We present an alternative definition of discrete-time coined quantum walks convenient for capturing a rather broad spectrum of a walker's behavior on arbitrary graphs. It includes and covers both the geometry of possible walker's positions with interconnecting links and the prescribed rule in which directions the walker will move at each vertex. While the former allows for the analysis of inhomogeneous quantum walks on graphs with vertices of varying degree, the latter offers us to choose, investigate, and compare quantum walks with different shift operators. The synthesis of both key ingredients constitutes a well-suited playground for analyzing percolated quantum walks on a quite general class of graphs. Analytical treatment of the asymptotic behavior of percolated quantum walks is presented and worked out in details for the Grover walk on graphs with maximal degree 3. We find that for these walks with cyclic shift operators, the existence of an edge-3 coloring of the graph allows for nonstationary asymptotic behavior of the walk. For different shift operators, the general structure of localized attractors is investigated, which determines the overall efficiency of a source-to-sink quantum transport across a dynamically changing medium. As a simple nontrivial example of the theory, we treat a single-excitation transport on a percolated cube.

We consider the simultaneous coupling of a qubit system to two qubit probes, designed to measure noncommuting qubit observables when working in isolation. While the single meter model usually corresponds to an unsharp measurement of a qubit operator, the double meter model usually describes an informationally complete measurement. The double meter positive operator measurement can be characterized by three vectors associated with the space of Hermitian tracesless observables of the system. The dimension of the linear space generated by these vectors (Bloch rank) is equal to the number of independent operators (or the number of independent Bloch-vector components) which can be estimated. $\mathbb{S}$, the subspace of parameters associated with informationally incomplete measurements (IICs), is characterized either analytically or numerically, and their Bloch rank is used to classify the IICs. Bloch rank of the “simultaneous measurement” of two Pauli matrices is shown to be 2 if the isolated measurements are projective and 3 if they are weak; however, two-meter weak measurements are expected to converge more slowly than their single-meter counterparts.

We propose a quantum reservoir engineering approach for stabilizing Bell states of two superconducting qubits. The system under consideration consists of two linearly coupled superconducting transmission line resonators and two separated flux qubits, one of which is interacted with one resonator. Applying external driving fields to tailor appropriate qubit-resonator interactions, we show that dissipative photons of the resonators can be exploited to autonomously drive and stabilize the two flux qubits into an approximate Bell state at the stationary state. Because of using the dissipative dynamical process, the present approach does not need to well prepare the initial state of the system and exactly monitor the evolution time. Compared with previous schemes, the present one has the remarkable features that the generation of the entangled state is implemented at a single-photon quantum level, and all four Bell states can be generated and stabilized on demand by changing the external driving parameters. Our result may have useful applications for the realization of quantum computation with superconducting quantum circuits.

We propose a measurement scheme that validates the preparation of an $n$-qubit stabilizer state. The scheme involves a measurement of $n$ Pauli observables, a priori determined from the stabilizer state and which can be realized using single-qubit gates. Based on the proposed validation scheme, we derive an explicit expression for the worst-case fidelity, i.e., the minimum fidelity between the stabilizer state and any other state consistent with the measured data. We also show that the worst-case fidelity can be certified, with high probability, using $O\left(n^2\right)$ copies of the state.

High-order above-threshold ionization (HATI) of the ${{\mathrm{H}}_2}^{+}$ ion by a linearly polarized laser field is investigated theoretically using numerical solutions of the full three-dimensional time-dependent Schrödinger equation (TDSE). The photoelectron spectrum is calculated in two ways: by projecting the final wave function onto continuum states satisfying the incoming boundary condition and by using the window-operator method. Our numerical simulations show that the shape of the corresponding photoelectron energy spectra depends on the internuclear distance. For small internuclear distances the obtained HATI spectrum is very similar to the HATI spectrum for atomic targets. By increasing the internuclear distance, i.e., by stretching the molecule, some features emerge in the spectra. The cutoff position of the high-energy photoelectron spectrum extends from $10U_p$ ($U_p$ is the electron ponderomotive energy) for small internuclear distances up to above $18U_p$ for very large internuclear distances. The second observed feature is that, with the increase of the internuclear distance, a low-energy plateau appears which is much higher than the above-mentioned extended plateau. For the internuclear distance of 18 a.u. this plateau extends up to $6U_p$. These features are further investigated by using solutions of the classical equation of motion for the electron in the strong laser field and by using quantum-orbit theory. The results of classical analysis are confirmed using two quantum-mechanical methods based on the analysis of the electron time-dependent probability density and of the electron energy-resolved probability density, obtained from the TDSE solutions.

