We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While the Landau-Zener transition probabilities depend sensitively on the system parameters, much more precision may be obtained using the acquired phase, quantified by the quantum Fisher information. This information scales with a power of the elapsed time for the quantum case, whereas it is time independent if the transition probabilities alone are used. We add coherent control to the system and increase the permitted maximum precision in this time-dependent quantum system. The case of multiple passes before measurement, Landau-Zener-Stueckelberg interferometry, is considered, and we demonstrate that proper quantum control can cause the quantum Fisher information about the oscillation frequency to scale as $T^4$, where $T$ is the elapsed time. These results are foundational for frequency standards and quantum clocks.

Collective measurements on large quantum systems together with a majority voting strategy can lead to a violation of the Clauser-Horne-Shimony-Holt Bell inequality. In the presence of many entangled pairs, this violation decreases quickly with the number of pairs and vanishes for some critical pair number that is a function of the noise present in the system. Here we show that a different binning strategy can lead to a more substantial Bell violation when the noise is sufficiently small. Given the relation between the critical pair number and the source noise, we then present an experiment where the critical pair number is used to quantify the quality of a high visibility photon pair source. Our results demonstrate nonlocal correlations using collective measurements operating on clusters of more than 40 photon pairs.

In any Bell test, loopholes can cause issues in the interpretation of the results, since an apparent violation of the inequality may not correspond to a violation of local realism. An important example is the coincidence-time loophole that arises when detector settings might influence the time when detection will occur. This effect can be observed in many experiments where measurement outcomes are to be compared between remote stations because the interpretation of an ostensible Bell violation strongly depends on the method used to decide coincidence. The coincidence-time loophole has previously been studied for the Clauser-Horne-Shimony-Holt and Clauser-Horne inequalities, but recent experiments have shown the need for a generalization. Here, we study the generalized “chained” inequality by Pearle, Braunstein, and Caves (PBC) with $N\ge 2$ settings per observer. This inequality has applications in, for instance, quantum key distribution where it has been used to reestablish security. In this paper we give the minimum coincidence probability for the PBC inequality for all $N\ge 2$ and show that this bound is tight for a violation free of the fair-coincidence assumption. Thus, if an experiment has a coincidence probability exceeding the critical value derived here, the coincidence-time loophole is eliminated.

Branciard et al. [Phys. Rev. Lett. 104, 170401 (2010)] first characterized the correlations arising in an entanglement swapping network under the assumption that the sources generating the initially uncorrelated quantum systems are independent. Precisely speaking, Branciard et al. [Phys. Rev. Lett. 104, 170401 (2010) and later in Phys. Rev. A 85, 032119 (2012)] analyzed the importance of bilocal (source independence) assumption to lower the restrictions over correlations for revealing quantumness in the network where each of two sources generates a bipartite entangled state. In this context, one may find interest to characterize correlations in a network involving independent sources which can correlate more than two initially uncorrelated multipartite entangled quantum systems. Our present topic of discussion basically analyzes such a network scenario. Specifically, we introduce a trilocal network scenario where each of three sources independently generates a tripartite entangled quantum system, thereby exploring the role of source independence assumption to exploit nonlocality in a network involving multipartite entanglement analogous to bilocal assumption in a network where only bipartite entanglement was considered. Interestingly, genuine entanglement content did not turn out to be an essential requirement for exploiting nonlocality in such a scenario. Moreover, it is interesting to explore whether such a scenario can be generalized so as to characterize correlations arising in a network involving $n$ number of $n$-partite systems for any finite value of $n\ge 4$ under source independence assumption.

We present a comprehensive experimental and theoretical investigation on the LMM, LMN, and LNN normal Auger spectra of xenon, which reveal excellent agreement with theory when core-hole lifetimes of the two-hole final states are taken into account. Generally, the spectra turned out to be highly complex due to a strong overlap of the Auger transitions subsequent to $2s_{1/2}^{-1}$, $2p_{1/2}^{-1}$, and $2p_{3/2}^{-1}$ ionization. This overlap is due to the splitting of the three initial $L$ core holes and the different final $M$ and $N$ core holes being on the same order of magnitude of several hundred eV. The Auger transitions are assigned in detail based on the theoretical results. Most of the $MM$, $MN$, and $NN$ final states are described well based on $jj$ coupling. In addition, we present a detailed assignment of the resonant $L{M}_{45}{M}_{45}$ Auger transition subsequent to the $2s\to 6p$, $7p$ and $2p\to 5d$, $6d$ excitations.

Approximate functionals for the exchange-correlation energy of electrons often draw on explicit or implicit models for the exchange-correlation hole. Here we focus on the spherically averaged exchange hole ${\rho }_{\mathrm{X}}(\mathbf{r},u)$, which depends on the reference point $\mathbf{r}$ and on the electron-electron distance $u$. We extend the well-known [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)] second-order Taylor-series expansion in $u$ to fourth order and we show that the fourth-order term can add important additional information that is particularly relevant for molecules compared to atoms. Drawing on these findings, we explore exchange functionals that depend on the fourth-order term of the expansion of ${\rho }_{\mathrm{X}}(\mathbf{r},u)$. We also find that Gaussian basis set expansions, frequently used in electronic structure codes, result in unsatisfactory representations of the fourth-order term.

