We extend the adiabatic theory of strong-field ionization of molecules including nuclear motion developed in our previous paper [J. Svensmark et al., Phys. Rev. A 101, 053422 (2020)] to describe rescattering processes. The adiabatic regime in which the electronic timescale is much smaller than that of the nuclei and laser field is considered. The asymptotics of rescattering parts of the solution to the time-dependent Schrödinger equation (TDSE) and ionization amplitude are obtained, and thus vibrationally resolved photoelectron momentum distributions (PEMDs) in the whole range of the photoelectron momentum are found. The ionization dynamics is described in terms of a nuclear wave packet in the molecular ion created as a result of ionization of the molecule, its evolution until rescattering, and a nuclear wave packet after rescattering. This complements the three-step model by accounting for what happens with the nuclear subsystem between ionization and rescattering events. A uniform asymptotics defining the PEMDs near a backward rescattering caustic is obtained, which enables one to extract the nuclear wave packet after rescattering from the PEMDs. The theory is illustrated by comparing its predictions with accurate numerical results obtained by solving the TDSE for a one-dimensional molecule with one electronic and one internuclear degree of freedom modeling ${\mathrm{H}}_2$.

We study theoretically a Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover of two-species ions in a three-dimensional quantum plasma at zero temperature. Central to this crossover is an effective short-ranged, attractive interaction potential between the ions shielded by the surrounding degenerate electrons. The interaction range and magnitude can be tuned nonmonotonically by varying the carrier density of the quantum plasma. Low-energy collisions between two ions are characterized by the $s$-wave scattering length when the interaction range and the inter-ion spacing are comparable. We show that the $s$-wave scattering length can be changed from $-\infty$ to $\infty$, leading to a BCS-BEC crossover driven purely by the plasma density. Through numerical and analytical calculations, we find that the quantum acoustic waves in the plasma exhibit distinct dispersion relations in the different regimes, providing a route to probe the crossover. Our paper shows that the quantum plasma may offer a different platform to quantum simulate the BEC-BCS crossover and exotic phases with added tunability that might be difficult to achieve in conventional solid-state systems and ultracold atom gases.

A quantum nature of vacuum is expected to affect electromagnetic fields in vacuum as a nonlinear correction, yielding nonlinear Maxwell's equations. We extend the finite-difference time-domain (FDTD) method in the case that the nonlinear electromagnetic Lagrangian is quartic with respect to the electric field and magnetic flux density. With this extension, the nonlinear Maxwell's equations can be numerically solved without making any assumptions on the electromagnetic field. We demonstrate examples of self-modulations of nonlinear electromagnetic waves in a one-dimensional cavity, in particular, in a timescale beyond an applicable range of linear approximation. A momentarily small nonlinear correction can accumulate and a comparably large self-modulation can be achieved in a long timescale even though the electromagnetic field is not extremely strong. Further, we analytically approximate the nonlinear electromagnetic waves in the cavity and clarify the characteristics, for example, how an external magnetic flux density changes the self-modulations of phase and polarization.

We study the ability to implement unitary maps on states of the $I=9/2$ nuclear spin in ${}^{87}\mathrm{Sr}$, a $d=10$ dimensional (qudecimal) Hilbert space, using quantum optimal control. Through a combination of nuclear spin resonance and a tensor ac Stark shift, by solely modulating the phase of a radio-frequency magnetic field, the system is quantum controllable. Alkaline-earth-metal atoms, such as ${}^{87}\mathrm{Sr}$, have a very favorable figure of merit for such control due to narrow intercombination lines and the large hyperfine splitting in the excited states. We numerically study the quantum speed limit, optimal parameters, and the fidelity of arbitrary state preparation and full SU(10) maps, including the presence of decoherence due to optical pumping induced by the light-shifting laser. We also study the use of robust control to mitigate some dephasing due to inhomogeneities in the light shift. We find that with an rf Rabi frequency of ${\mathrm{\Omega }}_{\text{rf}}$ and 0.5% inhomogeneity in the the light shift we can prepare an arbitrary Haar-random state in a time $T=4.5\pi /{\mathrm{\Omega }}_{\text{rf}}$ with average fidelity $\langle {\mathcal{F}}_{\psi }\rangle =0.9992$, and an arbitrary Haar-random SU(10) map in a time $T=24\pi /{\mathrm{\Omega }}_{\text{rf}}$ with average fidelity $\langle {\mathcal{F}}_U\rangle =0.9923$.

