Geometric phase is an indispensable element for achieving robust and high-fidelity quantum gates due to its built-in noise-resilience feature. However, due to the complexity of manipulation and the intrinsic leakage of the encoded quantum information to a non-logical-qubit basis, the experimental realization of universal nonadiabatic holonomic quantum computation is very difficult. Here we propose to implement scalable nonadiabatic holonomic quantum computation with a decoherence-free subspace encoding on a two-dimensional square superconducting transmon-qubit lattice, where only the two-body interaction of neighboring qubits, from the simplest capacitive coupling, is needed. Meanwhile, we introduce qubit-frequency driving to achieve tunable resonant coupling for the neighboring transmon qubits, and thus avoid the leakage problem. In addition, our presented numerical simulation shows that high-fidelity quantum gates can be obtained, verifying the advantages of the robustness and scalability of our scheme. Therefore, our scheme provides a promising way towards the physical implementation of robust and scalable quantum computation.

It is known that noisy topological quantum codes are related to random-bond Ising models where the order-disorder phase transition in the classical model is mapped to the error threshold of the corresponding topological code. On the other hand, there is a dual mapping between classical spin models and quantum Calderbank-Shor-Steane (CSS) states where the partition function of a classical model defined on a hypergraph $H$ is written as an inner product of a product state and a CSS state on dual hypergraph $\tilde{H}$. It is then interesting to see what the interpretation is of the classical phase transition in the random-bond Ising model within the framework of the above duality, and whether such an interpretation has any connection to the error threshold of the corresponding topological CSS code. In this paper, we consider the above duality relation specifically for a two-dimensional random-bond Ising model. We show that the order parameter of this classical system is mapped to a coherence order parameter in a noisy Toric code model. In particular, a quantum phase transition from a coherent phase to a noncoherent phase occurs when the initial coherent state is affected by two sequences of bit-flip quantum channels where a quenched disorder is induced by measurement of the errors after the first channel. On the other hand, the above transition is directly related to the error threshold of the Toric code model. Accordingly, and since the noisy process can be applied to other topological CSS states, we conclude that the dual correspondence can also provide a useful tool for the study of error thresholds in different topological CSS codes.

We propose a Wigner-like inequality suitable for testing the hypothesis of realism. We show that this inequality is identical neither to the well-known Wigner inequality nor to the Leggett-Garg inequality in Wigner form. The obtained inequality is suitable for testing realism not only in quantum mechanical systems, but also in quantum field systems. Also we propose a mathematically consistent derivation of the Leggett-Garg inequality in Wigner form, which was recently presented in the literature, for three and $n$ distinct moments of time. Contrary to these works, our rigor derivation uses Kolmogorov axiomatics of probability theory. We pay special attention to the construction and studies of the spaces of elementary outcomes. Based on the Leggett-Garg inequality in Wigner form for $n$ distinct moments of time we prove that any unitary evolution of a quantum system contradicts the concept of macroscopic realism. We show that application of the concept of macroscopic realism to any quantum system leads to “freezing” of the system in the initial state. It is shown that for a particle with an infinite number of observables the probability to find a pair of the observables in some defined state is zero, even if the operators of these observables commute. This fact might serve as an additional logical argument for the contradiction between quantum theory and classical realism.

A fully relativistic approach to evaluating the correlation effects in highly charged ions is presented. The interelectronic-interaction contributions of first and second orders in $1/Z$ are treated rigorously within the framework of bound-state quantum electrodynamics, whereas the calculations of the third- and higher-order contributions are based on the Dirac-Coulomb-Breit Hamiltonian. The developed approach allows one to deal with single as well as degenerate or quasidegenerate states. We apply this approach to the calculations of the correlation contributions to the $n=1$ and $n=2$ energy levels in heliumlike ions. The obtained contributions are combined with the one-electron QED, screened QED, nuclear recoil, and nuclear polarization corrections to get the total theoretical predictions for the ionization and transition energies in high-$Z$ heliumlike ions.

The alignment parameter $A_{20}$ of ${}_{73}\mathrm{Ta}, {}_{74}\mathrm{W}$, and ${}_{79}\mathrm{Au}$ ions after $L_3$ subshell ionization by electron impact has been determined experimentally and theoretically in the wide energy range $(1.02–10.2)E_{L_3}$, where $E_{L_3}$ is the $L_3$ ionization threshold. The $A_{20}$ values have been deduced from measurements of the $L\ell$ ($L_3\to M_1$), $L{\alpha }_2$ ($L_3\to M_4$), and $L{\alpha }_1$ ($L_3\to M_5$) x-ray angular distributions using thin targets. The beam energies have been selected above the threshold energy of each $L$ subshell in order to also investigate the influence of the Coster-Kronig transitions on the anisotropy of x-ray emission. The results provide a clear indication of alignment and agree with calculations carried out within the plane-wave Born approximation up to about $6E_{L_3}$, but an unpredicted inversion in the sign of $A_{20}$ is observed above this energy.

