ultracold collisions of Li and Cs atoms in the presence of superimposed electric and magnetic fields. We show that electric fields induce resonances through couplings between the $s$- and $p$-wave scattering channels and modify the scattering length to a great extent. Electric-field-induced resonances lead to the anisotropy of ultracold scattering and provide the diagnostics for magnetic $p$-wave resonances in ultracold gases. We show that the electric field couplings may shift the positions of $s$-wave magnetic resonances, thereby making the electric field control of ultracold atoms possible even far away from $p$-wave resonances. Finally, we demonstrate that electric fields may rotate and spin up the collision complex of ultracold atoms at substantial rates.

We study the photoemission spectra of the hydrogen molecular ion for various geometrical arrangements. For different angles between the internuclear axis and the polarization vector, we calculate the angular distribution and analyze the results in terms of the symmetries and partial-wave contributions to the spectra. Contrary to previous studies we find that the angular distribution is not aligned with the internuclear axis or the polarization vector. The alignment is determined by the coherent superposition of $\sigma \to \sigma$ and $\sigma \to \pi$ transition amplitudes and by the relative contributions from the different partial waves, strongly dependent on the photoelectron energy.

We have studied the system of hard-core bosons on a two-dimensional optical lattice using a variational algorithm based on projected entangled-pair states. We have investigated the ground-state properties of the system as well as the responses of the system to sudden changes in the parameters. We have compared our results to mean-field results based on a Gutzwiller ansatz.

The far-field emission of two-dimensional stadium-shaped dielectric cavities is investigated. Microlasers with such shape present a highly directional emission. We provide experimental evidence of the dependence of the emission directionality on the shape of the stadium, in good agreement with ray numerical simulations. We develop an analytical geometrical optics model which permits to account for the main observed features. Wave numerical calculations confirm the results.

A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser (a laser with self-similar propagation of ultrashort pulses), is used as a variational wave function to solve the Gross-Pitaevskii equation for a wide range of interaction parameters. The variational form interpolates between the noninteracting density profile and the strongly interacting Thomas-Fermi profile smoothly. The simple form of the ansatz is modified for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground-state density profile and energy are in very good agreement with both the analytical solutions in the limiting cases of interaction and the numerical solutions in the intermediate regime.

We point out that the Rashba and Dresselhaus spin-orbit interactions in two dimensions can be regarded as a Yang-Mills non-Abelian gauge field. The physical field generated by the gauge field gives the electron wave function a spin-dependent phase which is frequently called the Aharonov-Casher phase. Applying on an $AB$ ring this non-Abelian field together with the usual vector potential, we can make the interference condition completely destructive for one component of the spin while completely constructive for the other component of the spin over the entire energy range. This enables us to construct a perfect spin filter.

We present a scheme for realization of quantum-mechanical weak values of observables using entangled photons produced in parametric down-conversion. We consider the case when the signal and idler modes are respectively in a coherent state and vacuum. We use a low-efficiency detector to detect the photons in the idler mode. This weak detection leads to a large displacement and fluctuations in the signal field’s quantum state which can be studied by monitoring the photon number and quadrature distributions. This also demonstrates the effect of weak measurement of one partner on its twin.

Decoherence-free subspaces (DFS’s) in systems of dipole-dipole interacting multilevel atoms are investigated theoretically. It is shown that the collective state space of two dipole-dipole interacting four-level atoms contains a four-dimensional DFS. We describe a method that allows us to populate the antisymmetric states of the DFS by means of a laser field, without the need for a field gradient between the two atoms. We identify these antisymmetric states as long-lived entangled states. Further, we show that any single-qubit operation between two states of the DFS can be induced by means of a microwave field. Typical operation times of these qubit rotations can be significantly shorter than for a nuclear spin system.

Quantum key distribution (QKD) can be used to generate secret keys between two distant parties. Even though QKD has been proven unconditionally secure against eavesdroppers with unlimited computation power, practical implementations of QKD may contain loopholes that may lead to the generated secret keys being compromised. In this paper, we propose a phase-remapping attack targeting two practical bidirectional QKD systems (the “plug-and-play” system and the Sagnac system). We showed that if the users of the systems are unaware of our attack, the final key shared between them can be compromised in some situations. Specifically, we showed that, in the case of the Bennett-Brassard 1984 (BB84) protocol with ideal single-photon sources, when the quantum bit error rate (QBER) is between 14.6% and 20%, our attack renders the final key insecure, whereas the same range of QBER values has been proved secure if the two users are unaware of our attack; also, we demonstrated three situations with realistic devices where positive key rates are obtained without the consideration of Trojan horse attacks but in fact no key can be distilled. We remark that our attack is feasible with only current technology. Therefore, it is very important to be aware of our attack in order to ensure absolute security. In finding our attack, we minimize the QBER over individual measurements described by a general POVM, which has some similarity with the standard quantum state discrimination problem.