Collisions of two fermionic dimers near the unitary limit are studied using exact four-particle equations for transition operators in momentum space. Universal properties of dimer-dimer phase shifts and effective range expansion (ERE) parameters are determined. The inclusion of the fourth-order momentum term in the ERE significantly extends its validity to higher collision energies. The dimer-dimer scattering length and effective range are determined in the unitary limit as well as their corrections arising due to the finite range of the two-fermion interaction. These results are of considerably higher accuracy as compared to previous works, but confirm most of the previous results except for the lattice effective field theory calculations.

Using the recently developed Bloch-state tomography technique, the quasimomentum $\mathbf{k}$-dependent Bloch states ${[sin\left({\theta }_{\mathbf{k}}/2\right),-cos\left({\theta }_{\mathbf{k}}/2\right)e^{i{\varphi }_{\mathbf{k}}}]}^T$ of a two-band tight-binding model with two sublattices can be mapped out. We show that if we prepare the initial Bloch state as the lower-band eigenstate of a topologically trivial Haldane Hamiltonian $H_i$ and then quench the Haldane Hamiltonian to $H_f$, the time-dependent azimuthal phase ${\varphi }_{\mathbf{k}}\left(t\right)$ supports two types of vortices. The first type of vortices is static, with the corresponding Bloch vectors pointing to the north pole (${\theta }_{\mathbf{k}}=0$). The second type of vortices is dynamical, with the corresponding Bloch vectors pointing to the south pole (${\theta }_{\mathbf{k}}=\pi$). In the $(k_x,k_y,t)$ space, the linking number between the trajectories of these two types of vortices exactly equals the Chern number of the lower band of $H_f$, which provides an alternative method to directly map out the topological phase boundaries of the Haldane model.

We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order Rényi entanglement entropy $S_2$ can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge $c$. We discuss the adiabatic preparation of the ground state at half filling and small hopping parameter $J/U$, where we expect a CFT with $c=1$. We provide two complementary methods to estimate and subtract the classical entropy generated by the experimental preparation and imaging processes. We compare numerical calculations for the classical O(2) model with a chemical potential on a ($1+1$)-dimensional lattice, and the quantum Bose-Hubbard Hamiltonian implemented in the experiments. $S_2$ is very similar for the two models and follows closely the Calabrese-Cardy scaling, $(c/8)ln\left(N_s\right)$, for $N_s$ sites with open boundary conditions, provided that the large subleading corrections are taken into account.

We propose and experimentally demonstrate dynamic nonlinear optical holograms by introducing the concept of computer-generated holograms for second-harmonic generation of a structured fundamental wave with a specially designed wave front. The generation of Laguerre-Gaussian second-harmonic beams is investigated in our experiment. Such a method, which only dynamically controls the wave front of the fundamental wave by a spatial light modulator, does not need domain inversion in nonlinear crystals and hence is a more flexible way to achieve the off-axis nonlinear second-harmonic beams. It can also be adopted in other schemes and has potential applications in nonlinear frequency conversion, optical signal processing, and real-time hologram, etc.

We consider the spontaneous emission of a two-level quantum emitter, such as an atom or a quantum dot, in a modulated time-dependent environment with a photonic band gap. An example of such an environment is a dynamical photonic crystal or any other environment with a band gap whose properties are modulated in time, in the effective mass approximation. After introducing our model of a dynamical photonic crystal, we show that it allows new possibilities to control and tailor the physical features of the emitted radiation, specifically its frequency spectrum. In the weak-coupling limit and in an adiabatic case, we obtain the emitted spectrum and we show the appearance of two lateral peaks due to the presence of the modulated environment, separated from the central peak by the modulation frequency. We show that the two side peaks are not symmetric in height, and that their height ratio can be exploited to investigate the density of states of the environment. Our results show that a dynamical environment can give further possibilities to modify the spontaneous emission features, such as its spectrum and emission rate, with respect to a static one. Observability of the phenomena we obtain is discussed, as well as relevance for tailoring and engineering radiative processes.

Experimental measurements and calculations of stimulated Raman adiabatic passage transfer efficiencies were made on a sodium gas starting from the $3{}^2{S}_{1/2}$ electronic ground state, passing through the $3{}^2{P}_{1/2}$ and/or the $3{}^2{P}_{3/2}$ to the $5{}^2{S}_{1/2}$ state. The lasers used in the experiments had a pulse width of several picoseconds and were close to the Fourier transform limit. Although the linewidth of the laser was much smaller than the spin orbit splitting between the $3{}^{2}P_{1/2}$ and $3{}^{2}P_{3/2}$ states, Experiments and calculations reveal that both 3p states play a role in the transfer efficiency when the lasers are tuned to resonance through the $3{}^2{P}_{1/2}$ state, revealing evidence of quantum interference between the competing pathways.

