Weak-value amplification (WVA) has recently become an important technique for parameter estimation, owing to its ability to enhance the signal-to-noise ratio by amplifying extremely small signals with proper postselection strategies. In this paper, we propose an adaptive WVA scheme to achieve the highest Fisher information when using an unbalanced pointer. Different from previous schemes, the adaptive WVA scheme is associated with a real-time update on the postselection states with the help of feedback information from the outcomes, and the “extremely small” condition set on the parameter of interest is relaxed. By applying this scheme to a time-delay measurement scenario, we show by numerical simulation that the precision achieved in our scheme is several times higher than the standard WVA scheme. Our result might open a path for improving the WVA technique in a more flexible and robust way.

We propose a realization of a synthetic random flux model in a two-dimensional optical lattice. Starting from Bose-Hubbard Hamiltonian for two atom species, we show how to use fast-periodic modulation of the system parameters to construct a random gauge field. We investigate the transport properties of such a system and describe the impact of time-reversal symmetry breaking and correlations in disorder on Anderson localization length.

Studying $K$-shell hollow atom spectra broadens our knowledge on femtosecond phenomena in atomic physics, chemistry, and biology. Recent synchrotron measurements of the two-electron one-photon (TEOP) transitions of low-$Z$ atoms have shown discrepancies between experiment and theoretical predictions of the TEOP relative intensities and their linewidths. The discrepancies seem to be a result of an incomplete description of an atomic response to the strong perturbation due to the $K$-shell double photoionization (DPI). A theoretical attempt, based on the multiconfiguration Dirac-Fock relativistic configuration interaction method, is presented for Mg, Al, and Si atoms. It is demonstrated that both the branching ratios and the TEOP linewidths can be closely reproduced by taking into account the influences of the core and valence electron correlations, open-shell valence configuration, and the outer-shell ionization and excitation processes following the $K$-shell DPI.

The divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under infinitesimal perturbations, and characterize Pauli dynamical semigroups exhibiting such a property. We construct collision models with factorized environment particles, which realize additivity and multiplicativity of generators of CP divisible maps. A mixture of dynamical maps is obtained with the help of correlated environment. The mixture of ultimate CP divisible processes is shown to result in a class of eternal CP indivisible evolutions. We explicitly find collision models leading to weakly and essentially non-Markovian Pauli dynamical maps.

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

It was suggested that two entangled fermions can behave like a single boson and that the bosonic quality is proportional to the degree of entanglement between the two particles. The relation between bosonic quality and entanglement is quite natural if one takes into account the fact that entanglement appears in bound states of interacting systems. However, entanglement can still be present in spatially separated subsystems that no longer interact. These systems are often the subject of studies on quantum nonlocality and foundations of quantum physics. Here, we ask whether an entangled spatially separated fermionic pair can exhibit bosonic properties. We show that under certain conditions the answer to this question can be positive. In particular, we propose a nonlocal bunching scenario in which two such pairs form an analog of a two-partite bosonic Fock state.

We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such continuous-variable measurements is established in two main steps, making use of the symmetry of quantum evolution under time reversal. Namely, we first construct a twofold version of scattershot boson sampling in which, as opposed to the original proposal, both legs of a collection of two-mode squeezed vacuum states undergo parallel linear-optical transformations. This twofold scattershot model yields, as a corollary, an instance of boson sampling from Gaussian states where photon counting is hard to simulate. Then, a time-reversed setup is used to exhibit a boson sampling model in which the simulation of Gaussian measurements—namely the outcome of eight-port homodyne detection—is proven to be computationally hard. These results illustrate how the symmetry of quantum evolution under time reversal may serve as a tool for analyzing the computational complexity of novel physically motivated computational problems.

Trapped-ion quantum platforms are subject to “anomalous” heating due to interactions with electric-field noise sources of nature not yet completely known. There is ample experimental evidence that this noise originates at the surfaces of the trap electrodes, and models assuming fluctuating pointlike dipoles are consistent with observations, but the exact microscopic mechanisms behind anomalous heating remain undetermined. Here we show how a two-ion probe displays a transition in its dissipation properties, enabling experimental access to the mean orientation of the dipoles and the spatial extent of dipole-dipole correlations. This information can be used to test the validity of candidate microscopic models, which predict correlation lengths spanning several orders of magnitude. Furthermore, we propose an experiment to measure these effects with currently available traps and techniques.

We show that the interplay between spin-orbit coupling and Zeeman splitting in atomic systems can lead to the existence of bound states in the continuum (BICs) supported by trapping potentials. Such states have energies falling well within the continuum spectrum, but nevertheless they are localized and fully radiationless. We report the existence of BICs, in some cases in exact analytical form, in systems with tunable spin-orbit coupling and show that the phenomenon is physically robust. We also found that BIC states may be excited in spin-orbit-coupled Bose-Einstein condensates, where under suitable conditions they may be metastable with remarkably long lifetimes.

