A charged particle in a magnetic field possesses discrete energy levels associated with particle rotation around the field lines. The radiative transitions between these levels are the well-known cyclotron transitions. We show that a bound complex of particles with a nonzero net charge displays analogous transitions between the states of confined motion of the entire complex in the field. The latter bound-ion cyclotron transitions are affected by a coupling between the collective and internal motions of the complex and, as a result, differ from the transitions of a “reference” bare ion with the same mass and charge. We analyze the cyclotron transitions for complex ions by including the coupling within a rigorous quantum approach. Particular attention is paid to comparison of the transition energies and oscillator strengths to those of the bare ion. Selection rules based on integrals of collective motion are derived for the bound-ion cyclotron transitions analytically, and the perturbation and coupled-channel approaches are developed to study the transitions quantitatively. Representative examples are considered and discussed for positive and negative atomic and cluster ions.

We extended the multiconfiguration Hartree-Fock (MCHF) + effective charge (EFC) method for double photoionization of atoms and investigated the effect of valence-electron correlation in the double $K$-shell photoionization of atomic beryllium. We used the MCHF method, which accounts for electron correlations, to calculate the initial-state wave function. The wave functions for the two continuum electrons in the final state are calculated in the angle-dependent EFC approximation. The actual interaction potential between the two final-state continuum electrons is approximated by the EFC, which is determined variationally. We studied the effect of valence shell electron correlation on the $K$-shell double photoionization of beryllium for both equal and unequal sharing of excess photon energies at four fixed scattered electron directions in order to study the effects near the double $K$-shell ionization threshold. We found considerable effect of valence shell correlation in the triple-differential cross section for double photoionization of the beryllium atom at each of the excess photon energies.

The SU(1,1) interferometer can be thought of as a Mach-Zehnder interferometer with its linear beam splitters replaced with parametric nonlinear optical processes. We consider the cases of bright- and vacuum-seeded SU(1,1) interferometers using intensity or homodyne detectors. A simplified truncated scheme with only one nonlinear interaction is introduced, which not only beats conventional intensity detection with a bright seed, but can saturate the phase-sensitivity bound set by the quantum Fisher information. We also show that the truncated scheme achieves a sub-shot-noise phase sensitivity in the vacuum-seeded case, despite the phase-sensing optical beams having no well-defined phase.

We propose a robust realization of the two-photon quantum Rabi model in a trapped-ion setting based on a continuous dynamical decoupling scheme. In this manner the magnetic dephasing noise, which is identified as the main obstacle to achieve long-time coherent dynamics in ion-trap simulators, can be safely eliminated. More specifically, we investigate the ultrastrong coupling regime of the two-photon quantum Rabi model whose realization in trapped ions involves second-order sideband processes. Hence, the resulting dynamics becomes unavoidably slow and more exposed to magnetic noise requiring an appropriate scheme for its elimination. Furthermore, we discuss how dynamical decoupling methods take a dual role in our protocol, namely they remove the main source of decoherence from the dynamics while they actively define the parameter regime of the simulated model.

Photon pairs produced by parametric down-conversion or four-wave mixing can interfere with each other in multiport interferometers or carry entanglement between distant nodes for use in entanglement swapping. This requires the photons to be spectrally pure to ensure good interference and have high heralding efficiency to know accurately the number of photons involved and to maintain high rates as the number of photons grows. Spectral filtering is often used to remove noise and define spectral properties. For heralded single photons high purity and heralding efficiency are possible by filtering the heralding arm, but when both photons in typical pair sources are filtered, we show that the heralding efficiency of one or both of the photons is strongly reduced even by ideal spectral filters with 100% transmission in the passband: any improvement in reduced-state spectral purity from filtering comes at the cost of lowered heralding efficiency. We consider the fidelity to a pure, lossless single photon, symmetrize it to include both photons of the pair, and show this quantity is intrinsically limited for sources with spectral correlation. We then provide a framework for this effect for benchmarking common photon-pair sources and present an experiment where we vary the photon filter bandwidths and measure the increase in purity and corresponding reduction in heralding efficiency.

