Quantum approximate optimization algorithm (QAOA) is a hybrid algorithm whose control parameters are classically optimized. In addition to the variational parameters, the right choice of hyperparameter is crucial for improving the performance of any optimization model. Control depth, or the number of variational parameters, is considered as the most important hyperparameter for QAOA. In this paper we investigate the control depth selection with an automatic algorithm based on proximal gradient descent. The performances of the automatic algorithm are demonstrated on seven-node and ten-node max-cut problems, which show that the control depth can be significantly reduced during the iteration whereas achieving an sufficient level of optimization accuracy. With theoretical convergence guarantee, the proposed algorithm can be used as an efficient tool for choosing the appropriate control depth as a replacement of random search or empirical rules. Moreover, the reduction of control depth will induce a significant reduction in the number of quantum gates in circuit, which improves the applicability of QAOA on noisy intermediate-scale quantum devices.

We demonstrate a supersolid-like spatially periodic square- and honeycomb-lattice crystallization of droplets in addition to the commonly studied triangular-lattice crystallization in a cylindrically symmetric quasi-two-dimensional trapped dipolar condensate, using a beyond-mean-field model including a quantum-fluctuation Lee-Huang-Yang-type interaction. These three types of crystallization of droplets may appear for the same atomic interaction and the same trap frequencies. The energies $E$ of all three crystallizations as a function of the number $N$ of atoms satisfy the universal scaling relation $E\sim N^{0.4}$, indicating that all three arrangements of the droplets should be energetically probable processes of phenomenological interest. The state of square-lattice crystallization may have the central site occupied or unoccupied, corresponding to a parity-symmetric or parity-antisymmetric state, respectively. The state of square-lattice crystallization with the occupied central site and the state of triangular-lattice crystallization, for a fixed $N$, constitute two quasidegenerate ground states, while the other states are low-lying excited states. This makes the square-lattice crystallization with the occupied central site an ideal candidate for future experimental observation.

We introduce models of one-dimensional $n(\ge 3)$-body problems that undergo phase transition from a continuous scale-invariant phase to a discrete scale-invariant phase. In this paper, we focus on identical spinless particles that interact only through two-body contacts. Without assuming any particular cluster-decomposition property, we first classify all possible scale-invariant two-body contact interactions that respect unitarity, permutation invariance, and translation invariance in one dimension. We then present a criterion for the breakdown of continuous scale invariance to discrete scale invariance. Under the assumption that the criterion is met, we solve the many-body Schrödinger equation exactly; we obtain the exact $n$-body bound-state spectrum as well as the exact $n$-body $S$-matrix elements for arbitrary $n\ge 3$, all of which enjoy discrete scale invariance or log periodicity. Thanks to the boson-fermion duality, these results can be applied equally well to both bosons and fermions. Finally, we demonstrate how the criterion is met in the case of $n=3$; we determine the exact phase diagram for the scale-invariance breaking in the three-body problem of identical bosons and fermions. The zero-temperature transition from the unbroken phase to the broken phase is the Berezinskii-Kosterlitz-Thouless-like transition discussed in the literature.

The radiative transfer equation (RTE) models the transport of light inside photonic scattering samples such as paint, foam, and tissue. Analytic approximations to solve the RTE fail for samples with strong absorption and dominant anisotropic scattering and predict unphysical negative energy densities and the diffuse flux in the wrong direction. Here we fully characterize the unphysical regions of three popular approximations to the RTE for a slab, namely the $P_1$ approximation (or diffusion approximation), the $P_3$ approximation, and a popular modification to $P_3$ that corrects the forward scattering in the approximation. We find that the $\delta$ function correction to $P_3$ eliminates the unphysical range in the forward scattering. In addition, we compare the predictions of these analytical methods to exact Monte Carlo simulations for the physical and unphysical regions. We present maps of relative errors for the albedo and the anisotropy of the scatterers for a realistic index contrast typical of a polymer slab in air and optical thickness. The relative error maps provide a guideline for the accuracy of the analytical methods to interpret experiments on light transport in photonic scattering slabs. Our results show that the $P_1$ approximation is significantly inaccurate to extract transport parameters unless the sample scatters purely isotropic and elastic. The $P_3$ approximation exceeds $P_1$ in terms of accuracy in its physical range for moderate absorption, and the $P_3$ with the $\delta$ function correction is the most accurate approximation considered here for the forward direction.

