The Hamiltonian and evolution time of a quantum unitary system completely determine a unitary operator, which turns an initial state ${\rho }_0$ into its time-evolved state ${\rho }_t$ and may also turn another state ${\sigma }_0$ into its time-evolved state ${\sigma }_t$. Although the two pairs of states $({\rho }_0,{\rho }_t)$ and $({\sigma }_0,{\sigma }_t)$ are governed by the same Hamiltonian and experience equal evolution periods, their state distances are not necessarily equal to each other. Specifically, the evolution operator contains information about the evolution other than that reflected by two specific states connected through it. As a matter of fact, two pairs of states with different state distances may have equal path distances. Here we propose a geometric measure for the path distance contained in a quantum unitary evolution, which depends only on the unitary operator itself and is independent of any pair of states connected through it. This path distance meets the basic requirements for a good measure of distance and is valid during the whole evolution process, no matter how long the evolution time is. This path distance is bounded by the path length of the evolution from above and by the Bures angle between the two states connected through it from below. It has potential applications in quantum information processing, such as providing another way to study the optimal control between two quantum states. We finally present the form of Hamiltonian to realize a unitary operator on demand.

With the increasing commercial availability of quantum information processing devices the need for testing them efficiently for their specified functionality will arise. Complete quantum channel characterization is out of the question for anything more than the simplest quantum channels for one or two qubits. Quantum functional testing leads to a decision problem with outcomes corresponding to the rejection or acceptance of the claim of the producer that the device parameters are within certain specifications. In this context, we introduce and analyze three ingredients that can speed up this decision problem: the iteration of the channel, efficient decision criteria, and nongreedy adaptive experimental design.

We conduct a systematic study of quantum circuits composed of multiple-control $Z$-rotation (mczr) gates as primitives, since they are widely used components in quantum algorithms and also have attracted much experimental interest in recent years. We establish a circuit-polynomial correspondence to characterize the functionality of quantum circuits over the mczr gate set with continuous parameters. An analytic method for exactly synthesizing such quantum circuit to implement any given diagonal unitary matrix with an optimal gate count is proposed, which also enables the circuit depth optimal for specific cases with pairs of complementary gates. Furthermore, we present a gate-exchange strategy together with a flexible iterative algorithm for effectively optimizing the depth of any mczr circuit, which can also be applied to quantum circuits over any other commuting gate set. Besides the theoretical investigation, the practical performance of our circuit synthesis and optimization techniques is further evaluated numerically on two typical examples in quantum computing, including diagonal Hermitian operators and quantum approximate optimization algorithm circuits with tens of qubits, which can demonstrate a reduction in circuit depth by 33.40% and 15.55% on average over relevant prior works, respectively. Therefore, our methods and results provide a pathway for implementing quantum circuits and algorithms on recently developed devices.

Laser-induced tunneling ionization triggers a broad class of strong-field phenomena in the attosecond community. The understanding and application of these ultrafast phenomena require accurate knowledge of the position information for the tunneling electron wave packet (EWP). Here, with strong-field photoelectron holography, we theoretically demonstrate a scheme to retrieve the position of the EWP emitted from molecules in the direction perpendicular to the tunnel. In our scheme, the photoelectron momentum distributions from strong-field tunneling ionization are obtained by solving the time-dependent Schrödinger equation. When the molecule is aligned with a nonzero angle to the linearly polarized laser field, a distinct shift of the holographic pattern in the photoelectron momentum distribution is observed. With the quantum-orbit model, we demonstrate that the shift of the holographic pattern is caused by a nonzero initial transverse position of the EWP immediately after tunneling. By tracing their exact correspondence and examining the shift of the holographic pattern, the transverse emission position of the tunnel-ionized EWP is probed accurately. Furthermore, we demonstrate that the complex Coulomb interaction can be safely canceled in our scheme by performing the scheme for both of the model molecules with the short-range and Coulomb potentials. The validity and accuracy of our scheme are confirmed by its application to different molecules, alignments, and laser parameters.

