The defining characteristic of an exceptional point (EP) in the parameter space of a family of operators is that, upon encircling the EP, eigenstates are permuted. When one encircles multiple EPs, the question arises how to properly compose the effects of the individual EPs. This was thought to be ambiguous. We show that one can solve this problem by considering based loops and their deformations. The theory of fundamental groups allows us to generalize this technique to arbitrary degeneracy structures like exceptional lines in a three-dimensional parameter space. As permutations of three or more objects form a non-Abelian group, the next question that arises is whether one can experimentally demonstrate this noncommutative behavior. This requires at least two EPs of a family of operators that have at least three eigenstates. A concrete implementation in a recently proposed $\mathcal{PT}$ symmetric waveguide system is suggested as an example of how to experimentally check the composition law and show the non-Abelian nature of non-Hermitian systems with multiple EPs.

Quantum control of phonons has become a focus of attention for developing quantum technologies. Here, we present a proposal to realize phonon blockade in a quadratically coupled optomechanical system, where a strong nonlinear interaction between photons and phonons can be induced by an external field coherently driving the cavity and the effective coupling strength is tunable by adjusting the amplitude of the driving field. This optically induced nonlinearity is different from standard methods for the realization of phonon blockade, where the nonlinearity is achieved by coupling the mechanical system to superconducting qubits. We both analytically and numerically study the phonon statistical properties via the steady-state solution of the second-order correlation function and find phonon blockade can be efficiently realized for a large cooperativity of the system, which is achievable based on the optically enhanced nonlinear coupling and high quality mechanical system.

We experimentally investigate the unitarity-limited behavior of the three-body loss near a $p$-wave Feshbach resonance in a single-component Fermi gas of ${}^6\mathrm{Li}$ atoms. At the unitarity limit, the three-body loss coefficient $L_3$ exhibits universality in the sense that it is independent of the interaction strength and follows the predicted temperature scaling law of $L_3\propto T^{-2}$. When decreasing the interaction strength from the unitarity regime, the three-body loss coefficient as a function of the interaction strength and temperature can be described by the theory based on the association of an excited resonant quasibound state and its relaxation into a deep stable dimer by collision with a third atom in the framework of the standard Breit-Wigner theoretical approach. The results reported here are important to understand the properties of a resonant $p$-wave Fermi gas in the prospect of quantum few- and many-body physics.

The interaction of a two-level system (TLS) with a single bosonic mode (BM) is one of the most fundamental processes in quantum optics. Microscopically, it is described by the quantum Rabi model (QRM). Here we propose a versatile implementation of this model based on single trapped cold atoms. Assuming realistic experimental conditions, we show that our approach is not restricted to the Jaynes-Cummings regime but also allows exploring the regimes of ultrastrong coupling, deep strong coupling, and dispersive deep strong coupling. In contrast to most other QRM platforms, all important system parameters, i.e., the emitter-field detuning and the coupling strength of the emitter to the mode, can be dynamically tuned over a wide range. The quantum state of the BM and the TLS can be prepared and read-out using standard cold-atom techniques, enabling the study of the QRM and its dynamics with unprecedented control. Our scheme implements the TLS using atomic Zeeman states, while the atom's vibrational states in the trap represent the BM. The coupling is mediated by a suitable fictitious magnetic field pattern. Finally, we show that our scheme also enables the implementation of important generalizations, namely, the driven QRM, the QRM with quadratic coupling, or the Dicke model.

It has long been recognized that certain quantum correlations are incompatible with a particular assumption about classical causal structure. Given a causal structure of unknown classicality, the presence of such correlations certifies the nonclassical nature of the causal structure in a device-independent fashion. In structures where all parties share a common resource, these nonclassical correlations are also known as nonlocal correlations. Any constraint satisfied by all correlations which are classically compatible with a given causal structure defines a causal compatibility criterion. Such criteria were recently derived for the triangle structure (E. Wolfe et al., arXiv:1609.00672) in the form of polynomial inequalities, begging the question of whether any of those inequalities admit violation by quantum correlations. Numerical investigation suggests that they do not, and we further conjecture that the set of correlations admitted by the classical triangle structure is equivalent to the set of correlations admitted by its quantum generalization whenever the three observable variables are binary. Our main contribution in this work, however, is the derivation of causal compatibility inequalities for the triangle structure which do admit quantum violation. This provides a robust-to-noise witness of quantum correlations in the triangle structure. We conclude by considering the possibility of quantum resources potentially qualitatively different from those known previously.