We establish, within the second quantization method, the general dipole-dipole Hamiltonian interaction of a system of $n$-level atoms. The variational energy surface of the $n$-level atoms interacting with $\ell$-mode fields and under the Van Der Waals forces is calculated with respect to the tensorial product of matter and electromagnetic field coherent states. This is used to determine the quantum phase diagram associated with the ground state of the system and quantify the effect of the dipole-dipole Hamiltonian interaction. By considering real induced electric dipole moments, we find the quantum phase transitions for 2- and 3-level atomic systems interacting with one and two modes of the electromagnetic field, respectively. The corresponding order of the transitions is established by means of Ehrenfest classification; for undetermined cases, we propose two procedures: one based on the difference of the expectation value of the Casimir operators of the 2-level subsystems, and another based on maximizing the Bures distance between neighbor variational solutions.

We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this annealing protocol allows avoidance of first-order quantum phase transitions of selected models, resulting in an exponential speedup compared with standard quantum annealing, provided that the initial state of the algorithm is close in Hamming distance to the target one. Here, we show that decoherence can significantly modify this conclusion: by resorting to the adiabatic master equation approach, we simulate the dynamics of the ferromagnetic $p$-spin model with $p=3$ under independent and collective dephasing. For both models of decoherence, we show that the performance of open system ARA is far less sensitive to the choice of the initial state than its unitary counterpart, and, most significantly, that open system ARA by and large loses its time to solution advantage compared to standard quantum annealing. These results suggest that as a stand-alone strategy ARA is unlikely to experimentally outperform standard “forward” quantum annealing, and that error mitigation strategies will likely be required in order to realize the benefits of ARA in realistic, noisy settings.

We consider a topological Hamiltonian and establish correspondence between its eigenstates and the resource for a causal-order game introduced by Oreshkov et al. [Nat. Commun. 3, 1092 (2012)], known as the process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of the success probabilities of the game. As a result, we show that the ground state of the model can be related to the optimal strategy of the causal-order game. Subsequently, we observe that at the point of maximum violation of the classical bound in the causal-order game, the corresponding quantum many-body model undergoes a second-order quantum phase transition. The correspondence equally holds even when we generalize the game for a higher number of parties.

Photoelectron emission Wigner time delay for $K$-shell ionization of a nitrogen molecule is studied theoretically in the frame of a molecular reference for parallel and perpendicular orientations of the molecule with respect to the electric field vector of linearly polarized ionizing light. Electronic structure calculations are performed by the single center method for photoelectron kinetic energies from 5 to 20 eV and at different levels of approximation. Thereby, the influence of core relaxation effects and interchannel coupling on the $1s$-photoemission time delays, computed across the ${\sigma }^{*}$-shape resonance, is investigated in detail. The present theoretical results can be considered as reliable predictions for future experiments.

We investigate the resonant enhancement of nonlinear interactions in a three-mode cavity optomechanical system with two mechanical oscillators. Using the Keldysh Green's function technique, we find that nonlinear effects on the cavity density of states can be greatly enhanced by the resonant interaction of two phononic polaritons, due to their small effective dissipation. In the large detuning limit and taking into account an upper bound on the achievable dressed coupling, the optimal point for probing the nonlinear effect is obtained, showing that such a three-mode system can exhibit significant nonlinear features also for relatively small values of $g/\kappa$.

