Quantum optimal control represents a powerful technique to enhance the performance of quantum experiments by engineering the controllable parameters of the Hamiltonian. However, the computational overhead for the necessary optimization of these control parameters drastically increases as their number grows. We devise a variant of a gradient-free optimal-control method by introducing the idea of phase-modulated driving fields, which allows us to find optimal control fields efficiently. We numerically evaluate its performance and demonstrate the advantages over standard Fourier-basis methods in controlling an ensemble of two-level systems showing an inhomogeneous broadening. The control fields optimized with the phase-modulated method provide an increased robustness against such ensemble inhomogeneities as well as control-field fluctuations and environmental noise, with one order of magnitude less of average search time. Robustness enhancement of single quantum gates is also achieved by the phase-modulated method. Under environmental noise, an XY-8 sequence constituted by optimized gates prolongs the coherence time by $50\%$ compared with standard rectangular pulses in our numerical simulations, showing the application potential of our phase-modulated method in improving the precision of signal detection in the field of quantum sensing.

The addition of a photon into the same mode as a coherent state produces a nonclassical state that has interesting features, including quadrature squeezing and a sub-Poissonian photon-number distribution. The squeezed nature of photon-added coherent (PAC) states potentially offers an advantage in quantum sensing applications. Previous theoretical works have employed a single-mode treatment of PAC states. Here, we use a continuous-mode approach that allows us to model PAC state pulses. We study the properties of a single-photon and coherent-state wave packet superimposed with variable temporal and spectral overlap. We show that, even without perfect overlap, the state exhibits a sub-Poissonian number distribution, second-order quantum correlations, and quadrature squeezing for a weak coherent state. We also include propagation loss in waveguides and study how the fidelity and other properties of PAC state pulses are affected.

The Griffiths-McCoy singularity is a phenomenon characteristic of low-dimensional disordered quantum spin systems, in which the magnetic susceptibility shows singular behavior as a function of the external field even within the paramagnetic phase. We study whether this phenomenon is observed in the transverse-field Ising model with disordered ferromagnetic interactions on the quasi-two-dimensional diluted Chimera graph both by quantum Monte Carlo simulations and by extensive experiments on the D-Wave quantum annealer used as a quantum simulator. From quantum Monte Carlo simulations, evidence is found for the existence of the Griffiths-McCoy singularity in the paramagnetic phase. The experimental approach on the quantum hardware produces results that are less clear cut due to the intrinsic noise and errors in the analog quantum device but can nonetheless be interpreted to be consistent with the existence of the Griffiths-McCoy singularity as in the Monte Carlo case. This is the first experimental approach based on an analog quantum simulator to study the subtle phenomenon of Griffiths-McCoy singularities in a disordered quantum spin system, through which we have clarified the capabilities and limitations of the D-Wave quantum annealer as a quantum simulator.

Masking information is a protocol that encodes quantum information into a bipartite entangled state while the information is completely unknown to local systems. This paper explicitly studies the structure of the set of maskable states and its relation to hyperdisks. We prove that, although the qubit states which can be masked must locate on a single hyperdisk, the set of maskable states can consist of two or more hyperdisks for high-dimensional cases. Our results may shed light on several research fields of quantum information theory, such as the structure of entangled states and the local discrimination of bipartite states.

We present a comprehensive theoretical study of the cross-resonance gate operation covering estimates for gate parameters and gate error as well as analyzing spectator qubits and multiqubit frequency collisions. Starting from the Josephson nonlinearity and by accounting for the eigenstates renormalization, due to counterrotating terms, we derive a starting model for the cross-resonance gate with modified qubit-qubit interaction and drive matrix elements. Employing time-dependent Schrieffer-Wolff perturbation theory, we derive an effective Hamiltonian for the cross-resonance gate with estimates for the gate parameters calculated up to the fourth order in drive amplitude. The model with renormalized eigenstates lead to 10%–15% relative correction of the effective gate parameters compared to Kerr theory. We find that gate operation is strongly dependent on the ratio of qubit-qubit detuning and anharmonicity. In particular, we characterize five distinct regions of operation, and propose candidate parameter choices for achieving high gate speed and low coherent gate error when the cross-resonance tone is equipped with an echo pulse sequence. Furthermore, we generalize our method to include a third spectator qubit and characterize possible detrimental multiqubit frequency collisions.

