A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first contribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i) the observed sequence of measurements (quantum tracks) corresponding to a single experiment converges to a limit point, and that (ii) the limit point is random over the ensemble of the experiments, being distributed as a zero-mean Gaussian random variable with a variance at most equal to the ground-state variance. As a second contribution, the richer scenario where the oscillator is coupled with a frozen (i.e., at the ground state) ensemble of independent quantum oscillators is considered. A sharply different behavior emerges: under the same measurement scheme, here we observe that the measurement sequences are essentially divergent. Such a rigorous statistical analysis of the sequential measurement process might be useful for characterizing the main quantities that are currently used for inference, manipulation, and monitoring of many quantum systems. Several interesting properties of the quantum tracks evolution, as well as of the associated (quantum) threshold crossing times, are discussed and the dependence upon the main system parameters (e.g., the choice of the measurement sampling time, the degree of interaction with the environment, the measurement device accuracy) is elucidated. At a more fundamental level, it is seen that, as an application of basic quantum mechanics principles, a sharp difference exists between the intrinsic randomness unavoidably present in any quantum system, and the extrinsic randomness arising from the environmental coupling, i.e., the randomness induced by an external source of disturbance.

Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of complete-positive trace-preserving maps is no longer valid. The departure from complete positivity means many useful bounds, such as entropy production, Holevo, and data processing inequality are no longer applicable to such systems. We address these issues by deriving a generalized bound for entropy valid for quantum dynamics with arbitrary system-environment correlations. We employ superchannels, which map quantum operations performed by the experimenter, represented in terms of completely positive maps, to states. Our bound has information-theoretic applications, as it generalizes the data processing inequality and the Holevo bound. We prove that both data processing inequality and the Holevo are valid even when a system is correlated with the environment.

Quantum walks are promising for information processing tasks because in regular graphs they spread quadratically more rapidly than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson localization, with their wave function staying within a finite region even in the infinite time limit, with a probability exponentially close to 1. It is thus important to understand when a quantum walk will be Anderson localized and when we can expect it to spread to infinity even in the presence of disorder. In this work we analyze the response of a one-dimensional quantum walk—the split-step walk—to different forms of static disorder. We find that introducing static, symmetry-preserving disorder in the parameters of the walk leads to Anderson localization. In the completely disordered limit, however, a delocalization transition occurs, and the walk spreads subdiffusively to infinity. Using an efficient numerical algorithm, we calculate the bulk topological invariants of the disordered walk and find that the disorder-induced Anderson localization and delocalization transitions are governed by the topological phases of the quantum walk.

A well-known cryptographic primitive is the so-called random access code. Namely, Alice is to send to Bob one of two bits, so that Bob has the choice of which bit he wants to learn about. However, at any time, Alice should not learn Bob's choice, and Bob should learn only the bit of his choice. The task is impossible to accomplish by means of either classical or quantum communication. On the other hand, a concept of correlations stronger than quantum ones, exhibited by the so-called Popescu-Rohrlich box, was introduced and widely studied. In particular, it is known that the Popescu-Rohrlich box enables simulation of the random access code with the support of one bit of communication. Here, we propose a quantum analog of this phenomenon. Namely, we define an analog of a random access code, where instead of classical bits, one encodes qubits. We provide a quantum nonsignaling box that if supported with two classical bits, allows one to simulate a quantum version of a random access code. We point out that two bits are necessary. We also show that a quantum random access code cannot be fully quantum: when Bob inputs the superposition of two choices, the output will be in a mixed state rather than in a superposition of required states.

In this paper, we introduce a simple and natural bipartite Bell scenario by considering the correlations between two parties defined by general measurements in one party and dichotomic ones in the other. We show that unbounded Bell violations can be obtained in this context. Since such violations cannot occur when both parties use dichotomic measurements, so far our setting can be considered as the simplest one where this phenomenon can be observed. Our example is essentially optimal in terms of the outputs and the Hilbert space dimension.

We show experimentally that field-free one-dimensional (1D) alignment of 1,4-diiodobenzene molecules embedded in helium nanodroplets, induced by a single, linearly polarized 200-fs laser pulse, can be significantly enhanced by using two or four optimally synchronized laser pulses. The strongest degree of 1D alignment is obtained with four pulses and gives $\langle {cos}^2\theta \rangle >0.60$. Besides the immediate implications for molecular frame studies, our results pave the way for more general manipulation of rotational motion of molecules in He droplets.