We investigate the qubit in the hierarchical environment where the first layer is just one lossy cavity while the second layer is the $N$-coupled lossy cavities. In the weak-coupling regime between the qubit and the first-layer environment, the dynamics crossovers from Markovian to non-Markovian and from no-speedup to speedup can be realized by controlling the hierarchical environment. We find that the coupling strength between two nearest-neighbor cavities and the number of cavities in the second-layer environment have the opposite effect on the non-Markovian dynamics and speedup evolution of the qubit. However, in the case of strong coupling between the qubit and the first-layer environment, we can be surprised to find that, compared with the original non-Markovian dynamics, the added second-layer environment cannot play a beneficial role on the speedup of the dynamics of the system. In addition, a phenomenon can be noticed that the complete opposite role of the coupling strength between two nearest-neighbor cavities (the number of cavities) in the second-layer environment in the above weak- and strong-coupling regimes.

We studied the change of the nonlocal correlation of the entanglement in Rindler space-time by showing that the Unruh effect can be interpreted as a noisy quantum channel having a complete positive and trace preserving map with an “operator sum representation.” It is shown that the entanglement fidelity is obtained in analytic form from the operator sum representation, which agrees well numerically with the entanglement monotone and the entanglement measure obtained previously. Nonzero entropy exchange between the system $Q$ and region II of the Rindler wedge indicates the nonlocal correlation between causally disconnected regions. We have also shown the subadditivity of entropies numerically.

We study the prospects of using transitions from the ytterbium ground state to metastable states ${}^{3}P_2^{\mathrm{o}}$ at $E=19710.388{\mathrm{cm}}^{-1}$ and $4f^{13}5d6s^2(J=2)$ at $E=23188.518{\mathrm{cm}}^{-1}$ as clock transitions in an optical lattice clock. Having more than one clock transition in Yb could benefit the search for new physics beyond the Standard Model via studying the nonlinearity of King's plot or the time variation of the ratio of the frequencies of two clock transitions. We calculate the lifetime of the states, relevant transition amplitudes, systematic shifts, and the sensitivities of the clock transitions to a variation of the fine-structure constant and to the gravitational potential. We find that both transitions can probably support high accuracy, approaching what is already achieved for the ${}^{1}S_0-{}^{3}P_0^{\mathrm{o}}$ clock transition.

We study far- and near-field magnetic and electric multipole moments induced in the ground state of the Dirac one-electron atom placed in a weak $2^L$-pole magnetostatic field. The analysis is carried out within the framework of the first-order Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997);J. Phys. B 30, 2747(E) (1997)]. Closed-form analytical expressions for multipole magnetizabilities ${\chi }_L$, magnetic nuclear shielding constants ${\sigma }_{\mathrm{M}L\to \mathrm{M}L}$, the far-field magnetic-to-electric cross-susceptibilities ${\chi }_{\mathrm{M}L\to \mathrm{E}(L\mp 1)}$, and the near-field counterparts ${\sigma }_{\mathrm{M}L\to \mathrm{E}(L\mp 1)}$ of the latter are derived. The formulas obtained for ${\chi }_L$ and ${\sigma }_{\mathrm{M}L\to \mathrm{M}L}$ are much simpler than those available in the literature. We establish the relationship ${\chi }_{\mathrm{M}L\to \mathrm{E}(L\mp 1)}={\alpha }_{\mathrm{E}(L\mp 1)\to \mathrm{M}L}$, where ${\alpha }_{\mathrm{E}(L\mp 1)\to \mathrm{M}L}$ are the multipole far-field electric-to-magnetic susceptibilities discussed in our previous paper [Szmytkowski and Łukasik, Phys. Rev. A 93, 062502 (2016)]. It is also found that when the atom is placed in superimposed weak and static electric and magnetic fields of respective multipolarities $2^{L_1}$ and $2^{L_2}$, such that $L_1=L_2\mp 1$, then the second-order correction to the ground-state energy contains an additional term entangling both fields and involving the cross-susceptibility ${\alpha }_{\mathrm{E}{L}_1\to \mathrm{M}{L}_2}={\chi }_{\mathrm{M}{L}_2\to \mathrm{E}{L}_1}$.

