Through dedicated measurements in the optical regime we demonstrate that ptychography can be applied to reconstruct complex-valued object functions that vary with time from a sequence of spectral measurements. A probe pulse of approximately 1 ps duration, time delayed in increments of 0.25 ps, is shown to recover dynamics on a ten times faster time scale with an experimental limit of approximately 5 fs.

We address the dynamics of nonclassicality for a quantum system interacting with a noisy fluctuating environment described by a classical stochastic field. As a paradigmatic example, we consider a harmonic oscillator initially prepared in a maximally nonclassical state, e.g., a Fock number state or a Schrödinger-cat-like state, and then coupled to either a resonant or a nonresonant external field. Stochastic modeling allows us to describe the decoherence dynamics without resorting to approximated quantum master equations and to introduce non-Markovian effects in a controlled way. A detailed comparison among different nonclassicality criteria and a thorough analysis of the decoherence time reveal a rich phenomenology whose main features may be summarized as follows: (i) Classical memory effects increase the survival time of quantum coherence and (ii) a detuning between the natural frequency of the system and the central frequency of the classical field induces revivals of quantum coherence.

We describe a set of measurement protocols for performing nonclassicality tests and the verification of entangled superposition states of macroscopic continuous variable systems, such as nanomechanical resonators. Following earlier works, we first consider a setup where a two-level system is used to indirectly probe the motion of the mechanical system via Ramsey measurements and discuss the application of this method for detecting nonclassical mechanical states. We then show that the generalization of this technique to multiple resonator modes allows the conditioned preparation and the detection of entangled mechanical superposition states. The proposed measurement protocols can be implemented in various qubit-resonator systems that are currently under experimental investigation and find applications in future tests of quantum mechanics at a macroscopic scale.

Although the simulation of quantum chemistry is one of the most anticipated applications of quantum computing, the scaling of known upper bounds on the complexity of these algorithms is daunting. Prior work has bounded errors due to discretization of the time evolution (known as “Trotterization”) in terms of the norm of the error operator and analyzed scaling with respect to the number of spin orbitals. However, we find that these error bounds can be loose by up to 16 orders of magnitude for some molecules. Furthermore, numerical results for small systems fail to reveal any clear correlation between ground-state error and number of spin orbitals. We instead argue that chemical properties, such as the maximum nuclear charge in a molecule and the filling fraction of orbitals, can be decisive for determining the cost of a quantum simulation. Our analysis motivates several strategies to use classical processing to further reduce the required Trotter step size and estimate the necessary number of steps, without requiring additional quantum resources. Finally, we demonstrate improved methods for state preparation techniques which are asymptotically superior to proposals in the simulation literature.

We experimentally explore the state space of three qubits on a nuclear magnetic resonance (NMR) quantum-information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a nontrivial combination of Greenberger-Horne-Zeilinger (GHZ) and $W$-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and $W$ states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and $W$ states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the $W$ state, we demonstrate this method of reconstruction by comparing it to the directly tomographed three-qubit state.

Measurement-device-independent quantum key distribution (MDI-QKD) can remove all the side-channel attacks from imperfections in the detection side. However, finite-size resources undoubtedly influence its performance and the achievable finite secret key rates of MDI-QKD are typically lower than that of standard decoy-state QKD. In this paper, we introduce the efficient decoy-state method with biased basis choice into the finite-key analysis and propose a decoy-state protocol for MDI-QKD. By applying vacuum + weak decoy-state method, we analytically derive concise formulas for estimating the lower bound of single-photon yield and the upper bound of phase error rate in the case of finite resources. The simulations show that proper basis choice combined with deliberate intensity choice can substantially enhance the performance of decoy-state MDI-QKD and, without a full optimization program, our protocol can bring a long-distance implementation (168 km on standard optical fiber) of MDI-QKD with a reasonable data size of total transmitting signals $\left(N={10}^{15}\right)$.

A set of stabilizer operations augmented by some special initial states known as “magic states” gives the possibility of universal fault-tolerant quantum computation. However, magic state preparation inevitably involves nonideal operations that introduce noise. The most common method to eliminate the noise is magic state distillation (MSD) by stabilizer operations. Here we propose a hybrid MSD protocol by connecting a four-qubit $H$-type MSD with a five-qubit $T$-type MSD in order to overcome the shortcomings of the previous MSD protocols. The hybrid MSD protocol further integrates distillable ranges of different existing MSD protocols and provides considerable improvement in qubit cost. Moreover, we experimentally demonstrate the four-qubit $H$-type MSD protocol using nuclear magnetic resonance technology, together with the previous five-qubit MSD experiment, to show the feasibility of the hybrid MSD protocol.