We consider the quantum effect of slow-light dark soliton (SLDS) in a cold atomic gas with defocusing Kerr nonlinearity via electromagnetically induced transparency (EIT). We calculate the quantum fluctuations of the SLDS by solving the relevant non-Hermitian eigenvalue problem describing the quantum fluctuations and find that only one zero mode is allowed. This is different from the quantum fluctuations of bright solitons, where two independent zero modes occur. We rigorously prove that the eigenmodes, which consist of continuous modes and the zero mode, are biorthogonal and constitute a complete biorthonormalized basis, useful for the calculation on the quantum fluctuations of the SLDS. We demonstrate that, due to the large Kerr nonlinearity contributed from the EIT effect, a significant quantum squeezing of the SLDS can be realized; the squeezing efficiency can be manipulated by the Kerr nonlinearity and the soliton's amplitude, which can be much higher than that of bright solitons. Our work contributes to efforts for developing quantum nonlinear optics and non-Hermitian physics and for possible applications in quantum information processing and precision measurements.

In this paper we carry out a theoretical investigation on the propagation of spatiotemporal solitons (light bullets) in the nonlinear metamaterial waveguides. Our theoretical study is based on the formulation of Lagrangian variational analysis with a suitable ansatz, followed by a split-step Fourier method in confirming the previous outcomes numerically. A particular emphasis is given to obtain the conditions on the system parameters for stable dynamics in negative as well as positive index regimes of metamaterial waveguides. Similar to the conventional medium, the three-dimensional (3D) light bullets are highly unstable in metamaterials with the Kerr-type nonlinearity alone. However, in the negative index regime of metamaterials, the stable propagation of light bullets may occur in the normal dispersion regime balancing with defocusing cubic nonlinearity and focusing quintic nonlinearity. As in the conventional case, the stable dynamics is also observed in the case of anomalous dispersion with focusing cubic nonlinearity and defocusing quintic nonlinearity in the positive index regime. To test the solitonic nature of the 3D light bullets in the metamaterials, we also numerically investigate the collision dynamics of two light bullets. The study shows that the spatiotemporal soliton propagates without any change, except perhaps some phase shift after a collision with another spatiotemporal soliton in competing cubic and quintic nonlinear metamaterials. The improper balancing between the linear and nonlinear effects results to form the bullet molecules in a distorted form with a large amount of energy after interaction, and in the long run, oscillations of the light bullets grow and the bullets become filaments. We observed the same collision dynamics in both the negative and positive refractive index regimes of the metamaterial.

We present theoretical models for quantum-optical mode-selective filters and mirrors using continuous-variable teleportation. We call these devices telefilters and telemirrors, respectively. Both devices act as the identity channel on a mode of interest from an input multimode field while filtering or reflecting all the orthogonal modes. We utilize these models to analyze a causality problem in relativistic quantum optics, specifically the apparently acausal transmission and propagation of temporally delocalized wave packets through mode-selective mirrors. First, we show how telemirrors, and thus mode-selective operations generally, enact a fundamental time delay on such wave packets, which is necessary in order to prevent violations of causality. We next consider teleporting the independent temporal components of the input field separately and continuously, that is, performing operations on the fly. In this scenario, the telemirror transmits the mode of interest as well as orthogonal modes which carry with them uncorrelated noise. In this scenario, the device may be considered mode discriminating but not mode selective.

We analytically investigate the sensitivity of Kerr nonlinear phase estimation in a Mach-Zehnder interferometer with two-mode squeezed vacuum states. We find that such a metrological scheme could access a sensitivity scaling over the Boixo et al.'s generalized sensitivity limit [S. Boixo et al., Phys. Rev. Lett. 98, 090401 (2007)], which is saturable with celebrated NOON states. We also show that parity detection is a quasioptimal measurement which can nearly saturate the quantum Cramér-Rao bound in the aforementioned situation. Moreover, we further clarify the supersensitive performance observed in the above scheme is due to the restriction of Boixo et al.'s generalized sensitivity limit (BGSL) to probe states with fixed photon numbers. To conquer this problem, we generalize the BGSL into the case with probe states of a fluctuating number of photons, to which our scheme belongs.

A partial-wave method is developed to deal with small molecules dominated by a central atom as an extension of earlier single-center methods. In particular, a model potential for the water molecule is expanded over a basis of spherical harmonics. A finite-element method is employed to generate local polynomial functions in subintervals to represent the radial part of the wave function. The angular parts of the wave function are represented by spherical harmonics. The problem of Stark resonances is treated with the exterior complex scaling method which incorporates a wave-function discontinuity at the scaling radius. The resultant non-Hermitian matrix eigenvalue problem yields resonance positions and widths (decay rates). We present these dc Stark shifts and exponential decay rates for the valence orbitals $1b_1, 3a_1$, and the bonding orbital $1b_2$. Furthermore, comparison is made with total molecular decay rates and dc shifts obtained recently within the Hartree-Fock and coupled-cluster approaches.