We present measure synchronization (MS) in a bosonic Josephson junction with spin-orbit coupling. The two atomic hyperfine states are coupled by a Raman dressing scheme, and they are regarded as two orientations of a pseudo-spin-$1/2$ system. A feature specific to a spin-orbit-coupled (SOC) bosonic Josephson junction is that the transition from non-MS to MS dynamics can be modulated by Raman laser intensity, even in the absence of interspin atomic interaction. A phase diagram of non-MS and MS dynamics as functions of Raman laser intensity and Josephson tunneling amplitude is presented. Taking into account interspin atomic interactions, the system exhibits MS breaking dynamics resulting from the competition between intraspin and interspin atomic interactions. When interspin atomic interactions dominate in the competition, the system always exhibits MS dynamics. For interspin interaction weaker than intraspin interaction, a window for non-MS dynamics is present. Since SOC Bose-Einstein condensates provide a powerful platform for studies on physical problems in various fields, the study of MS dynamics is valuable in researching the collective coherent dynamical behavior in a spin-orbit-coupled bosonic Josephson junction.

Until now, the known set of absolute optical instruments has been limited to those containing high levels of symmetry. Here, we demonstrate a method of mathematically constructing refractive index profiles that result in asymmetric absolute optical instruments. The method is based on the analogy between geometrical optics and classical mechanics and employs Lagrangians that separate in Cartesian coordinates. In addition, our method can be used to construct the index profiles of most previously known absolute optical instruments, as well as infinitely many different ones.

We study the structure of the eigenstates and the dynamics of a system that undergoes an excited-state quantum phase transition (ESQPT). The analysis is performed for two-level pairing models characterized by a $\mathrm{U}(n+1)$ algebraic structure. They exhibit a second-order phase transition between two limiting dynamical symmetries represented by the $\mathrm{U}\left(n\right)$ and $\mathrm{SO}(n+1)$ subalgebras. They are, or can be mapped onto, models of interacting bosons. We show that the eigenstates with energies very close to the ESQPT critical point, $E_{\text{ESQPT}}$, are highly localized in the $\mathrm{U}\left(n\right)$ basis. Consequently, the dynamics of a system initially prepared in a $\mathrm{U}\left(n\right)$-basis vector with energy $\mathcal{E}\sim E_{\text{ESQPT}}$ may be extremely slow. Signatures of an ESQPT can therefore be found in the structures of the eigenstates and in the speed of the system evolution after a sudden quench. Our findings can be tested experimentally with trapped ions.

In this paper we introduce parity-time- $(\mathcal{PT}$-) symmetric perturbation to a one-dimensional Lieb lattice, which is otherwise $\mathcal{P}$ symmetric and has a flat band. In the flat band there is a multitude of degenerate dark states and the degeneracy $N$ increases with the system size. We show that the degeneracy in the flat band is completely lifted due to the non-Hermitian perturbation in general, but it is partially maintained with the half-gain–half-loss perturbation and its $\mathsf{V}$ variant that we consider. With these perturbations, we show that both randomly positioned states and pinned states at the symmetry plane in the flat band can undergo thresholdless $\mathcal{PT}$ breaking. They are distinguished by their different rates of acquiring non-Hermicity as the $\mathcal{PT}$-symmetric perturbation grows, which are insensitive to the system size. Using a degenerate perturbation theory, we derive analytically the rate for the pinned states, whose spatial profiles are also insensitive to the system size. Finally, we find that the presence of weak disorder has a strong effect on modes in the dispersive bands but not on those in the flat band. The latter respond in completely different ways to the growing $\mathcal{PT}$-symmetric perturbation, depending on whether they are randomly positioned or pinned.

We define a family of binary-outcome $n$-party $m\le n$ settings per party Bell inequalities whose members require the least detection efficiency for their violation among all known inequalities of the same type. This gives upper bounds for the minimum value of the critical efficiency—below which no violation is possible—achievable for such inequalities. For $m=2$, our family reduces to the one given by Larsson and Semitecolos in 2001 [Phys. Rev. A 63, 022117 (2001)]. For $m>2$, a gap remains between these bounds and the best lower bounds. The violating state near the threshold efficiency always approaches a product state of $n$ qubits.

Measurement-based quantum computation is a model for quantum information processing utilizing local measurements on suitably entangled resource states for the implementation of quantum gates. A complete characterization for universal resource states is still missing. It has been shown that symmetry-protected topological order in one dimension can be exploited for the protection of certain quantum gates in measurement-based quantum computation. In this paper we show that the two-dimensional (2D) plaquette states on arbitrary lattices exhibit nontrivial symmetry-protected topological order in terms of symmetry fractionalization and that they are universal resource states for quantum computation. Our results of the nontrivial symmetry-protected topological order on arbitrary 2D lattices are based on an extension of the recent construction by Chen et al. [Phys. Rev. B 87, 155114 (2013)] on the square lattice.

Lifetimes of the $6d{}^{2}D_{3/2}$ and $6d{}^{2}D_{5/2}$ states in Fr are determined from calculations of the radiative transition amplitudes of the allowed electric dipole $\left(E1\right)$ and the forbidden electric quadrupole $\left(E2\right)$ and magnetic dipole $\left(M1\right)$ channels which were performed using the second-order many-body perturbation theory and the coupled-cluster method at different levels of approximations in the relativistic framework. The values obtained for these two quantities are 540(10) and 1704(32) ns, respectively. These relatively long lifetimes and the large electric dipole parity-non-conserving amplitudes of $7s{}^{2}S_{1/2}\to 6d{}^{2}D_{3/2,5/2}$ transitions strongly favor Fr as a leading candidate for the measurement of parity nonconservation arising from the neutral-current weak interaction and the nuclear anapole moment. In another important application, these $6D$ states in Fr can be used efficiently for resonance ionization spectroscopic techniques to carry out precise measurements of the properties of the higher excited states due to the long lifetimes of these states.

