We introduce high-order dynamical decoupling strategies for open-system adiabatic quantum computation. Our numerical results for the random-unitary map model demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding which allows computation to proceed alongside decoupling, can dramatically enhance the fidelity of adiabatic quantum computation in spite of decoherence.

Although important for detecting entanglement, the transpose operation cannot be directly realized in laboratory because it is a nonphysical operation. It is, however, possible to find an approximate transpose operation using the method known as the structural physical approximation (SPA); recently, SPA-based implementations of the transpose and partial transpose have been demonstrated for a single-qubit [Phys. Rev. A 83, 020301(R) (2011)] and an entangled two-qubit system [Phys. Rev. Lett. 107, 160401 (2011)]. In this work, we expand SPA-transpose to a three-dimensional quantum system: a qutrit. The photonic qutrit state is encoded in the polarization, and path degrees of freedom of a single-photon and the SPA-transpose operation, which is based on measurement and preparation of quantum states, is implemented with linear optics. Our work paves the way toward entanglement detection for higher-dimensional quantum systems.

Sequential double ionization of argon induced by elliptically polarized laser pulses at the over-the-barrier ionization regime is investigated with a fully classical model. We provide futher detail beyond that found in our previous paper [Phys. Rev. Lett. 109, 053004 (2012)] and show that all of the experimental observations, including the evolution of the ion momentum spectra as a function of laser intensity, the intensity-dependent ratio for the parallel and antiparallel electron emissions, and the release times of both electrons for various laser pulses, are excellently reproduced by our classical model. Our results indicate that the classical treatment is very valid and accurate in describing strong-field ionization, providing a simple and intuitive way to investigate the complex electron correlations in strong-field double and multiple ionizations.

Molecular hydrogen ion (H${{}_2}^{+}$) dissociation paths of bond softening (BS) and above threshold dissociation (ATD) are investigated exploiting few-cycle chirped laser pulses. 7-fs laser pulses are temporally broadened in a controlled way by the imposed positive chirp covering the range 7–55 fs. The dissociation of the H${{}_2}^{+}$ molecules via the BS and ATD paths is then systematically monitored as a function of the pulses duration in conditions of equal H${{}_2}^{+}$ yield. The experimental data show distinctive characteristics both in the energy dissociation spectral structure as well as in the yield as the pulse duration broadens. The interpretation of our experimental findings is supported by ab initio calculations based on the H${{}_2}^{+}$ dissociation time-dependent Schrödinger equation (TDSE) in a strong laser field, thus shedding light into the details of the underlying dissociation dynamics involving few-cycle pulses. The results are also analyzed within the Floquet picture discussing certain limits of its applicability. Finally, our experimental findings show strong molecular alignment for durations longer than 20 fs.

We study the thermodynamics near the generic (density-driven) superfluid–Mott-insulator transition in the three-dimensional Bose-Hubbard model using the nonperturbative renormalization-group approach. At low energy, the physics is controlled by the Gaussian fixed point and becomes universal. Thermodynamic quantities can then be expressed in terms of the universal scaling functions of the dilute Bose gas universality class while the microscopic physics enters only via two nonuniversal parameters, namely, the effective mass $m^{*}$ and the “scattering length” $a^{*}$ of the elementary excitations at the quantum critical point between the superfluid and Mott-insulating phases. A notable exception is the condensate density in the superfluid phase which is proportional to the quasiparticle weight $Z_{\mathrm{qp}}$ of the elementary excitations. The universal regime is defined by $m^{*}{a}^{*}{}^{2}T\ll 1$ and $m^{*}{a}^{*}{}^2\left|\delta \mu \right|\ll 1$ or, equivalently, $|\overline{n}-{\overline{n}}_c|a^{*}{}^3\ll 1$, where $\delta \mu =\mu -{\mu }_c$ is the chemical potential shift from the quantum critical point $(\mu ={\mu }_c,T=0)$ and $\overline{n}-{\overline{n}}_c$ the doping with respect to the commensurate density ${\overline{n}}_c$ of the $T=0$ Mott insulator. We compute $Z_{\mathrm{qp}}$, $m^{*}$, and $a^{*}$ and find that they vary strongly with both the ratio $t/U$ between hopping amplitude and onsite repulsion and the value of the (commensurate) density ${\overline{n}}_c$. Finally, we discuss the experimental observation of universality and the measurement of $Z_{\mathrm{qp}}$, $m^{*}$, and $a^{*}$ in a cold-atomic gas in an optical lattice.

Single-photon cooling is a recently introduced method to cool atoms and molecules for which standard methods might not be applicable. We numerically examine this method in a two-dimensional wedge trap as well as in a two-dimensional harmonic trap. An element of the method is a small optical box with “diodic” walls which moves slowly through the external potential and catches atoms irreversibly. We show that the cooling efficiency of the method can be improved by optimizing the trajectory of this box.

