We consider the problem of optimally decoding a quantum error correction code—that is, to find the optimal recovery procedure given the outcomes of partial “check” measurements on the system. In general, this problem is NP hard. However, we demonstrate that for concatenated block codes, the optimal decoding can be efficiently computed using a message-passing algorithm. We compare the performance of the message-passing algorithm to that of the widespread blockwise hard decoding technique. Our Monte Carlo results using the five-qubit and Steane’s code on a depolarizing channel demonstrate significant advantages of the message-passing algorithms in two respects: (i) Optimal decoding increases by as much as 94$\%$ the error threshold below which the error correction procedure can be used to reliably send information over a noisy channel; and (ii) for noise levels below these thresholds, the probability of error after optimal decoding is suppressed at a significantly higher rate, leading to a substantial reduction of the error correction overhead.

We perform a detailed analysis of how high-order harmonic generation (HHG) and above-threshold ionization (ATI) can be controlled by a time-delayed attosecond-pulse train superposed to a strong, near-infrared laser field. In particular we show that the high-order harmonic and photoelectron intensities, the high-order harmonic plateau structure and cutoff energies, and the ATI angular distributions can be manipulated by changing this delay. This is a direct consequence of the fact that the attosecond pulse train can be employed as a tool for constraining the instant an electronic wave packet is ejected in the continuum. A change in such initial conditions strongly affects its subsequent motion in the laser field, and thus HHG and ATI. In our studies, we employ the strong-field approximation and explain the features observed in terms of interference effects between various electron quantum orbits. Our results are in agreement with recent experimental findings and theoretical studies employing purely numerical methods.

We investigate the long-time limit of quantum localization of the kicked Rydberg atom. The kicked Rydberg atom is shown to possess in addition to the quantum localization time ${\tau }_L$ a second crossover time $t_D$ where quantum dynamics diverges from classical dynamics towards increased instability. The quantum localization is shown to vanish as either the strength of the kicks at fixed principal quantum number or the quantum number at fixed kick strength increases. The survival probability as a function of frequency in the transient localization regime ${\tau }_L<t<t_D$ is characterized by highly irregular, fractal-like fluctuations.

We have studied the multiphoton dissociation dynamics of the ${\tilde{E}}^{\prime }{}^{1}A_1^{{}^{\prime }}$ Rydberg state of ammonia $\left({\mathrm{NH}}_3\right)$ on a homebuilt femtosecond pump-probe system by resonance-enhanced multiphoton ionization photoelectron (REMPI-PE) spectroscopy. The highly excited Rydberg state, ${\tilde{E}}^{\prime 1}{A}_1^{\prime }$, of ammonia was accessed by two $267\mathrm{nm}$ pump photons and then ionized by a $401\mathrm{nm}$ probe pulse delayed in time. The variation of the REMPI-PE spectra of ammonia with pump-probe delay time provides valuable information on the dynamics of the excited intermediate accessed by the pump pulse. We find that the Frank-Condon preferred transition during ionization does not occur for $\mathrm{\Delta }{\upsilon }_1=0$ but for $\mathrm{\Delta }{\upsilon }_1=1$, which implies that the intermediate has a different geometry from the ionic ground state. Different dynamical behavior has been observed for each of the transitions $\mathrm{\Delta }{\upsilon }_1=0,1,2,3$, giving a full temporal description of the excited intermediate state by projection onto the eigenspace of the ionic ground state.

We consider a one-dimensional mean-field-hydrodynamic model of a two-component degenerate Fermi gas in an external trap, each component representing a spin state of the same atom. We demonstrate that the interconversion between them (linear coupling), imposed by a resonant electromagnetic wave, transforms the immiscible binary gas into a miscible state, if the coupling constant, $\kappa$, exceeds a critical value, ${\kappa }_{\mathrm{cr}}$. The effect is predicted in a variational approximation, and confirmed by numerical solutions. Unlike the recently studied model of a binary Bose-Einsten condensate with the linear coupling, the components in the immiscible phase of the binary fermion mixture never fill two separated domains with a wall between them, but rather form antilocked ($\pi$-phase-shifted) density waves. Another difference from the bosonic mixture is spontaneous breaking of symmetry between the two components in terms of the numbers of atoms in them, $N_1$ and $N_2$. The latter effect is characterized by the parameter $\nu \equiv (N_1-N_2)∕(N_1+N_2)$ (only $N_1+N_2$ is a conserved quantity), the onset of miscibility at $\kappa ⩾{\kappa }_{\mathrm{cr}}$ meaning a transition to $\nu \equiv 0$. At $\kappa <{\kappa }_{\mathrm{cr}}$, $\nu$ features damped oscillations as a function of $\kappa$. We also briefly consider an asymmetric model, with a chemical-potential difference between the two components. The relation between the imbalance in the spin population, induced by the linear coupling, and the developing spatial structure resembles the known Larkin-Ovchinnikov-Fulde-Ferrell states in the Fermi mixture. Dynamical states, when $\kappa$ is suddenly switched from zero to a value exceeding ${\kappa }_{\mathrm{cr}}$, are considered too. In the latter case, the system features oscillatory relaxation to the mixed state.

