A method for synthesizing dynamical decoupling (DD) sequences is presented, which can tailor these sequences to a given set of qubits, environments, instruments, and available resources using partial information of the system. The key concept behind the generation of the DD sequences involves not only extricating the strong dependence on the coupling strengths according to the “optimal control,” but also exploiting the “refocus” technique used conventionally to obtain DD sequences. The concept is a generalized one that harmonizes optimal control and designing of DD sequences.

Quantum steering has recently been formalized in the framework of a resource theory of steering, and several quantifiers have already been introduced. Here, we propose an information-theoretic quantifier for steering called intrinsic steerability, which uses conditional mutual information to measure the deviation of a given assemblage from one having a local-hidden-state model. We thus relate conditional mutual information to quantum steering and introduce monotones that satisfy certain desirable properties. The idea behind the quantifier is to suppress the correlations that can be explained by an inaccessible quantum system and then quantify the remaining intrinsic correlations. A variant of the intrinsic steerability finds operational meaning as the classical communication cost of sending the measurement choice and outcome to an eavesdropper who possesses a purifying system of the underlying bipartite quantum state that is being measured.

The two-photon transition $5S-5P-5D$ in rubidium vapor is investigated by detecting the fluorescence from the $6P_{3/2}$ state when the atomic system is excited by the combined action of a cw diode laser and a frequency comb. The cw laser plays a role as a velocity-selective filter and allows for sub-Doppler spectroscopy over a large spectral range including the $5D_{3/2}$ and $5D_{5/2}$ states. For a counterpropagating beam configuration, the response of each atomic velocity group is well characterized within the Doppler profile and the excited hyperfine levels are clearly resolved. The contribution of the optical pumping to the direct two-photon process is also revealed. The results are well described in a frequency domain picture by considering the interaction of each velocity group with the cw laser and the modes of the frequency comb.

The study of $N$-qubit mixed symmetric separable states is a longstanding challenging problem as no unique separability criterion exists. In this regard, we take up the $N$-qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer an elegant mathematical analysis since the dimension of the Hilbert space is reduced from $2^N$ to $N+1$. Since there exists a one-to-one correspondence between the spin-$j$ system and an $N$-qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of the spin-density matrix. Further, we use a geometric multiaxial representation (MAR) of the density matrix to characterize the mixed symmetric separable states. Since the separability problem is NP-hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the $P$-distribution function $\lambda (\theta ,\varphi )$. We show that the $N$-qubit mixed symmetric separable states can be visualized as a uniaxial system if the distribution function is independent of $\theta$ and $\varphi$. We further choose a distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the $N$-qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two-qubit mixed symmetric separable state. We also observe that there exists a correspondence between the separability and classicality of states.

By the numerical solution to the time-dependent Schrödinger equation, we observe a remarkable asymmetry in the photoelectron streaking spectra when the ${\mathrm{He}}^{+}$ ion is ionized by an attosecond pulse from the $2s$ state in the presence of a weak infrared pulse. An analytical theory based on the modified perturbation theory is developed to quantitatively account for the underlying mechanism. We find that a transition occurs between the degenerate $2s$ and $2p$ states under the influence of the infrared electric field before the arrival of the attosecond pulse. The observed asymmetry in the attosecond streaking is formed by the interference of photoelectrons ionized from the $2s$ and $2p$ states. Using the sensitivity of the asymmetry to the infrared (IR) electric field at the moment of attosecond photoionization, we show that the present finding provides a highly reliable way to fully characterize the IR waveform in the streaking experiment.

Nonadiabatic decay rates for a radio-frequency-dressed magnetic trap are calculated using Fermi's golden rule: that is, we examine the probability for a single atom to make transitions out of the dressed trap and into a continuum in the adiabatic limit, where perturbation theory can be applied. This approach can be compared to the semiclassical Landau-Zener theory of a resonant dressed atom trap, and it is found that, when carefully implemented, the Landau-Zener theory overestimates the rate of nonadiabatic spin-flip transitions in the adiabatic limit. This indicates that care is needed when determining requirements on trap Rabi frequency and magnetic-field gradient in practical atom traps.

By studying the zero-temperature and nonzero-temperature phase diagrams of the ferromagnetic spin-1 Bose-Hubbard model under an external magnetic field, we find that the competition between ferromagnetism and the quadratic Zeeman energy yields two superfluid phases, which feature discontinuous first-order phase transitions between them for a strongly spinor Bose gas such as ${}^7\mathrm{Li}$, contrary to the corresponding continuum system.

We study the superradiant evolution of a set of $N$ two-level systems spontaneously radiating under the effect of phase-breaking mechanisms. We investigate the dynamics generated by nonradiative losses and pure dephasing, and their interplay with spontaneous emission. Our results show that in the parameter region relevant to many solid-state cavity quantum electrodynamics experiments, even with a dephasing rate much faster than the radiative lifetime of a single two-level system, a suboptimal collective superfluorescent burst is still observable. We also apply our theory to the dilute excitation regime, often used to describe optical excitations in solid-state systems. In this regime, excitations can be described in terms of bright and dark bosonic quasiparticles. We show how the effect of dephasing and losses in this regime translate into intermode scattering rates and quasiparticle lifetimes.