Dark and gray soliton-like states are shown to emerge from numerically constructed superpositions of translationally invariant eigenstates of the interacting Bose gas in a toroidal trap. The exact quantum many-body dynamics reveals a density depression with ballistic spreading that is absent in classical solitons. A simple theory based on finite-size bound states of holes with quantum-mechanical center-of-mass motion quantitatively explains the time-evolution and predicts quantum effects that could be observed in ultracold gas experiments. The soliton phase step is found relevant for explaining finite-size effects in numerical simulations. An invariant fundamental soliton width is shown to deviate from the Gross-Pitaevskii predictions in the interacting regime and vanishes in the Tonks-Girardeau limit.

We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a two-dimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [N. Dogra, F. Brennecke, S. D. Huber, and T. Donner, Phys. Rev. A 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flottat et al. [T. Flottat, L. de Forges de Parny, F. Hébert, V. G. Rousseau, and G. G. Batrouni, Phys. Rev. B 95, 144501 (2017)]. The salient differences concern the stability of the supersolid phases, which we discuss in detail. Finally, we discuss differences and analogies between the ground-state properties of all-connected bosons with the ones predicted for repulsively interacting dipolar bosons in two dimensions.

Cavity-embedded quantum emitters show strong modifications of free space radiation properties such as an enhanced decay known as the Purcell effect. The central parameter is the cooperativity $C$, the ratio of the square of the coherent cavity coupling strength over the product of cavity and emitter decay rates. For a single emitter, $C$ is independent of the transition dipole moment and dictated by geometric cavity properties such as finesse and mode waist. In a recent work [Phys. Rev. Lett. 119, 093601 (2017)], we have shown that collective excitations in ensembles of dipole-dipole coupled quantum emitters show a disentanglement between the coherent coupling to the cavity mode and spontaneous free space decay. This leads to a strong enhancement of the cavity cooperativity around certain collective subradiant antiresonances. Here, we present a quantum Langevin equations approach aimed at providing results beyond the classical coupled dipoles model. We show that the subradiantly enhanced cooperativity imprints its effects onto the cavity output field quantum correlations while also strongly increasing the cavity-emitter system's collective Kerr nonlinear effect.

Light interaction with random linear or nonlinear media is always an interesting scheme to study Anderson localization of photons and phase-matching-free nonlinear optics. Here, a cavity-enhanced second-harmonic generation (SHG) process in a random nonlinear material was experimentally demonstrated. Compared to the conventional random laser action based on the photoluminescence (PL) effect, this cavity-enhanced SHG indicates a possible Anderson localization of the nonlinear signals by ring cavities and widens the response wave band due to the flexible frequency conversion in the nonlinear process. The combination of the random cavity scheme and the random quasi-phase-matching scheme will provide us another way to break phase-matching limitations, with locally high conversion efficiency. This work suggests important progress on nonlinear Anderson localization and indicates many potential applications, such as a band-tunable random nonlinear laser, phase-matching-free nonlinear optics, and even focusing or imaging through random nonlinear media with a nice conversion efficiency.

Bound states and resonances are physically important solutions of the time-independent Schrödinger equation for a given quantum-mechanical potential. One can find these states using numerical analysis techniques by searching for poles of the scattering amplitude, or equivalently by locating the zeros of particular transcendental complex-valued functions. We show that the evolution of these solutions displays much deeper behavior than one may assume when parameters of the potential are varied, giving insight into the relationship between different types of solutions.

Ongoing experimental activity aims at calorimetric measurements of thermodynamic indicators of quantum integrated systems. We study a model of a driven qubit in contact with a finite-size thermal electron reservoir. The temperature of the reservoir changes due to energy exchanges with the qubit and an infinite-size phonon bath. Under the assumption of weak coupling and weak driving, we model the evolution of the qubit-electron temperature as a hybrid master equation for the density matrix of the qubit at different temperatures of the calorimeter. We compare the temperature evolution with an earlier treatment of the qubit-electron model, where the dynamics were modeled by a Floquet master equation under the assumption of drive intensity much larger than the qubit-electron coupling squared. We numerically and analytically investigate the predictions of the two mathematical models of dynamics in the weak-drive parametric region. We numerically determine the parametric regions where the two models of dynamics give distinct temperature predictions and those where their predictions match.

We demonstrate that incomplete quantum tomography can give conclusive information in experimental realizations. We divide the state space into a union of multiple disjoint subsets and determine conclusively to which of the subsets a system, prepared in completely unknown state, belongs. In other words, we construct and solve membership problems. Our membership problems are partitions of the state space into a union of four disjoint sets formed by fixing two maximally entangled reference states and boundary values of a fidelity function “radius” between the reference states and the unknown preparation. We study the necessary and sufficient conditions of the measurements that solve these membership problems conclusively. We construct and experimentally implement such informationally incomplete measurement on two-photon polarization states with combined one-qubit measurements, and we solve the membership problem in example cases.