In his recent article [Phys. Rev. A 95, 060101(R) (2017)], Adler questions the usefulness of the bound found in our experimental search for genuine effects of hypercomplex quantum mechanics [Nat. Commun. 8, 15044 (2017)]. Our experiment was performed using a black-box (instrumentalist) approach to generalized probabilistic theories; therefore, it does not assume a priori any particular underlying mechanism. From that point of view our experimental results do indeed place meaningful bounds on the possible effects of “postquantum theories,” including quaternionic quantum mechanics. In his article, Adler compares our experiment to nonrelativistic and Möller formal scattering theories within quaternionic quantum mechanics. With a particular set of assumptions, he finds that quaternionic effects would likely not manifest themselves in general. Although these assumptions are justified in the nonrelativistic case, a proper calculation for relativistic particles is still missing. Here, we provide a concrete relativistic example of Klein-Gordon scattering wherein the quaternionic effects persist. We note that when the Klein-Gordon equation is formulated using a Hamiltonian formalism it displays a so-called “indefinite metric,” a characteristic feature of relativistic quantum wave equations. In Adler's example this is directly forbidden by his assumptions, and therefore our present example is not in contradiction to his work. In complex quantum mechanics this problem of an indefinite metric is solved in a second quantization. Unfortunately, there is no known algorithm for canonical field quantization in quaternionic quantum mechanics.

We discuss the possibility of using optical dipole forces for Sisyphus cooling of ions stored in a Penning trap by addressing the specific case of the molecular cooling candidate ${{\mathrm{C}}_2}^{-}$. Using a GPU accelerated code for Penning trap simulations, which we extended to include the molecule-light interaction, we show that this scheme can decrease the time required for cooling by an order of magnitude with respect to Doppler cooling. In our simulation we found that a reduction of the axial anion temperature from $10\mathrm{K}$ to $50\mathrm{mK}$ in around $10\mathrm{s}$ is possible. The temperature of the radial degrees of freedom was seen to thermalize to $150\mathrm{mK}$. Based on the laser-cooled ${{\mathrm{C}}_2}^{-}$, a study on the sympathetic cooling of anions with masses 1–50 nucleon was performed, covering relevant candidates for investigations of chemical anion reactions at ultracold temperatures as well as for antimatter studies.

Concentric cavities can lead to strong photon-atom coupling without a need for high finesse or small physical-cavity volume. In this proof-of-principle experiment we demonstrate coupling of single Rb atoms to an 11-mm-long near-concentric cavity with a finesse $F=138\left(2\right)$. Operating the cavity $1.7\left(1\right)\mu \mathrm{m}$ shorter than the critical length, we observe an atom-cavity coupling constant $g_0=2\pi \times 5.0\left(2\right)$ MHz which exceeds the natural dipole decay rate $\gamma$ by a factor of $g_0/\gamma =1.7\left(1\right)$.

A solution to the second measurement problem, determining what prior microscopic properties can be inferred from measurement outcomes (“pointer positions”), is worked out for projective and generalized (POVM) measurements, using consistent histories. The result supports the idea that equipment properly designed and calibrated reveals the properties it was designed to measure. Applications include Einstein's hemisphere and Wheeler's delayed choice paradoxes, and a method for analyzing weak measurements without recourse to weak values. Quantum measurements are noncontextual in the original sense employed by Bell and Mermin: if $[A,B]=[A,C]=0,[B,C]\ne 0$, the outcome of an $A$ measurement does not depend on whether it is measured with $B$ or with $C$. An application to Bohm's model of the Einstein-Podolsky-Rosen situation suggests that a faulty understanding of quantum measurements is at the root of this paradox.

We show that it is possible to use a quantum walk to find a path from one marked vertex to another. In the specific case of $M$ stars connected in a chain, one can find the path from the first star to the last one in $O\left(M\sqrt{N}\right)$ steps, where $N$ is the number of spokes of each star. First we provide an analytical result showing that by starting in a phase-modulated highly superposed initial state we can find the path in $O(M\sqrt{N}logM)$ steps. Next, we improve this efficiency by showing that the recovery of the path can also be performed by a series of successive searches when we start at the last known position and search for the next connection in $O\left(\sqrt{N}\right)$ steps leading to the overall efficiency of $O\left(M\sqrt{N}\right)$. For this result we use the analytical solution that can be obtained for a ring of stars of double the length of the chain.

The fragmentation dynamics of an endohedral fullerene, $\mathrm{S}{\mathrm{c}}_3\mathrm{N}@{\mathrm{C}}_{80}$, after absorption of a soft-x-ray photon, has been studied with an ion-ion-coincidence momentum-imaging technique. Molecular inner-shell ionization at 406.5 eV, targeting the Sc ($2p$) shell of the encapsulated $\mathrm{S}{\mathrm{c}}_3\mathrm{N}$ moiety and the C ($1s$) shell of the ${\mathrm{C}}_{80}$ cage, leads to the cage fragmentation through evaporation of ${\mathrm{C}}_2$, emission of small molecular carbon ions (${\mathrm{C}}_n{}^{+}$, $n\le 24$), and release of Sc and Sc-containing ions associated with the carbon cage opening or fragmentation. The predominant charge states of Sc and Sc-containing ionic fragments are $+1$ despite an effective Sc valence of 2.4, indicating that charge transfer or redistribution plays an important role in the fragmentation of the encaged $\mathrm{S}{\mathrm{c}}_3\mathrm{N}$. Sequential emission of two out of the three Sc atoms of the encaged moiety, via Coulomb explosion in the form of $\mathrm{S}{\mathrm{c}}^{+}$ or Sc-containing ions, is significant. We also find that the resonant excitation of the Sc ($2p$) shell electrons significantly increased the yield of the parent $\mathrm{S}{\mathrm{c}}_3\mathrm{N}@{\mathrm{C}}_{80}$ and its fragment ions, partially attributed to the collision of the energetic Auger electrons from the Sc site with the carbon cage.