Atomic or molecular assemblies irradiated with intense hard x-ray pulses, such as those emitted from x-ray free-electron lasers (XFELs), are subject to a strong ionization, which also releases electrons from atomic inner shells. The resulting core-hole states relax via various channels, including fluorescence and Auger decay. The latter is the predominant relaxation channel for light elements and typically occurs on a time scale of 1–10 fs. In dense samples, the core-hole ions may already undergo electron-impact ionizations during this time due to the abundance of highly energetic photoelectrons and Auger electrons. In this study we perform an ab initio calculation of the electron-impact-ionization cross sections of ions with an arbitrary electronic configuration at zero temperature. This allows us to evaluate and compare impact-ionization cross sections for ions in ground and “exotic” electronic states (e.g., with a few core holes), which may be formed during their interaction with intense x-ray pulses. We show that the impact-ionization cross sections for ions of the same charge, but with varying electronic configurations, may significantly differ. This finding has to be taken into account in any modeling tool treating the relaxation of atoms after high-energy-impact collision, e.g., simulations dedicated for coherent x-ray diffraction imaging of nanocrystals and single biological macromolecules, or laser-created plasma studies. Our computationally efficient ab initio calculation scheme can be easily incorporated in such simulation schemes.

Synthetic fields applied to ultracold quantum gases can realize topological phases that transcend conventional Bose and Fermi-liquid paradigms. Raman laser beams in particular are under scrutiny as a route to create synthetic fields in neutral gases to mimic ordinary magnetic and electric fields acting on charged matter. Yet external laser beams can impose heating and losses that make cooling into many-body topological phases challenging. We propose that atomic or molecular dipoles placed in optical lattices can realize a topological phase without synthetic fields by placing them in certain frustrated lattices. We use numerical modeling on a specific example to show that the interactions between dipolar fermions placed in a kagome optical lattice spontaneously break time-reversal symmetry to lead to a topological Mott insulator, a chiral topological phase generated entirely by interactions. We estimate realistic entropy and trapping parameters to argue that this intriguing phase of matter can be probed with quantum gases using a combination of recently implemented technologies.

The process of coherent x-ray emission by an ultrarelativistic electron crossing a system of two targets, thick amorphous upstream and ultrathin crystalline downstream, is considered. It is shown that transformation of the electromagnetic field around the particle after its emission from the upstream target influences upon characteristics of radiation produced by the electron in the downstream target. The considered radiation is an interfering sum of parametric x-ray radiation and diffracted transition radiation. It is demonstrated that in the present case the properties of the x-ray pulse differ both from the ones typical for thick and ultrathin crystals and depend on the distance between the targets. At multi-GeV electron energies, such dependence is observable within macroscopically large values of this distance. Special attention is drawn to the study of the influence of the downstream target finiteness on radiation characteristics. It is shown that it results in the dependence of radiation yield on separation between the targets for macroscopically large values of such separation even at sub-GeV electron energies.

We theoretically investigate the transport properties of a weak coherent input field scattered by an ensemble of $\mathrm{\Lambda }$-type atoms coupled to a one-dimensional photonic crystal waveguide. In our model, the atoms are randomly located in the lattice along the crystal axis. We analyze the transmission spectrum mediated by the tunable long-range atomic interactions and observe the highest-energy dip. The results show that the highest-energy dip location is associated with the number of the atoms, which provides an accurate measuring tool for the emitter-waveguide system. We also quantify the influence of a Gaussian inhomogeneous broadening and the dephasing on the transmission spectrum, concluding that the highest-energy dip is immune to both the inhomogeneous broadening and the dephasing. Furthermore, we study photon-photon correlations of the reflected field and observe quantum beats. With tremendous progress in coupling atoms to photonic crystal waveguides, our results may be experimentally realizable in the near future.

We propose a method to deterministically prepare a desired quantum state in a one-dimensional (1D) continuum by a shaped photon pulse. This method is based on time reversal of the quantum emission process. We show that the desired quantum state such as a Dicke or timed Dicke state can be successfully prepared with very high fidelity even if the dissipation to the environment is non-negligible and the pulse shaping is not perfect. We also show that large quantum entanglement between emitters can be created by just a single-photon pulse. This method is experimentally feasible in a 1D waveguide QED or a circuit QED system.