In this paper, the dynamics of an unbalanced two-ion crystal comprising the “target” and the “sensor” ions confined in a Penning trap along the magnetic-field axis has been studied. First, the low amplitude regime is addressed. In this regime, the overall potential including the Coulomb repulsion between the ions can be considered harmonic and the axial, magnetron, and reduced-cyclotron modes split up into the so-called stretch and common modes, that are generalizations of the well-known “breathing” and “center-of-mass” motions of a balanced crystal made of two ions. By using optical detection to measure the frequencies of the modes of the crystal, and of the sensor ion on its own, in the quantum regime of motion, it will be possible to determine the target ion's free-cyclotron frequency. The nonharmonicity of the Coulomb interaction is also discussed since this causes large systematic effects, which are minimized due to the high sensitivity of the optical detection method when the crystal is cooled to the ground state of motion in the Penning trap.

Recent experiments [D. Pengel, S. Kerbstadt, L. Englert, T. Bayer, and M. Wollenhaupt, Phys. Rev. A 96 043426 (2017)] have measured the photoelectron momentum distribution for three-photon ionization of potassium by counter-rotating circularly polarized 790-nm laser pulses. The distribution displays spiral vortices, arising from the interference of ionizing wave packets with different magnetic quantum numbers. The high level of multidimensional detail observed in the distribution makes this an ideal case in which to demonstrate the accuracy of emerging theoretical techniques applicable to such problems. We use the $R$-matrix with time dependence approach to investigate this process. We calculate the full-dimensional photoelectron momentum distribution, and compare against a set of planar projections of this distribution previously measured in experiment.

We investigate a generic dynamical theory to characterize by quantum quenches the topological quantum phases defined for the equilibrium ground state and study the emergent topology of quantum dynamics when the quenches start from a deep trivial (far from the phase boundary) or shallow trivial (close to the phase boundary) phase to topological regimes. Two dynamical schemes are examined: One is to characterize topological phases via quantum dynamics induced by a single quench along an arbitrary axis of (pseudo)spin polarization, and the other applies a set of quenches with respect to all (pseudo)spin axes. These two schemes are both built on the so-called dynamical bulk-surface correspondence, which shows that the $d$-dimensional ($d\mathrm{D}$) topological phases with integer invariants can be characterized by the dynamical topological pattern emerging on particular $(d-1)\mathrm{D}$ momentum subspaces called band inversion surfaces (BISs). We show that the first dynamical scheme works for both deep and shallow quenches, while for the second scheme, an emergent topological transition, associated with topological charges crossing BISs, is predicted in the joint quench dynamics. A generic criterion for the emergent transition is precisely obtained. Above the criterion (deep quench regime), quantum dynamics on BISs can directly characterize the topology of the postquench Hamiltonian. Below the criterion (shallow quench regime), the quench dynamics may depict a new dynamical topology; the postquench topology can be characterized by the emergent topological invariant plus the total charges moving outside the region enclosed by BISs. We illustrate our results by numerically calculating the 2D quantum anomalous Hall model, which has been realized in ultracold atoms. This work broadens the way to classify topological phases by nonequilibrium quantum dynamics and is feasible for experimental realization.

We investigate the Lipkin-Meshkov-Glick model coupled to a thermal bath. Since the isolated model itself exhibits a quantum phase transition, we explore the critical signatures of the open system. Starting from a system-reservoir interaction written in positive-definite form, we find that the position of the critical point remains unchanged, in contrast to the popular mean-field prediction. Technically, we employ the polaron transform to be able to study the full crossover regime from the normal to the symmetry-broken phase, which allows us to investigate the fate of quantum-critical points subject to dissipative environments. The signatures of the phase transition are reflected in observables such as magnetization, stationary mode occupation, or waiting-time distributions.