In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites $\alpha$ and $\beta$ may be obtained directly from $S_{\alpha \beta }\left(\omega \right)$, the (suitably normalized) two-port measurement between sites $\alpha$ and $\beta$ at frequency $\omega$. This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.

Quantum contextuality turns out to be a necessary resource for universal quantum computation and important in the field of quantum information processing. It is therefore of interest both for theoretical considerations and for experimental implementation to find new types and instances of contextual sets and develop methods of their optimal generation. We present an arbitrarily exhaustive hypergraph-based generation of the most explored contextual sets [Kochen-Specker (KS) ones] in 4, 6, 8, 16, and 32 dimensions. We consider and analyze 12 KS classes and obtain numerous properties of theirs, which we then compare with the results previously obtained in the literature. We generate several thousand additional types and instances of KS sets, including all KS sets in three of the classes and the upper part of a fourth set. We make use of the McKay-Megill-Pavičić (MMP) hypergraph language, algorithms, and programs to generate KS sets strictly following their definition from the Kochen-Specker theorem. This approach proves to be particularly advantageous over the parity-proof-based ones (which prevail in the literature) since it turns out that only a very few KS sets have a parity proof (in six KS classes <0.01% and in one of them 0%). MMP hypergraph formalism enables a translation of an exponentially complex task of solving systems of nonlinear equations, describing KS vector orthogonalities, into a statistically linearly complex task of evaluating vertex states of hypergraph edges, thus exponentially speeding up the generation of KS sets and enabling us to generate billions of novel instances of them. The MMP hypergraph notation also enables us to graphically represent KS sets and to visually discern their features.

We experimentally demonstrated an all-fiber-based unidimensional continuous-variable quantum key distribution (CV QKD) protocol and analyzed its security under collective attack in realistic conditions. A pulsed balanced homodyne detector, which could not be accessed by eavesdroppers, with phase-insensitive efficiency and electronic noise, was considered. Furthermore, a modulation method and an improved relative phase-locking technique with one amplitude modulator and one phase modulator were designed. The relative phase could be locked precisely with a standard deviation of 0.5° and a mean of almost zero. Secret key bit rates of 5.4 kbps and 700 bps were achieved for transmission fiber lengths of 30 and 50 km, respectively. The protocol, which simplified the CV QKD system and reduced the cost, displayed a performance comparable to that of a symmetrical counterpart under realistic conditions. It is expected that the developed protocol can facilitate the practical application of the CV QKD.

We consider the explicit construction of resource states for measurement-based quantum information processing. We concentrate on special-purpose resource states that are capable to perform a certain operation or task, where we consider unitary Clifford circuits as well as non-trace-preserving completely positive maps, more specifically probabilistic operations including Clifford operations and Pauli measurements. We concentrate on $1\to m$ and $m\to 1$ operations, i.e., operations that map one input qubit to $m$ output qubits or vice versa. Examples of such operations include encoding and decoding in quantum error correction, entanglement purification, or entanglement swapping. We provide a general framework to construct optimal resource states for complex tasks that are combinations of these elementary building blocks. All resource states only contain input and output qubits, and are hence of minimal size. We obtain a stabilizer description of the resulting resource states, which we also translate into a circuit pattern to experimentally generate these states. In particular, we derive recurrence relations at the level of stabilizers as key analytical tool to generate explicit (graph) descriptions of families of resource states. This allows us to explicitly construct resource states for encoding, decoding, and syndrome readout for concatenated quantum error correction codes, code switchers, multiple rounds of entanglement purification, quantum repeaters, and combinations thereof (such as resource states for entanglement purification of encoded states).

The security of quantum key distribution (QKD) protocols hinges upon features of physical systems that are uniquely quantum in nature. We explore the role of quantumness, as qualified by quantum contextuality, in a QKD scheme. A QKD protocol based on the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) contextuality scenario using a three-level quantum system is presented. We explicitly show the unconditional security of the protocol by a generalized contextuality monogamy relationship based on the no-disturbance principle. This protocol provides a new framework for QKD which has conceptual and practical advantages over other protocols.

