We study the entanglement dynamics of an open quantum system composed of two identical two-level subsystems in a common stationary environment undergoing Markovian dissipation, with the help of a set of physical parameters defined with the collective transition coefficients of the system. We then systematically investigate the steady-state entanglement of such a system and obtain the necessary and sufficient condition for steady-state entanglement when it is initial-state dependent. We also show in particular conditions for steady-state entanglement in some circumstances and propose in general a conjecture for the necessary and sufficient condition when it is independent of the initial state.

Quantum process tomography is an experimental technique to fully characterize an unknown quantum process. Standard quantum process tomography suffers from exponentially scaling of the number of measurements with the increasing system size. In this work, we put forward a quantum machine learning algorithm which approximately encodes the unknown unitary quantum process into a relatively shallow depth parametric quantum circuit. We demonstrate our method by reconstructing the unitary quantum processes resulting from the quantum Hamiltonian evolution and random quantum circuits up to eight qubits. Results show that those quantum processes could be reconstructed with high fidelity, while the number of input states required are at least two orders of magnitude less than required by the standard quantum process tomography.

Quantum sensors, offering novel sensing and imaging technologies beyond the capabilities of any classical device, enable harnessing new technologies from atomic clocks and nanoscale microscopy to gravitational wave detection and delicate biological measurements. We consider the performance of $W$-type quantum states as the probe for the networked quantum sensors. Providing an analytic result on the metrological performance of networked quantum sensors, we attain a criterion for the enhancement of the distributed phase estimations in networked quantum sensors. This insight enables us to compare the metrological power of certain quantum states. We also consider schemes that enable the generation and utility of such entangled quantum probes in practical settings.

In this paper, definitions of the unification condition, the hierarchy condition, and three kinds of monogamy relations for multipartite quantum correlation measures are given and discussed. A computable multipartite multimode Gaussian quantum correlation measure ${\mathcal{M}}^{\left(k\right)}$ is proposed for any $k$-partite multimode continuous-variable systems with $k\ge 2$. The value of ${\mathcal{M}}^{\left(k\right)}$ only depends on the covariance matrices of continuous-variable states, is invariant under any permutation of subsystems, has no ancilla problem, is nonincreasing under $k$-partite local Gaussian channels (particularly, invariant under $k$-partite locally Gaussian unitary operations), and vanishes on $k$-partite product states. For a $k$-partite Gaussian state $\rho , {\mathcal{M}}^{\left(k\right)}\left(\rho \right)=0$ if and only if $\rho$ is a $k$-partite product state. Moreover, ${\mathcal{M}}^{\left(k\right)}$ satisfies the unification condition and the hierarchy condition that a multipartite quantum correlation measure should obey. We also show that ${\mathcal{M}}^{\left(k\right)}$ is not strongly monogamous but completely monogamous and tightly monogamous.

In this work we present a general quantum-mechanical and statistical formulation of the process of interactions of external test particles with plasmas, considering the calculation of the energy-loss coefficients, including energy losses, mean-free paths, and straggling, and describing in detail the differences between protons, positrons, and electrons. Two relevant aspects contained in this formulation are studied: the competing action of loss and gain processes in the interaction with the plasma, and the role of thermal fluctuations in those interactions. We propose two different approaches to evaluate processes of electronic interactions in plasmas. To formulate the first approach we introduce modifications to the quantum-wave-packet dielectric method, which provides a reliable description over wide ranges of plasma densities and temperatures as compared with full quantum-mechanical dielectric theory. The second approach is a semiclassical dielectric method. It consists of including statistical quantum distributions and restrictions in the energy-loss expression, combined with the classical dielectric function for hot plasmas obtained from the linearized Vlasov-Poisson equation. We compare the results from both methods on an extensive range of parameters that include low, intermediate, and high energies, with densities and temperatures going from normal laboratory conditions to very high values, such as those of interest for studies on inertial fusion, Tokamak plasmas, and astrophysical media. We give also special consideration to the case of electrons, where the restrictions imposed by the identity with plasma electrons produce important effects.

The optical generation of high-order harmonics is known to have a strong polarization dependence: In contrast to linearly polarized excitation, circularly polarized light induces practically no harmonics. In the current paper we focus on atomic targets, the case when a well-established physical picture explains the effect: For circular polarization, the photoionized electrons never return to their parent nuclei, and the energy they gained while being accelerated by the field is not transferred into high-order harmonic radiation. This is essentially a picture that is based on real-space electron trajectories (or the dynamics of the wave functions). Here, we provide an alternative description that uses the discrete Sturmian basis, and points out how quantum mechanical interference effects and selection rules can explain the polarization dependence of the process. This emphasizes the importance of space-time symmetries during the process of high-order harmonic generation.

