Genuinely entangled subspaces (GESs) are those subspaces of multipartite Hilbert spaces that consist only of genuinely multiparty entangled pure states. They are natural generalizations of the well-known notion of completely entangled subspaces, which by definition are void of fully product vectors. Entangled subspaces are an important tool of quantum information theory as they directly lead to constructions of entangled states, since any state supported on such a subspace is automatically entangled. Moreover, they have also proven useful in the area of quantum error correction. In our recent contribution [M. Demianowicz and R. Augusiak, Phys. Rev. A 98, 012313 (2018)], we have studied the notion of a GES qualitatively in relation to so-called nonorthogonal unextendible product bases and provided a few constructions of such subspaces. The main aim of the present work is to perform a quantitative study of the entanglement properties of GESs. First, we show how one can attempt to compute analytically the subspace entanglement, defined as the entanglement of the least-entangled vector from the subspace, of a GES and illustrate our method by applying it to a new class of GESs. Second, we show that certain semidefinite programming relaxations can be exploited to estimate the entanglement of a GES and apply this observation to a few classes of GESs revealing that in many cases the method provides the exact results. Finally, we study the entanglement of certain states supported on GESs, which is compared to the obtained values of the entanglement of the corresponding subspaces, and find the white-noise robustness of several GESs. In our study we use the (generalized) geometric measure as the quantifier of entanglement.

We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansatze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion, and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of $E_4=-2.220\pm 0.179$ MeV may be compared with the exact deuteron ground-state energy $-2.224$ MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.

Dynamical evolution of systems with sparse Hamiltonians can always be recognized as continuous-time quantum walks (CTQWs) on graphs. In this paper, we analyze the short-time asymptotics of CTQWs. In recent studies, it was shown that for the classical diffusion process the short-time asymptotics of the transition probabilities follows power laws whose exponents are given by the usual combinatorial distances of the nodes. Inspired by this result, we perform a similar analysis for CTQWs in both closed and open systems, including time-dependent couplings. For time-reversal symmetric coherent quantum evolutions, the short-time asymptotics of the transition probabilities is completely determined by the topology of the underlying graph analogously to the classical case, but with a doubled power-law exponent. Moreover, this result is robust against the introduction of on-site potential terms. However, we show that time-reversal symmetry-breaking terms and noncoherent effects can significantly alter the short-time asymptotics. The analytical formulas are checked against numerics, and excellent agreement is found. Furthermore, we discuss in detail the relevance of our results for quantum evolutions on particular network topologies.

We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of polarizabilities. Due to the lack of separation of the total momentum from the internal degrees of freedom, the notion of polarizability of the bound state immersed in the continuum spectrum of the global motion is nontrivial. We introduce a bound-continuum perturbation theory and obtain a complete formula for the equation of motion for a polarizable bound system, such as atom, ion, or the nucleus. This formula may find applications when high precision is sought and small effects due polarizabilities are important.

We report experimental investigations of two-body fragmentation of ${\mathrm{C}}_2{{\mathrm{H}}_2}^{2+}$ induced by 1 keV electron collision utilizing an ion momentum imaging spectrometer. With the ion-ion coincidence measurement, dissociation channels ${\mathrm{C}}_2{{\mathrm{H}}_2}^{2+}\to {\mathrm{H}}^{+}+{\mathrm{C}}_2{\mathrm{H}}^{+}$ (deprotonation) and ${\mathrm{C}}_2{{\mathrm{H}}_2}^{2+}\to {{\mathrm{H}}_2}^{+}+{{\mathrm{C}}_2}^{+}$ (${{\mathrm{H}}_2}^{+}$ formation) are directly identified, while the symmetric breakup ${\mathrm{C}}_2{{\mathrm{H}}_2}^{2+}\to \mathrm{C}{\mathrm{H}}^{+}+\mathrm{C}{\mathrm{H}}^{+}$ channel and vinylidene decarbonation ${\mathrm{C}}_2{{\mathrm{H}}_2}^{2+}\to {\mathrm{C}}^{+}+\mathrm{C}{{\mathrm{H}}_2}^{+}$ channel are not well separated in the measured time-of-flight (TOF) correlation map. In this work, by taking advantage of the independence of kinetic energy release (KER) on the dissociation angle, we are able to disentangle the events from the TOF map. Consequently, KER distributions for all four fragmentation channels are deduced, and the relative branching ratios are precisely determined from the measurements. By comparing the measured KER values with the previous calculated potential energy surfaces, pathways for the fragmentation channels are assigned.