In electromagnetically induced transparency, the scattering rate of a probe beam is greatly reduced due to destructive interference between two dressed atomic states produced by a strong laser beam. Here we show that a similar reduction in the single-photon scattering rate can be achieved by tuning a probe beam to be halfway between the resonant frequencies of two modes of a cavity. This technique is expected to be useful in enhancing two-photon absorption while reducing losses due to single-photon scattering.

When two distinguishable photons are simultaneously input into a nonlinear system, the output photons undergo nonlinear optical effects of the cross–Kerr type. Theoretical quantification of this two-photon cross–Kerr effect requires, in principle, a fully quantum-mechanical analysis involving heavy computation. In this paper, we propose a method for evaluating the two-photon cross–Kerr effect using a semiclassical optical response theory. The semiclassical method enables precise evaluation of the cross–Kerr effect with greatly reduced computation. The validity of the method is confirmed using a model nonlinear system.

The dynamics of nonlinear optical conversion in the high-intensity femtosecond pump regime has been studied in gaseous media over a wide pressure range. The existence of two different types of optical supercontinua, structured and structureless, has been found in a number of atomic (argon, krypton) and molecular (methane) gases. The structured optical supercontinuum exhibits a typical oscillationlike spectral structure, resulting from self-phase modulation in neutrals and plasma. The structureless optical supercontinuum is completely dense, and its main properties cannot be explained within the self-phase modulation mechanism. The structureless optical supercontinuum is attributed to Bremsstrahlung radiation from electrons that tunnel through the bound potential inside the atoms or molecules under a strong optical field. The basic properties of the structureless optical supercontinuum have now been revealed experimentally.

Coherent population trapping (CPT) in a three-level atomic medium pumped by two subsequent short optical pulses is considered under the condition of negligible population decay from the excited optical state. It is shown that the amount of atomic population transferred to the excited state by the combined action of the pulses strongly depends on the phase of the ground-state coherence excited by the first pulse at the arrival time of the second pulse. Oscillatory behavior of optical excitation efficiency on the time delay between the pulses is predicted. It is also shown that saturating optical pulses can produce population inversion in a resonantly pumped quasi-two-level system. A class of solid materials in which the predicted phenomena can be observed at room temperature is found. It includes some rare-earth and transition-metal doped dielectric crystals where Orbach relaxation between ground-state Zeeman states is suppressed: ruby, alexandrite, and several others. On the basis of the theoretical predictions, experimental observation of Ramsey fringes in CPT spectrum of ruby is reported.

We analyzed the security of the secure direct communication protocol based on the secret transmitting order of particles recently proposed by Zhu, Xia, Fan, and Zhang[Phys. Rev. A 73, 022338 (2006)] and found that this scheme is insecure if an eavesdropper, say Eve, wants to steal the secret message with Trojan horse attack strategies. The vital loophole in this scheme is that the two authorized users check the security of their quantum channel only once. Eve can insert another spy photon, an invisible photon, or a delay one in each photon which the sender Alice sends to the receiver Bob, and capture the spy photon when it returns from Bob to Alice. After the authorized users check the security, Eve can obtain the secret message according to the information about the transmitting order published by Bob. Finally, we present a possible improvement of this protocol.

We investigate boundary critical phenomena from a quantum-information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Rényi entropy $S_{\alpha }$, which includes the von Neumann entropy $(\alpha \to 1)$ and the single-copy entanglement $(\alpha \to \infty )$ as special cases. We identify the contribution of the boundaries to the Rényi entropy, and show that there is an entanglement loss along boundary renormalization group (RG) flows. This property, which is intimately related to the Affleck-Ludwig $g$ theorem, is a consequence of majorization relations between the spectra of the reduced density matrix along the boundary RG flows. We also point out that the bulk contribution to the single-copy entanglement is half of that to the von Neumann entropy, whereas the boundary contribution is the same.

Bloch oscillations in a frequency-chirped optical lattice are a powerful tool to transfer coherently many photon momenta to atoms. We have used this method to measure accurately the ratio $h∕m_{\mathrm{Rb}}$. In this paper we detail the experimental procedure and we present a complete analysis of the different systematic effects. They yield a global relative uncertainty of 13 parts per ${10}^9$ (ppb). The measured value of $h∕m_{\mathrm{Rb}}$ is $4.59135929\left(6\right)\times {10}^{-9}{\mathrm{m}}^2{\mathrm{s}}^{-1}$. The deduced value of the fine-structure constant is ${\alpha }^{-1}=137.03599884$ (91) with a relative uncertainty of $6.7\mathrm{ppb}$.

We consider the effects of decoherence on Landau-Zener crossings encountered in a large-scale adiabatic-quantum-computing setup. We analyze the dependence of the success probability—i.e., the probability for the system to end up in its new ground state—on the noise amplitude and correlation time. We determine the optimal sweep rate that is required to maximize the success probability. We then discuss the scaling of decoherence effects with increasing system size. We find that those effects can be important for large systems, even if they are small for each of the small building blocks.