We present an experimental determination of the electron-impact ionization cross section of the $1s2s{}^{3}S$ state of helium, for which there is a serious long-lasting discrepancy between theory and experiment. A technique for the production of a fast, intense beam of helium in the $1s2s{}^{3}S$ state only has been developed for this purpose, based on photodetachment of the ${\mathrm{He}}^{-}$ anion. The cross section is measured using the animated crossed beam technique. The present results are much lower than the experimental data of Dixon et al. [J. Phys. B 9, 2617 (1976)] and are in excellent agreement with the calculation of Fursa and Bray [J. Phys. B 36, 1663 (2003)].

The ability to generate and tune quantized persistent supercurrents is crucial for building superconducting or atomtronic devices with novel functionalities. In ultracold atoms, previous methods for generating quantized supercurrents are generally based on dynamical processes to prepare atoms in metastable excited states. Here, we show that arbitrary quantized circulation states can be adiabatically prepared and tuned as the ground state of a ring-shaped Bose-Einstein condensate by utilizing spin–orbital-angular-momentum (SOAM) coupling and an external potential. There exists superfluid hysteresis for tuning supercurrents between different quantization values with nonlinear atomic interactions, which is explained by developing a nonlinear Landau-Zener theory. Our work will provide a powerful platform for studying SOAM-coupled ultracold atomic gases and building atomtronic circuits.

We analyze the connection between Bell inequality violations and symmetric extendibility of quantum states. We prove that 2-qubit reduced states of multiqubit symmetric pure states do not violate the Bell Clauser-Horne-Shimony-Holt (CHSH) inequality. We then prove the more general converse that any 2-qubit state that violates the CHSH inequality cannot have a symmetric extension. We extend our analysis to qudits and provide a test for symmetric extendibility of 2-qudit states. We show that if a 2-qudit Bell inequality is monogamous, then any 2-qudit state that violates this inequality does not have a symmetric extension. For the specific case of 2-qutrit states, we use numerical evidence to conjecture that the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality is monogamous. Hence, the violation of the CGLMP inequality by any 2-qutrit state could be a sufficient condition for the nonexistence of its symmetric extension.

We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time $\text{poly}({log}_2\left(N\right),d,\kappa ,1/\epsilon )$, where $N$ is the size of the data set, $d$ is the number of adjustable parameters, $\kappa$ is the condition number of the design matrix, and $\epsilon$ is the desired precision in the output. We also show that the polynomial dependence on $d$ and $\kappa$ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

Genuine multipartite entanglement has been found in some spin chain systems. However, genuine multipartite nonlocality is much rarer than genuine multipartite entanglement. Here we present genuine multipartite nonlocality in a spin chain system. After introducing the definition of genuine multipartite nonlocality and a multipartite Bell-type inequality, we construct a group of joint measurements for the inequality in a one-dimensional ferromagnetic $N$-qubit chain with nearest-neighbor $XXZ$ interaction, and many violations to the inequality have been found. The violations do indicate that genuine multipartite nonlocality exists in this ferromagnetic spin-1/2 chain system. Last but not least, we also calculate genuine multipartite entanglement concurrence in the same spin chain to demonstrate the difference and relationship between genuine multipartite nonlocality and genuine multipartite entanglement.

We address measurement-based generation of quantum coherence in continuous variable systems. We consider Gaussian measurements performed on Gaussian states and focus on two scenarios: In the first one, we assume an initially correlated bipartite state shared by two parties and study how correlations may be exploited to remotely create quantum coherence via measurement back action. In particular, we focus on conditional states with zero first moments, so as to address coherence due to properties of the covariance matrix. We consider different classes of bipartite states with incoherent marginals and show that the larger the measurement squeezing, the larger the conditional coherence. Homodyne detection is thus the optimal Gaussian measurement to remotely generate coherence. We also show that for squeezed thermal states there exists a threshold value for the generated coherence which separates entangled and separable states at a fixed energy. Finally, we briefly discuss the tripartite case and the relationship between tripartite correlations and the conditional two-mode coherence. In the second scenario, we address the steady-state coherence of a system interacting with an environment which is continuously monitored. In particular, we discuss the dynamics of an optical parametric oscillator in order to investigate how the coherence of a Gaussian state may be increased by means of time-continuous Gaussian measurement on the interacting environment.

Quantum memories, capable of storing single photons or other quantum states of light, to be retrieved on demand, offer a route to large-scale quantum information processing with light. A promising class of memories is based on far-off-resonant Raman absorption in ensembles of $\mathrm{\Lambda }$-type atoms. However, at room temperature these systems exhibit unwanted four-wave mixing, which is prohibitive for applications at the single-photon level. Here, we show how this noise can be suppressed by placing the storage medium inside a moderate-finesse optical cavity, thereby removing the main roadblock hindering this approach to quantum memory.