The time-dependent complete-active-space self-consistent-field (TD-CASSCF) method for the description of multielectron dynamics in intense laser fields is presented, and a comprehensive description of the method is given. It introduces the concept of frozen-core (to model tightly bound electrons with no response to the field), dynamical-core (to model electrons tightly bound but responding to the field), and active (fully correlated to describe ionizing electrons) orbital subspaces, allowing compact yet accurate representation of ionization dynamics in many-electron systems. The classification into the subspaces can be done flexibly, according to simulated physical situations and desired accuracy, and the multiconfiguration time-dependent Hartree-Fock (MCTDHF) approach is included as a special case. To assess its performance, we apply the TD-CASSCF method to the ionization dynamics of one-dimensional lithium hydride (LiH) and LiH dimer models, and confirm that the present method closely reproduces rigorous MCTDHF results if active orbital space is chosen large enough to include appreciably ionizing electrons. The TD-CASSCF method will open a way to the first-principles theoretical study of intense-field-induced ultrafast phenomena in realistic atoms and molecules.

We show that the quasiadiabatic evolution of a system governed by the Dicke Hamiltonian can be described in terms of a self-induced quantum many-body metrological protocol. This effect relies on the sensitivity of the ground state to a small symmetry-breaking perturbation at the quantum phase transition, which leads to the collapse of the wave function into one of two possible ground states. The scaling of the final-state properties with the number of atoms and with the intensity of the symmetry-breaking field can be interpreted in terms of the precession time of an effective quantum metrological protocol. We show that our ideas can be tested with spin-phonon interactions in trapped ion setups. Our work points to a classification of quantum phase transitions in terms of the capability of many-body quantum systems for parameter estimation.

We derive an exact lower bound to a universal measure of frustration in degenerate ground states of quantum many-body systems. The bound results in the sum of two contributions: entanglement and classical correlations arising from local measurements. We show that average frustration properties are completely determined by the behavior of the maximally mixed ground state. We identify sufficient conditions for a quantum spin system to saturate the bound, and for models with twofold degeneracy we prove that average and local frustration coincide.

We present experimental evidence of the successful closed-loop optimization of the dynamics of cold atoms in an optical lattice. We optimize the loading of an ultracold atomic gas minimizing the excitations in an array of one-dimensional (1D) tubes (3D-1D crossover) and we perform an optimal crossing of the quantum phase-transition from a superfluid to a Mott insulator in a 3D lattice. In both cases we enhance the experiment performances with respect to those obtained via adiabatic dynamics, effectively speeding up the process by more than a factor three while improving the quality of the desired transformation.

An arbitrary quantum-optical process (channel) can be completely characterized by probing it with coherent states using the recently developed coherent-state quantum process tomography (QPT) [Lobino et al., Science 322, 563 (2008)]. In general, precise QPT is possible if an infinite set of probes is available. Thus, realistic QPT of infinite-dimensional systems is approximate due to a finite experimentally feasible set of coherent states and its related energy-cutoff approximation. We show with explicit formulas that one can completely identify a quantum-optical Gaussian process just with a few different coherent states without approximations like the energy cutoff. For tomography of multimode processes, our method exponentially reduces the number of different test states, compared with existing methods.

We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation space of the observable algebra, once a state is chosen. In this approach, which is based on the Gel'fand-Naimark-Segal construction, the study of subsystems becomes particularly clear. We explicitly show how the problems associated with the partial trace for the study of entanglement of identical particles are readily overcome. In particular, a suitable entanglement measure is proposed that can be applied to systems of particles obeying Fermi, Bose, para-, and even braid-group statistics. The generality of the method is also illustrated by study of the time evolution of subsystems emerging from restriction to subalgebras. Problems related to anomalies and quantum epistemology are also discussed.