Grover's quantum search algorithm drives a quantum computer from a prepared initial state to a desired final state by using selective transformations of these states. Here, we analyze a framework when one of the selective transformations is replaced by a more general unitary transformation. Our framework encapsulates several previous generalizations of the Grover's algorithm. We show that the general quantum search algorithm can be improved by controlling the transformations through an ancilla qubit. As a special case of this improvement, we get a faster quantum algorithm for the two-dimensional spatial search.

We construct coefficient matrices of size $2^{\ell }$ by $2^{n-\ell }$ associated with pure $n$-qubit states and prove the invariance of the ranks of the coefficient matrices under stochastic local operations and classical communication (SLOCC). The ranks give rise to a simple way of partitioning pure $n$-qubit states into inequivalent families and distinguishing degenerate families from one another under SLOCC. Moreover, the classification scheme via the ranks of coefficient matrices can be combined with other schemes to build a more refined classification scheme. To exemplify we classify the nine families of four qubits introduced by Verstraete et al. [Phys. Rev. A 65, 052112 (2002)] further into inequivalent subfamilies via the ranks of coefficient matrices, and as a result, we find 28 genuinely entangled families and all the degenerate classes can be distinguished up to permutations of the four qubits. We also discuss the completeness of the classification of four qubits into nine families.

We consider the formation of ultrashort spatiotemporal optical waveforms in arrays of carbon nanotubes. We use a short-wave approximation to derive a generic two-dimensional sine-Gordon equation, describing ultrashort soliton evolution in such nanomaterials. This model was derived by using a rigorous application of the reductive perturbation formalism (multiscale analysis) for the Maxwell equations and for the corresponding Boltzmann kinetic equation for the distribution function of electrons in carbon nanotubes. We show numerically diffractionless and dispersionless robust propagation over large distances (with respect to the wavelength) of few-cycle (2+1)-dimensional spatiotemporal solitons in the form of optical breathers.

We theoretically investigate a cavity quantum electrodynamics system in which a high-$Q$ whispering-gallery-mode (WGM) microresonator interacts with multiple diamond nanocrystals each containing a single nitrogen-vacancy (NV) center. With a tapered fiber waveguide coupling the WGMs, the transmission spectrum of the system exhibits a twofold-splitting phenomenon, where the first fold of splitting originates from the nanocrystals’ Rayleigh scattering and the second fold stems from the NV center dipole coupling with the WGMs. The interacting system can serve as a platform to generate quantum entanglement between two NV centers embedded in distant diamond nanocrystals. Our further study reveals that the Rayleigh scattering of the nanocrystals plays a positive role in generating entanglement in some cases. The analytical results show that the relatively strong scattering leads to a larger concurrence for the fixed dipole-cavity detunings. This investigation may hold potential for solid-state quantum information processing applications.

In excellent agreement with our numerical simulations of Shor's algorithm, equipped with a truncated quantum Fourier transform of bandwidth $b$, we find that its performance scales $\sim$$2^{-{\xi }_{b}n}$, where $n$ is the number of qubits, ${\xi }_b=1.1\times 2^{-2b}$, and the bandwidth $b$ is the number of quantum states coupled by the quantum Fourier transform. Nonexponential behavior is observed for small $n$ and explained analytically. The large-$n$ exponential scaling implies that $b=7$ is sufficient to operate a 1000-qubit quantum computer running Shor's algorithm on the $95\%$ performance level and implies hardware savings of the order of half a million rotation gates.

We investigate the estimation of a small interaction parameter from the outcomes of weak quantum measurements implemented by the interaction. The relation of weak values and sensitivity is explained and the different contributions of postselected results are identified using experimental data. The results show how weak values can be used to control the distribution of input state sensitivity between different postselected outcomes.

We reappraise some of the hybrid classical-quantum models proposed in the literature with the goal of retrieving some of their common characteristics. In particular, first, we analyze in detail the Peres-Terno argument regarding the inconsistency of hybrid quantizations of the Sudarshan type. We show that to accept such hybrid formalism entails the necessity of dealing with additional degrees of freedom beyond those in the straight complete quantization of the system. Second, we recover a similar enlargement of degrees of freedom in the so-called statistical hybrid models. Finally, we use Wigner's quantization of a simple model to illustrate how in hybrid systems the subsystems are never purely classical or quantum. A certain degree of quantumness (classicality) is being exchanged between the different sectors of the theory, which in this particular unphysical toy model makes them undistinguishable.

The quantum receiver is an important tool for overcoming the standard quantum limit (SQL) of discrimination errors in optical communication. We theoretically study the quantum receivers for discriminating ternary and quaternary phase-shift-keying coherent states in terms of average error rate and mutual information. Our receiver consists of on-off–type photon detectors and displacement operations without electrical feedforward operations. We show that for the ternary signals, the receiver shows a reasonable gain from the SQL even without feedforward. This scheme is realizable with the currently available technology. For the quaternary signals feedforward operation is crucial to overcome the SQL with imperfect devices. We also analytically examine the asymptotic limit of the performance of the proposed receiver with respect to the number of feedforward steps.

