We present a method for engineering harmonic frequency combs (HFCs) in the terahertz spectral region. This approach involves interfacing a quantum cascade laser (QCL) with an external reflector featuring frequency-dependent reflectivity. A notable advantage of this method over existing ones is its dual functionality in shaping HFCs, allowing for control over both the frequency offset and comb spacing based on the external reflectivity profile. Moreover, the resulting HFCs manifest as sequences of short pulses in the time domain. Consequently, our method enables the generation of ultrashort picosecond pulses passively, providing a distinct alternative to conventional pulse generation systems reliant on active bias current modulation, which struggle with modulation frequencies significantly higher than the first beat note. This offers intriguing prospects for utilizing HFCs in pump and probe spectroscopy, a field already recognized in the literature as one of the most compelling applications of these states. Furthermore, we demonstrate that these HFCs can be triggered from an initial condition of free-running unlocked dynamics, eliminating the need for assuming free-running comb emission. Thus, the utilization of an external, frequency-dependent reflector is capable of enhancing the coherence of the QCL emission.

We study the crossing of the quantum phase transition in the transverse-field Ising model after modulating the magnetic field at an arbitrary rate, exploring the critical dynamics from the slow to the sudden-quench regime. We do so by analyzing the defect density, the complete kink-number distribution, and its cumulants upon completion of a linearized quench. Our analysis relies on the diagonalization of the model using the standard Jordan-Wigner and Fourier transformations, along with the exact solution of the time evolution in each mode in terms of parabolic cylinder functions. The free-fermion nature of the problem dictates that the kink-number distribution is associated with independent and distinguishable Bernoulli variables, each with a success probability $p_k$. We employ a combination of convergent and asymptotic series expansions to characterize $p_k$ without restrictions on the driving rate. When the latter is approximated by the Landau-Zener formula, the kink density is described by the Kibble-Zurek mechanism, and higher-order cumulants follow a universal power-law behavior, as recently predicted theoretically and verified in the laboratory. By contrast, for moderate and sudden-driving protocols, the cumulants exhibit a nonuniversal behavior that is not monotonic on the driving rate and changes qualitatively with the cumulant order. The kink-number statistics remain sub-Poissonian for any driving rate, as revealed by an analysis of the cumulant ratios that vary nonmonotonically from the sudden- to the slow-driving regime. Due to the determination of $p_k$ for an arbitrary rate, our study provides a complete analytical understanding of kink-number statistics from the slow-driving regime to the sudden-quench limit.

Dynamical quantum phase transition is a nonstationary analog of the equilibrium quantum phase transitions that may occur after global quenches across a quantum phase transition in systems. In this work, we investigate the quench dynamics of single-particle tight-binding quasiperiodic lattices, where the quenching process originates and terminates within the same phases. Intriguingly, the system under quench dynamics undergoes an energy-dependent dynamical quantum phase transition, characterized by the singularities of the Loschmidt echo in time scale. Specifically, we find disentangling behavior between static and dynamical quantum phase transitions for eigenenergies excluding band edges. Remarkably, the connection between static and dynamical quantum phase transitions does not hold generally for all eigenenergies. Our findings suggest the existence of dynamical phase transitions inside the band energies without crossing the critical point under certain conditions. Our results pave the way to a deeper understanding of the energy-dependent nonequilibrium quench dynamics.

This paper presents the quantum Möbius-Escher-Penrose hypergraph, drawing inspiration from paradoxical constructs such as the Möbius strip and Penrose's “impossible objects.” The hypergraph is constructed using faithful orthogonal representations in Hilbert space, thereby embedding the graph within a quantum framework. Additionally, a quasiclassical realization is achieved through two-valued states and partition logic, leading to an embedding within a Boolean algebra. This dual representation delineates the distinctions between classical and quantum embeddings, with a particular focus on contextuality, highlighted by violations of exclusivity and completeness, quantified through classical and quantum probabilities. The paper also examines violations of Boole's conditions of possible experience using correlation polytopes, underscoring the inherent contextuality of the hypergraph. These results offer deeper insights into quantum contextuality and its intricate relationship with classical logic structures.