For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to nondegenerate wave functions. However, in two dimensions, the symmetry of the box or microstrip antenna is an important feature, the details of which have often been overlooked in the literature. In the high-symmetry cases of a disk, square, or equilateral triangle, the wave functions for both boundary conditions are grouped into two distinct classes, which are one- and two-dimensional representations of the respective point groups, $C_{\infty v}, C_{4v}$, and $C_{3v}$. Here we present visualizations of representative wave functions for both boundary conditions and both one- and two-dimensional representations of those point groups. For the nondegenerate or doubly degenerate one-dimensional representation wave functions, color contour plots are presented. The nominally doubly degenerate two-dimensional representation wave functions are presented as common nodal points and/or lines, the patterns of which are invariant under all operations of the respective point group. The wave functions with the Neumann boundary conditions have important consequences for the coherent terahertz emission from the intrinsic Josephson junctions in the high-temperature superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$: the enhancement of the output power from electromagnetic cavity resonances is strong only for nondegenerate wave functions.

We consider hierarchically implemented quantum error correction (HI-QEC), in which the fidelities of logical qubits are differentially optimized to enhance the capabilities of quantum devices in scientific applications. By employing qubit representations that propagate hierarchies in simulated systems to those in logical qubit noise sensitivities, heterogeneity in the distribution of physical-to-logical qubits can be systematically structured. For concreteness, we estimate HI-QEC's impact on surface code resources in computing low-energy observables to fixed precision, finding up to approximately $60\%$ reductions in qubit requirements plausible in early error-corrected simulations. Hierarchical qubit maps are also possible without error correction in qubit and qudit systems where fidelities are nonuniform, either unintentionally or by design. Hierarchical optimizations are another element in the codesign process of quantum computations, including quantum simulations for nuclear and particle physics.

Among various quantum-key-distribution (QKD) protocols, the round-robin differential-phase- shift (RRDPS) protocol has a unique feature where its security is guaranteed without monitoring the signal disturbance. Moreover, this protocol has the remarkable property of being robust against source imperfections, assuming that the emitted pulses are independent. Unfortunately, some experiments with high-speed QKD systems confirmed the violation of the independence due to pulse correlations, and therefore the lack of a security proof, without taking into account this effect is an obstacle for guaranteeing the implementation security. In this paper, we show that the RRDPS protocol is secure against any source imperfections by establishing a security proof with the pulse correlations. The proof is simple in the sense that we make only three experimentally simple assumptions on the source. Our numerical simulation based on the proof shows that the long-range pulse correlation does not cause a significant impact on the key rate, which reveals another striking feature of the RRDPS protocol. Our security proof is thus effective and applicable to a wide range of practical sources and paves the way to realizing truly secure QKD in high-speed systems.

A scheme for optimizing quantum gates in quantum computation on decoherence-free subspaces using optimal control theory is presented. Compared with the previous scheme, this scheme possesses the following properties: (i) efficiency in finding control sequences, specifically in a system without controllable exchange interaction where the previous method is difficult to handle; (ii) robustness against control errors; and (iii) showing better performance than the robust GRAPE method under stochastic noise. As an application, we work out the control sequences for the not, quantum phase, and cnot gates.

${}^{229}\mathrm{Th}$ is a promising candidate for developing nuclear optical clocks and searching for new physics beyond the standard model. For this purpose, it is important to have accurate knowledge of the nuclear properties of ${}^{229}\mathrm{Th}$. In this work, we calculate hyperfine-structure (HFS) constants for the lowest four states of ${}^{229}\mathrm{Th}^{3+}$ using the relativistic coupled-cluster method based on the Gaussian basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with the lowest-order quantum electrodynamics (QED) correction is the starting point, and all linear and nonlinear terms of single and double excitations are included in the coupled-cluster calculation. Combining the measured HFS constants [Campbell et al., Phys. Rev. Lett. 106, 223001 (2011)] and the present atomic calculations, we extract the magnetic dipole moment, $\mu =0.359\left(9\right)$, and the electric quadrupole moment, $Q=2.95\left(7\right)$, of the ${}^{229}\mathrm{Th}$ nucleus. Our magnetic dipole moment is perfectly consistent with the recommended value from the all-order calculation by Safronova et al. [Phys. Rev. A 88, 060501(R) (2013)], but our electric quadrupole moment is smaller than their recommended value by about $5\%$. A detailed analysis indicates that the nonlinear terms of single and double excitations, not included in the all-order calculation, are crucial to produce a precise $Q$ value for ${}^{229}\mathrm{Th}$. In addition, we also report the magnetic octupole hyperfine-structure constants and some important nondiagonal hyperfine transition matrix elements, which are required for further extraction of the magnetic octupole moment $\mathrm{\Omega }$ of ${}^{229}\mathrm{Th}$ nucleus.