The total two-photon decay rate of hydrogenlike ions is studied using relativistic quantum electrodynamics. In particular, we analyze how finite nuclear size and QED vacuum polarization corrections affect the decay rate. To calculate these corrections, a finite basis set method based on $B$ splines is used for the generation of quasicomplete atomic spectra and, hence, of the relativistic Green's function. By making use of this $B$-spline approach, high precision calculations have been performed for the $2s_{1/2}\to 1s_{1/2}+2\gamma$ and $2p_{1/2}\to 1s_{1/2}+2\gamma$ decay of hydrogenlike ions along the entire isoelectronic sequence. The results of these calculations show that both QED and finite nuclear size effects are comparatively weak for the $2s_{1/2}\to 1s_{1/2}+2\gamma$ transition. In contrast, they are much more pronounced for the $2p_{1/2}\to 1s_{1/2}+2\gamma$ decay, where, for hydrogenlike uranium, the decay rate is reduced by 0.484% due to the finite nuclear size and enhanced by 0.239% if the vacuum polarization is taken into account.

The negative ion of lanthanum, $\mathrm{L}{\mathrm{a}}^{\text{–}}$, has one of the richest bound state spectra observed for an atomic negative ion and has been proposed as a promising candidate for laser-cooling applications. In the present experiments, $\mathrm{L}{\mathrm{a}}^{\text{–}}$ was investigated using tunable infrared photodetachment spectroscopy. The relative signal for neutral atom production was measured with a crossed ion-beam–laser-beam apparatus over the photon energy range 585–920 meV (2120–1350 nm) to probe the continuum region above the La neutral atom ground state. Eleven prominent peaks were observed in the $\mathrm{L}{\mathrm{a}}^{\text{–}}$ photodetachment cross section due to resonant excitation of quasibound transient negative ion states in the continuum, which subsequently autodetach. In addition, thresholds were observed for photodetachment from several bound states of $\mathrm{L}{\mathrm{a}}^{\text{–}}$ to both ground and excited states of La. The present results provide information on the excited state structure and dynamics of $\mathrm{L}{\mathrm{a}}^{\text{–}}$ that depend crucially on multielectron correlation effects.

The electron-impact excitation from the ground state to the excited $1s2p_{3/2}$ ${}^{3}P_2$ energy level and the subsequent magnetic-quadrupole radiative decay $1s2p_{3/2}{}^{3}P_2\to 1s^2{}^{1}S_0$ of heliumlike ${\mathrm{Tl}}^{79+}$ ions with nuclear spin $I=1/2$ have been investigated by employing the multiconfigurational Dirac-Fock method and the relativistic distorted-wave theory. Special attention has been paid to the effects of the hyperfine interaction on the angular distribution of the emitted magnetic-quadrupole line. To this end, we considered heliumlike spin-1/2 ${}_{81}{}^{187}\mathrm{Tl}^{79+}$, ${}_{81}{}^{205}\mathrm{Tl}^{79+}$, and ${}_{81}{}^{207}\mathrm{Tl}^{79+}$ ions with rather large nuclear magnetic dipole moment ${\mu }_I$. It is found that the hyperfine interaction lowers significantly the anisotropy of the angular distribution of the magnetic-quadrupole line emitted from these spin-1/2 ions for all considered impact electron energies, compared with the results for ${\mathrm{Tl}}^{79+}$ ions with zero nuclear spin. In particular, the angular distribution becomes first less and less anisotropic as the impact energy increases up to about 4.4 times the excitation threshold, for which it becomes fully isotropic. For even higher impact energies, the angular distribution becomes again anisotropic, although with inverse emission pattern. We also find that the angular distribution is quite sensitive to the magnetic moment ${\mu }_I$ with a more isotropic distribution for spin-1/2 ions with larger ${\mu }_I$. This ${\mu }_I$ sensitivity of the angular distribution may therefore (help) probe important information about the nuclear magnetic dipole moment of spin-1/2 isotopes.