We present a method for optimizing the location of the fermion ground-state nodes using a combination of diffusion Monte Carlo (DMC) and projected gradient descent (PGD). A PGD iteration shifts the parameters of an arbitrary node-fixing trial function in the opposite direction of the DMC energy gradient, while maintaining the cusp condition for atomic electrons. The energy gradient is calculated from DMC walker distributions by one of three methods we derive from an exact analytical expression. We combine our energy gradient calculation methods with different gradient-descent algorithms and a projection operator that maintains the cusp condition. We apply this stochastic PGD method to trial functions of Be, ${\mathrm{Li}}_2$, and Ne, all consisting of a single Slater determinant with randomized parameters, and find that the nodes dramatically improve to the same DMC energy as nodes optimized by variational Monte Carlo. Our method, therefore, departs from the standard procedure of optimizing the nodes with a non-DMC scheme such as variational Monte Carlo, density-functional theory, or configuration-interaction-based calculation, which do not directly minimize the DMC energy.

We present experimental observations of bimodal solitons in a solid state three-level maser cooled to millikelvin temperatures. The maser is built on a highly dilute ${\text{Fe}}^{3+}$ spin ensemble hosted by a high-purity ${\text{Al}}_2{\text{O}}_3$ crystal constituting a high-quality factor whispering-gallery-mode resonator. The maser is pumped through one of these modes, near 31 GHz, generating two signals near 12.04 GHz from two distinct modes, 8 MHz apart. The system demonstrates three regimes, namely, a continuous-wave regime, a dense soliton regime, and a sparse soliton regime. These results open other avenues for studying nonlinear wave phenomena using microwave systems as well as different applications of solitons in this part of the electromagnetic spectrum.

We propose a mechanism to achieve real energy spectra via Hermitian subspace in non-Hermitian systems. As an illustrative example, we investigate a system composed of two identical Su-Schrieffer-Heeger (SSH) chains connected by a lossy site in each unit cell. Although the system as a whole is non-Hermitian, it is able to support Dirac points that coexist with exceptional points, exactly exhibiting real eigenenergies. The real spectra and coexistence of different singularities are inherited from two virtual decoupled subsystems after a transformation that comprises a Hermitian SSH chain and a non-Hermitian Lieb lattice. Furthermore, we show the two subsystems both experience topological phase transition by tuning coupling strength, allowing the exploration of Hermitian and non-Hermitian topological edge modes at the same time. In aid of Hermitian subspace, the waves could evolve without dissipation depending on initial injection, which contributes to coherent splitters with locked phase and intensity in two SSH layers. The proposed model can be realized in evanescently coupled optical waveguide arrays and further extended to other tight-binding systems.

The practical applications of chiral discrimination are usually limited by the weak chiral response of enantiomers and the high complexity of detection methods. Here, we propose to use the C lines (i.e., lines of polarization singularities) emerged in light scattering by a metal sphere to detect small chiral particles. Using full-wave numerical simulations and analytical multipole expansions, we determined the absorption dissymmetry of deep-subwavelength helices (i.e., chiral particles) at different positions on the C lines. We find that the absorption dissymmetry can be much larger than that induced by circularly polarized plane-wave excitation, and it can be attributed to the asymmetric absorption of the induced electric and magnetic dipoles. We also show that the absorption dissymmetry strongly depends on the anisotropy of the helices. The results may find applications in optical manipulations, optical sensing, and chiral quantum optics.

Coherence has been an important key for numerous applications of quantum physics ranging from quantum metrology to quantum information. We report here a theoretical paper demonstrating how maximally created coherence results in the squeezing of a cavity field coupled to a coherently driven single quantum dot. We employ a polaron master equation theory for accurately incorporating the impact of exciton-phonon coupling on squeezing.