An algorithm for simulation of quantum many-body dynamics having su$(2)$ spectrum-generating algebra is developed. The algorithm is based on the idea of dynamical coarse-graining. The original unitary dynamics of the target observables—the elements of the spectrum-generating algebra—is simulated by a surrogate open-system dynamics, which can be interpreted as weak measurement of the target observables, performed on the evolving system. The open-system state can be represented by a mixture of pure states, localized in the phase space. The localization reduces the scaling of the computational resources with the Hilbert-space dimension $n$ by factor $n^{3/2}(\ln \hspace{0.5em}n){}^{-1}$ compared to conventional sparse-matrix methods. The guidelines for the choice of parameters for the simulation are presented and the scaling of the computational resources with the Hilbert-space dimension of the system is estimated. The algorithm is applied to the simulation of the dynamics of systems of $2\times {10}^4$ and $2\times {10}^6$ cold atoms in a double-well trap, described by the two-site Bose-Hubbard model.

We consider a subwavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small, thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. The behavior of the electromagnetic field in the extreme nonlinear regime is very peculiar and characterized by interesting features such as the transverse power flow reversing. In order to probe this regime, we consider a class of fields (transverse magnetic nonlinear guided waves) admitting full analytical description and show that these waves are allowed to propagate even in media with $\epsilon <0$ and $\mu >0$ since the nonlinear polarization produces a positive overall effective permittivity. The considered nonlinear waves exhibit, in addition to the mentioned features, a number of interesting properties like hyperfocusing induced by the phase difference between the field components.

The dynamical entanglement of two spin-qubits coupled to an $\mathit{XY}$ spin-chain with a three-site interaction environment is studied. The dynamical process of disentanglement is numerically and analytically investigated. In the strong-coupling region, the three-site interaction can dramatically accelerate the decay of the entanglement between the two spin-qubits. However, in the weak-coupling region, the role of this interaction in the process of disentanglement depends on the strength of the three-site interaction; for example, in some specific intervals, this interaction can remarkably delay the process of disentanglement.

We generalize the Lieb-Robinson theorem to systems whose Hamiltonian is the sum of local operators whose commutators are bounded.

We show that qubit decoherence due to zero-temperature energy relaxation can be almost completely suppressed by using the quantum uncollapsing (measurement reversal) procedure. To protect a qubit state, a partial quantum measurement moves it toward the ground state, where it is kept during the storage period, while the second partial measurement restores the initial state. This procedure preferentially selects the cases without energy decay events. Stronger decoherence suppression requires smaller selection probability; a desired point in this trade-off can be chosen by varying the measurement strength. The experiment can be realized in a straightforward way using the superconducting phase qubit.

We propose a scheme to measure the quantum state of a nanomechanical oscillator cooled near its ground state of vibrational motion. This is an extension of the nonlinear atomic homodyning technique scheme first developed to measure the intracavity field in a micromaser. It involves the use of a detector atom that is simultaneously coupled to the resonator via a magnetic interaction and to (classical) optical fields via a Raman transition. We show that the probability for the atom to be found in the ground state is a direct measure of the Wigner characteristic function of the nanomechanical oscillator. We also investigate the back-action effect of this destructive measurement on the state of the resonator.

All-versus-nothing (AVN) proofs show the conflict between Einstein, Podolsky, and Rosen’s elements of reality and the perfect correlations of some quantum states. Given an $n$-qubit state distributed between $m$ parties, we provide a method with which to decide whether this distribution allows an $m$-partite AVN proof specific for this state using only single-qubit measurements. We apply this method to some recently obtained $n$-qubit $m$-particle states. In addition, we provide all inequivalent AVN proofs with less than nine qubits and a minimum number of parties.

We present a detailed description of an architecture for fault-tolerant quantum computation, which is based on the cluster model of encoded qubits. In this cluster-based architecture, concatenated computation is implemented in a quite different way from the usual circuit-based architecture where physical gates are recursively replaced by logical gates with error-correction gadgets. Instead, some relevant cluster states, say fundamental clusters, are recursively constructed through verification and postselection in advance for the higher-level one-way computation, which namely provides error-precorrection of gate operations. A suitable code such as the Steane seven-qubit code is adopted for transversal operations. This concatenated construction of verified fundamental clusters has a simple transversal structure of logical errors, and achieves a high noise threshold $~3\%$ for computation by using appropriate verification procedures. Since the postselection is localized within each fundamental cluster with the help of deterministic bare controlled-$Z$ gates without verification, divergence of resources is restrained, which reconciles postselection with scalability.