Atom and, more recently, molecule interferometers are used in fundamental research and industrial applications. Most atom interferometers rely on gratings made from laser beams, which can provide high precision, but cannot reach very short wavelengths and require complex laser systems to function. Contrary to this, simple monolithic interferometers cut from single crystals offer (sub) nanometer wavelengths with an extreme level of stability and robustness. Such devices were conceived and demonstrated several decades ago for neutrons and electrons. Here, we propose a monolithic design for a thermal-beam molecule interferometer based on (quantum) reflection. We show, as an example, how a reflective, monolithic interferometer (Mach-Zehnder type) can be realized for a helium beam using $\mathrm{Si}\left(111\right)\text{−}\mathrm{H}(1\times 1)$ surfaces, which have previously been demonstrated to act as very robust and stable diffractive mirrors for neutral helium atoms.

The generalization of the area theorem is derived for the case of a pulse circulating inside a ring laser cavity. In contrast to the standard area theorem, which is valid for a single pass of a traveling pulse through a resonant medium, the obtained generalized area theorem takes into account the medium-assisted nonlinear self-action effects through the medium excitation left by the pulse at the previous round-trip in the cavity. The generalized area theorem was then applied to the theoretical description of the dynamics of a single-section ring-cavity laser and the steady solutions for the pulse area and for the medium parameters were found both in the limit of a lumped model and for a spatially extended system. The derived area theorem can be used for the convenient analytical description of different coherent photonic devices, such as coherently mode-locked lasers or pulse compressors, as well as for the analysis of the photon echo formation in cavity-based setups.

Cluster states are versatile quantum resources and an essential building block for measurement-based quantum computing. The possibility to generate cluster states in specific systems may thus serve as an indicator regarding if and to what extent these systems can be harnessed for quantum technologies and quantum information processing in particular. Here, we apply this analysis to networks of degenerate optical parametric oscillators (DOPOs), also called coherent Ising machines (CIMs). CIMs are distinguished by their highly flexible coupling capabilities, which makes it possible to use them, e.g., to emulate large spin systems. As CIMs typically operate with coherent states (and superpositions thereof), it is natural to consider cluster states formed by superpositions of coherent states, i.e., coherent cluster states. As we show, such coherent cluster states can, under ideal conditions, be generated in DOPO networks with the help of beam splitters and classical pumps. Our subsequent numerical analysis provides the minimum requirements for the generation of coherent cluster states under realistic conditions. Moreover, we discuss how nonequilibrium pumps can improve the generation of coherent cluster states. In order to assess the quality of the cluster-state generation, we map the generated states to an effective spin space using modular variables, which allows us to apply entanglement criteria tailored for spin-based cluster states.

We study the emission spectrum of two distant qubits strongly coupled to a waveguide by using the numerical and analytical approaches, which are beyond the Markovian approximation and the rotating-wave approximation. The numerical approach combines the Dirac-Frenkel time-dependent variational principle with the multiple Davydov $D_1$ ansatz. A transformed rotating-wave approximation (TRWA) treatment and a standard perturbation (SP) are used to analytically calculate the emission spectrum. It is found that the variational approach and the TRWA treatment yield accurate emission spectra of the two distant qubits in certain strong-coupling regimes while the SP breaks down. The emission spectrum is found to be asymmetric irrespective of the two-qubit distance and exhibits a single peak, double peaks, and multiple peaks depending on the two-qubit distance as well as the initial states. In sharp contrast with the single-qubit case, the excited-state populations of the two qubits can ultraslowly decay due to the subradiance even in the presence of a strong qubit-waveguide coupling, which in turn yields an ultranarrow emission line. Our results provide insights into the emission spectral features of the two distant qubits in the strong light-matter coupling regime.

Bound-state formation is a classic feature of quantum mechanics, where a particle localizes in the vicinity of an attractive potential. This is typically understood as the particle lowering its potential energy. In this article, we discuss a paradigm where bound states arise purely due to kinetic-energy considerations. This phenomenon occurs in certain nonmanifold spaces that consist of multiple smooth surfaces that intersect one another. The intersection region can be viewed as a singularity where dimensionality is not defined. We demonstrate this idea in a setting where a particle moves on $M$ spaces $(M=2,3,4,...)$, each of dimensionality $D$ ($D=1,2$, and 3). The spaces intersect at a common point, which serves as a singularity. To study quantum behavior in this setting, we discretize space and adopt a tight-binding approach. We generically find a ground state that is localized around the singular point, bound by the kinetic energy of “shuttling” among the $M$ surfaces. We draw a quantitative analogy between singularities on the one hand and local attractive potentials on the other. To each singularity, we assign an equivalent potential that produces the same bound state wave function and binding energy. The degree of a singularity $M$ (the number of intersecting surfaces) determines the strength of the equivalent potential. With $D=1$ and $D=2$, we show that any singularity creates a bound state. This is analogous to the well-known fact that any attractive potential creates a bound state in one and two dimensions. In contrast, with $D=3$, bound states appear only when the degree of the singularity exceeds a threshold value. This is analogous to the fact that in three dimensions, a threshold potential strength is required for bound-state formation. We discuss implications for experiments and theoretical studies in various domains of quantum physics.