Precision comparison experiments on bound states of matter and antimatter rely on the production of corresponding systems at low temperatures and in sufficient numbers. In this paper we propose a scheme for the pulsed production of highly excited protonium (Pn) in a Penning-Malmberg trap at low kinetic energies of tens of meV. The scheme relies on the resonant-charge-exchange reaction ${\mathrm{H}}^{*}+\overline{p}\to {\mathrm{Pn}}^{*}+e^{-}$ where Rydberg excited hydrogen and antiprotons ($\overline{p}$) interact to form ${\mathrm{Pn}}^{*}$. The reagent H($n=30,l=2$) is created from laser photodetached and excited hydrogen anions (${\mathrm{H}}^{-}$), which are initially trapped and mixed in a plasma together with electrons and antiprotons at low kinetic energies. We discuss a three-step pulsed laser excitation using rate equations. A semiclassical Monte Carlo approach leads to a formation rate of ${10}^5$ Pn per 20 s when assuming a production temperature of 100 K. The formed Pn are internally excited in states with average principal quantum number $\langle n\rangle \approx 1200$ having lifetimes that can reach seconds. The proposed scheme is therefore particularly interesting for experiments aiming at the study of cold antimatter and purely baryonic systems for precision experiments (charge neutrality, gravity, spectroscopy), as performed at the antiproton decelerator facility at CERN.

X-ray-assisted nuclear excitation by electron capture (NEEC) into inner-shell atomic holes in a plasma environment generated by strong optical lasers is investigated theoretically. The considered scenario involves the interaction of a strong optical laser with a solid-state nuclear target leading to the generation of a plasma. In addition, intense x-ray radiation from the X-ray Free Electron Laser (XFEL) produces inner-shell holes in the plasma ions, into which NEEC may occur. As a case study, we consider the 4.85-keV transition starting from the 2.4-MeV long-lived ${}^{93\mathrm{m}}\mathrm{Mo}$ isomer that can be used to release the energy stored in this metastable nuclear state. We find that the recombination into $2p_{1/2}$ inner-shell holes is most efficient in driving the nuclear transition. The generation of inner-shell holes while the plasma is at a temperature of a few hundred eV can allow optimal conditions for NEEC, which are otherwise reached for steady-state plasma conditions in thermodynamical equilibrium only at few keV. The combination of x-ray and optical lasers presents two advantages: First, NEEC rates can be maximized at plasma temperatures where the photoexcitation rate remains low. Second, with mJ-class optical lasers and an XFEL repetition rate of 10 kHz, the NEEC excitation number can reach $\approx 1$ depleted isomer per second and is competitive with scenarios recently envisaged at petawatt-class lasers.

We propose an approach to characterizing the depths of optical lattices, in which either an atomic gas is given a finite initial momentum or, alternatively, a corresponding “walking” configuration is applied to the optical lattice itself. This leads to high-amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a simplified model yielding an analytic formula describing such oscillations for a gas assumed to be at zero temperature. This model is extended to include atoms with initial momenta detuned from our chosen initial value, before analyzing the full finite-temperature response of the system. Finally, we present a steady-state solution to the finite-temperature system, which in principle makes possible the measurement of both the lattice depth and the initial temperature of the atomic gas from a single common data set.

On a two-dimensional planar parity-time-($\mathcal{PT}$-)symmetric nonlinear magnetic metamaterial, consisting of split-ring dimers with balanced gain and loss, discrete breather solutions can be found. We extend these studies and by numerical calculations reveal the existence of further stable, long-lived oscillations, with certain frequencies, in the breather spectrum. We describe these oscillations in terms of an analytical breather theory, and show that they can be interpreted as superpositions of a breather oscillation and a plane wave. We coin the term “hybrid breather” solutions for these solutions.