We consider a spin-orbit-coupled Bose-Einstein condensate with nonlocal Rydberg interactions confined in a toroidal trap. Our results show that the interplay among nonlocal Rydberg interactions, contact interactions, spin-orbit coupling, and the external toroidal trap can give rise to a rich variety of ground-state phases, such as lump necklace, chiral supersolid, standing- and plane-wave supersolid, and so on. Furthermore, we clarify the different breaking of symmetry induced by system parameters. Finally, the limiting case of a quasi-one-dimensional ring has also been investigated, and our analytical results agree well with the Gross-Pitaevskii numerical simulations. We also give an experimental protocol to observe these states in future experiments.

We demonstrate one-dimensional Doppler cooling of a beam of buffer-gas-cooled barium monofluoride (BaF) molecules. This represents a key step towards further cooling and trapping of BaF molecules. The dependencies of the cooling efficiency on the detuning of laser, the intensity of the laser, and the bias field are systematically studied. Furthermore, the numerical simulations with a Monte Carlo method agree quite well with our data.

Cavity ring-up spectroscopy (CRUS) can be used to sense ultrafast phenomena with a timescale of a nanosecond and it has been experimentally demonstrated in whispering-gallery-mode (WGM) microresonators. Here, we present a modification of CRUS in which the intensity of the monochromatic laser used to excite a WGM microresonator is changed from one nonzero value to another nonzero value within a very short time. The modification doubles the sampling rate of CRUS at almost no cost, which is important in ultrafast sensing. We first give a theory of the modified CRUS and then show its experimental observation. The obtained results make the developing CRUS more complete.

We propose and design a high-brightness, ultracompact electrically pumped GaSb-based laser source of entangled photons generated by mode-matched intracavity parametric down-conversion of lasing modes. To describe the nonlinear mixing in highly dispersive and dissipative waveguides, we develop a nonperturbative quantum theory of parametric down-conversion of waveguide modes which takes into account the effects of modal dispersion, group and phase mismatch, propagation, dissipation, and coupling to noisy reservoirs. We extend our theory to the regime of quantized pump fields with an approach based on the propagation equation for the state vector which solves the nonperturbative boundary-value problem of the parametric decay of a quantized single-photon pump mode and can be generalized to include the effects of dissipation and noise. Our formalism is applicable to a wide variety of three-wave mixing propagation problems. It provides convenient analytic expressions for interpreting experimental results and predicting the performance of monolithic quantum photonic systems.

Classical random walks on finite graphs have an underrated property: a walk from any vertex can reach every other vertex in finite time, provided they are connected. Discrete-time quantum walks on finite connected graphs, however, can have infinite hitting times. This phenomenon is related to graph symmetry, as previously characterized by the group of direction-preserving graph automorphisms that trivially affect the coin Hilbert space. If a graph is symmetric enough (in a particular sense), then the associated quantum walk unitary will contain eigenvectors that do not overlap a set of target vertices for any coin-flip operator. These eigenvectors span the infinite-hitting-time (IHT) subspace. Quantum states in the IHT subspace never reach the target vertices, leading to infinite hitting times. However, this is not the whole story: the graph of the three-dimensional cube does not satisfy this symmetry constraint, yet quantum walks on this graph with certain symmetric coins can exhibit infinite hitting times. We study the effect of coin symmetry by analyzing the group of coin-permutation symmetries (CPSs): graph automorphisms that act nontrivially on the coin Hilbert space but leave the coin operator invariant. Unitaries using highly symmetric coins with large CPS groups, such as the permutation-invariant Grover coin, are associated with higher probabilities of never arriving, as a result of their larger IHT subspaces.

Phase-space features of the Wigner flow for generic one-dimensional systems with a Hamiltonian $H^W(q,p)$ constrained by the ${\partial }^2{H}^W/\partial q\partial p=0$ condition are analytically obtained in terms of Wigner functions and Wigner currents. Liouvillian and stationary profiles are identified for thermodynamic (TD) and Gaussian quantum ensembles to account for exact corrections due to quantum modifications over a classical phase-space pattern. General results are then specialized to the Harper Hamiltonian system, which, besides working as a feasible test platform for the framework here introduced, admits a statistical description in terms of TD and Gaussian ensembles, where the Wigner flow properties are all obtained through analytical tools. Quantum fluctuations over the classical regime are therefore quantified through probability and information fluxes whenever the classical Hamiltonian background is provided. Besides allowing for a broad range of theoretical applications, our results suggest that such a generalized Wigner approach works as a probe for quantumness and classicality of Harper-like systems in a framework which can be extended to any quantum system described by Hamiltonians in the form of $H^W(q,p)=K\left(p\right)+V\left(q\right)$.