The high-order harmonic generation induced by a polarization-skewed laser pulse is studied by numerically simulating the time-dependent Schrödinger equation. For the polarization-skewed laser pulse, each cycle points to different directions and steers the electron to different directions. The polarization of the harmonics generated by each cycle coincides with the polarization of the driving laser cycle. By synthesizing the harmonics, an attosecond pulse train is formed. In the train, each attosecond pulse is almost linearly polarized, but the adjacent pulses have different polarizations. To demonstrate the advantage of such an attosecond pulse train, we implement it to singly ionize the hydrogen atom. The photoelectron triggered by each attosecond pulse in the train has different momentum distribution, and the overall photoelectron momentum distribution presents fascinating structures, from which the ultrafast ionization can be recorded.

Wave propagation on the surface of cylinders exhibits interferometric self-imaging, much like the Talbot effect in the near-field diffraction at periodic gratings. We report the experimental observation of the cylindrical Talbot carpet in weakly guiding ring-core fibers for classical light fields. We further show that the ring-core fiber acts as a higher-order optical beamsplitter for single photons, whose output can be controlled by the relative phase between the input light fields. By also demonstrating high-quality two-photon interference between indistinguishable photons sent into the ring-core fiber, our findings open the door to applications in optical telecommunications as a compact beam multiplexer as well as in quantum information processing tasks as a scalable realization of a linear optical network.

We consider a homogeneously pumped photon gas coupled to a dye medium and investigate how its steady state is affected when varying the pump power, the photon cavity lifetime, and the cutoff frequency. We study how the interplay between pumping, loss, and dye-induced thermalization influences the selection of the cavity modes that acquire large occupation. Depending on the parameter regime, the latter can be related either to lasing of (typically multiple) modes or to equilibrium-like photon condensation in the ground mode. We calculate and explain the phase diagram of the system, with a particular emphasis on the role played by mode competition that occurs in the regime of weak cavity loss.

Here we put into practice the concept of blind client-server quantum computation, in which a client with limited quantum power controls the execution of a quantum computation on a powerful server, without revealing any details of the computation. In particular, it is a three-node setting in which an oracular quantum computation can be executed blindly. In this Blind Oracular Quantum Computation (BOQC), the oracle (Oscar) is another node, with limited power, who acts in cooperation with the client (Alice) to supply quantum information to the server so that the oracle part of the quantum computation can also be executed blindly. We develop tests of this protocol using two- and three-qubit versions of the exact Grover algorithm (i.e., with database sizes $4\le N\le 8$), obtaining optimal implementations of these algorithms within a gate array scheme and the blinded cluster-state scheme. We discuss the feasibility of executing these protocols in state-of-the-art three-node experiments using nitrogen-vacancy diamond electronic and nuclear qubits.

Classical models with complex energy landscapes represent a perspective avenue for the near-term application of quantum simulators. Until now, many theoretical works studied the performance of quantum algorithms for models with a unique ground state. However, when the classical problem is in a so-called clustering phase, the ground-state manifold is highly degenerate. As an example, we consider a 3-XORSAT model defined on simple hypergraphs. The degeneracy of classical ground-state manifold translates into the emergence of an extensive number of $Z_2$ symmetries, which remain intact even in the presence of a quantum transverse magnetic field. We establish a general duality approach that restricts the quantum problem to a given sector of conserved $Z_2$ charges and use it to study how the outcome of the quantum adiabatic algorithm depends on the hypergraph geometry. We show that the tree hypergraph which corresponds to a classically solvable instance of the 3-XORSAT problem features a constant gap, whereas the closed hypergraph encounters a second-order phase transition with a gap vanishing as a power law in the problem size. The duality developed in this work provides a practical tool for studies of quantum models with classically degenerate energy manifold and reveals potential connections between glasses and gauge theories.