We develop methods for performing quantum teleportation of the total spin variables of an unknown state, using quantum nondemolition measurements, spin projection measurements, and classical communication. While, theoretically, teleportation of high-dimensional states can be attained with the assumption of generalized Bell measurements, this is typically experimentally nontrivial to implement. We introduce two protocols and show that on average, the teleportation succeeds in teleporting the spin variables of a spin coherent state with average zero angular error in the ideal case, beating classical strategies based on quantum state estimation. In a single run of the teleportation, there is an angular error at the level of $\sim 0.1$ radians for large ensembles. A potential physical implementation for the scheme is with atomic ensembles and quantum nondemolition measurements performed with light. We analyze the decoherence of the protocols and find that the protocol is robust even in the limit of large ensemble sizes.

We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature (London) 619, 282 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the scaling of the total evolution time with the size of the system. We also explore extensions of the circuit, including the use of time-dependent Hamiltonians and reverse digitized annealing. Additionally, we propose that classical, approximate quantum simulators can be used for the proposal step instead of the original real-hardware implementation. We observe that tensor-network simulators, even with unconverged settings, can maintain a scaling advantage over standard classical samplers. This may extend the utility of quantum-enhanced Monte Carlo as a quantum-inspired algorithm, even before the deployment of large-scale quantum hardware.

We report on the emergence of a highly nonclassical collective behavior in quantum parametric oscillators, which we name quantum hyperspin, induced by a tailored nonlinear interaction. This is the second quantized version of classical multidimensional spherical spins, as $XY$ spins in two dimensions, and Heisenberg spins in three dimensions. In the phase space, the quantum hyperspins are represented as spherical shells whose radius scales with the number of particles in a way such that it cannot be factorized even in the limit of large particle number. We show that the nonlinearly coupled quantum oscillators form a high-dimensional entangled state that is surprisingly robust with respect to the coupling with the environment. Such a behavior results from a properly engineered reservoir. Networks of entangled quantum hyperspins are a new approach to quantum simulations for applications in computing, Ising machines, and high-energy physics models. We analyze from first principles through ab initio numerical simulations the properties of quantum hyperspins, including the interplay of entanglement and coupling frustration.

Vortex beams are exotic states of classical light fields that contain orbital angular momentum (OAM) due to their space-dependent phases. While the experimental realization of intense low-frequency optical vortices has led to the discovery and application of OAM conservation in high-harmonic generation, there is not a comparable signature of light's OAM on photoelectrons. Here we propose using a linear combination of vortex modes, referred to as a vector vortex beam, for strong-field ionization of atoms. We then demonstrate that the input vortex beam's position-dependent phase can be obtained from the resulting electron momentum distribution following strong-field ionization. We validate this method by performing classical trajectory Monte Carlo simulations and comparing momentum distributions corresponding to different ionization locations within the beam profile, demonstrating that one can unambiguously determine the ionizing radiation's OAM index. These results are suitable for the added control offered by vortex light compared to Gaussian or plane-wave radiation in intense light-matter interactions.

Quantum machine learning aims to improve learning methods through the use of quantum computers. If it is to ever realize its potential, many obstacles need to be overcome. A particularly pressing one arises at the prediction stage because the outputs of quantum learning models are inherently random. This creates an often considerable overhead, as many executions of a quantum learning model have to be aggregated to obtain an actual prediction. In this work, we analyze when quantum learning models can evade this issue and produce predictions in a near-deterministic way—paving the way to single-shot quantum machine learning. We give a rigorous definition of single shotness in quantum classifiers and show that the degree to which a quantum learning model is near deterministic is constrained by the distinguishability of the embedded quantum states used in the model. Opening the black box of the embedding, we show that if the embedding is realized by quantum circuits, a certain depth is necessary for single shotness to be even possible. We conclude by showing that quantum learning models cannot be single shot in a generic way and trainable at the same time.