Dynamically corrected gates are extended to non-Markovian open quantum systems where limitations on the available controls and/or the presence of control noise make existing analytical approaches unfeasible. A computational framework for the synthesis of dynamically corrected gates is formalized that allows sensitivity against non-Markovian decoherence and control errors to be perturbatively minimized via numerical search, resulting in robust gate implementations. Explicit sequences for achieving universal high-fidelity control in a singlet-triplet spin qubit subject to realistic system and control constraint are provided, which simultaneously cancel to the leading order the dephasing due to non-Markovian nuclear-bath dynamics and voltage noise affecting the control fields. Substantially improved gate fidelities are predicted for current laboratory devices.

Most quantum entanglement investigations are focused on two qubits or some finite (small) chain structure, since the infinite chain structure is a considerably cumbersome task. Therefore, the quantum entanglement properties involving an infinite chain structure is quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by an infinite chain. Thus, in this paper we consider an entangled diamond chain with Ising and anisotropic Heisenberg (Ising-XXZ) coupling. Two interstitial particles are coupled through Heisenberg coupling or simply two-qubit Heisenberg, which could be responsible for the emergence of entanglement. These two-qubit Heisenberg operators are interacted with two nodal Ising spins. An infinite diamond chain is organized by interstitial-interstitial and nodal-interstitial (dimer-monomer) site couplings. We are able to get the thermal average of the two-qubit operator, called the reduced two-qubit density operator. Since these density operators are spatially separated, we could obtain the concurrence (entanglement) directly in the thermodynamic limit. The thermal entanglement (concurrence) is constructed for different values of the anisotropic Heisenberg parameter, magnetic field, and temperature. We also observed the threshold temperature via the parameter of anisotropy, Heisenberg and Ising interaction, external magnetic field, and temperature.

Recently discovered processes of volume reflection and multiple volume reflection of charged particles in bent crystals are accompanied by specific electromagnetic (e.m.) radiation. The mechanism of radiation emission is quite complex due to the coexistence of different regimes for particle dynamics, resulting in e.m. generation with features characteristic of each regime. We present a simulation taking into consideration both the nondipole nature and arbitrary multiplicity of radiation accompanying volume reflection. This approach is worked out for electrons or positrons of any energy and is based on the local straight-crystal approximation and Baier-Katkov formula for radiation, the integration of which is considerably facilitated by the fast Fourier transform method. The radiation generated by multiple volume reflection with vertical and skew planes has been studied, too. A large axial contribution to the hard part of the radiative energy loss spectrum as well as the strengthening of planar radiation, with respect to the single volume reflection case, in the soft part of the spectrum are demonstrated. Both the wide spectrum and high intensity make this type of radiation quite suitable for the conversion of electron and positron beams to hard $\gamma$ radiation.

We discuss the production of ultracold molecules in their electronic ground state by photoassociation employing electronically excited states with ion-pair character and strong spin-orbit interaction. A short photoassociation laser pulse drives a nonresonant three-photon transition for alkali-metal atoms colliding in their lowest triplet state. The excited-state wave packet is transferred to the ground electronic state by a second laser pulse, driving a resonant two-photon transition. After analyzing the transition matrix elements governing the stabilization step, we discuss the efficiency of population transfer using transform-limited and linearly chirped laser pulses. Finally, we employ optimal control theory to determine the most efficient stabilization pathways. We find that the stabilization efficiency can be increased by one and two orders of magnitude when using linearly chirped and optimally shaped laser pulses, respectively.

The nonadiabatically coupled dynamics of electrons and nuclei is investigated for the ozone molecule on the attosecond time scale. A coherent superposition of nuclear wave packets located on different electronic states in the Chappuis and in the Hartley bands are created by pump pulses. The multiconfiguration time-dependent Hartree method is used to solve the coupled nuclear quantum dynamics in the framework of the adiabatic separation of the time-dependent Schrödinger equation including nonadiabatic couplings. Our nuclear wave-packet calculations demonstrate that the coherence between Hartley state B and one of the Chappuis states (Chappuis 1) is significantly large, while it is almost negligible for the other two cases (between Hartley B and Chappuis 2 or between Chappuis 1 and Chappuis 2). At present we limited our description of the electronic motion to the Franck-Condon region only due to the localization of the nuclear wave packets around this point during the first 5–6 fs.

Using the perturbative approach, it is demonstrated that the widths of the density and second-order correlation function of atoms scattered from a quasicondensate in a Raman process are sensitive to the phase fluctuations induced by the nonzero temperature of the mother cloud. It is also shown how these widths evolve during expansion of the halo of scattered atoms. It is also argued that if the Raman scattering is preceded by expansion of the mother cloud, the density of atoms widens substantially, while the second-order correlation function remains practically unchanged. These results are useful for planning future Raman scattering experiments and indicate the degree of spatial resolution of atom-position measurements necessary to detect the temperature dependence of the quasicondensate. All the calculations are performed using experimental parameters of a metastable ${}^4$He${}^{*}$ quasicondensate of the Palaiseau group.