We investigate topological features of a one-dimensional photonic quasicrystal within the context of $\mathcal{PT}$ symmetry. Via the scattering characteristics, we analyze various properties of a particular mirrored structure, which supports topological edge modes in its band gaps. These interface modes display a nontrivial dependence on the quasiperiodic geometry, even in a passive system. Subsequently, the tailored addition of gain and loss generates curious $\mathcal{PT}$-like features. For example, the quasicrystal high density of modes leads to complicated mode-merging behaviors between edge and band modes, such as the symmetry recovery phenomenon. Furthermore, anisotropic transmission resonances (connected with unidirectional invisibility) are also present, but they display richer patterns in comparison to previously studied periodic structures. Additionally, we examine lasing effects in detail, with numerics and a simple Fabry-Pérot model. The large variety of mode-merging behaviors opens the way to laser resonance engineering.

In this paper we present a trajectory-based formulation of entanglement dynamics by employing the Wigner function. The linear entropy of a single trajectory is derived based on the trajectory evolution of the Wigner function. The entanglement dynamics with a separable Gaussian initial state is investigated using different values of Planck's constant $\hslash$ in the evolution of the trajectories, while quantum-classical correspondence in entanglement dynamics is investigated. In addition, we show why chaos can increase entanglement rapidly through analytical results and physical pictures of the underlying dynamics in phase space.

The conundrum parameter-operator of time in quantum mechanics, as well as the time-energy uncertainty relation and the tunneling delay time, have recently been addressed in attosecond optical ionization experiments. Dirac's formulation of the electron's relativistic quantum mechanics (RQM) allows the introduction of a dynamical self-adjoint time operator, representing an internal time of the system. Its relation to the parametric (laboratory) time is derived. Its relevance to the tunneling measurements in these experiments is exhibited, namely, as the time it takes the wave packet to cross the exit point of the barrier, thus justifying considering this time operator an additional observable in RQM.

We discuss protection of a quantum state that goes through a noise process by measurements and operations before and after the noise process. In our previous work, we showed the nonexistence of “truly quantum” protocols that protect an unknown qubit state against depolarizing noise better than “classical” ones. Toward identifying the class of noise processes that is optimally suppressed by such a “classical” protocol, we extend our previous result in two directions. First, we show that the statement is also true in any finite-dimensional Hilbert spaces, which was previously conjectured; the optimal protocol is either the do nothing protocol or the discriminate and reprepare protocol, depending on the strength of the noise. Second, in the case of a single qubit, we show that essentially the same conclusion holds for any unital noise. Thus, the noise must be nonunital for a control protocol beyond “classical” ones to exist.

We compare the performance of quantum annealing (QA, through Schrödinger dynamics) and simulated annealing (SA, through a classical master equation) on the $p$-spin infinite range ferromagnetic Ising model, by slowly driving the system across its equilibrium, quantum or classical, phase transition. When the phase transition is second order ($p=2$, the familiar two-spin Ising interaction) SA shows a remarkable exponential speed-up over QA. For a first-order phase transition ($p\ge 3$, i.e., with multispin Ising interactions), in contrast, the classical annealing dynamics appears to remain stuck in the disordered phase, while we have clear evidence that QA shows a residual energy which decreases towards zero when the total annealing time $\tau$ increases, albeit in a rather slow (logarithmic) fashion. This is one of the rare examples where a limited quantum speedup, a speedup by QA over SA, has been shown to exist by direct solutions of the Schrödinger and master equations in combination with a nonequilibrium Landau-Zener analysis. We also analyze the imaginary-time QA dynamics of the model, finding a $1/{\tau }^2$ behavior for all finite values of $p$, as predicted by the adiabatic theorem of quantum mechanics. The Grover-search limit $p\left(\mathrm{odd}\right)=\infty$ is also discussed.

Quantum technologies are developing powerful tools to generate and manipulate coherent superpositions of different energy levels. Envisaging a new generation of energy-efficient quantum devices, here we explore how coherence can be manipulated without exchanging energy with the surrounding environment. We start from the task of converting a coherent superposition of energy eigenstates into another. We identify the optimal energy-preserving operations, both in the deterministic and in the probabilistic scenario. We then design a recursive protocol, wherein a branching sequence of energy-preserving filters increases the probability of success while reaching maximum fidelity at each iteration. Building on the recursive protocol, we construct efficient approximations of the optimal fidelity-probability trade-off, by taking coherent superpositions of the different branches generated by probabilistic filtering. The benefits of this construction are illustrated in applications to quantum metrology, quantum cloning, coherent state amplification, and ancilla-driven computation. Finally, we extend our results to transitions where the input state is generally mixed and we apply our findings to the task of purifying quantum coherence.

