The uncertainty principle determines the distinction between the classical and the quantum world. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum information theory, the Shannon entropy is used as an appropriate measure to express the uncertainty relation. Improving the bound of the entropic uncertainty relation is of great importance. The bound can be varied by considering an extra quantum system as the quantum memory which is correlated with the measured quantum system. One can extend the bipartite quantum-memory-assisted entropic uncertainty relation to the tripartite one in which the memory is split into two parts. Here, a lower bound is obtained for the tripartite quantum-memory-assisted entropic uncertainty relation. This lower bound has two extra terms compared with the lower bound in Renes and Boileau [J. M. Renes and J.-C. Boileau, Phys. Rev. Lett. 110, 020402 (2013)] which depends on the conditional von Neumann entropy, the Holevo quantity, and the mutual information. It is shown that the bound is tighter than other bounds derived earlier. It also leads to a lower bound for the quantum secret key rate. In addition, it is applied to obtain the states for which both the strong subadditivity and the Koashi-Winter inequalities turn into equalities.

Device-independent protocols based on Bell nonlocality, such as quantum key distribution and randomness generation, must ensure no adversary can have prior knowledge of the measurement outcomes. This requires a measurement independence assumption: that the choice of measurement is uncorrelated with any other underlying variables that influence the measurement outcomes. Conversely, relaxing measurement independence allows for a fully “causal” simulation of Bell nonlocality. We construct the most efficient such simulation, as measured by the mutual information between the underlying variables and the measurement settings, for the Clauser-Horne-Shimony-Holt (CHSH) scenario, and find that the maximal quantum violation requires a mutual information of just $\sim 0.080$ bits. Any physical device built to implement this simulation allows an adversary to have full knowledge of a cryptographic key or “random” numbers generated by a device-independent protocol based on violation of the CHSH inequality. We also show that a previous model for the CHSH scenario, requiring only $\sim 0.046$ bits to simulate the maximal quantum violation, corresponds to the most efficient “retrocausal” simulation, in which future measurement settings necessarily influence earlier source variables. This may be viewed either as an unphysical limitation of the prior model or as an argument for retrocausality on the grounds of its greater efficiency. Causal and retrocausal models are also discussed for maximally entangled two-qubit states, as well as superdeterministic, one-sided, and zigzag causal models.

The double-well problem for the two-dimensional Dirac equation is solved for a family of quasi-one-dimensional potentials in terms of confluent Heun functions. We demonstrate that for a double well separated by a barrier, both the energy-level splitting associated with the wave-function overlap of well states and the gap size of the avoided crossings associated with well and barrier state repulsion can be controlled via the parameters of the potential. The transitions between the two states comprising a doublet, as well as transitions across the pseudogaps are strongly allowed, highly anisotropic, and, for realistic graphene devices, can be tuned to fall within the highly desirable terahertz frequency range.

Renormalization group ideas and effective operators are introduced to efficiently prepare ground states of massive lattice field theories on digital quantum devices. This is accomplished with a systematic approximation through localized unitaries that removes an exponentially costly barrier in the spatial volume of the quantum simulation. With these methods, classically computed ground states in a spatial volume $L$, containing a few Compton wavelengths, can be used to determine operators for preparing the ground state toward the thermodynamic limit with a precision improving as $e^{-mL}$ on beyond-classical quantum registers. Due to the exponential spatial decay of correlations in massive theories and the double exponential suppression of digitization artifacts in the number of qubits representing the scalar field, the derived fixed-point quantum circuits are expected to be relevant for simulations of quantum field theories throughout the evolution from small-scale near-term quantum devices to large-scale fault-tolerant quantum computers.

The Lee-Yang zeros are one-to-one mapped to zeros in the coherence of a probe spin coupled to a many-body system. Here, we propose two different types of Lee-Yang dephasing channels, where the partition functions vanish at Lee-Yang zeros, and study the spin squeezing under them. Under the first type of channels where probes are coupled to their own bath, we find that the performance of spin squeezing is improved and its maximum only depends on the initial state. Moreover, the centers of all the concurrence vanishing domains are corresponding to the Lee-Yang zeros. Under the second type of the channel where probes are coupled to one bath together, the performance of spin squeezing is not improved, however, the concurrence shares almost the same properties under both channels. These results provide experimental possibilities in many-body physics and give an alternative perspective on the relationship between the entanglement and spin squeezing in probes-bath systems.

Gaussian cluster states are ideal infinitely squeezed states. In practice it is possible to construct only approximated version of them with finite squeezing. Here we show how to determine the specific multimode squeezing transformation, which generates a faithful approximation of any given Gaussian cluster state.