We present an entanglement purification protocol (EPP) to reconstruct some maximally hybrid entangled states (HESs) from nonmaximally mixed HESs. We use simple linear optical elements such as a polarization beam splitter (PBS) and beam splitter (BS) to achieve this task. Meanwhile, it is shown that the parity-check gates acted by PBS and BS are enough to complete the task, and the controlled-not (cnot) gates or similar logic operations are not needed. Unlike the current EPPs, this protocol can purify not only the conventional bit-flip error and phase-flip error but also the dissipation error coming from the photon loss of the coherent state. It can also be extended to achieve the purification for multiphoton and multicoherent state HES. This protocol may be useful in current hybrid quantum repeaters.

We propose a quantum-electrodynamics scheme for implementing the discrete-time, coined quantum walk with the walker corresponding to the phase degree of freedom for a quasimagnon field realized in an ensemble of nitrogen-vacancy centers in diamond. The coin is realized as a superconducting flux qubit. Our scheme improves on an existing proposal for implementing quantum walks in cavity quantum electrodynamics by removing the cumbersome requirement of varying drive-pulse durations according to mean quasiparticle number. Our improvement is relevant to all indirect-coin-flip cavity quantum-electrodynamics realizations of quantum walks. Our numerical analysis shows that this scheme can realize a discrete quantum walk under realistic conditions.

We investigate the impact of an electric field on the structure of ultra-long-range polar diatomic rubidium Rydberg molecules. Both the $s$-wave and $p$-wave interactions of the Rydberg electron and the neutral ground-state atom are taken into account. In the presence of the electric field the angular degree of freedom between the electric field and the internuclear axis acquires vibrational character and we encounter two-dimensional oscillatory adiabatic potential energy surfaces with an antiparallel equilibrium configuration. The electric field allows shifting of the corresponding potential wells in such a manner that the importance of the $p$-wave interaction can be controlled and the individual wells are energetically lowered at different rates. As a consequence the equilibrium configuration and corresponding energetically lowest well move to larger internuclear distances for increasing field strength. For strong fields the admixture of nonpolar molecular Rydberg states leads to the possibility of exciting the large angular momentum polar states via two-photon processes from the ground state of the atom. The resulting properties of the electric dipole moment and the vibrational spectra are analyzed with varying field strength.

We explore possible pathways for the creation of ultracold polar $\mathrm{NaK}$ molecules in their absolute electronic and rovibrational ground state starting from ultracold Feshbach molecules. In particular, we present a multichannel analysis of the electronic ground and $\text{K}\left(4p\right)+\text{Na}\left(3s\right)$ excited-state manifold of NaK, analyze the spin character of both the Feshbach molecular state and the electronically excited intermediate states and discuss possible coherent two-photon transfer paths from Feshbach molecules to rovibronic ground-state molecules. The theoretical study is complemented by the demonstration of stimulated Raman adiabatic passage from the $X{}^1{\Sigma }^{+}$($v=0$) state to the $a{}^3{\Sigma }^{+}$ manifold on a molecular beam experiment.

We report on the realization of quantum degenerate gas mixtures of the alkaline-earth-metal element strontium with the alkali-metal element rubidium. A key ingredient of our scheme is sympathetic cooling of Rb by Sr atoms that are continuously laser cooled on a narrow-linewidth transition. This versatile technique allows us to produce ultracold gas mixtures with a phase-space density of up to 0.06 for both elements. By further evaporative cooling we create double Bose-Einstein condensates of ${}^{87}$Rb with either ${}^{88}$Sr or ${}^{84}$Sr, reaching more than $1\times {10}^5$ condensed atoms per element for the ${}^{84}$Sr-${}^{87}$Rb mixture. These quantum gas mixtures constitute an important step towards the production of a quantum gas of polar, open-shell RbSr molecules.

We propose an exactly solvable waveguide lattice incorporating an inhomogeneous coupling coefficient. This structure provides classical analogs to the squeezed number and squeezed coherent intensity distribution in quantum optics where the propagation length plays the role of a squeezed amplitude. The intensity pattern is obtained in a closed form for an arbitrary distribution of the initial beam profile. We have also investigated the phase transition to the spatial Bloch-like oscillations by adding a linear gradient to the propagation constant of each waveguide ($\alpha$). Our analytical results show that the Bloch-like oscillations appear above a critical value for the linear gradient of the propagation constant ($\alpha >{\alpha }_c$). The phase transition (in the propagation properties of the waveguide) is a result of competition between discrete and Bragg diffraction. Moreover, the light intensity decays algebraically along each waveguide at the critical point while it falls off exponentially below the critical point ($\alpha <{\alpha }_c$).

