We compare several instances of pure-state Belavkin weighted square-root measurements from the standpoint of minimum-error discrimination of quantum states. The quadratically weighted measurement is proven superior to the so-called “pretty good measurement” (PGM) in a number of respects: (1) Holevo’s quadratic weighting unconditionally outperforms the PGM in the case of two-state ensembles, with equality only in trivial cases. (2) A converse of a theorem of Holevo is proven, showing that a weighted measurement is asymptotically optimal only if it is quadratically weighted. Counterexamples for three states are constructed. The cube-weighted measurement of Ballester, Wehner, and Winter is also considered. Sufficient optimality conditions for various weights are compared.

In this paper we calculated the relativistic corrections to transition frequencies ($q$ factors) of Fe I for the transitions from the even- and odd-parity states to the ground state. We also carried out isotope-shift calculations in Fe I and Fe II.

Theory and experiment are compared for the electron-impact single ionization of Mg and ${\text{Al}}^{+}$. Nonperturbative $R$ matrix with pseudostates (RMPS) and time-dependent close-coupling (TDCC) calculations have been carried out that exhibit large reductions from perturbative distorted-wave results of 38% for Mg and 20% for ${\text{Al}}^{+}$. Experimental single-ionization data available for Mg and ${\text{Al}}^{+}$ are in reasonable accord with distorted-wave data and lie substantially above the new theoretical results. Rate coefficients, necessary for the collisional-radiative modeling of Mg and Al plasmas were generated from the RMPS ionization cross sections. In the collisional-ionization region near the ionization threshold, the resulting rates were found to be up to two times lower for Mg and three times lower for ${\text{Al}}^{+}$ than the rates generated from experimental data.

We propose a method for the production of ultracold molecular ions. This method utilizes sympathetic cooling due to the strong collisions between appropriately chosen molecular ions and laser-cooled neutral atoms to realize ultracold internal ground-state molecular ions. In contrast to other experiments producing cold molecular ions, our proposed method efficiently cools both the internal and external molecular-ion degrees of freedom. The availability of an ultracold, absolute ground-state sample of molecular ions would have broad impact to fields as diverse as quantum chemistry, astrophysics, and fundamental physics and may lead to the development of a robust scalable quantum computer.

We present a theoretical study on proton energy loss in solid targets of atomic number greater than 54. Fully relativistic wave functions and binding energies are obtained by solving numerically the Dirac equation. Ab initio calculations are developed for the first (stopping) and second (straggling) moments of the energy transferred from the ion to the target electrons. The shellwise local plasma approximation is employed for the inner shells, and the Mermin dielectric function is employed for the valence electrons. The dielectric response of each subshell is calculated separately, including in this way the screening among the electrons of the same binding energy. Results for stopping and straggling cross sections of protons in Au, Pb, and Bi are compared with the available experimental data. The theoretical stopping results are very good in the case of Au, reproducing the experimental data in an extensive energy region (10 keV–100 MeV). For Pb and Bi, the stopping results agree with the measurements for energies above 300 keV, for which the inner shells play a major role. However, we found some difficulties around the stopping maximum. For the energy-loss straggling, we obtained reasonably good agreement with the experiments for the three targets studied.

We report on the electronic structure of the ${\text{C}}_{60}{\text{-C}}_{240}$ multiwalled fullerene (onion) near the Fermi level. The analytical expressions for the hybridizations of the $\pi$ orbitals on the fullerene shells were derived. The difference between the Fermi levels of individual fullerenes is obtained. The highest occupied molecular orbital–lowest unoccupied molecular orbital energy gap for the ${\text{C}}_{60}{\text{-C}}_{240}$ carbon fullerene onion is calculated. The charge transfer from the outer shell to the inner shell in the base state of the onion is determined. Splitting and the shift of the energy levels of the onion as a result of intershell interaction are predicted.

We describe the preparation of atom-number states with strongly interacting bosons in one dimension or spin-polarized fermions. The procedure is based on a combination of weakening and squeezing of the trapping potential. For the resulting state, the full atom-number distribution is obtained. Starting with an unknown number of particles $N_i$, we optimize the sudden change in the trapping potential which leads to the Fock state of $N_f$ particles in the final trap. Nonzero temperature effects as well as different smooth trapping potentials are analyzed. A simple criterion is provided to ensure the robust preparation of the Fock state for physically realistic traps.

We present a family of exact vector-soliton solutions for the coupled nonlinear Schrödinger equations with tunable interactions and harmonic potential, and then apply the model to investigate the dynamics of solitons and collisions between two orthogonal solitons in the case with equal interaction parameters. Our results show that the exact vector-soliton solutions can be obtained with arbitrary tunable interactions as long as a proper harmonic potential is applied. The dynamics of solitons can be controlled by the Feshbach resonance and the collisions are essentially elastic and do not depend on the initial conditions.

Classical fields counterpart of the ideal Bose gas statistics in a trap is investigated by performing calculations in the canonical ensemble. There exists the optimal cutoff which allows to match the full probability distribution of the condensate population by its classical counterpart. Universal scaling of that cutoff with temperature and dimensionality is derived.

We show that ultrafast surface science studies using the laser-assisted photoelectric effect can benefit from longer-wavelength infrared dressing beams. We compare soft-x-ray photoemission from a Pt(111) surface dressed by 1300 and 780 nm light. Using 1300 nm light, the amplitude of the laser-assisted photoelectric signal is enhanced sevenfold compared with 780 nm. This allows lower dressing laser intensity to be used, which dramatically suppresses undesirable processes such as above-threshold photoemission, desorption, and distortion of the photoemission spectrum due to space charge. This work enables ultrafast studies of surface-adsorbate systems and attosecond electron dynamics over a wider energy range.