Quantum repeaters have been proposed as a way of extending the reach of quantum communication. First-generation approaches use entanglement swapping to connect entangled links along a long-distance channel. Recently, there have been proposals for first-generation quantum repeaters for continuous variables. In this paper, we present an improved continuous-variable (CV) repeater scheme using optimal Gaussian entanglement swapping. Our scheme uses the noiseless linear amplifier for entanglement distillation. We show that with the simplest configuration of the noiseless linear amplifier and under the assumption of good quantum memories and perfect sources and detectors, our scheme beats the direct transmission upper limit for shorter distances and can offer advantages over previous CV repeater schemes.

We consider the problem of pulsed biexciton preparation in a quantum dot, and we show that a pulse sequence with a simple on-off-on modulation can achieve complete preparation of the target state faster than the commonly used constant and hyperbolic secant pulses. The durations of the pulses composing the sequence are obtained from the solution of a transcendental equation. Furthermore, using numerical optimal control, we demonstrate that for a wide range of values of the maximum pulse amplitude, the proposed pulse sequence prepares the biexciton state in the numerically obtained minimum time for the specific system under consideration. We finally show with numerical simulations that, even in the presence of dissipation and dephasing, high levels of biexciton-state fidelity can be generated in short times.

State-of-the-art argon $KLL$ Auger spectra measured using photon energies of $h\nu =3216$ and 3400 eV are presented along with an Ar $\left[1s\right]$ photoelectron spectrum (square brackets indicate holes in the respective orbital). The two different photon energies used for measuring the Auger spectra allow distinguishing between the shake transitions during the Auger decay and the Auger transitions of the photoelectron satellites. A complete assignment of satellite transitions is provided, partially based on configuration-interaction calculations. In addition, Ar $\left[1s3(s,p)\right]n^{\prime }{l}^{\prime }\to \left[2p^2{(}^1{D}_2)\right]$ transitions are observed, which can be explained by knock-down transitions leading to a direct exchange of angular momentum between the excited electron and the Auger electron. The lifetime broadenings of the Ar $\left[2s\right]$ single-core-hole state and the $\left[2s^2\right]$ and $\left[2s2p\right]$ double-core-hole states are also determined, confirming previously observed trends for double-core-hole states.

Peik and Tamm [Europhys. Lett. 61, 181 (2003)] proposed a nuclear clock based on the isomeric transition between the ground state and the first excited state of thorium-229. This transition was recognized as a potentially sensitive probe of possible temporal variation of the fine-structure constant, $\alpha$. The sensitivity to such a variation can be determined from measurements of the mean-square charge radius and quadrupole moment of the different isomers. However, current measurements of the quadrupole moment are yet to achieve an accuracy high enough to resolve nonzero sensitivity. Here we determine this sensitivity using existing measurements of the change in the mean-square charge radius, coupled with the ansatz of constant nuclear density. The enhancement factor for $\alpha$ variation is $K=-(0.82\pm 0.25)\times {10}^4$. For the current experimental limit, $\delta \alpha /\alpha \lesssim {10}^{-17}$ per year, the corresponding frequency shift is $\sim 200$ Hz per year. This shift is six orders of magnitude larger than the projected accuracy of the nuclear clock, paving the way for increased accuracy of the determination of $\delta \alpha$ and interaction strength with low-mass scalar dark matter. We verify that the constant-nuclear-density ansatz is supported by nuclear theory and propose how to verify it experimentally. We also consider a possible effect of the octupole deformation on the sensitivity to $\alpha$ variation and calculate the effects of $\alpha$ variation in a number of Mössbauer transitions.

We consider hyperfine-mediated effects for clock transitions in ${}^{176}\mathrm{Lu}^{+}$. Mixing of fine-structure levels due to the hyperfine interaction brings about modifications to the Landé $g$-factors and the quadrupole moment for a given state. Explicit expressions are derived for both the $g$-factor and quadrupole corrections, for which leading-order terms arise from the nuclear magnetic dipole coupling. High accuracy measurements of the $g$-factors for the ${}^1{S}_0$ and ${}^3{D}_1$ hyperfine levels are carried out, and they provide an experimental determination of the leading-order correction terms.

The free complement $s_{ij}$-assisted $r_{ij}$ ($\mathrm{FC}{r}_{ij}{s}_{ij}^n$) theory was developed as a variational method for solving the Schrödinger equations of atoms and molecules. This theory permits only a single correlated $r_{ij}$ term in each complement function (cf) and the other $r_{ij}$ terms are replaced with $s_{ij}=r_{ij}^2$ terms so that the variational calculations are performed within one- to four-electron integrals. We developed the $r_{ij}$-extended Löwdin formula for the antisymmetrization of $r_{ij}$-included nonorthogonal functions and implemented one- to four-electron Slater atomic integral codes necessary for the present calculations. The cf selection technique was introduced to reduce the number of degrees of freedom efficiently without much loss of accuracy. These methods were applied to the lowest quintet ${}^{5}S^o\left({sp}^3\right)$ state of a carbon atom, which is an excited state of a carbon atom but most important for chemical bonds. The chemical accuracy was achieved with the absolute solution of $\mathrm{\Delta }E=0.215\mathrm{kcal}/\mathrm{mol}$ from the estimated exact energy: The number of the cf's used was 4577 but reduced to only 129 after utilizing the cf selection technique for obtaining the chemical accuracy $\mathrm{\Delta }E<1\mathrm{kcal}/\mathrm{mol}$. Thus, the present theory can realize accurate variational calculations of many-electron systems with compact wave functions if the required three- and four-electron integrals are practically available.