We determine the local symmetries and local transformation properties of certain many-body states called translationally invariant matrix product states (TIMPSs). We focus on physical dimension $d=2$ of the local Hilbert spaces and bond dimension $D=3$ and use the procedure introduced in Sauerwein et al. [Phys. Rev. Lett. 123, 170504 (2019)] to determine all (including nonglobal) symmetries of those states. We identify and classify the stochastic local operations assisted by classical communication (SLOCC) that are allowed among TIMPSs. We scrutinize two very distinct sets of TIMPSs and show the big diversity (also compared to the case $D=2$) occurring in both their symmetries and the possible SLOCC transformations. These results reflect the variety of local properties of MPSs, even if restricted to translationally invariant states with low bond dimension. Finally, we show that states with nontrivial local symmetries are of measure zero for $d=2$ and $D>3$.

Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation, and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian generator of CTQWs, which are the complex phases along the loops of the underlying graph, was acknowledged for its interest in optimizing or suppressing transport on specific topologies. We argue that the quantum-classical distance, a figure of merit which was introduced to capture the difference in dynamics between a CTQW and its classical, stochastic counterpart, guides the optimization of parameters of the Hamiltonian to achieve better quantum transport on cycle graphs and spatial search for the quantum speed limit without an oracle on complete graphs, the latter also implying fast uniform mixing. We compare the variations of this quantity with the 1-norm of coherence and the inverse participation ratio, showing that the quantum-classical distance is linked to both, but in a topology-dependent relation, which is key to spot the most interesting quantum evolution in each case.

The effect of instantaneous spectral diffusion (ISD) on gate operations in rare-earth-ion-doped crystals is an important question to answer for the future of rare-earth quantum computing. Here we present a microscopic modeling that highlights the stochastic nature of the phenomenon and use it to investigate ISD errors on single-qubit gate operations. Furthermore, we present a method to estimate the total error from many different error sources by only studying subsystems containing one error source at a time. This allows us to estimate the total ISD error from all nonqubit dopants in the vicinity of a qubit. We conclude that optical pumping techniques must be used to empty the frequency regions around the qubit transitions from absorption (transmission windows) in order to suppress the ISD errors. Despite using such windows, there remains a roughly $0.3\%$ risk that a qubit has an ISD error larger than the error from other sources. In those cases, the qubit can be discarded and its frequency channel can be reused by another qubit. However, in most cases the ISD errors are significantly smaller than other errors, thus opening up the possibility to perform noisy intermediate-scale quantum (NISQ) algorithms despite ISD being present.

We have measured and calculated fully differential cross sections for vibrational dissociation following capture in 75-keV $p+{\mathrm{H}}_2$ collisions. For a molecular orientation perpendicular to the projectile beam axis and parallel to the transverse momentum transfer we observe a pronounced interference structure. The positions of the interference extrema suggest that the interference term is afflicted with a phase shift which depends on the projectile scattering angle. However, no significant dependence on the kinetic-energy release was observed. Considerable discrepancies between our calculations and experimental data were found.

We analyze the photoexcitation of atoms with a single valence electron by cylindrically polarized Laguerre-Gaussian beams. Theoretical analysis is performed within the framework of first-order perturbation theory and by expanding the vector potential of the Laguerre-Gaussian beam in terms of its multipole components. For cylindrically polarized Laguerre-Gaussian beams, we show that the (magnetic) sub-components of electric-quadrupole field vary significantly in the beam cross section with beam waist and radial distance from the beam axis. We discuss the influence of varying magnetic multipole components in the beam cross section on the sublevel population of a localized atomic target. In addition, we calculate the total excitation rate of electric-quadrupole transition $(4s{}^{2}S_{1/2}\to 3d{}^{2}D_{5/2})$ in a mesoscopic target of a ${\mathrm{Ca}}^{+}$ ion. These calculations shows that the total rate of excitation is sensitive to the beam waist and the distance between the center of the target and the beam axis. However, the excitation by a cylindrically polarized Laguerre-Gaussian beam is found more efficient in driving electric-quadrupole transition in the mesoscopic atomic target than the circularly polarized beams.

The quantum features of ultrashort-pulse optical parametric oscillators (OPOs) are investigated theoretically in the nonlinear regime near and above threshold. Viewing the pulsed OPO as a multimode open quantum system, we rigorously derive a general input-output model that features nonlinear coupling among many cavity (i.e., system) signal modes and a broadband single-pass (i.e., reservoir) pump field. Under appropriate assumptions, our model produces a Lindblad master equation with multimode nonlinear Lindblad operators describing two-photon dissipation and a multimode four-wave-mixing Hamiltonian describing a broadband, dispersive optical cascade, which we show is required to preserve causality. To simplify the multimode complexity of the model, we employ a supermode decomposition to perform numerical simulations in the regime where the pulsed supermodes experience strong single-photon nonlinearity. We find that the quantum nonlinear dynamics induces pump depletion as well as corrections to the below-threshold squeezing spectrum predicted by linearized models. We also observe the formation of non-Gaussian states with Wigner-function negativity and show that the multimode interactions with the pump, both dissipative and dispersive, can act as effective decoherence channels. Finally, we briefly discuss some experimental considerations for potentially observing such quantum nonlinear phenomena with ultrashort-pulse OPOs on nonlinear nanophotonic platforms.