We have investigated the collisional properties of ${}^{41}\text{K}$ atoms at ultracold temperatures. To demonstrate the possibility of using ${}^{41}\text{K}$ as a coolant, a Bose-Einstein condensate of ${}^{41}\text{K}$ atoms in the stretched state $\left(F=2,m_F=2\right)$ was created by direct evaporative cooling in a magnetic trap. An upper bound of the three-body loss coefficient for atoms in the condensate was determined to be $4\left(2\right)\times {10}^{-29}{\text{cm}}^{-6}{\text{s}}^{-1}$. A Feshbach resonance in the $F=1,m_F=-1$, state was observed at 51.35(10) G, which is in good agreement with theoretical prediction.

We study the effects of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the ground-state properties of the Heisenberg $XY$ spin chain by means of the fidelity susceptibility, order parameter, and entanglement entropy. Our results show that the DM interaction could influence the distribution of the regions of quantum phase transitions and cause different critical regions in the $XY$ spin model. Meanwhile, the DM interaction has effective influence on the degree of entanglement of the system and could be used to increase the entanglement of the spin system.

We examine a situation that $n$ eavesdroppers attack the Bennett-Brassard cryptographic protocol via their own optimal and symmetric strategies. Information gain and mutual information with sender for each eavesdropper are explicitly derived. The receiver’s error rate for the case of arbitrary $n$ eavesdroppers can be derived using a recursive relation. Although the first eavesdropper can get mutual information without disturbance arising due to other eavesdroppers, subsequent eavesdropping generally increases the receiver’s error rate. Other eavesdroppers cannot gain information on the input signal sufficiently. As a result, the information each eavesdropper gains becomes less than optimal one.

We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasicyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Skor-Steane construction do not need to satisfy the dual-containing property as long as preshared entanglement is available to both sender and receiver. We can use this to avoid the many four cycles which typically arise in dual-containing LDPC codes. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product algorithm (SPA). It is well known that in the SPA, cycles of length 4 make successive decoding iterations highly correlated and hence limit the decoding performance. We show the principle of constructing quantum QC-LDPC codes which require only small amounts of initial shared entanglement.

Secure key distribution between two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? Recently, a semiquantum key distribution protocol was presented [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501 (2007)], in which one of the parties (Bob) is classical, and yet, the protocol is proven to be completely robust against an eavesdropping attempt. Here we extend that result much further. We present two protocols with this constraint and prove their complete robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate parties could notice. One protocol presented here is identical to the one referred to above; however, its robustness is proven here in a much more general scenario. The other protocol is very different as it is based on randomization.

Plasma-screening effects are investigated on three-photon bound-bound transitions in hydrogen atoms embedded in weakly coupled plasmas. In the present context, we discuss a set of basis functions for the pseudostate method. The basis functions are obtained from the modified wave functions for screening Coulomb potential (Debye model) using the Ritz variation method. The calculated energy eigenvalues for various Debye lengths agree well with the other theoretical results. Our calculated transition amplitudes for free-atom case agree excellently with the existing results in the literature. We have calculated the three-photon transition matrix elements for various Debye lengths, showing the strong plasma effects on the three-photon bound-bound transition amplitudes for the plasmas-embedded hydrogen atom.

We demonstrate the use of a periodic train of half-cycle pulses to maintain strongly-localized wave packets in very-high-$n$ $\left(n\sim 300\right)$ Rydberg atoms that travel in near-circular orbits about the nucleus. This motion can be followed for hundreds of orbital periods and mimics the original Bohr model of the hydrogen atom which envisioned an electron in circular classical orbit about the nucleus.

We report measurements of near-resonance light scattering from an ultracold sample of ${}^{87}\text{R}\text{b}$ atoms formed in a magneto-optical trap (MOT). Time-dependent measurements of scattering of probe radiation tuned in the vicinity of the $F=1\to F^{\prime }=0$ hyperfine transition of the $D_2$ resonance line reveal dynamics due to Zeeman optical pumping on this transition in competition with diffusive light scattering in the optically dense sample. Zeeman mixing effects due to small residual magnetic fields also play an important role in the scattered light dynamics and reveal surprising sensitivity to the field strength. The various processes are examined as a function of probe-laser power, detuning from atomic resonance, and the presence or absence of the spatially inhomogeneous MOT quadrupole field.

In this work we demonstrate, by means of numerical simulations, the possibility of replicating matter-wave vortices in a Bose-Einstein condensate trapped in a double-well potential. The most remarkable result is the generation of replicas of an initial vortex state located in one side of the double potential, which evolves into two copies, each one located in one of the potential minima. A simple linear theory gives the basic explanation of the phenomenon and predicts experimental realistic conditions for observation. A complementary strategy of easy experimental implementation to dramatically decrease the replication time is presented and numerically tested for the general case of nonlinear atomic interactions.

We simulate a trapped quasi-two-dimensional Bose gas using a classical field method. To interpret our results we identify the uniform Berezinskii-Kosterlitz-Thouless (BKT) temperature $T_{\text{BKT}}$ as where the system phase-space density satisfies a critical value. We observe that density fluctuations are suppressed in the system well above $T_{\text{BKT}}$ when a quasicondensate forms as the first occurrence of degeneracy. At lower temperatures, but still above $T_{\text{BKT}}$, we observe the development of appreciable coherence as a prominent finite-size effect, which manifests as bimodality in the momentum distribution of the system. At $T_{\text{BKT}}$ algebraic decay of off-diagonal correlations occurs near the trap center with an exponent of 0.25, as expected for the uniform system. Our results characterize the low-temperature phase diagram for a trapped quasi-two-dimensional Bose gas and are consistent with observations made in recent experiments.