We present a family of quantum money schemes with classical verification which display a number of benefits over previous proposals. Our schemes are based on hidden matching quantum retrieval games and they tolerate noise up to $23\%$, which we conjecture reaches $25\%$ asymptotically as the dimension of the underlying hidden matching states is increased. Furthermore, we prove that $25\%$ is the maximum tolerable noise for a wide class of quantum money schemes with classical verification, meaning our schemes are almost optimally noise tolerant. We use methods in semidefinite programming to prove security in a substantially different manner to previous proposals, leading to two main advantages: first, coin verification involves only a constant number of states (with respect to coin size), thereby allowing for smaller coins; second, the reusability of coins within our scheme grows linearly with the size of the coin, which is known to be optimal. Last, we suggest methods by which the coins in our protocol could be implemented using weak coherent states and verified using existing experimental techniques, even in the presence of detector inefficiencies.

The efficiency of optical trapping is determined by the atomic dynamic dipole polarizability, whose real and imaginary parts are associated with the potential energy and photon-scattering rate, respectively. In this article we develop a formalism to calculate analytically the real and imaginary parts of the scalar, vector, and tensor polarizabilities of lanthanide atoms. We assume that the sum-over-state formula comprises only transitions involving electrons in the valence orbitals like $6s,5d,6p$, and $7s$, while transitions involving $4f$ core electrons are neglected. Applying this formalism to the ground level of configuration $4f^{q}6s^2$, we restrict the sum to transitions implying the $4f^{q}6s6p$ configuration, which yields polarizabilities depending on two parameters: an effective transition energy and an effective transition dipole moment. Then, by introducing configuration-interaction mixing between $4f^{q}6s6p$ and other configurations, we demonstrate that the imaginary part of the scalar, vector, and tensor polarizabilities is very sensitive to configuration-interaction coefficients, whereas the real part is not. The magnitude and anisotropy of the photon-scattering rate are thus strongly related to the details of the atomic electronic structure. Those analytical results agree with our detailed electronic-structure calculations of the energy levels, Landé $g$ factors, transition probabilities, polarizabilities, and van der Waals $C_6$ coefficients, previously performed on erbium and dysprosium and presently performed on holmium. Our results show that, although the density of states decreases with increasing $q$, the configuration interaction between $4f^{q}6s6p,4f^{q-1}5d6s^2$, and $4f^{q-1}5d^{2}6s$ is surprisingly stronger in erbium ($q=12$) than in holmium ($q=11$), itself stronger than in dysprosium ($q=10$).

In our previous work S. Bubin et al., Chem. Phys. Lett. 647, 122 (2016), it was established that complex explicitly correlated one-center all-particle Gaussian functions (CECGs) provide effective basis functions for very accurate nonrelativistic molecular non-Born-Oppenheimer calculations. In this work, we advance the molecular CECGs approach further by deriving and implementing algorithms for calculating the leading relativistic corrections within this approach. The algorithms are tested in the calculations of the corrections for all 23 bound pure vibrational states of the ${\mathrm{HD}}^{+}$ ion.

We use accurate ab initio and quantum scattering calculations to explore the prospects for sympathetic cooling of the heavy molecular radical $\mathrm{SrOH}{(}^2{\mathrm{\Sigma }}^{+})$ by ultracold Li atoms in a magnetic trap. Our ab initio calculations show that the chemical reaction between spin-polarized Li and SrOH, which occurs on the triplet Li-SrOH potential energy surface (PES), is strongly endothermic and hence energetically forbidden at ultralow temperatures. The chemical reaction $\mathrm{Li}\left({}^{2}S\right)+\mathrm{SrOH}{(}^2{\mathrm{\Sigma }}^{+})\to \mathrm{Sr}\left({}^{1}S\right)+\mathrm{LiOH}{(}^1{\mathrm{\Sigma }}^{+})$ occurs barrierlessly on the singlet PES and is exothermic by 2505 ${\mathrm{cm}}^{-1}$. A two-dimensional PES for the triplet electronic state of Li-SrOH is calculated ab initio using the partially spin-restricted coupled cluster method with single, double, and perturbative triple excitations and a large correlation-consistent basis set. The highly anisotropic PES has a deep global minimum in the skewed Li-HOSr geometry with $D_e=4932{\mathrm{cm}}^{-1}$ and saddle points in collinear configurations. Our quantum scattering calculations predict low spin-relaxation rates in fully spin-polarized Li + SrOH collisions with the ratios of elastic to inelastic collision rates well in excess of 100 over a wide range of magnetic fields (1–1000 G) and collision energies (${10}^{-5}$ to 0.1 K), suggesting favorable prospects for sympathetic cooling of SrOH molecules with spin-polarized Li atoms in a magnetic trap. We find that spin relaxation in Li + SrOH collisions occurs via a direct mechanism mediated by the magnetic dipole-dipole interaction between the electron spins of Li and SrOH, and that the indirect (spin-rotation) mechanism is strongly suppressed. The upper limit to the Li + SrOH reaction rate coefficient calculated for the singlet PES using adiabatic capture theory is found to decrease from $4\times {10}^{-10}{\mathrm{cm}}^3$/s to a limiting value of $3.5\times {10}^{-10}{\mathrm{cm}}^3$/s with decreasing temperature from 0.1 K to 1 $\mu \mathrm{K}$.