The consensus on the mechanism of atomic excitation in an intense laser field has not been reached so far because the proposed mechanisms may dominate in different regimes. In this paper, we show a clear transition of the underlying physical mechanism of strong-field atomic excitation from multiphoton resonance to coherent recapture by investigating the intensity dependence of the yields of neutral excited atoms $\left({\mathrm{Ar}}^{*}\right)$ and singly charged ions $\left({\mathrm{Ar}}^{+}\right)$ of argon experimentally and theoretically. Our results indicate that, for 400 nm, the multiphoton resonance mechanism plays a significant role at low intensity and coherent recapture mechanism becomes important at high intensity. While for 800 nm, distinctive out-of-phase oscillations of ${\mathrm{Ar}}^{*}$ and ${\mathrm{Ar}}^{+}$ yields are identified, implying that coherent recapture mechanism dominates. Our work provides a more comprehensive understanding of the atomic excitation mechanism in an intense laser field.

Recent studies in high-harmonic spectroscopy of condensed matter mainly focused on the bulk of the system under consideration. In this work we investigate the response of thin, hexagonal nanoribbons to an intense laser pulse that is linearly polarized along the ribbon. Such nanoribbons are prime examples of two-dimensional systems that are bulklike in one direction and finite in the other direction. Despite the atomically thin scale in the direction perpendicular to the linearly polarized driving laser field, the emitted harmonics are elliptically polarized if an alternating onsite potential and Haldane hopping is taken into account. For given hoppings, we find a sudden change of the helicity for a certain harmonic order. The origin of this flip is traced back to phase differences between the components of Bloch states.

We calculate the Bose-Einstein-condensate (BEC) occupation statistics vs the interparticle interaction in a dilute gas with a nonuniform condensate in a box trap within the Bogoliubov approach. The results are compared against the previously found BEC-occupation statistics in (i) an ideal gas and (ii) a weakly interacting gas with a uniform condensate. In particular, we reveal and explicitly describe an appearance of a nontrivial transition from the ideal gas to the Thomas-Fermi regime. The results include finding the main regimes of the BEC statistics—the anomalous non-Gaussian thermally dominated fluctuations and the Gaussian quantum-dominated fluctuations—as well as a crossover between them and their manifestations in a mesoscopic system. Remarkably, we show that the effect of the boundary conditions, imposed at the box trap, on the BEC fluctuations does not vanish in the thermodynamic limit of a macroscopic system even in the presence of the interparticle interactions. Finally, we discuss a challenging problem of an experimental verification of the theory of the BEC fluctuations addressing a much deeper level of the many-body statistical physics than usually studied quantities related to the mean condensate occupation.

Optical trapping efficiency for silver nanoparticles is theoretically estimated using dipole approximation and generalized Lorenz-Mie theory, including higher-order optical nonlinear effects. Here, we show a reversal in asymmetry of axial trapping potential due to Fano resonance is observed, along with a splitting of trapping potential well due to optical nonlinearity. Further, it is shown that there exists a limit for particle size beyond which the particle cannot be trapped and how this limit can be extended by harnessing optical nonlinearity under femtosecond pulsed excitation.

We investigate thermo-phonon transport and its nontrivial Berry-phase-like effect in an optomechanical system with a squeezed vacuum injection. By taking the cumulant generation function approach the exact expressions of the thermo-phonon flux and optomechanical Berry phase are derived analytically. Further, the quantum master equation approach is invoked to verify the analytical results of the transport properties. It is shown that the steady-state thermo-phonon flux can be modulated by varying optically the nonequilibrium characteristics of the system via the squeezed vacuum. In particular, an adiabatic modulation of squeezing parameters induces an optomechanical Berry-phase-like effect and as a result provides an additional geometric phonon response across the macroscopic mechanical motion near the quantum regime, which can also be seen as a consequence of the asymmetric jumping probability between transition associated with phonon absorption and emission in a thermal bath. The present method and results are general and can be straightforwardly extended to any multimode oscillator systems and therefore pave the way to the thermal noise energy harvesting and rectification in coupled oscillator systems with inertial terms.

A scheme is proposed to enhance the photon blockade effect in a hybrid optomechanical system with a $\mathrm{\Lambda }$-type atom driven by the microwave. Through analyzing the conventional and unconventional blockade mechanisms, we find that the enhanced photon blockade effect can be attributed to two aspects: (i) The nonresonant coupled $\mathrm{\Lambda }$-type atom reconstructs the anharmonic eigenenergy spectrum and (ii) the microwave driving field promotes the destructive quantum interference for two-photon excitation. By means of the joint enhancement effect, the perfect photon blockade, i.e., the second-order correlation function $g^{\left(2\right)}\left(0\right)\simeq 0$, can be achieved without the strong single-photon optomechanical coupling as reported in the standard optomechanical system. All the analyses and derivations are further verified via simulating numerically the quantum master equation of the initial Hamiltonian, showing good agreement between analytical and numerical results. Moreover, the optimal parameter relation is given to optimize the photon blockade and maximize the occupancy probability of single-photon excitation at the same time. Our scheme provides a feasible method to engineer a high-quality and efficient single-photon source.