We theoretically investigate optomechanical coupling between a single-wall carbon nanotube and a high-$Q$ whispering gallery microcavity. The anisotropy in the refractive index of the nanotube results in polarization-sensitive optomechanical coupling. Moreover, the band structure of the nanotube leads to a strong dependence of the coupling strength on wavelength. In particular, strong and pure dissipative coupling can be achieved at the absorption resonance frequency of the nanotube, and the single-photon coupling strength can exceed $10\text{kHz}$. This strong coupling induces dissipative cooling of the nanotube oscillation, and ground-state cooling can be achieved.

We examine the geometric structure of qutrit state space by identifying the outcome probabilities of symmetric informationally complete (SIC) measurements with quantum states. We categorize the infinitely many qutrit SICs into eight SIC families corresponding to independent orbits of the extended Clifford group. Every SIC can be uniquely identified from a set of geometric invariants that we use to establish several properties of the convex body of qutrits, which include a simple formula describing its extreme points, an expression for the rotation between the probability vectors for distinct qutrit SICs, and a polar equation for its boundary states.

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the currently widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in place or move in a fixed direction, e.g., rightward or upward. While both formulations are essentially equivalent, the present approach leads us to consider discrete Fourier transforms, which eventually results in obtaining explicit expressions for the wave functions in terms of finite sums and allows the use of efficient algorithms based on the fast Fourier transform. The wave functions here obtained govern the probability of finding the particle at any given location but determine as well the exit-time probability of the walker from a fixed interval, which is also analyzed.

We use local adiabatic evolution to experimentally create and determine the ground-state spin ordering of a fully connected Ising model with up to 14 spins. Local adiabatic evolution—in which the system evolution rate is a function of the instantaneous energy gap—is found to maximize the ground-state probability compared with other adiabatic methods while requiring knowledge only of the lowest $\sim$$N$ of the $2^N$ Hamiltonian eigenvalues. We also demonstrate that the ground-state ordering can be experimentally identified as the most probable of all possible spin configurations, even when the evolution is highly nonadiabatic.

We analyze entanglement classes for permutation-symmetric states for $n$ qudits (i.e., $d$-level systems), with respect to local unitary operations (LU equivalence) and stochastic local operations and classical communication (SLOCC equivalence). In both cases, we show that the search can be restricted to operations where the same local operation acts on all qudits, and we provide an explicit construction for it. Stabilizers of states in the form of one-particle operations preserving permutation symmetry are shown to provide a coarse-grained classification of entanglement classes. We prove that the Jordan form of such one-particle operators is a SLOCC invariant. We find, as representatives of those classes, a discrete set of entangled states that generalize the Greenberger-Horne-Zeilinger and $W$ states for the many-particle qudit case. In the latter case, we introduce the excitation state as a natural generalization of the $W$ state for $d>2$.

We study the resilience of the surface code to decoherence caused by the presence of a bosonic bath. This approach allows us to go beyond the standard stochastic error model commonly used to quantify decoherence and error threshold probabilities in this system. The full quantum mechanical system-bath dynamics is computed exactly over one quantum error correction cycle. Since all physical qubits interact with the bath, space-time correlations between errors are taken into account. We compute the fidelity of the surface code as a function of the quantum error correction time. The calculation allows us to map the problem onto an Ising-like statistical spin model with two-body interactions and a fictitious temperature which is related to the inverse bath coupling constant. The model departs from the usual Ising model in the sense that interactions can be long ranged and can involve complex exchange couplings; in addition, the number of allowed configurations is restricted by the syndrome extraction. Using analytical estimates and numerical calculations, we argue that, in the limit of an infinite number of physical qubits, the spin model sustains a phase transition which can be associated to the existence of an error threshold in the surface code. An estimate of the transition point is given for the case of nearest-neighbor interactions.