Higher-order topological superfluids have gapped bulk and symmetry-protected Majorana zero modes with various localizations. Motivated by recent advances, we present a proposal for synthesizing multiorder topological superfluids that support various Majorana zero modes in ultracold atomic gases. For this purpose, we use the two-dimensional optical superlattice that introduces a spatial modulation to the spin-orbit coupling in one direction, providing an extra degree of freedom for the emergent higher-order topological state. We find the topologically trivial superfluids, first-order and second-order topological superfluids, as well as different topological phase transitions among them with respect to the experimentally tunable parameters. Besides the conventional transition characterized by the Chern number associated with the bulk gap closing and reopening, we find the system can support the topological superfluids with Majorana corner modes, but the topological phase transition undergoes no gap-closing of bulk bands. Instead, the transition is refined by the quadrupole moment and signaled out by the gap-closing of edge states. The proposal is based on the $s$-wave interaction and is valid using existing experimental techniques, which unifies multiorder topological phase transitions in a simple but realistic system.

Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single-photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this Letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave packets that can excite a given superposition of these bound states. As specific examples, we study bound-state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.

The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. In QAOA, a quantum circuit is trained—by repeatedly adjusting circuit parameters—to solve a problem instance. Several recent findings have reported parameter concentration effects in QAOA and their presence has become one of folklore: while empirically observed, the concentrations have not been defined and analytical approaches remain scarce, focusing on limiting system sizes while neglecting parameter scaling as system size increases. We found that optimal QAOA circuit parameters concentrate as an inverse polynomial in the problem size, providing an optimistic result for improving circuit training. Our results are analytically demonstrated for QAOA at $p=1,2$ (corresponding to 2 and 4 tunable parameters, respectively). The technique is also applicable for higher depths wherein the concentration effect is cross verified numerically. Parameter concentrations allow for training on a fraction $w<n$ of qubits to assert that these parameters are nearly optimal on $n$ qubits, thereby reducing training time.

Understanding the quantum properties of many-body states is important in the fields of both quantum information and condensed-matter physics. For this purpose, we generalize the basic concept of the anticommutator from two operators to the many-body case. Some key properties are given for the many-body anticommutators, and examples are provided for Pauli operators and density matrices. Using these results and techniques from the symmetry group, in a straightforward way, we give the normalization of the completely symmetric states with Majorana's stellar representations. Our developed method will help to pave the way in the study of many-body symmetric systems.

The core of security proofs of quantum key distribution (QKD) is the estimation of a parameter that determines the amount of privacy amplification that the users need to apply in order to distill a secret key. To estimate this parameter using the observed data, one needs to apply concentration inequalities such as random sampling theory or Azuma's inequality. The latter can be straightforwardly employed in a wider class of QKD protocols, including those that do not rely on basis-independent sources such as the loss-tolerant (LT) protocol. However, when applied to real-life finite-length QKD experiments, Azuma's inequality typically results in substantially lower secret-key rates. Here we propose an alternative security analysis of the LT protocol against general attacks, for both its prepare-and-measure and measurement-device-independent versions, that is based on random sampling theory. Consequently, our security proof provides considerably higher secret-key rates than the previous finite-key analysis based on Azuma's inequality. This work opens up the possibility of using random sampling theory to provide alternative security proofs for other QKD protocols.

A constellation of $N=d-1$ Majorana stars represents an arbitrary pure quantum state of dimension $d$ or a permutation-symmetric state of a system consisting of $n$ qubits. We generalize the latter construction to represent in a similar way an arbitrary symmetric pure state of $k$ subsystems with $d$ levels each. For $d\ge 3$, such states are equivalent, as far as rotations are concerned, to a collection of various spin states, with definite relative complex weights. Following Majorana's lead, we introduce a multiconstellation, consisting of the Majorana constellations of the above spin states, augmented by an auxiliary, “spectator” constellation, encoding the complex weights. Examples of stellar representations of symmetric states of four qutrits, and two spin-3/2 systems, are presented. We revisit the Hermite and Murnaghan isomorphisms, which relate multipartite states of various spins, number of parties, and even symmetries. We show how the tools introduced can be used to analyze multipartite entanglement and to identify optimal quantum rotosensors, i.e., pure states which are maximally sensitive to rotations around a specified axis, or averaged over all axes.

Passive side-channel attacks in quantum key distribution (QKD) aim at obtaining information about the quantum signals without disturbing them and hence compromise real-world QKD security. Currently, there are no reliable tools for the assessment of QKD signal generation imperfections. In this work we propose a generic experimental method which allows to upper-bound QKD light-source imperfections and directly integrate them into the modern security proofs. The method relies on Hong-Ou-Mandel interference between different emitted signals: the maximum interference visibility reveals overall signal distinguishability that could lead to passive side-channel information leakage. We apply it for the standard decoy-state BB84 protocol and calculate a lower bound on the secret key rate for realistic values of interference visibility. The method can be readily implemented in practical QKD setups and is especially relevant for multiple-laser QKD systems such as the one installed on the Micius satellite.