In the current quest for efficient and experimentally feasible platforms for implementation of multimode squeezing and entanglement in the continuous variable regime, we underpin and complement our results on the generation of versatile multimode entanglement and cluster states in nonlinear waveguide arrays presented by Barral et al., arXiv:1912.11154 [Phys. Rev. Appl. (to be published)]. We present detailed derivations of the equations that describe the propagation of light through this system, and then we focus on parameter regimes where these equations can be solved analytically. These analytical solutions build an intuition for the wide landscape of quantum states that are accessible through the activation of pumping, coupling, and measurement schemes. Furthermore, we showcase the acquired insights by using one of the identified analytical solutions to exhibit the generation, optimization, and scalability of spatial linear cluster states.

It has been proposed that quantum features of the gravitational field can be exposed experimentally by employing gravity as a mediator of entanglement. We show that in order to witness this type of entanglement experimentally, strong limits on acceleration noise, which has been neglected in previous work, must be overcome. In the case of two particles of similar mass, Casimir-Polder forces lead to a fundamental limit of tenths of $\mathrm{fm}{\mathrm{s}}^{-2}/\sqrt{\mathrm{Hz}}$. Limits are between three and six orders of magnitude less strict for two particles of unequal mass, depending on collisional decoherence.

We study solutions to the quantum trajectory evolution of $N$-mode open quantum systems possessing a time-independent Hamiltonian, linear Heisenberg-picture dynamics, and Gaussian measurement noise. In terms of the mode annihilation and creation operators, a system will have linear Heisenberg-picture dynamics under two conditions. First, the Hamiltonian must be quadratic. Second, the Lindblad operators describing the coupling to the environment (including those corresponding to the measurement) must be linear. In cases where we can solve the $2N$-degree polynomials that arise in our calculations, we provide an analytical solution for initial states that are arbitrary (i.e., they are not required to have Gaussian Wigner functions). The solution takes the form of an evolution operator, with the measurement-result dependence captured in $2N$ stochastic integrals over these classical random signals. The solutions also allow the positive operator-valued measure (POVM), which generates the probabilities of obtaining measurement outcomes, to be determined. To illustrate our results, we solve some single-mode example systems, with the POVMs being of practical relevance to the inference of an initial state, via quantum state tomography. Our key tool is the representation of mixed states of quantum mechanical oscillators as state vectors rather than state matrices (albeit in a larger Hilbert space). Together with methods from Lie algebra, this allows a more straightforward manipulation of the exponential operators comprising the system evolution than is possible in the original Hilbert space.

It has been shown that certain quantum walks give rise to relativistic wave equations, such as the Dirac and Weyl equations, in their long-wavelength limits. This intriguing result raises the question of whether something similar can happen in the multiparticle case. We construct a one-dimensional quantum cellular automaton (QCA) model, which matches the quantum walk in the single particle case and which approaches the quantum field theory of free fermions in the long-wavelength limit. However, we show that this class of constructions does not generalize to higher spatial dimensions in any straightforward way and that no construction with similar properties is possible in two or more spatial dimensions. This rules out the most common approaches based on QCAs. We suggest possible methods to overcome this barrier while retaining locality.

In this work, the multicenter continuum-distorted-wave (CDW) eikonal-initial-state (EIS) model is introduced. In contrast to previously reported CDW EIS analyses for electron-molecule collisions, in which the ionized electron interacted with the molecular ion via a one-center effective potential, the multicenter nature of the molecular ion is explicitly taken into account. Results obtained for electron-impact ionization of oriented ${\mathrm{H}}_2$ molecules at the fully differential level are presented and contrasted with recent experimental data and reported theoretical calculations obtained with the time-dependent close-coupling method. The present results suggest that this simple molecule still represents a challenging target from a theoretical point of view and that many aspects of the ionization process at the fully differential level remain to be understood.