We propose a quantum interface protocol based on two quantum nondemolition (QND) interactions arranged either in sequence or in parallel. Since the QND coupling arises naturally in interactions between light and a macroscopic ensemble of atoms, or between light and a micromechanical oscillator, the proposed interface is capable of transferring a state of light onto these matter systems. The transfer itself is perfect and deterministic for any quantum state, for arbitrarily small interaction strengths, and for arbitrarily large noise of the target system. It requires an all-optical preprocessing with a coupling stronger than that between the light and the matter, and a displacement feed-forward correction of the matter system. We also suggest a probabilistic version of the interface, which eliminates the need for the feed-forward correction at the cost of a reduced success rate. An application of the interface can be found in the construction of a quantum memory or in the state preparation for quantum sensing.

An $(n,m,p)$ random access code (RAC) makes it possible to encode $n$ bits in an $m$-bit message in such a way that a receiver of the message can guess any of the original $n$ bits with probability $p$ greater than $\frac{1}{2}$. In quantum RACs (QRACs), one transmits $n$ qubits. The full set of primitive entanglement-assisted random access codes (EARACs) is introduced, in which parties are allowed to share a two-qubit singlet. It is shown that via a concatenation of these, one can build for any $n$ an $(n,1,p)$ EARAC. QRACs for $n>3$ exist only if parties also share classical randomness. We show that EARACs outperform the best of known QRACs not only in the success probabilities but also in the amount of communication needed in the preparatory stage of the protocol. Upper bounds on the performance of EARACs are given and shown to limit also QRACs.

Entanglement refers to the inability of many-body quantum mechanical systems to be separated into independent subsystems. This has been well investigated in systems consisting of two entangled subsystems. In larger systems, more complex types of entanglement exist. In a system consisting of three subsystems (e.g., qubits), it is possible that all three subsystems are entangled with each other in a way that cannot be reduced to bipartite entanglement, and it is known that two different, inequivalent forms of tripartite entanglement exist such as the GHZ and $W$ states (GHZ denotes “Greenberger-Horne-Zeilinger”). Here, we investigate a particularly interesting system with competing one-, two-, and three-body interactions. Its ground state can be a product state, a GHZ state, or a $W$ state, depending on the type and strength of the spin-spin couplings. By varying an external control parameter, the system can be made to undergo quantum transitions between the various ground-state-entanglement phases. We implement the system in an NMR quantum simulator and use adiabatic evolution of the effective Hamiltonian to drive the system through the quantum transitions. In the experimental and numerical simulations, we check the suitability of different observables for making the quantum transitions visible and for characterizing the different phases.

In this paper we discuss the optimization of Sturmian basis functions by studying bound atomic systems within the configuration interaction method. Our investigation clearly shows how the fulfillment of correct physical boundary conditions at short and large distances from the nucleus improves the convergence rate of the method. This is illustrated first through a one-electron atom, and then with the two-electron systems. For the ground state of the helium atom, and with 35 Sturmian functions per electron and angular momenta, we obtain an energy of $-2.903\hspace{0.5em}712\hspace{0.5em}820$ a.u., outperforming previous similar calculations [Bromley and Mitroy, Int. J. Quantum Chem. 107, 1150 (2007)].

The dynamic dipole polarizabilities for Li atoms and Be${}^{+}$ ions in the $2\hspace{0.5em}{}^{2}S$ and $2\hspace{0.5em}{}^{2}P$ states are calculated using the variational method with a Hylleraas basis. The present polarizabilities represent the definitive values in the nonrelativistic limit. Corrections due to relativistic effects are also estimated. Analytic representations of the polarizabilities for frequency ranges encompassing the $n=3$ excitations are presented. The recommended polarizabilities for ${}^7\mathrm{Li}$ and ${}^9\mathrm{Be}$${}^{+}$ are $164.11\pm 0.03$ $a_0^3$ and $24.489\pm 0.004$ $a_0^3$, respectively.

Relativistic cross sections for electron-impact ionization including quantum electrodynamic effects are studied for hydrogenlike ions in the two-potential formalism. Results are compared with other theoretical calculations and experimental data. Effects of the transverse-photon interaction as well as vacuum polarization potential between charges are analyzed. Systematic behaviors along the H-isoelectronic sequence are summarized.