Noiseless linear amplifiers (NLAs) provide a powerful tool to achieve long-distance continuous-variable (CV) quantum key distribution (QKD) in the presence of realistic setups with nonunit reconciliation efficiency. We address a NLA-assisted CV QKD protocol implemented via realistic physical NLAs, namely, quantum scissors and single-photon catalysis, and compare their performance with respect to the ideal NLA $g^{\widehat{n}}$. We investigate also the robustness of two schemes against inefficient conditional detection and discuss the two alternative scenarios in which the gain associated with the NLA is either fixed or optimized.

Optimal quantum control of continuous variable systems poses a formidable computational challenge because of the high-dimensional character of the system dynamics. The framework of quantum invariants can significantly reduce the complexity of such problems, but it requires the knowledge of an invariant compatible with the Hamiltonian of the system in question. We explore the potential of a Gaussian invariant that is suitable for quadratic Hamiltonians with any given number of motional degrees of freedom for quantum optimal control problems that are inspired by current challenges in ground-state to ground-state shuttling of trapped ions.

Many-body perturbation theory is implemented to calculate the isotope shifts of $4s$, $4p_{1/2}$, $4p_{3/2}$, $3d_{3/2}$, and $3d_{5/2}$ energy levels of ${\mathrm{Ca}}^{+}$ for even isotopes $A=40$, 42, 44, 46, 48. The results are presented for mass shift and field shift, as well as for higher-order field shifts, quadratic mass shift, nuclear polarization correction, and the cross term between field and mass shifts. Additionally, we examine King-plot nonlinearities introduced by higher-order isotope-shift corrections to the combinations of $3d_{3/2}\to 4s$, $3d_{5/2}\to 4s$, and $4p_{1/2}\to 4s$ transitions. For these transitions, second-order mass shift and nuclear polarization correction are identified as the dominant sources of King-plot nonlinearity.

Differential studies of the proton-helium scattering problem using the two-center wave-packet convergent close-coupling approach is extended to the calculation of the ionization cross section differential in the electron emission energy and the projectile scattering angle. The results obtained using the correlated two-electron and effective one-electron methods are in reasonably good agreement with experiment. While the shape of the doubly differential cross section generally agrees with the results of the experiment, at some emission energies its magnitude does not. This appears consistent with similar disagreement seen in the singly differential cross section at the same emission energies.

We experimentally measure the photoelectron momentum distributions of multiphoton ionization of aligned ${\mathrm{N}}_2$ molecules at 400 nm. The phase structure of the ionized electron wave packet is probed with a weak parallelly polarized field at 800 nm. By inspecting the two-color phase-resolved photoelectron interference fringes, we observe a relative phase shift between the yields of above-threshold ionization and sideband peaks that depends on the molecular alignment angle. With the support of molecular strong-field approximation, we show the measured alignment-dependent relative phase shift is associated with the initial phase of electron wave packet dictated by the molecular orbital at the ionization exit, which is mapped into the intracycle interference. We find that the initial phase which depends on the molecular alignment can be modulated by the two-color synthesized fields and decreases with increasing photoelectron energy. Finally, we demonstrate the alignment-dependent phase shift in momentum space allows the retrieval of the relative spatial displacement for electrons at the ionization exit in position space between different alignments.

We propose the redistribution-reconfiguration (red-rec) algorithm to prepare large configurations of atoms using programmable arrays of optical traps. Red-rec exploits simple heuristics and exact subroutines to solve atom reconfiguration problems on grids. It admits a fast and efficient implementation suitable for real-time operation. We numerically quantify its performance using realistic physical parameters and operational constraints, in both the absence and presence of loss. Red-rec enables assembling large configurations of atoms with high mean success probability. Fast preparation times are achieved by harnessing parallel control operations that actuate multiple traps simultaneously. Faster preparation times are achieved by rejecting configurations of atoms containing fewer atoms than a given threshold. However, the number of traps required to prepare a compact-centered configuration of atoms on a grid with a probability of 0.5 scales as the 3/2 power of the number of desired atoms. This finding highlights some of the challenges associated with scaling up configurations of atoms beyond tens of thousands of atoms.