We show that entanglement of pure multiparty states can be quantified by means of quantum uncertainties of certain basic observables through the use of a measure that was initially proposed by Klyachko et al. [Appl. Phys. Lett. 88, 124102 (2006)] for bipartite systems.

The discrimination of any pair of unknown quantum states is performed by devices processing three parts of inputs: copies of the pair of unknown states we want to discriminate are, respectively, stored in two program systems and copies of data, which is guaranteed to be one of the unknown states, in a third system. We study the efficiency of such programmable devices with the inputs prepared with $n$ and $m$ copies of unknown qubits used as programs and data, respectively. By finding a symmetry in the average inputs, we apply the Jordan-basis method to derive their optimal unambiguous discrimination and minimum-error discrimination schemes. The dependence of the optimal solutions on the a priori probabilities of the mean input states is also demonstrated.

In this paper we provide an operational method to detect multipartite entanglement in ensemble-based quantum computing. This method is based on the concept of the entanglement witness. We decompose the entanglement witness for each class of multipartite entanglement into nonlocal operations in addition to local measurements. Individual single-qubit measurements are performed simultaneously; hence complete detection of entanglement is performed in a single-run experiment. In this sense, our scheme is superior to the generally used entanglement witnesses that require a number of experiments and preparation of copies of quantum state for detection of entanglement.

We have used the hyperspherical adiabatic representation to describe the system of three identical bosons in a spin stretched state interacting through an attractive $1∕r$ potential. A proposal has been forwarded to enable the experimental realization of such a system in cold trapped atoms using extremely off-resonant laser fields [Phys. Rev. Lett., 84, 5687 (2000)]. We have obtained the effective potentials, channel functions, and nonadiabatic couplings for this gravitylike interaction, allowing us to calculate the ground-state energy with accuracy that substantially improves upon previous results. We have similarly calculated the energies for the first four $0^{+}$ excited states. These results show that the simple adiabatic hyperspherical approximation offers an accurate description for such a system. Further, since the effective potentials have a long-range $1∕R$ attraction, the properties of the excited states follow from the well-known results for Rydberg states. We have also analyzed the possible geometries and vibrational modes for this system.

We have studied the influence of a static magnetic field on the high harmonic radiation that is caused by the motion of an atomic electron along the laser propagation direction. Different from the ordinary high harmonic spectrum which has been studied under the influence of a static magnetic field, we found that the spectrum of the harmonic radiation polarized in the laser propagation direction is quite sensitive to an additional static magnetic field. The signal heights of this spectrum can be substantially affected by a relatively weak static magnetic field of the order of $30\mathrm{T}$ directed along the magnetic-field vector of the linearly polarized laser pulse. This dependence of the signal strength on the external magnetic field has clear potential to be employed as a means to measure magnetic fields.

The binding energies and magnetic susceptibilities for states evolving from $1s_{1∕2}$, $2s_{1∕2}$, $2p_{1∕2}$, $2p_{3∕2}$, $3s_{1∕2}$, $3d_{3∕2}$, and $3d_{5∕2}$ are calculated using power-series solutions of the Dirac equation for hydrogenic atoms in static and uniform magnetic $B$. The accuracy of the binding energies for low and medium magnetic fields exceeds that of previous variational calculations. In the low-magnetic-field limit the highly accurate values of energies are used to determine the relativistic Paschen-Back effect and relativistic magnetic susceptibilities by expansion of the fully relativistic energy into power series of the parameter $B∕Z^2$. The linear term of this series is related to the relativistic Paschen-Back effect and the square term is proportional to the relativistic dipole magnetic susceptibility of the atom.

For a condensate in a one-dimensional ring geometry, we compare the thermodynamic properties of three conceptually different classical field techniques: stochastic dynamics, microcanonical molecular dynamics, and the “classical field method.” Starting from nonequilibrium initial conditions, all three methods approach steady states whose distribution and correlation functions are in excellent agreement with an exact evaluation of the partition function in the high-temperature limit. Our study helps to establish these various classical field techniques as powerful nonperturbative tools for systems at finite temperatures.

We describe theoretically the dynamics of the off-resonant superradiant Raman scattering of light in a prolate atomic Bose-Einstein condensate, from the initial stages governed by quantum fluctuations to the subsequent semiclassical regime, and within a multimode theory that fully accounts for propagation effects. Our results are in good agreement with recent experimental results that exploit Raman superradiance as an imaging technique to probe the long-range coherence of condensates, including the observed time-dependent spatial features, and account properly for the macroscopic shot-to-shot fluctuations resulting from the quantum noise that initiates the superradiance process.