We theoretically investigate high-order harmonic generation (HHG) in one-dimensional model solids with linearly polarized laser pulses. By identifying crystal-momentum-resolved contributions, we show that the reason behind the odd-order harmonics-dominated harmonic spectrum originates from the interferences between harmonics generated by different crystal momentum channels. Symmetry analysis show that constructive interferences between odd-order harmonics and destructive interferences between even-order harmonics are determined by the inversion symmetry of the band dispersion and the time translation symmetry of the laser field. We also propose and numerically demonstrate a method to select the short and long trajectories for HHG in solids. It is shown that the classical trajectories predicted by quasiclassical model are associated with the quantum orbits that originate from a single crystal momentum channel. However, the classical trajectories predicted by the recollision model are associated with all of the crystal momentum channels in the entire first Brillouin zone, and the interferences between harmonics generated by different crystal momentum channels play a key role in the formation of recollision quantum orbits. Moreover, we find that the effect of dephasing time is the damping of the current rather than changing the harmonic phases. The present results may contribute to disentangling the underlying mechanism of HHG in solids.

In two-dimensional bosonic systems ultrasoft interactions develop an interesting phenomenology that ultimately leads to the appearance of supersolid phases in free space conditions. While suggested in early theoretical works and despite many further analytical efforts, the appearance of these exotic phases as well as the detailed shape of the ground-state phase diagrams have not been established yet. Here we develop a variational mean-field calculation for a generic quantum system with cluster-forming interactions. We show that by including the restriction of a fixed integer number of particles per cluster the ground-state phase diagram can be obtained in great detail. The great detail includes the determination of coexistence regimes of crystals of different occupancy as well as crystals with superfluid phases. To illustrate the application of the method we consider the softened van der Waals potential, for which the phase diagram is known via quantum Monte Carlo simulations. For densities other than that corresponding to the single-particle crystal, our results show very good quantitative agreement with the simulations regarding the location of the superfluid transitions. Additionally, the phase diagrams suggest that the solid-superfluid coexistence could be a reliable marker to locate supersolidity.

We propose a method for generating programmable interactions in one- and two-dimensional trapped-ion quantum simulators. Here we consider the use of optical tweezers to engineer the sound-wave spectrum of trapped ion crystals. We show that this approach allows us to tune the interactions and connectivity of the ion qubits beyond the power-law interactions accessible in current setups. We demonstrate the experimental feasibility of our proposal using realistic tweezer settings and experimentally relevant trap parameters to generate the optimal tweezer patterns to create target spin-spin interaction patterns in both one- and two-dimensional crystals. Our approach will advance quantum simulation in trapped-ion platforms as it allows them to realize a broader family of quantum spin Hamiltonians.

Spin ensembles coupled to optical cavities provide a powerful platform for engineering synthetic quantum matter. Recently, we demonstrated that cavity-mediated infinite-range interactions can induce fast scrambling in a Heisenberg $\mathrm{XXZ}$ spin chain [Phys. Rev. Research 2, 043399 (2020)]. In this paper, we analyze the kaleidoscope of quantum phases that emerge in this system from the interplay of these interactions. Employing both analytical spin-wave theory as well as numerical density-matrix renormalization group calculations, we find that there is a large parameter regime where the continuous $U\left(1\right)$ symmetry of this model is spontaneously broken and the ground state of the system exhibits $\mathrm{XY}$ order. This kind of symmetry breaking and the consequent long-range order is forbidden for short-range interacting systems by the Mermin-Wagner theorem. Intriguingly, we find that the $\mathrm{XY}$ order can be induced by even an infinitesimally weak infinite-range interaction. Furthermore, we demonstrate that in the $U\left(1\right)$ symmetry-broken phase, the half-chain entanglement entropy violates the area law logarithmically. Finally, we discuss a proposal to verify our predictions in state-of-the-art quantum emulators.

We investigate a species selective cooling process of a trapped $\mathrm{SU}\left(N\right)$ Fermi gas using entropy redistribution during adiabatic loading of an optical lattice. Using high-temperature expansion of the Hubbard model, we show that when a subset $N_A<N$ of the single-atom levels experiences a stronger trapping potential in a certain region of space, the dimple, it leads to improvement in cooling as compared to an $\mathrm{SU}\left(N_A\right)$ Fermi gas only. We show that optimal performance is achieved when all atomic levels experience the same potential outside the dimple and we quantify the cooling for various $N_A$ by evaluating the dependence of the final entropy densities and temperatures as functions of the initial entropy. Furthermore, considering ${}^{87}\mathrm{Sr}$ and ${}^{173}\mathrm{Yb}$ for specificity, we provide a quantitative discussion of how the state selective trapping can be achieved with readily available experimental techniques.

We investigate a theoretical model for a dynamic Moiré grating which is capable of producing slow and stopped light with improved performance when compared with a static Moiré grating. A Moiré grating superimposes two grating periods, which creates a narrow slow light resonance between two band gaps. A Moiré grating can be made dynamic by varying its coupling strength in time. By increasing the coupling strength the reduction in group velocity in the slow light resonance can be improved by many orders of magnitude while still maintaining the wide bandwidth of the initial, weak grating. We show that for a pulse propagating through the grating this is a consequence of altering the pulse spectrum, and therefore the grating can also perform bandwidth modulation. Finally we present a possible realization of the system via an electro-optic grating by applying a quasistatic electric field to a poled ${\chi }^{\left(2\right)}$ nonlinear medium.