A simple approximate version of the Fock-space relativistic coupled-cluster method is developed and applied for modeling the spin-orbit-coupling effect in the $A^1{\mathrm{\Sigma }}_{\left(u\right)}^{+}$ and $b^3{\mathrm{\Pi }}_{\left(u\right)}$ states of the heavy alkali diatomics RbCs and ${\mathrm{Cs}}_2$. Numerical stability in a wide range of molecular geometries is achieved at the cost of a very moderate loss of accuracy for low-lying states and negligibly small deviations of the computational scheme from strict size consistency. The adiabatic potential energy curves computed for the $(2,3)0^{+}$ (RbCs) and $(1,2)0_u^{+}$ (${\mathrm{Cs}}_2$) states are converted into “quasidiabatic” potentials and effective spin-orbit-coupling functions via projection of the scalar relativistic states onto the subsets of fully relativistic states. A detailed comparison of the present ab initio results with their experimental and preceding theoretical counterparts is performed.

We present the results of a study of ionization of Xe atoms by a pair of phase-locked pulses, which is characterized by interference produced by the twin peaks. Two types of interference are considered: ordinary optical interference, which changes the intensity of the composite pulse and thus the ion yield, and a quantum interference, in which the excited electron wave packets interfere. We use the measured ${\mathrm{Xe}}^{+}$ yield as a function of the temporal delay and/or relative phase between the peaks to monitor the interferences and compare their relative strengths. We model the interference with a pulse intensity function and by calculating the ionization yield with the time-dependent Schrödinger equation. Our results provide insight into optimal control pulses generated with learning algorithms. The results also show that the relative phase between peaks of a control pulse, along with small features such as distortions and imperfections in the wings of an ideal shape, play a significant role in the control process.

We present a generalized velocity gauge form of the relativistic laser-matter interaction. In comparison with the (equivalent) regular minimal coupling description, this form of light-matter interaction results in superior convergence properties for the numerical solution of the time-dependent Dirac equation. This applies both to the numerical treatment and, more importantly, to the multipole expansion of the laser field. The advantages of the alternative gauge is demonstrated in hydrogen by studies of the dynamics following the impact of superintense laser pulses of extreme ultraviolet wavelengths and subfemtosecond duration.

Low-energy above-threshold ionization by a midinfrared laser field is investigated in terms of a commonly used semiclassical model. The mapping of the initial conditions (initial transverse velocity and initial phase of the field) on the final drift momenta that is mediated by Newton's equation of motion is approximated by three Coulomb interactions, which occur at the exit of the tunnel and during the subsequent hard and soft interactions that occur when the electron revisits the ion. The mapping exhibits a particular caustic structure in the area of the low-energy structure, which has the shape of the butterfly catastrophe.

Bose-Einstein condensates (BECs) confined in a two-dimensional (2D) harmonic trap are known to possess a hidden 2D Schrödinger symmetry, that is, the Schrödinger symmetry modified by a trapping potential. Spontaneous breaking of this symmetry gives rise to a breathing motion of the BEC, whose oscillation frequency is robustly determined by the strength of the harmonic trap. In this paper, we demonstrate that the concept of the 2D Schrödinger symmetry can be applied to predict the nature of three-dimensional (3D) collective modes propagating along a condensate confined in an elongated trap. We find three kinds of collective modes whose existence is robustly ensured by the Schrödinger symmetry, which are physically interpreted as one breather mode and two Kelvin-ripple complex modes, i.e., composite modes in which the vortex core and the condensate surface oscillate interactively. We provide analytical expressions for the dispersion relations (energy-momentum relation) of these modes using the Bogoliubov theory [D. A. Takahashi and M. Nitta, Ann. Phys. 354, 101 (2015)]. Furthermore, we point out that these modes can be interpreted as “quasi-massive-Nambu-Goldstone (NG) modes”, that is, they have the properties of both quasi-NG and massive NG modes: quasi-NG modes appear when a symmetry of a part of a Lagrangian, which is not a symmetry of a full Lagrangian, is spontaneously broken, while massive NG modes appear when a modified symmetry is spontaneously broken.

Motivated by a recent experiment [L. F. Livi et al., Phys. Rev. Lett. 117, 220401 (2016)], we study the ground-state properties of interacting fermions in a one-dimensional optical lattice clock with spin-orbit coupling. As the electronic and the hyperfine-spin states in the clock-state manifolds can be treated as effective sites along distinct synthetic dimensions, the system can be considered as multiple two-leg ladders with uniform magnetic flux penetrating the plaquettes of each ladder. As the interorbital spin-exchange interactions in the clock-state manifolds couple individual ladders together, we show that exotic interaction-induced vortex states emerge in the coupled-ladder system, which compete with existing phases of decoupled ladders and lead to a rich phase diagram. Adopting the density matrix renormalization group approach, we map out the phase diagram, and investigate in detail the currents and the density-density correlations of the various phases. Our results reveal the impact of interactions on spin-orbit coupled systems, and are particularly relevant to the ongoing exploration of spin-orbit coupled optical lattice clocks.