Positron-impact electronic excitation cross sections, mean excitation energies, and mass stopping power of the ${\mathrm{H}}_2$ molecule have been calculated for energies from 10 eV up to 2 keV using the convergent close-coupling method that utilizes single- and two-center expansions. Results are compared to previous studies. Application of Bragg's rule of stopping power additivity is discussed by comparing results obtained for atomic (H) and molecular (${\mathrm{H}}_2$) targets for positron impact.

In this article we study quantum phases and the phase diagram of a Fermi-Hubbard model under periodic driving that has been realized in recent cold-atom experiments, in particular, when the driving frequency is nearly resonant with the interaction energy. Due to the driving, the effective Hamiltonian contains a correlated hopping term where the density occupation strongly modifies the hopping strength. Focusing on half filling, in addition to the charge- and spin-density wave phases, large regions of ferromagnetic phase and phase separation are discovered in the weakly interacting regime. The mechanism of this ferromagnetism is attributed to the correlated hopping, because the hopping strength within a ferromagnetic domain is normalized to a larger value than the hopping strength across the domain. Thus, the kinetic energy drives the system into a ferromagnetic phase. We note that this is a different mechanism, in contrast to the well-known Stoner mechanism for ferromagnetism where the ferromagnetism is driven by interaction energy.

In the present paper, we consider the steady state of Fermi atoms coupled to a shaken cavity field at half filling. This shaking generates a time-dependent dynamical optical lattice with backaction on the atomic degrees of freedom. In the high-frequency limit, the shaken dynamical optical lattice produces interesting cavity-field-dependent long-range hoppings, including the nearest-, next-nearest-, and next-next-nearest-neighbor hoppings. They can change the band structures of the system and thus induce nontrivial topological superradiant phases, especially with a large winding number and four degenerate edge states. We also briefly address possible experimental observations of the predicted topological superradiant phases. Our results provide an alternative way to explore novel many-body physics in cavity quantum electrodynamics systems.

We consider a one-dimensional two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2)-symmetry-breaking near-resonant odd- wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.

Most of the self–accelerating beams have monotonous single-channel bending structures, which greatly limit their applications in many fields such as microscopic imaging and particle manipulation. In this paper, the self-accelerating cusp beams with variable numbers of multichannel bending structures are generated to demonstrate the optical transportation and accumulation of micrometer polystyrene particles. The transportation velocity and optical force profiles of the microparticles moving along the bending channels of cusp beams are analyzed. Parallel particle transportation and particle accumulation manipulation from all the bending channels are further demonstrated. These results will inspire a lot of promising applications for self-accelerating beams especially in three-dimensional optical micromanipulation.

Squeezed spin states have important applications in quantum metrology and sensing. It has been shown by Sørensen and Mølmer [Phys. Rev. A 66, 022314 (2002)] that an effective one-axis-twisting interaction can be realized in a cavity setup via a double off-resonance stimulated Raman scattering, resulting in a noise reduction scaling $\propto 1/N^{2/3}$ with $N$ being the atom number. Here, we show that, by making an appropriate change of the initial input spin state, it is possible to produce a one-axis-twisting spin squeezing via a single off-resonance stimulated Raman scattering, which thus can greatly simplify the realistic implementation. We also show that the one-axis-twisting interaction can be transformed into a more efficient two-axis-twisting interaction by rotating the collective spin while coupling to the cavity, yielding a Heisenberg limited noise reduction $\propto 1/N$. Considering the noise effects due to atomic decoherence and cavity decay, we find that substantial squeezing is still attainable with current laboratory techniques.

We study the influence of short-range quantum correlations and classical spatial correlations on the phase diagram of the dissipative XYZ model by using a Gutzwiller Monte Carlo method and a cluster Gutzwiller ansatz for the wave function. Considering lattices of finite size we confirm the emergence of a region with ferromagnetic correlations and two paramagnetic regions and show the emergence of a region with a buildup of ferromagnetic correlations completely missed by mean-field theory. The inclusion of short-range quantum correlations causes drastic alterations of the mean-field correlation functions but our results show that the inclusion of long-range quantum correlations or the use of more sophisticated methods is needed to quantitatively match the exact results. A study of the susceptibility tensor shows that reciprocity is broken, a feature not observed in closed quantum systems. Furthermore, increasing the magnetic field suppresses the magnetization; this is also in contrast with closed quantum systems.