In this work, we report a general reflection model to describe the reflected behaviors of a Gaussian beam near photonic Dirac point at the optical interface. With spin polarized electromagnetic waves strikes near the single Dirac point on Dirac material interface, vortical phase distribution and spin inversion are demonstrated for reflected state, and we further develop a higher-order Poincaré sphere to describe the evolution of polarization states. It is possible to generate any desired Poincaré vortex beam on the sphere by modulating the incident polarization state of light. Moreover, we discuss the case of normal incidence around two adjacent Dirac points, reflection spectrum involves a couple of spin flip vortices corresponding to two points with the corresponding topological invariants, which are consistent with the Berry curvature and topological charge. These results can be extended to similar hyperbolic metamaterials with degenerate point, and inspire a different perspective for manipulating polarized vortex beam with photonic Dirac point.

We investigate theoretically and numerically the self-similar propagation of optical pulses in the presence of gain, positive Kerr nonlinearity, and positive (i.e., normal) dispersion of even order $m$. Starting from a modified nonlinear Schrödinger equation, separating the evolution of amplitude and phase, we find that the resulting equations simplify considerably in the asymptotic limit. Exact solutions to the resulting equations indicate that the temporal intensity profile follows a $1-T^{m/(m-1)}$ function with an $m$-dependent scaling relation, with a $T^{1/(m-1)}$ chirp, where $T$ is the pulse's local time. These correspond to a triangle and a step function, respectively, as $m\to \infty$. These results are borne out by numerical simulations, although we do observe indications of nonasymptotic behavior.

Loss compensation via inserting gain is of fundamental importance in different branches of photonics, nanoplasmonics, and metamaterial science. This effect has found an impressive implementation in the parity-time symmetric ($\mathcal{PT}$-symmetric) structures possessing balanced distribution of loss and gain. In this paper, we generalize this phenomenon to the asymmetric systems demonstrating loss compensation in the coupled multimode loss-gain dielectric waveguides of different radii. We show that similar to the $\mathcal{PT}$-symmetric coupled single-mode waveguides of identical radii, the asymmetric systems support the exceptional points called here the loss-compensation (LC) thresholds where the frequency spectrum undergoes a transition from complex to real values. Moreover, the LC thresholds can be obtained for dissimilar modes excited in the waveguides providing an additional degree of freedom to control the system response. In particular, changing loss and gain of asymmetric coupled waveguides, we observe loss compensation for TM and TE modes as well as for the hybrid HE and EH modes.

Cluster states are useful in many quantum information processing applications. In particular, universal measurement-based quantum computation (MBQC) utilizes two-dimensional cluster states [R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)] and topologically fault-tolerant MBQC requires cluster states of dimension 3 or higher [R. Raussendorf et al., New J. Phys. 9, 199 (2007)]. This work proposes a protocol to deterministically generate multidimensional photonic cluster states using a single atom-cavity system and time-delay feedback. The dimensionality of the cluster state increases linearly with the number of time-delay feedbacks. We first give a diagrammatic derivation of the tensor network states, which is valuable in simulating matrix product states and projected entangled pair states generated from sequential photons. Our method also provides a simple way to bridge and analyze the experimental imperfections and the logical errors of the generated states. In this method, we analyze the generated cluster states under realistic experimental conditions and address both one-qubit and two-qubit errors. Through numerical simulation, we observe an optimal atom-cavity cooperativity for the fidelity of the generated states, which is surprising given the prevailing assumption that higher-cooperativity systems are inherently better for photonic applications.

Entanglement verification and measurement is essential for experimental tests of quantum mechanics and also for quantum communication and information science. Standard methods of verifying entanglement in a bipartite mixed state require detection of both particles and involve coincidence measurement. We present a method that enables us to verify and measure entanglement in a two-photon mixed state without detecting one of the photons, i.e., without performing any coincidence measurement or postselection. We consider two identical sources, each of which can generate the same two-photon mixed state but they never emit simultaneously. We show that one can produce a set of single-photon interference patterns, which contain information about entanglement in the two-photon mixed state. We prove that it is possible to retrieve the information about entanglement from the visibility of the interference patterns. Our method reveals a distinct avenue for verifying and measuring entanglement in mixed states.

In their interesting paper [Phys. Rev. A 99, 032312 (2019)], Chen et al. consider the completely symmetric (CS) states, which are invariant under any index permutation. They proved that the CS states are separable if and only if they are a convex combination of real symmetric pure product states in Theorem 14, and claimed that any CS state in a two-qutrit system is separable in Theorem 20. We point out that their proof of Theorem 20 is flawed because of invalid assumptions. Furthermore, we present a sufficient and necessary condition for the separability of the CS states in two-qutrit systems.