This paper introduces a model for a few repulsively interacting particles trapped in a one-dimensional harmonic well and provides exact solutions for the three-particle case. This model is a hybrid of two other well-known systems, the Calogero model and the contact-interaction model, and coincides with them in limiting cases. However, those models have purely two-body interactions whereas this model has intrinsically few-body interactions. Comparing these three models provides clarifying distinctions among the properties of symmetry, separability, and integrability. The model's analytic solutions provide a useful basis to improve approximation schemes, especially near the unitary limit of hard-core contact interactions.

We present a time-dependent density-matrix renormalization group investigation of the quantum distillation process within the Fermi-Hubbard model on a quasi-one-dimensional ladder geometry. The term distillation refers to the dynamical, spatial separation of singlons and doublons in the sudden expansion of interacting particles in an optical lattice, i.e., the release of a cloud of atoms from a trapping potential. Remarkably, quantum distillation can lead to a contraction of the doublon cloud, resulting in an increased density of the doublons in the core region compared to the initial state. As a main result, we show that this phenomenon is not limited to chains that were previously studied. Interestingly, there are additional dynamical processes on the two-leg ladder such as density oscillations and self-trapping of defects that lead to a less efficient distillation process. An investigation of the time evolution starting from product states provides an explanation for this behavior. Initial product states are also considered since in optical lattice experiments, such states are often used as the initial setup. We propose configurations that lead to a fast and efficient quantum distillation.

We present a numerical study of the dynamic response of a confined superfluid Fermi gas to a rapid change of the scattering length (i.e., an interaction quench). Based on a fully microscopic time-dependent density-matrix approach within the full Bogoliubov–de Gennes formalism that includes a 3D harmonic confinement we simulate and identify the emergence of a Goldstone mode of the BCS gap in a cigar-shaped ${}^6\mathrm{Li}$ gas. By analyzing this Goldstone mode over a wide range of parameters, we show that its excitation spectrum is gapless and that its main frequency is not fixed by the trapping potential but that it is determined by the details of the quench. Thus we report the emergence of a pure Goldstone mode of the BCS gap that—in contrast to situations in many previous studies—maintains its gapless excitation spectrum predicted by the Goldstone theorem. Furthermore, we observe that the size-dependent superfluid resonances resulting from the atypical BCS-BEC crossover have a direct impact on this Goldstone mode. Finally, we find that the interaction quench-induced Goldstone mode leads to a low-frequency in-phase oscillation of the single-particle occupations with complete inversion of the lowest-lying single-particle states which could provide a convenient experimental access to the pure gapless Goldstone mode.

Coherent intense attosecond x-ray pulses could lead to a fast dynamical imaging of biological macromolecules and other material nanostructures with a unique combination of a record high temporal and spatial resolution. Plasma-based x-ray laser sources are capable of producing high-energy x-ray pulses but with relatively long picosecond duration. The sources based on high-harmonic generation (HHG) of a laser field allow one to produce much shorter pulses but of lower energy. We suggest two different paths towards intense subfemtosecond x-ray sources: (i) via efficient transformation of the picosecond radiation of the x-ray plasma lasers into the trains of subfemtosecond pulses in a resonantly absorbing medium, and (ii) via amplification of HHG radiation in the active medium of the x-ray plasma lasers. We show that essentially the same technique can be used for realization of both paths. This technique is a modulation of the parameters of the resonant transition (accordingly in absorbing or amplifying medium) produced under the action of a sufficiently strong infrared or optical field. We propose experimental realization of the suggested technique in the passive and/or active media of (i) Li iii ions modulated by the mid-IR laser field and (ii) C vi ions modulated by the optical laser radiation.

We investigate the occurrence of a phase transition, characterized by the spontaneous breaking of a discrete symmetry, in a driven-dissipative Bose-Hubbard lattice in the presence of two-photon coherent driving. The driving term does not lift the original $\text{U}\left(1\right)$ symmetry completely and a discrete ${\mathbb{Z}}_2$ symmetry is left. When driving the bottom of the Bose-Hubbard band, a mean-field analysis of the steady state reveals a second-order transition from a symmetric phase to a quasicoherent state with a finite expectation value of the Bose field. For larger driving frequency, the phase diagram shows a third region, where both phases are stable and the transition becomes of first order.