We study unconventional cavity optomechanics and the acoustic analog of radiation pressure to show the possibility of nonlinear coherent control of phonons in the acoustic quantum vacuum. Specifically, we study systems where a quantized optical field effectively modifies the frequency of an acoustic resonator. We present a general method to enhance such a nonlinear interaction by employing an intermediate qubit. Compared to conventional optomechanical systems, the roles of mechanical and optical resonators are interchanged, and the boundary condition of the phonon resonator can be modulated with an ultrahigh optical frequency. These differences allow to test some quantum effects with parameters which are far beyond the reach of conventional cavity optomechanics. Based on this interaction form, we show that various nonclassical quantum effects can be realized. Examples include an effective method for modulating the resonance frequency of a phonon resonator (e.g., a surface-acoustic-wave resonator), demonstrating mechanical parametric amplification, and the dynamical Casimir effect of phonons originating from the acoustic quantum vacuum. Our results demonstrate that unconventional optomechanics offers a versatile hybrid platform for quantum engineering of nonclassical phonon states in quantum acoustodynamics.

The observation of spatial quantum noise reduction, or spatial squeezing, with a large number of photons can lead to a significant advantage in quantum imaging and quantum metrology due to the scaling of the signal-to-noise ratio with the number of photons. Here we present a systematic study of the limiting factors that play a role on the measurement of spatial squeezing with an electron-multiplying charge-coupled device (EMCCD) camera in the limit of bright quantum states of light generated with a four-wave mixing process in an atomic vapor cell. We detect a total number of photons per beam of the order ${10}^8$ in $1\mu \mathrm{s}$ pulses, which corresponds to a photon flux per beam of the order of ${10}^{14}$ photons per second. We then investigate the role of different parameters, such as cell temperature, pump power, laser detunings, scattered pump background noise, and timing sequences for the image acquisition with the EMCCD camera, on the level of spatial squeezing. We identify critical parameters to obtain an optimum squeezing level and demonstrate that for bright beams it is essential to acquire images at a rate fast enough to overcome the effect of classical technical noise.

Chaotic whispering-gallery modes have significance both for optical applications and for our understanding of the interplay between wave phenomena and the classical ray limit in the presence of chaotic dynamics and openness. In strongly nonconvex geometries, a theorem by Mather rules out the existence of invariant curves in phase space corresponding to rays circulating in whispering-gallery patterns, so that no corresponding modes of this type are expected. Here, we discuss numerical computations of the electromagnetic fields in planar dielectric cavities that are strongly nonconvex because they are coupled to waveguides. We find a family of special states which retains many features of the chaotic whispering-gallery modes known from convex shapes: An intensity pattern corresponding to near-grazing incidence along extended parts of the boundary, and comparatively high-cavity $Q$ factors. The modes are folded into a figure-eight pattern, so overlap with the boundary is reduced in the region of self-intersection. The modes combine the phenomenology of chaotic whispering-gallery modes with an important technological advantage: The ability to directly attach waveguides without spoiling the $Q$ factor of the folded mode. Using both a boundary-integral method and the finite-difference time-domain technique, we explore the dependence of the phenomenon on wavelength in relation to cavity size, refractive-index contrast to the surrounding medium, and the degree of shape deformation. A feature that distinguishes folded from regular whispering-gallery modes is that a given shape will support high-$Q$ folded chaotic whispering-gallery modes only in certain wavelength windows.

The dynamical Sauter-Schwinger mechanism of pair creation by a time-dependent electric field composed of $N_{\mathrm{rep}}$ identical pulses is analyzed within the framework of spinor and scalar quantum electrodynamics. For linearly polarized pulses, both theories predict that a single eigenmode of the matter wave follows the dynamics of a two-level system. This dynamics, however, is governed by either a Hermitian (for spin-1/2 particles) or a pseudo-Hermitian (for spin-zero particles) Hamiltonian. Essentially, both theories lead to a Fraunhofer-type enhancement of the momentum distributions of created pairs. While in the fermionic case the enhancement is never perfect and it deteriorates with increasing the number of pulses in a train $N_{\mathrm{rep}}$, in the bosonic case we observe the opposite. More specifically, it is at exceptional points where the spectra of bosonic pairs scale exactly as $N_{\mathrm{rep}}^2$, and this scaling is even enhanced with increasing the number of pulses in a train.