By using the relativistic multiconfiguration Dirac-Fock method, we calculate the hyperfine-structure properties of the $2s2p{}^3\mathrm{P}_J$ state in ${}^9\mathrm{Be}$. The hyperfine-structure properties encompass first-order hyperfine-structure parameters, as well as second-order and third-order corrections caused by the off-diagonal hyperfine interaction. Based on our theoretical results, we reanalyze the previously reported measurement of the hyperfine interval for the $2s2p{}^{3}P$ state in ${}^9\mathrm{Be}$ [A. G. Blachman and A. Lurio, Phys. Rev. 153, 164 (1967)], yielding updated hyperfine-structure constants. Our results show that the hyperfine-structure constant $B$ of $2s2p{}^{3}P_1$ is notably sensitive to second-order correction. Conversely, accurately determining the hyperfine-structure constant $B$ of $2s2p{}^{3}P_2$ necessitates consideration of the magnetic octupole hyperfine interaction in the first-order hyperfine interaction equation. The updated hyperfine-structure constant $B$ of the $2s2p{}^{3}P_2$ state is found to be 1.4542(67) MHz, which is approximately $1.7\%$ larger than the previous value of 1.427(9) MHz [A. G. Blachman and A. Lurio, Phys. Rev. 153, 164 (1967)]. By combining our theoretical results with the updated hyperfine-structure constant for the $2s2p{}^{3}P_2$ state, we extract the electric quadrupole moment $Q$ of ${}^9\mathrm{Be}$ nucleus to be 0.05320(50) b. This value is consistent with the most recent determination using the few-body precision calculation method [Puchalski et al. Phys. Rev. Res. 3, 013293 (2021)]. Additionally, we discuss the reasons for the discrepancy between the electric quadrupole moment $Q$ obtained through few-body and previous many-body calculations.

Motivated by the recent realization of the Qi-Wu-Zhang (QWZ) model for the minimal spin-orbit-coupled quantum anomalous Hall phase in ultracold fermions, we introduce the on-site attractive interaction and map out the topological phase diagram for the Qi-Wu-Zhang-Hubbard (QWZH) model at the mean-field level. We show that, in addition to the conventional chiral topological superfluids (TSs) with nonzero Chern number, there is also an obstructed superfluid (OSF) with zero Chern number in the extended region of phase space. This phase is characterized by gapless edge states completely detaching from the bulk energy bands and two $Z_2$ numbers. We find the gapless edge states in OSF are protected by particle-hole symmetry and robust for the disorder. The appearance of OSF demonstrates that it is not sufficient to label TSs in the two-dimensional D class only by Chern numbers. These different topological phases in the attractive QWZH model can be detected experimentally by spin-resolved time-of-flight imaging. We also plot the phase diagram of the attractive QWZH model with one-dimensional spin-orbit coupling and find a series of TSs with gapless Dirac points. Considering the successful realization of the QWZ model and the tremendous progress in manipulating cold atom systems, our work provides a possible route to realize OSF in cold fermionic systems in the future.

Quantum mixtures of Bose gases with tunable $s$- and $p$-wave interactions offer a versatile platform to explore strongly correlated phases and exotic phenomena. While repulsive interactions often drive phase separation, the interplay of $p$-wave interactions with spin-density decoupling remains underexplored. In this work we employ the path-integral field theory to investigate the role of $p$-wave interactions in three-dimensional two-component Bose gas. We derive the Lee-Huang-Yang corrections to the ground-state energy and quantum depletion, revealing how $p$-wave interactions modify equations of state of the model system. Furthermore, we demonstrate that $p$-wave interactions predominantly renormalize the spin-sector effective mass in the language of decoupling the density and spin-density degrees of freedom. This effect manifests in the dynamic structure factor, computed via hydrodynamic theory, where Bragg spectroscopy can detect a tunable splitting between spin and density modes. Our results bridge theoretical predictions with experimental observables, offering insights into anisotropic interaction effects in quantum gases and their implications for probing emergent phases.

Terahertz radiation with tunable polarization and amplitude can facilitate applications in many fields such as biological diagnosis and terahertz imaging. Using the photocurrent model and far-field coherent superposition method, we show that two-color laser-induced air filaments can generate terahertz radiation with independent control on both its polarization and amplitude when a circularly polarized fundamental wave and an elliptically polarized second harmonic are adopted. The polarization of the terahertz radiation, including polarization angle and polarization ellipticity, can be controlled independently by tuning the initial relative phase between two-color components and the filament length, respectively. Meanwhile, by increasing the polarization ellipticity of the second harmonic from $-1$ (with polarization opposite to the fundamental wave) to 1, the amplitude of the terahertz radiation can be tuned continuously from 0 to its maximum with its polarization fixed at a desirable state. Our studies provide an all-optical method for the manipulation of multiple parameters of terahertz radiation, which is useful for terahertz science.