Recently, semi-device-independent protocols have attracted increasing attention, guaranteeing security with few hypotheses and experimental simplicity. In this paper, we demonstrate a many-outcome scheme with binary phase-shift keying (BPSK) for a semi-device-independent protocol based on the energy assumption. We show in theory that the number of certified random bits of the $d$-outcome system outperforms the standard scheme (binary outcomes). Furthermore, we compare the results of two well-known measurement schemes, homodyne detection and heterodyne detection. Taking into account the experimental imperfections, we discuss the experimental feasibility of the $d$-outcome design, and finally, we experimentally validate this approach with an experiment based on BPSK modulation and heterodyne detection.

Positron-electron annihilation spectra of benzene, deuterated benzene, and naphthalene were theoretically calculated as a function of positron collision energy using Feshbach vibrational resonance energies and widths, which can be obtained from the correlation-polarization-potential model. We found that the contribution of overtone excitations to the annihilation spectrum becomes large for the vibrational mode, where structural deformation along the corresponding vibrational coordinate significantly changes the positron binding energy and polarizability. This behavior occurs for the ${\nu }_2$ vibrational mode in benzene and deuterated benzene, corresponding to symmetric ring stretching. Since the incoming positron is dominantly attracted by the π electrons of benzene, we conclude that the ring stretching vibration largely affects the π-electron density of the benzene ring.

The theory of Bloch-electron dynamics for carriers in a homogeneous electric field of arbitrary time dependence is developed in consideration of the properties of multiphoton absorption (MPA) in semiconductors and insulators. The general approach is to utilize the accelerated Bloch-state representation (ABR) as a basis thereby treating the electric field exactly; also, the electric field is described in the vector potential gauge. In developing the ABR, the instantaneous eigenstates for the central Hamiltonian are obtained as the accelerated Bloch states and utilized to find the time-dependent solution to the Schrödinger equation. In introducing the Wigner-Weisskopf approximation (WWA), the transition probability amplitude between the states of the system is obtained and used in the application to MPA in semiconductors and insulators. The probability amplitude for MPA is derived for a plane-polarized radiation field. The periodicity of the time-dependent electric field serves as a principle time constant in developing the probability amplitude per period. Utilizing the WWA, the general MPA transition probability is derived for transitions between an arbitrary set of valence and conduction bands for a time-varying electric field in the $x$ direction. Within the WWA, the MPA transition probability, equivalent to the well-known Keldysh transition amplitude, is derived and expressed in terms of infinite-variable generalized Bessel functions and modified Bessel functions. The exact MPA result is analyzed in the small ($\lesssim {10}^6$ V/cm) and large ($\gtrsim {10}^8$ V/cm) electric field amplitude limits.

We investigate the formation of photon bound states in a system of interacting photons inside nanoscale wires. The photons interact through the exchange of vibrational modes induced along the waveguide mainly due to radiation pressure. The problem of many-body photons is treated in using the formalism of contour Green's functions under the $T$-matrix approximation. The complex pole of the $T$ matrix is a signature for the appearance of photon molecules. The analysis of such singularity provides the critical temperature at which the $T$-matrix approximation breaks down and photon molecules appear. For strongly interacting slow photons the amplitude of the photon-molecule wave function acquires a significant quantum nonlinear phase inside the nanowire. Photon bound states can be implemented for quantum information processing as quantum logic gates, e.g., for $\pi$ phase shift the photon molecule is shown to serve as a $Z$-controlled gate.

We demonstrate numerically the possibility of generation of vector platicons (or vector flat-top solitons) having orthogonally polarized components by the modulated pump at normal group velocity dispersion (GVD). Dynamics of this process can be controlled by pump polarization and depends on both the spectral interval between pumped modes and the difference of their free spectral ranges. We also show the possibility of the excitation of the hybrid soliton-platicon complexes (or hybrid complexes of bright and flat-top solitons) if pumped modes have alternating signs of the GVD coefficient.

We present a theoretical and experimental paper of the zero-field optical spin noise (OSN) spectrum for a thermal state alkali vapor in the strong spin-exchange coupling regime. We show that the OSN spectrum consists of two components corresponding to a positive and a negative hyperfine spin correlation (HSC). We quantify the power ratio of each HSC component to the total OSN as a function of probe's detuning. At some special detunings, the OSN spectrum contains only one kind of HSC. At far detunings, the negative HSC component holds more power than the positive one for alkali isotopes with nuclear-spin-number $I>1$. We also briefly discuss the effect of the negative HSC component on spin squeezing experiments.