This work deals with quantum graphs, focusing on the transmission properties they engender. We first select two simple diamond graphs, and two hexagonal graphs in which the vertices are all of degree 3, and investigate their transmission coefficients. In particular, we identified regions in which the transmission is fully suppressed. We also considered the transmission coefficients of some series and parallel arrangements of the two basic graphs, with the vertices still preserving the degree 3 condition, and then identified specific series and parallel compositions that allow for windows of no transmission. Inside some of these windows, we found very narrow peaks of full transmission, which are consequences of constructive quantum interference. Possibilities of practical use as the experimental construction of devices of current interest to control and manipulate quantum transmission are also discussed.

We derive a deterministic protocol to implement a general single-qubit positive operator-valued measure (POVM) on near-term circuit-based quantum computers. The protocol has a modular structure such that an $n$-element POVM is implemented as a sequence of $(n-1)$ circuit modules. Each module performs a two-element POVM. Two variations of the protocol are suggested—one optimal in terms of number of ancilla qubits, the other optimal in terms of number of qubit gate operations and quantum circuit depth. We use the protocol to implement two- and three-element POVMs on two publicly available quantum computing devices. The results we obtain suggest that implementing nontrivial POVMs could be within the reach of the current noisy quantum computing devices.

It is proven that entirely spin-free wave functions can be utilized in the basic definitions of the universal functionals in density-functional theory and spin-density-functional theory. Then, for the purpose of approximating these functionals, it is shown that the knowledge of certain properties of the functionals, such as those involving the coordinate scaling of just one of the spin densities, is made feasible precisely because the wave functions in the functional definitions are free of explicit spins. Among the examples, a conjectured spin-density scaling relation for the correlation energy is studied.

We theoretically investigate Rydberg atom pair potentials of Rb atoms in front of a perfectly conducting plate. The pair potentials are perturbed by both the Casimir-Polder potential acting on a single atom and the scattering contribution to the interatomic interaction. In contrast to the pair potentials in free space, at atom-surface distances $d_s\lesssim 4\mu \mathrm{m}$, avoided crossings appear. In the associated potential wells that are entirely due to dispersion interactions with the surface, there exist vibrational bound states, i.e., Rydberg macrodimers, with ground-state energies of up to $E=-68\mathrm{MHz}$ and radial expectation values of the order of several $\mu \mathrm{m}$.

Semiclassical electrodynamics (with quantum matter plus classical electrodynamics fields) is an appealing approach for studying light-matter interactions, especially for realistic molecular systems. However, there is no unique semiclassical scheme. On the one hand, intermolecular interactions can be described instantaneously by static two-body interactions connecting two different molecules, while a classical transverse $E$ field acts as a spectator at short distance; we will call this Hamiltonian no. I. On the other hand, intermolecular interactions can also be described as effects that are mediated exclusively through a classical one-body $E$ field without any quantum effects at all (assuming we ignore electronic exchange); we will call this Hamiltonian no. II. Moreover, one can also mix these two different Hamiltonians into a third, hybrid Hamiltonian, which preserves quantum electron-electron correlations for lower excitations but describes higher excitations in a mean-field way. To investigate which semiclassical scheme is most reliable for practical use, here we study the real-time dynamics of a minimalistic many-site model—a pair of identical two-level systems (TLSs)—undergoing either resonance energy transfer (RET) or collectively driven dynamics. While both approaches (no. 1 and no. 2) perform reasonably well when there is no strong external excitation, we find that no single approach is perfect for all conditions (and all methods fail when a strong external field is applied). Each method has its own distinct problems: Hamiltonian no. I performs best for RET but behaves in a complicated manner for driven dynamics; Hamiltonian no. II is always stable, but obviously fails for RET at short distances. One key finding is that, for externally driven dynamics, a full configuration-interaction description of Hamiltonian no. I strongly overestimates the long-time electronic energy, highlighting the not obvious fact that, if one plans to merge quantum molecules with classical light, a full, exact treatment of electron-electron correlations can actually lead to worse results than a simple mean-field electronic structure treatment. Future work will need to investigate (i) how these algorithms behave in the context of more than a pair of TLSs and (ii) whether or not these algorithms can be improved in general by including crucial aspects of spontaneous emission.