On the basis of the quasipotential approach to the bound-state problem in quantum electrodynamics we calculate hyperfine structure intervals $\mathrm{\Delta }{E}^{\text{HFS}}\left(2P_{1/2}\right)$ and $\mathrm{\Delta }{E}^{\text{HFS}}\left(2P_{3/2}\right)$ for $P$ states in muonic deuterium. The tensor method of projection operators for the calculation of the hyperfine structure of $P$ states with definite quantum numbers of total atomic momentum $F$ and total muon momentum $j$ in muonic deuterium is formulated. We take into account vacuum polarization, relativistic, quadrupole, and structure corrections of orders ${\alpha }^4,{\alpha }^5$, and ${\alpha }^6$. The obtained numerical values of hyperfine splittings are useful for the analysis of experimental data of the CREMA collaboration regarding muonic deuterium.

We measure the resonance line shape of atomic-vapor layers with nanoscale thickness confined between two sapphire windows. The measurement is performed by scanning a probe laser through resonance and collecting the scattered light. The line shape is dominated by the effects of Dicke narrowing, self-broadening, and atom-surface interactions. By fitting the measured line shape to a simple model we discuss the possibility to extract information about the atom-surface interaction.

We investigate the multielectron ionization dynamics of ${\mathrm{C}}_2{\mathrm{H}}_2$ subjected to intense few-cycle laser fields with the time-dependent Hartree-Fock approach, in which one-center method is employed with the finite-element discrete-variable representation and $B$-spline functions. It is found that, when the photon energy is close to the energy gap between the two inner orbitals, an inner-orbital single-photon resonant transition phenomenon occurs and plays an important role in the ionization process of the molecule. Furthermore, the ionization of inner electrons surpasses that of the electrons in the highest occupied molecular orbital (HOMO) at high laser intensities, which may be attributed to the effect of the spatial distributions of molecular orbitals. Moreover, this phenomenon will be enhanced by a reduction of the screen for electrons in the HOMO due to the ionization of inner electrons.

We present experimental and numerical studies of nonlinear magneto-optical rotation (NMOR) in rubidium vapor excited with resonant light tuned to the $5{}^2{S}_{1/2}\to 6{}^2{P}_{1/2}$ absorption line (421 nm). Contrary to the experiments performed to date on the strong $D_1$ or $D_2$ lines, in this case, the spontaneous decay of the excited state $6{}^2{P}_{1/2}$ may occur via multiple intermediate states, affecting the dynamics, magnitude, and other characteristics of NMOR. Comparing the experimental results with the results of modeling based on Auzinsh et al. [Phys. Rev. A 80, 053406 (2009)], we demonstrate that despite the complexity of the structure, NMOR can be adequately described with a model, where only a single excited-state relaxation rate is used.

We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time optimal at each crossing. We correct the field applying optimal control techniques in order to find the minimal evolution or quantum speed limit (QSL) time. We investigate its dependence as a function of the system parameters and show that the QSL time gets proportionally smaller to the well-known two-level case as the dimension of the system increases. Working at the QSL, we study the control fields derived from the optimization procedure and show that they present a very simple shape, which can be described by a few parameters. Based on this result, we propose a simple expression for the control field and show that the full time evolution of the control problem can be analytically solved.

A phase modulation technique to sensitively and selectively isolate multiple-quantum coherences in a femtosecond pump-probe setup is presented. By detecting incoherent observables and incorporating lock-in amplification, even weak signals of highly dilute samples can be acquired. Applying this method, efficient isolation of one- and two-photon quantum beats in a rubidium-doped helium droplet beam experiment is demonstrated and collective resonances are observed in a potassium vapor for the first time up to fourth order. Our approach provides promising perspectives for coherent time-resolved experiments in the deep UV and multidimensional spectroscopy schemes, in particular when mass-selective detection of particles in dilute gas-phase targets is possible.

The ionization and fragmentation dynamics of acetylene and the hydrogen molecule driven by strong short circularly polarized laser pulses are investigated within the framework of the time-dependent density-functional theory coupled with the Ehrenfest dynamics. The effects of alignment are considered and the dynamics is compared to that driven by linearly polarized pulses. It is found that the coupled ion-electron dynamics of both molecules driven by circularly polarized pulses follows the enhanced ionization mechanism, as was found in previous theoretical studies with linearly polarized pulses. A moderate localization asymmetry in the ionization dynamics of the hydrogen molecule was also found, in qualitative agreement with previous experimental investigations.