We investigate the performance of superconducting flux qubits for the adiabatic quantum simulation of long-distance entanglement (LDE), namely, a finite ground-state entanglement between the end spins of a quantum spin chain with open boundary conditions. As such, LDE can be considered an elementary precursor of edge modes and topological order. We discuss two possible implementations which simulate open chains with uniform bulk and weak end bonds, either with Ising or with $XX$ nearest-neighbor interactions. In both cases, we discuss a suitable protocol for the adiabatic preparation of the ground state in the physical regimes featuring LDE. In the first case, the adiabatic manipulation and the Ising interactions are realized using dc currents, while in the second case microwaves fields are used to control the smoothness of the transformation and to realize the effective $XX$ interactions. We demonstrate the adiabatic preparation of the end-to-end entanglement in chains of four qubits with realistic parameters and on a relatively fast time scale.

Boson sampling is a simple model for nonuniversal linear optics quantum computing using far fewer physical resources than universal schemes. An input state comprising vacuum and single-photon states is fed through a Haar-random linear optics network and sampled at the output by using coincidence photodetection. This problem is strongly believed to be classically hard to simulate. We show that an analogous procedure implements the same problem, using photon-added or -subtracted squeezed vacuum states (with arbitrary squeezing), where sampling at the output is performed via parity measurements. The equivalence is exact and independent of the squeezing parameter, and hence provides an entire class of quantum states of light in the same complexity class as boson sampling.

We present a solvable model of iterating cluster state protocols that lead to entanglement production, between contiguous blocks, of 1 ebit per iteration. This continues until the blocks are maximally entangled, at which stage an unravelling begins at the same rate until the blocks are unentangled. The model is a variant of the transverse-field Ising model and can be implemented with controlled-not and single-qubit gates. The interqubit entanglement as measured by the concurrence is shown to be zero for periodic chain realizations, while for open boundaries there are very specific instances at which these can develop. Thus we introduce a class of simply produced states with very large multipartite entanglement content of potential use in measurement-based quantum computing.

We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse field. Such a mapping is derived by rewriting the initial Hamiltonian in a new basis so that the final model in such a basis has a well-known approximated phase transition point. Specifically, we consider the toric codes and the color codes on various lattices with Ising perturbation. Our results provide a useful table to compare the robustness of the topological codes and to explicitly show that the robustness of the topological codes depends on triangulation of their underlying lattices.

The relativistic formulation of the Voigt profile is reported for the spontaneous emission from an atomic or molecular cloud, in coincidence with a given spectral line. We considered the simultaneous occurrence of homogeneous broadening and thermal broadening, this latter being determined by the relativistic Doppler effect. Our formula for the relativistic Voigt profile reproduces those characterizing the two available limit cases, namely, the relativistic Gaussian profile and the classical Voigt convolution. The relativistic deformation of the Voigt profile was carefully quantified at different temperatures, in the case of the molecular hydrogen spectrum.

Energy levels, lifetimes, and wave function compositions have been computed for all atomic states of the $4p^6$ and $4p^{5}4d$ configurations using the multiconfiguration Dirac-Hartree-Fock method. Calculations were done by parity and the configuration state function expansions were obtained by allowing single and double substitutions from the the $4p^6$ and $4p^{5}4d$ single references with orbitals in an orbital set that was extended to $n=7$ and all possible angular symmetries. Lifetimes are computed from $E1$, $E2$, and $M1$ transitions between these levels. Energy levels and transition energies (or wavelengths) are compared with other theory and experiment, when available. Transition data for the $4p^6{}^1{S}_0$ – $4p^{5}4dJ=1$ transitions are investigated in detail with respect to convergence of transition energies and the length and velocity forms of the line strengths. By classifying the upper states by $J$, parity $\left(\pi \right)$, and position, the compositions of the states with the same three quantum number change smoothly as a function of the nuclear charge $Z$ and transition energies and transition matrix elements can be approximated by polynomial expressions in $Z.$ A zero in the transition matrix element for the ${}^1{S}_0\text{−}{}^3{P}_1^o$ transition leads to a long lifetime at $Z\approx 58$.

Pump-probe spectroscopy has allowed the construction of the nuclear probability density $\rho (R,t)$ as a function of the internuclear bond distance $\left(R\right)$ and the time $\left(t\right)$ in diatomic molecules and consequent deduction of the nuclear flux density $j(R,t)$. Thus, the two observables $\left[\rho \right(R,t),j(R,t\left)\right]$ comprise a very detailed description of the nuclear motion in ultrafast molecular dynamics. Here a Fourier analysis of $j(R,t)$ is proposed and compared with the already existing Fourier analysis of $\rho (R,t)$. It is shown that the two power spectra $|\tilde{\rho }{(R,\omega ;T)|}^2$ and $|\tilde{j}{(R,\omega ;T)|}^2$ provide the same information in the frequency domain $\omega$, but entirely different information in the spatial domain (i.e., along the $R$ coordinate).