We demonstrate that radiation pressure force fields can be measured and reconstructed with a resolution of 0.3 fN (at a $99.7\%$ confidence level) using an ergodic ensemble of overdamped colloidal particles. The outstanding force resolution level is provided by the large size of the statistical ensemble built by recording all displacements from all diffusing particles, regardless of trajectory and time. This is only possible because the noise driving the particles is thermal, white, and stationary, so that the colloidal system is ergodic, as we carefully verify. Using an ergodic colloidal dispersion for performing ultrasensitive measurements of external forces is not limited to nonconservative optical force fields. Our experiments therefore give way to interesting opportunities in the context of weak force measurements in fluids.

We theoretically study the quantum-interference-induced photon blockade and antiblockade phenomenon in an atom-cavity QED system, where the destructive [constructive] interference between two different transition pathways prohibits [enhances] two-photon excitation. To begin with, we study a single-atom–cavity QED system where the atom or cavity is driven by a coherent pump field. We show that the cavity-driven case will lead to the quantum-interference-induced photon blockade under a specific condition, but such an interference-induced photon blockade cannot be realized in the atom-driven case. This is an important consequence of the pathways possible for the two types of drives. Then, we investigate the two-atom case, and find that an additional transition pathway appears in the atom-driven case. We show that this additional transition pathway results in the quantum-interference-induced photon blockade only when the atomic resonant frequency is different from the cavity mode frequency otherwise antiblockade occurs. Moreover, in this case, the condition for realizing the interference-induced photon blockade is independent of the system's intrinsic parameters, which can be used to generate antibunched photons in both weak and strong coupling regimes.

Quantum correlations become formidable tools for beating classical capacities of measurement. Preserving these advantages in practical systems, where experimental imperfections are unavoidable, is a challenge of the utmost importance. Here we propose and realize a quantum ghost imaging protocol stemming from the differential ghost imaging, a scheme elaborated so far in the limit of bright thermal light, particularly suitable in the relevant case of faint or sparse objects. The extension toward the quantum regime represents an important step as quantum correlations allow low-brightness imaging, desirable for reducing the absorption dose. Furthermore, we optimize the protocol in terms of signal-to-noise ratio, to compensate for the detrimental effects of detection noise and losses. We perform the experiment using spontaneous parametric down conversion light in a microscope configuration. The image is reconstructed exploiting nonclassical intensity correlation in the low photon flux regime, rather than photon pairs detection coincidences. On the one side, we validate the theoretical model and on the other we show the applicability of this technique by imaging biological samples.

We demonstrate a transversely polarized spin-exchange pumped noble gas comagnetometer which suppresses systematic errors from longitudinal polarization. Rb atoms as well as ${}^{131}\mathrm{Xe}$ and ${}^{129}\mathrm{Xe}$ nuclei are simultaneously polarized perpendicular to a pulsed bias field. Both Xe isotopes' nuclear magnetic resonance conditions are simultaneously satisfied by frequency modulation of the pulse repetition rate. The Rb atoms detect the Xe precession. We highlight the importance of magnetometer phase shifts when performing comagnetometry. For detection of nonmagnetic spin-dependent interactions the sensing bandwidth is 1 Hz, the white-noise level is $7\mu \mathrm{Hz}/\sqrt{\text{Hz}}$, and the bias instability is $\sim 1$ $\mu \mathrm{Hz}$.

In contrast with the three-dimensional result, the Beth-Uhlenbeck (BU) formula in one dimension contains an extra $-1/2$ term. The origin of this $-1/2$ term is explained using a spectral density approach. To be explicit, a $\delta$-function potential is used to show that the correction term arises from a pole of the density of states at zero energy. The spectral density method shows that this term is actually an artifact of the non-normalizability of the scattering states and an infrared cutoff regularization scheme has to be used to get the correct result in one dimension. The formal derivation of the BU formula would miss this term since it ignores the effects of the boundary terms. While the result is shown for the $\delta$-function potential, the method and result are valid for more general potentials. Additionally, the one-dimensional Levinson theorem can be extracted from the spectral density method using the asymptotic form of general potentials. The importance of the result lies in the fact that all these correction terms in one dimension have a universal source: a pole at zero energy. Similar calculations using quantum field-theoretical approaches (without explicit infrared cutoff regularization schemes) also show the same subtleties with the correction term originating from the zero energy scattering states (Appendix A).

In this paper, we explore the possibilities of realizing weak value amplification (WVA) using purely atomic degrees of freedom. Our scheme identifies the internal electronic states and external motional states of a single trapped ${}^{40}\mathrm{Ca}^{+}$ ion as the system degree and pointer degree, respectively, and their controllable weak coupling is provided by a bichromatic light field. In our experimental demonstration, by performing appropriate postselection on the internal states, a position displacement of $\sim 4\AA$ (in phase space) of the trapped ion is amplified to $\sim 10$ nm. The sensitivity of the amplification effect to the relative phase of the quantum state is also demonstrated. The high operational flexibility of this procedure allows fully exploration of the peculiarities of WVA.