The triply differential cross section of ionization excitation of helium, leaving the residual ion in the $n=2$ excited states, is evaluated for the kinematics considered experimentally by Dupré et al. [J. Phys. B 25, 259 (1992)]. The interaction of the incident electron with the target is described at the first order, while the interaction of the ejected electron with the residual ion is treated very accurately within the formalism of the Jacobi matrix method. In the quasiphoton limit and for low ejected electron energies, the presence of series of doubly excited states, mainly below the $n=3$ single ionization threshold in helium, makes the triply differential cross sections extremely sensitive to both the energy and the emission angle of the ejected electron. We show that the convolution of our results with a Gaussian energy profile, in which the full width at half-maximum corresponds to the energy resolution in the experiment, has a significant effect. Our results suggest that it is also important to account for the finite resolution on the measurement of the scattering angle when the experimental data are compared to the theoretical predictions. Comparison of our theoretical results convoluted both in energy and in angle with the experimental data demonstrates the importance of an accurate description of the helium spectrum. A possible two-step mechanism involving single ionization of the target followed by excitation of the core electron is proposed to explain the remaining discrepancies.

The interaction of electrons and atomic sodium was studied by using the momentum space coupled-channel optical method at low-impact energies. Total scattering cross sections have been calculated, and negative-ion resonances have been located. The present calculation results are in good agreement with available experimental data and previous theoretical results. We have obtained resonance features at $4.166$ and $4.502$ eV and also found possible resonance structures near the ionization threshold in the total cross sections.

Postexponential decay of the probability density of a quantum particle leaving a trap can be reproduced accurately, except for interference oscillations at the transition to the postexponential regime, by means of an ensemble of classical particles emitted with constant probability per unit time and the same half-life as the quantum system. The energy distribution of the ensemble is chosen to be identical to the quantum distribution, and the classical point source is located at the scattering length of the corresponding quantum system. A one-dimensional example is provided to illustrate the general argument.

We present energy- and angle-resolved photoionization from Xe in an ultrastrong laser field at ${10}^{19}$ $\mathrm{W}/$cm${}^2$. The observed yields are consistent with the tunneling ionization of Xe${}^{9+}$ to Xe${}^{24+}$. However, energy and angle-resolved photoelectron spectra show differences for electrons whose final energies are above or below 0.5 MeV, which is approximately the ponderomotive energy at these intensities. Above 0.5 MeV, the observed photoelectron cutoff energy (between 1 and 1.35 MeV), photoelectron energy spectra, and the angle-resolved photoelectron azimuthal distributions agree with a model using tunneling ionization, multiple charge states, a classical relativistic continuum, and nonparaxial three-dimensional (3D) focused laser field. Below 0.5 MeV the yields and angular distributions observed indicate dynamics not included within a classical, single electron model of the interaction.

We theoretically study multiphoton ionization of the Ca atom irradiated by the second (photon energy $3.1$ eV) and third (photon energy 4.65 eV) harmonics of Ti:sapphire laser pulses (photon energy $1.55$ eV). Because of the dense energy level structure the second and third harmonics of a Ti:sapphire laser are nearly single-photon resonant with the $4s4p$ ${}^1{P}^o$ and $4s5p$ ${}^1{P}^o$ states, respectively. Although two-photon ionization takes place through the near-resonant intermediate states with the same symmetry in both cases, it turns out that there are significant differences between them. The photoelectron energy spectra exhibit the absence or presence of substructures. More interestingly, the photoelectron angular distributions clearly show that the main contribution to the ionization processes by the third harmonic arises from the far-off-resonant $4s4p$ ${}^1{P}^o$ state rather than the near-resonant $4s5p$ ${}^1{P}^o$ state. These findings can be attributed to the fact that the dipole moment for the $4s^2$ ${}^1{S}^e-4s5p$ ${}^1{P}^o$ transition is much smaller than that for the $4s^2$ ${}^1{S}^e-4s4p$ ${}^1{P}^o$ transition.

The quantum regime of highly doubly excited states in two-electron atoms has, so far, been largely inaccessible both to numerical methods as well as to experiments. Recent advances in semiclassical closed orbit theory in combination with a quantum mapping approach have shown a new way into this region of high dynamical complexity. In particular, new scaling laws near the double-ionization threshold as well as the dominant semiclassical contributions to the total photoionization cross section can be identified. We will present this new approach here in all its detail. It is based on representing the photoionization cross section in terms of quantum maps. These quantum maps or quantum propagators are used as a starting point for developing an efficient numerical method for calculating cross sections. Furthermore, by writing the quantum operators in semiclassical approximations, it is possible to interpret the quantum results in terms of classical triple collision orbits and to derive threshold laws near the three-particle breakup point. Semiclassical and numerical quantum results show excellent agreement for a model system, namely collinear helium.