A general treatment of ultracold two-body scattering in the presence of isotropic spin-orbit coupling (SOC) is presented. Owing to the mixing of different partial-wave channels, scattering with SOC is in general a coupled multichannel problem. A systematic method is introduced to analytically solve a class of coupled differential equations by recasting the coupled-channel problem as a simple eigenvalue problem. The exact Green's matrix in the presence of SOC is found, which readily gives the scattering solutions for any two identical particles in any total angular momentum subspace having negligible center-of-mass momentum. Application of this formalism to two spin-1 bosons shows the ubiquitous low-energy threshold behavior for systems with isotropic SOC. A modified threshold behavior shows up, which does not occur for the spin-orbit coupled spin-$\frac{1}{2}$ system. We also confirm the parity-breaking mechanism for the spontaneous emergence of handedness, which has been proposed by Duan et al. [H. Duan, L. You, and B. Gao, Phys. Rev. A 87, 052708 (2013)]. Additionally, a two-body bound state is found for any arbitrarily small and negative scattering length. Our study sheds light on the few-body side of SOC physics and provides one step towards understanding ultracold scattering in a non-Abelian gauge field.

Low-energy electron-impact cross sections of helium among the ground and some low excited states are calculated using the $R$-matrix method. The convergences of the cross sections are checked systematically by using five sets of high-quality target states; i.e., including 5, 11, 19, 29, and 39 physical target states, respectively. Our calculated cross sections are in excellent agreement with the benchmark high-resolution experimental data. Compared with the recommended theoretical data, there is a deviation of about 6%, which suggests the recommended data may need a revision. Based on our calculation results, the influence of the Rydberg target states on the collision cross sections of the excited states is found to be similar to the case of the ground state; i.e., the amplitude of resonance structures will decrease with respect to the principal quantum number $n$ of Rydberg target states. This result should be very useful for providing the cross-section data in the whole energy regions with high quality, which would be of great importance in related scientific fields.

The scattering process of an x-ray photon by an excited and ionized many-electron atom with attosecond photon-electron contact interaction is theoretically investigated. The results of the authors' recent work [Hopersky et al., Phys. Rev. A 88, 032704 (2013)] are generalized for the cases of (a) arbitrary energy of the photon that prepares the scattering state and (b) the scattering of the photon by the continuous spectrum electron of the ionization state of the atom. The atom of Ne is considered as the object of the study. Along with the effects of normal Compton and elastic scattering, the existence of anomalous inelastic scattering is predicted. It may be assumed that this effect will become a basis for an experimental method of increasing the energy of the photons generated, for example, by a free-electron x-ray laser. It is determined that during the elastic scattering of a photon by an electron of the continuous spectrum, along with the known contribution from the $j_l$ Bessel function over the $l=0$ harmonic (Thomson scattering), there is also a contribution from Bessel functions with harmonics $l\in [1;\infty )$. The experimental discovery and application of the anomalous Compton photon scattering effect directly by the atomic electron of the continuous spectrum have their own practical interest.

We develop a model to calculate nonlinear polarization in a nondegenerate four-wave mixing in diamond configuration which includes the effects of hyperfine structure and Doppler broadening. We verify the model against the experiment with $5{}^2{S}_{1/2},5{}^2{P}_{3/2},5{}^2{D}_{3/2}$, and $5{}^2{P}_{1/2}$ levels of rubidium 85. Treating the multilevel atomic system as a combination of many four-level systems we are able to express the nonlinear susceptibility of a thermal ensemble in a low-intensity regime in terms of Voigt-type profiles and obtain an excellent conformity of theory and experiment within this complex system. The agreement is also satisfactory at high intensity and the analytical model correctly predicts the positions and shapes of resonances. Our results elucidate the physics of coherent interaction of light with atoms involving higher excited levels in vapors at room temperature, which is used in an increasing range of applications.

Transverse spin diffusion in a polarized, interacting Fermi gas leads to the Leggett-Rice effect, where the spin current precesses around the local magnetization. With a spin-echo sequence both the transverse diffusivity and the spin-rotation parameter $\gamma$ are obtained; the sign of $\gamma$ reveals the repulsive or attractive character of the effective interaction. In a trapped Fermi gas the spin diffusion equations become nonlinear, and their numerical solution exhibits an inhomogeneous spin state even at the spin-echo time. While the microscopic diffusivity and $\gamma$ increase at weak coupling, their apparent values inferred from the trap-averaged magnetization saturate in agreement with a recent experiment for a dilute ultracold Fermi gas.