Programmable arrays of optical traps enable the assembly of configurations of single atoms to perform controlled experiments on quantum many-body systems. Finding the sequence of control operations to transform an arbitrary configuration of atoms into a predetermined one requires solving an atom reconfiguration problem quickly and efficiently. A typical approach to solving atom reconfiguration problems is to use an assignment algorithm to determine which atoms to move to which traps. This approach results in control protocols that exactly minimize the number of displacement operations; however, this approach does not optimize for the number of displaced atoms or the number of times each atom is displaced, resulting in unnecessary control operations that increase the execution time and failure rate of the control protocol. In this work we propose the assignment-rerouting-ordering (ARO) algorithm to improve the performance of assignment-based algorithms in solving atom reconfiguration problems. The ARO algorithm uses an assignment subroutine to minimize the total distance traveled by all atoms, a rerouting subroutine to reduce the number of displaced atoms, and an ordering subroutine to guarantee that each atom is displaced at most once. The ordering subroutine relies on the existence of a partial ordering of moves that can be obtained using a polynomial-time algorithm that we introduce within the formal framework of graph theory. We numerically quantify the performance of the ARO algorithm in the presence and in the absence of loss and show that it outperforms the exact, approximation, and heuristic algorithms that we use as benchmarks. Our results are useful for assembling large configurations of atoms with high success probability and fast preparation time, as well as for designing and benchmarking novel atom reconfiguration algorithms.

Odd-even harmonic generation contains the system's dynamical symmetry breaking, and its decoding is desirable not only in understanding physics but also for applications of dynamics extraction. In this work we discover a simple universal relation between the odd-even harmonics and the asymmetry of the terahertz (THz)-assisted laser-atomic system: atoms in a primary midinfrared laser pulse combined with a THz laser. We demonstrate numerically and then derive analytically the dependence of the harmonic even-to-odd ratio on the THz electric field. Notably, the functional form of this dependency reveals a universal scaling independent of the parameters of both the primary pulse and atomic target. This universality inspires us to propose a pump-probe scheme for THz waveform sampling from the even-to-odd ratio, accessible from conventional compact setups.

In this paper, we study static bistability and mechanical cooling of a dissipative optomechanical cavity filled with a Kerr medium. The system exhibits optical bistability for a wide input-power range with the power threshold being greatly reduced, in contrast to the case of purely dissipative coupling. At the bistable regime, the membrane can be effectively cooled down to a few millikelvin from the room temperature under the unresolved sideband condition, where the effective mechanical temperature is a nonmonotonic function of intracavity intensity and reaches its minimum near the turning point of the upper stable branch. When the system is in the cryogenics environment, the effective mechanical temperature at the bistable regime shows a similar feature as in the room temperature case, but the optimal cooling appears at the monostable regime and approaches the mechanical ground state. Our results are of interest for further understanding bistable optomechanical systems, which have many applications in nonclassical state preparations and quantum information processing.

Moving objects with optical or acoustical waves are topics both of fundamental interest and of importance for a range of practical applications. One particularly intriguing example is the tractor beam, which pulls an object toward the wave's source, in opposition to the wave's momentum. In this study, we introduce a protocol that enables the identification of wave states that produce the optimal tractor force for arbitrary objects. Our method relies solely on the solution of a simple eigenvalue problem involving the system's measurable scattering matrix. Using numerical simulations, we demonstrate the efficacy of this wavefront shaping protocol for a representative set of different targets. Moreover, we show that the diffractive nature of waves enables the possibility of a tractor beam that works even for targets where a geometric optics approach fails to explain the pulling forces.

Kerr frequency combs generated in high-$Q$ microresonators offer an immense potential in many applications, and predicting and quantifying their behavior, performance, and stability is key to systematic device design. Based on an extension of the Lugiato-Lefever equation we investigate in this paper the perspectives of changing the pump scheme from the well-understood monochromatic pump to a dual-tone configuration simultaneously pumping two modes. For the case of anomalous dispersion we give a detailed study of the optimal choices of detuning offsets and division of total pump power between the two modes in order to optimize single-soliton comb states with respect to performance metrics like power conversion efficiency and bandwidth. Our approach allows us also to quantify the performance metrics of the optimal single-soliton comb states and determine their trends over a wide range of technically relevant parameters.