Electron-ion recombination observed in storage ring experiments shows a strong enhancement of the recombination rate for highly charged ions with low-energy electrons relative to what standard radiative recombination rates predict. We present detailed simulations of the toroid and solenoid regions of the electron cooler, analyzing the classical dynamics of an electron in the presence of the Coulomb field of the ion, the homogeneous magnetic field inside the cooler, and the transient electric field in the merging section. Both bound and continuum electron dynamics display partially chaotic motion. For bound states we observe stochastic and quasiperiodic $l$ mixing while for continuum electrons we find transient chaos characterized by a fractal generalized reflection function. We determine the modified radiative and field-induced recombination of the electron with a highly charged ion in a storage ring. The obtained absolute excess recombination rates are compared with the experimental data and, overall, reasonable agreement is found. The scaling of the rate with the average relative energy, the ion charge, the magnetic guiding field, and the electron-beam temperatures is analyzed.

Nonlinear magneto-optical Faraday rotation (NMOR) on the potassium D1 and D2 lines was used to study Zeeman relaxation rates in an antirelaxation paraffin-coated $3\text{−}\mathrm{cm}$-diameter potassium vapor cell. Intrinsic Zeeman relaxation rates of ${\gamma }^{NMOR}∕2\pi =2.0\left(6\right)\mathrm{Hz}$ were observed. The relatively small hyperfine intervals in potassium lead to significant differences in NMOR in potassium compared to rubidium and cesium. Using laser optical pumping, widths and frequency shifts were also determined for transitions between ground-state hyperfine sublevels of ${}^{39}\mathrm{K}$ atoms contained in the same paraffin-coated cell. The intrinsic hyperfine relaxation rate of ${\gamma }_{\mathit{expt}}^{\mathit{hf}}∕2\pi =10.6\left(7\right)\mathrm{Hz}$ and a shift of $-9.1\left(2\right)\mathrm{Hz}$ were observed. These results show that adiabatic relaxation gives only a small contribution to the overall hyperfine relaxation in the case of potassium, and the relaxation is dominated by other mechanisms similar to those observed in previous studies with rubidium.

The effect of spontaneous decay on the linear polarizability of an atom is typically included by adding imaginary parts to the frequency denominators that appear in the Kramers-Heisenberg formula. It has been shown for a two-level atom with radiative broadening that these (frequency-dependent) imaginary parts must be included in both the resonant and antiresonant frequency denominators [P. W. Milonni and R. W. Boyd, Phys. Rev. A 69, 023814 (2004)]; however, the expression obtained by Milonni and Boyd for the polarizability does not satisfy the optical theorem, if contributions from non-rotating-wave terms are included. In this paper, we derive a more accurate expression for the polarizability. The calculations are rather complicated and require that we go beyond the standard Weisskopf-Wigner approximation. We present calculations carried out in both the Heisenberg and Schrödinger pictures, since they offer complementary methods for understanding the dynamics of the Rayleigh scattering associated with the atomic polarizability. Moreover, it is shown that the shifts associated with the excited state are not the Lamb shifts of an isolated atom, but depend on the dynamics of the atom-field interaction. Our results for the polarizability are consistent with those obtained recently by Loudon and Barnett using a Green’s-function approach.

We present a theoretical analysis of spin-entanglement between a photoelectron and an Auger electron sequentially ejected from an atom (say, $A$) following the absorption of a single photon. Entanglement, both without and with spin-orbit interaction has been analyzed. In the former case, entanglement in a photo-Auger electron pair is generated only by the electrostatic Coulomb forces inside an atom and completely characterized merely by the multiplicities of the electronic states of $A$, $A^{{+}^{*}}$, $A^{2+}$ participating in the process, without using any protocols already suggested in the literature for this purpose. The presence of both the Coulomb and spin-orbit interactions, on the other hand, couples the entanglement of this bipartite state with the dynamics and kinematics of the whole process, as well as with the properties of the absorbed photon. In such cases, therefore, it is not possible to predict, a priori, the photo-Auger electron entanglement. These discussions have quantitatively been illustrated by several examples.

The high harmonic spectra of helium atoms which are exposed to external monochromatic linearly polarized laser fields are calculated by solving the time-dependent non-Hermitian Schrödinger equation. The entire electronic correlation effects with and without the presence of the field are included in our calculations. The full high-harmonic generation spectra (HGS) were calculated (and not only the intensities of the integer harmonics frequencies as calculated before by non-Hermitian quantum mechanics). The HGS were calculated when the helium atoms are initially in their ground state, or in the $1s2p$ excited state or in a superposition of the two field free states. In the first two cases only odd-order harmonics are obtained. However, in the latter, in addition to the odd-order harmonics also pronounced even-order harmonics are obtained. The even order peaks are much broader than the peaks of the odd-order high harmonics. The association of the widths of the peaks in the HGS with the lifetime of the photoinduced resonances which control the dynamics is discussed.

We investigate states of fermionic atoms across a broad Feshbach resonance in an optical superlattice which allows interaction only among a small number of lattice sites. The states are in general described by superpositions of atomic resonating valence bonds and dressed molecules. As one scans the magnetic field, level crossing is found between states with different symmetry properties, which may correspond to a quantum phase transition in the many-body case.