We propose that the ground term transition, $2p^5{}^{2}P_{3/2}-{}^{2}P_{1/2}$, for ions in the F-like isoelectronic sequence could be used to accurately test current methods to compute Breit and quantum-electrodynamic (QED) effects. These systems are of interest since correlation is small due to what we will label Layzer quenching. Using the multiconfiguration Dirac-Hartee-Fock method, we investigate how correlation, Breit and QED corrections vary along the sequence and show that QED dominates over correlation already for $Z\approx 20$. We also investigate the behavior of different QED effects as a function of the nuclear charge and find that the self-energy dominates for the mid-$Z$ range (40–80), but then decreases to change sign for $Z\approx 90$. For a few elements between $Z=85$ and 90 the vacuum polarization is the leading term, while for higher $Z$ the two QED contributions cancel. This opens up the possibility for these ions to carefully test the frequency-dependent transverse photon correction. The uncertainties of the treatment of the well-understood frequency-independent Breit correction and correlation are expected to be at least three orders of magnitude smaller than the QED and frequency-dependent transverse photon corrections for high $Z$. In this work we also compare and evaluate the results from three different methods to compute self-energies.

Interatomic Coulombic electron capture (ICEC) is an environment-assisted process in which a free electron can efficiently attach to an ion, atom or molecule by transferring the excess energy to a neighboring species. Absolute cross sections are necessary to evaluate the relative importance of this process. In this work, we employ the $R$-matrix method to compute ab initio these cross sections for a singly charged neon ion embedded in small helium clusters. Our results show that the ICEC cross sections are several orders of magnitude higher than anticipated and dominate other competing processes. Electron energy loss spectra on an absolute scale are provided for the ${\mathrm{Ne}}^{+}$@${\mathrm{He}}_{20}$ cluster. Such spectra exhibit an unambiguous signature of the ICEC process. The finding is expected to stimulate experimental observations.

When a photon is detected after passing through an interferometer one might wonder which path it took, and a meaningful answer can only be given if one has the means of monitoring the photon's whereabouts. We report the realization of a single-photon experiment for a two-path interferometer with path marking. In this experiment, the path of a photon (“signal”) through a Mach-Zehnder interferometer becomes known by unambiguous discrimination between the two paths. We encode the signal path in the polarization state of a partner photon (“idler”) whose polarization is examined by a three-outcome measurement: one outcome each for the two signal paths plus an inconclusive outcome. Our results agree fully with the theoretical predictions from a common-sense analysis of what can be said about the past of a quantum particle: The signals for which we get the inconclusive result have full interference strength, as their paths through the interferometer cannot be known; and every photon that emerges from the dark output port of the balanced interferometer has a known path.

The stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with increasing $N$ the system approaches a deterministic limit, indicating self-averaging with respect to its temporal unitary evolution. This phenomenon is quantified by the variance of the unitary matrix governing the time evolution of a finite-dimensional quantum system which, according to an asymptotic analysis, decreases at least as $1/N$. For a special class of protocols (when the averaged Hamiltonian commutes at different times), we prove that for finite $N$ the distance (according to the Frobenius norm) between the averaged evolution unitary operator generated by the Hamiltonian $H$ and the unitary evolution operator generated by the averaged Hamiltonian $\langle H\rangle$ scales as $1/N$. Numerical simulations enlarge this result to a broader class of noncommuting protocols.

Contextuality is the leading notion of nonclassicality for a single system. However, an experimental demonstration requires finding procedures that are operationally equivalent, which might seem impossible to achieve exactly. Here I focus on the simplest nontrivial case, four preparations and two tomographically complete binary measurements. Exploiting a subtle connection to the Clauser-Horne-Shimony-Holt scenario gives eight nonlinear inequalities which are together necessary and sufficient for the experimental statistics to admit a preparation noncontextual model in such a scenario. No fixed operational equivalences are required, removing a key difficulty with experimental tests of older preparation noncontextuality inequalities.

We study the performance of quantum error correction (QEC) on a system undergoing open-system (OS) dynamics. The noise on the system originates from a joint quantum channel on the system-bath composite, a framework that includes and interpolates between the commonly used system-only quantum noise channel model and the system-bath Hamiltonian noise model. We derive the perfect OSQEC conditions, with QEC recovery only on the system and not the inaccessible bath. When the noise is only approximately correctable, the generic case of interest, we quantify the performance of OSQEC using worst-case fidelity. We find that the leading deviation from unit fidelity after recovery is quadratic in the uncorrectable part, a result reminiscent of past work on approximate QEC for system-only noise, although the approach here requires the use of different techniques than in past work.