We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ polar molecule in its absolute ground state combined with a calculation of its rovibrational-hyperfine motion. We find that an electric field strength of $5.26\left(15\right)$ kV/cm and an angle of $54.7^{\circ }$ between this field and the polarization of the optical laser lead to a trapping design for ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$ molecules where decoherence due to electric field strength and laser-intensity fluctuations, as well as fluctuations in the direction of its polarization, are kept to a minimum. One-standard-deviation systematic and statistical uncertainties are given in parenthesis. Under such conditions, pairs of hyperfine-rotational states of $v=0$ molecules, used to induce tunable dipole-dipole interactions between them, experience ultrastable, matching trapping forces.

Thanks to their immense purity and controllability, dipolar Bose-Einstein condensates are an exemplar for studying fundamental nonlocal nonlinear physics. Here we show that a family of fundamental nonlinear waves—the dark solitons—are supported in trapped quasi-one-dimensional dipolar condensates and within reach of current experiments. Remarkably, the oscillation frequency of the soliton is strongly dependent on the atomic interactions, in stark contrast to the nondipolar case. Established analytical techniques are shown to not capture the simulated dynamics. These sensitive waves may act as mesoscopic probes of the underlying quantum matter field.

We numerically show that time-delayed coherent feedback controls the statistical output characteristics of driven quantum emitters. Quantum feedback allows us to enhance or suppress a wide range of classical and nonclassical features of the emitted quantum light. As an exemplary quantum system, we use a pumped cavity containing two emitters. By applying phase-selective feedback, we demonstrate that photon antibunching and bunching can be increased for a given set of parameters in orders of magnitude due to intrinsically and externally controllable quantum interferences. Our modeling is based on a fully non-Markovian quantum simulation of a structured photon continuum. We show that an approximative method in the Schrödinger picture allows a very good estimate for quantum feedback induced features for low pump rates.

In this paper, we address nonradiating and cloaking problems exploiting the surface equivalence principle, by imposing at any arbitrary boundary the control of the admittance discontinuity between the overall object (with or without cloak) and the background. After a rigorous demonstration, we apply this model to a nonradiating problem, appealing for anapole modes and metamolecules modeling, and to a cloaking problem, appealing for non-Foster metasurface design. A straightforward analytical condition is obtained for controlling the scattering of a dielectric object over a surface boundary of interest. Previous quasistatic results are confirmed and a general closed-form solution beyond the subwavelength regime is provided. In addition, this formulation can be extended to other wave phenomena once the proper admittance function is defined (thermal, acoustics, elastomechanics, etc.).

We present a study of collective multiphoton blockade in coherently driven atoms in a single-mode cavity. Considering two atoms strongly coupled to an optical cavity, we show that the two-photon blockade with two-photon antibunching, and the three-photon blockade with three-photon antibunching can be observed simultaneously. The three-photon blockade probes both dressed states in the two-photon and three-photon spaces. The two-photon and three-photon blockades strongly depend on the location of the two atoms in the strong-coupling regime. The asymmetry in the atom-cavity coupling constants opens pathways for multiphoton blockade which is also shown to be sensitive to the atomic decay and pumping strengths. The work presented here predicts many quantum statistical features due to the collective behavior of atoms and can be useful to generate nonclassical photon pairs.