We report the generation of an ultrashort soliton train by pumping two identical time-delayed femtosecond pulses in a third-order nonlinear composite medium with normal dispersion. The entire composite medium is composed of two segments, the first segment with self-focusing nonlinearity and the second segment with self-defocusing nonlinearity. In the self-focusing segment, a temporal pulse sequence is generated via the formation of a dark soliton train due to the nonlinearity acting on the modulation. In the self-defocusing segment, these temporal pulses can be effectively compressed into the controlled and isolated ultrashort solitons via the temporal compression method, as long as the time delay between double pulses and the ratio of the self-focusing segment are suitably set. Interestingly, when the ratio of the self-focusing segment is relatively small, a giant soliton can be produced by the combined effect of temporal compression and soliton collision, which exhibits an extremely high intensity and a significant redshift but does not need to follow the $\mathsf{L}$-shaped intensity probability distribution.

We present a system capable of generating programmable polarization and frequency-bin hyperentangled photon pairs in an integrated photonic device. The structure is composed of ring resonators, each generating photon pairs with the same polarization in two pairs of frequency bins via spontaneous four-wave mixing. By combining several rings and controlling the amplitude and phase of the pump field, one can construct several hyperentangled states in a piece-by-piece fashion. For example, we consider a system composed of four rings and show that the density operator of the generated state describes a polarization and frequency-bin hyperentangled state. Finally, we calculate the expected generation rate and discuss the device efficiency.

Bipartite entangled states between a qubit and macroscopically distinct states of a mesoscopic system, known as micro-macro entangled states, are emerging resources for quantum information processing. One main challenge in generating such states in the laboratory is their fragility to environmental noise. We analyze this fragility in detail for single-particle noise by identifying what factors play a role in the robustness and quantifying their effect. There is a trade-off between the macroscopicity of a micro-macro entangled state and the robustness of its bipartite entanglement to environmental noise. We identify symmetric micro-macro entangled states as the most robust states to single-particle noise. We show that the robustness of bipartite entanglement of such states to single-particle noise decreases as the second order of macroscopicity, which identifies a regime where the bipartite entangled state is both robust and macroscopic. Our result is a step towards retaining quantum characteristics on large scales and experimental realization of micro-macro entangled spin states and their use for connecting separated qubits. Moreover, it advances our understanding of quantum to classical transition.

Permutation puzzles, such as the Rubik's Cube and the 15 puzzle, are enjoyed by the general public and mathematicians alike. Here we introduce quantum versions of permutation puzzles where the pieces of the puzzles are replaced with indistinguishable quantum particles. The moves in the puzzle are achieved by swapping or permuting the particles. We show that simply permuting the particles can be mapped to a classical permutation puzzle, even though the identical particles are entangled. However, we obtain a genuine quantum puzzle by adding a quantum move: the square root of swap. The resulting puzzle cannot be mapped to a classical permutation puzzle. We focus predominately on the quantization of the $2\times 2$ slide puzzle and briefly treat the $2\times 2\times 1$ Rubik's Cube.

This paper introduces an algorithm designed to approximate quantum transformation matrix with a restricted number of gates by using the block decomposition technique. Addressing challenges posed by numerous gates in handling large qubit transformations, the algorithm provides a solution by optimizing gate usage while maintaining computational accuracy. Inspired by the block decompose algorithm, our approach processes transformation matrices in a blockwise manner, enabling users to specify the desired gate count for flexibility in resource allocation. Simulations validate the effectiveness of the algorithm in approximating transformations with significantly fewer gates, enhancing quantum computing efficiency for complex calculations.

Lasers are the workhorse of quantum engineering in the atomic-molecular-optic community. However, phase noise of the laser, which can be especially large in popular semiconductor-based lasers, can limit gate fidelity. Here we present a fully fiberized instrument detecting and correcting the fast, submicrosecond, phase fluctuations of lasers. We demonstrate a measurement noise floor of less than 0.1 ${\mathrm{Hz}}^2$/Hz and a noise suppression of more than 20 dB for Fourier frequencies in the 1–10 MHz region (reaching up to 30 dB at 3 MHz), where noise is critical for Rydberg-based quantum gates. We observe the improvement offered by this fast-phase-noise eater on a Raman transition driven by two such stabilized lasers. These measurement and correction techniques are important tools for high-fidelity manipulation of the excited electronic states of atoms and molecules.