We study the protocol of qudit teleportation using quantum systems subjected to several kinds of noise for arbitrary dimensionality $d$. We consider four classes of noise: dit-flip, $d$-phase-flip, dit-phase-flip, and depolarizing noise, each of them corresponding to a family of Weyl operators, introduced via Kraus formalism. We derive a general expression for the average fidelity of teleportation in arbitrary dimension $d$ for any combination of noise on the involved qudits. Under a different approach we derive the average fidelity of teleportation for a more general scenario involving the $d$-dimensional generalization of amplitude damping noise as well. We show that all possible scenarios may be classified in four different behaviors and discuss the cases in which it is possible to improve the fidelity by increasing the associated noise fractions. All our results are in agreement with previous analysis for the case of qubits [R. Fortes and G. Rigolin, Phys. Rev. A 92, 012338 (2015)].

The planned measurement of optical resonances in singly ionized lawrencium $(Z=103)$ requires accurate theoretical predictions to narrow the search window. We present high-precision, ab initio calculations of the electronic spectra of ${\mathrm{Lr}}^{+}$ and its lighter homologue lutetium $(Z=71)$. We have employed the state-of-the-art relativistic Fock space coupled cluster approach as well as the configuration interaction with many-body perturbation theory $(\mathrm{CI}+\mathrm{MBPT})$ method to calculate atomic energy levels, g factors, and transition amplitudes and branching ratios. Our calculations are in close agreement with experimentally measured energy levels and transition strengths for the homologue ${\mathrm{Lu}}^{+}$, and are well converged for ${\mathrm{Lr}}^{+}$, where we expect a similar level of accuracy. These results present large-scale, systematic calculations of ${\mathrm{Lr}}^{+}$ and will serve to guide future experimental studies of this ion.

The motion of neutral, polarizable atoms (also called neutral particles in this work) in the field of the Bessel beam is considered. It is shown in the numerical way that the Bessel rings, i.e., the regions of high energy concentration, can trap particles of positive polarizability (atoms in red-detuned beams). This trapping occurs only in the plane perpendicular to the wave propagation, and the motion along the beam is unrestricted. When the beam is superposed with the plane wave of the same frequency propagating in the same direction, the particles are guided along helices, fixed in space. The shape of these helices depends on the parameters characterizing the electromagnetic fields but not on the initial state of guided particles. Depending on the vorticity of the Bessel beam, these helices can be made left- or right-handed. In the special case of zero vorticity, the helices are degenerated to the true, three-dimensional rings, which can serve as three-dimensional traps. The emerging structure of potential valleys can be applied to parallel guidance or capture several independent atoms, each in its own trap.

We experimentally investigate strong-field dissociative Rydberg excitation (DRE) of ${\mathrm{O}}_2$ molecules by using the photoelectron photoion coincidence spectrum, in which the outgoing neutral Rydberg fragments created by the strong laser fields are postionized by the weak static dc field of the spectrometer and afterwards detected as charged particles. The peak positions of the sum-kinetic energy release (KER) spectrum of the ejected nuclear fragments and electrons of the dissociative single ionization (DSI) channel are measured to be similar to that of the DRE channel, although their nuclear KER spectra are distinct. It indicates that the same number of photons is absorbed by the molecule in accessing the DRE and DSI channels, which are partitioned by the electron and nuclear fragments with various proportions. Different pathways towards the DRE and DSI channels are discussed based on the correlated dynamics of the nuclear fragments and electrons. Our results show that the DRE channel observed here is mostly accessed by the multiphoton resonance excitation process.

We investigate experimentally the possibility of enhancing the production of $2{}^{3}S$ positronium atoms by driving the $1{}^{3}S$–$3{}^{3}P$ and $3{}^{3}P$–$2{}^{3}S$ transitions, overcoming the natural branching ratio limitation of spontaneous decay from $3{}^{3}P$ to $2{}^{3}S$. The decay of $3{}^{3}P$ positronium atoms toward the $2{}^{3}S$ level has been efficiently stimulated by a 1312.2 nm broadband IR laser pulse. The dependence of the stimulating transition efficiency on the intensity of the IR pulse has been measured to find the optimal enhancement conditions. A maximum relative increase of $\times (3.1\pm 1.0)$ in the $2{}^{3}S$ production efficiency, with respect to the case in which only spontaneous decay is present, was obtained.