We report on the observation of resonance enhanced high-order harmonic generation (HHG) from a dense medium composed of indium or tin nanoparticles. Unlike previous studies of resonance enhanced high harmonics from laser produced plasma plume from a prepulse, we generate HHG directly, thus eliminating the undesired contributions from various components in the plasma. We discuss the mechanisms for our observed resonance effect in the absence of preionized particles and the implications of the experimental results on the HHG mechanism in metal nanoparticles.

The resonant dipole-dipole interaction between highly excited Rydberg levels dominates the interaction of neutral atoms at short distances scaling as $1/r^3$. Here we take advantage of the combined effects of strong dipole-dipole interaction and multifrequency driving fields to propose one type of selective Rydberg pumping mechanism. In the computational basis of two atoms $\left\{\right|00\rangle ,|01\rangle ,|10\rangle ,|11\rangle \}$, this mechanism allows $|11\rangle$ to be resonantly pumped upwards to the single-excited Rydberg states while the transitions of the other three states are suppressed. From the perspective of mathematical form, we achieve an analogous Förster resonance for ground states of neutral atoms. The performance of this selective Rydberg pumping is evaluated using the definition of fidelity for a controlled-$Z$ gate, which manifests a characteristic robustness to the deviation of interatomic distance, fluctuation of Förster resonance defect, and spontaneous emission of double-excited Rydberg states. As applications of this mechanism, we discuss in detail the preparation of the maximally entangled symmetric state for two atoms via ground-state blockade, and the maximally entangled antisymmetric state via engineered spontaneous emission, within the state-of-the-art experiments, respectively.

When an atom or molecule is illuminated by a short laser pulse, the intense electric field couples different electronic states promptly and alters the final products. Detecting such interaction processes in a time-resolved way requires techniques with unprecedented time resolution and is important for applications such as coherent chemical reaction control. Here by solving the time-dependent Schrödinger equation, we demonstrate that the time evolution of complex amplitudes of bound electronic states during the interaction with an optical laser pulse can be extracted with high accuracy using attosecond streaking.

Due to their coherence properties, dilute atomic gas Bose-Einstein condensates seem a versatile platform for controlled creation of mesoscopically entangled states with a large number of particles and allow controlled studies of their decoherence. However, the creation of such states intrinsically involves many-body quantum dynamics that cannot be captured by mean-field theory and, thus, invalidates the most common methods for the description of condensates. We follow up on a proposal in which a condensate cloud as a whole is brought into a superposition of two different spatial locations by mapping entanglement from a strongly interacting Rydberg atomic system onto the condensate using off-resonant laser dressing [Phys. Rev. Lett. 115 040401 (2015)]. A variational many-body ansatz akin to recently developed multiconfigurational methods allows us to model this entanglement mapping step explicitly, while still preserving the simplicity of mean-field physics for the description of each branch of the superposition. In the second part of the article, we model the decoherence process due to atom losses in detail. Altogether we confirm earlier estimates that tightly localized clouds of 400 atoms can be brought into a quantum superposition of two locations about $3\mu \mathrm{m}$ apart and remain coherent for about 1 ms.

We consider a one-dimensional trapped spin-1 Bose gas and numerically explore families of its solitonic solutions, namely antidark-dark-antidark (ADDAD), as well as dark-antidark-dark (DADD) solitary waves. Their existence and stability properties are systematically investigated within the experimentally accessible easy-plane ferromagnetic phase by means of a continuation over the atom number as well as the quadratic Zeeman energy. It is found that ADDADs are substantially more dynamically robust than DADDs. The latter are typically unstable within the examined parameter range. The dynamical evolution of both of these states is explored and the implication of their potential unstable evolution is studied. Some of the relevant observed possibilities involve, e.g., symmetry-breaking instability manifestations for the ADDAD, as well as splitting of the DADD into a right- and a left-moving dark-antidark pair with the antidarks residing in a different component as compared with prior to the splitting. In the latter case, the structures are seen to disperse upon long-time propagation.

Interfacing unbiased quantum Monte Carlo simulations with state-of-the-art analytic continuation techniques, we obtain exact numerical results for dynamical density and spin correlations in the attractive Hubbard model, describing a spin-balanced two-dimensional cold Fermi gas on an optical lattice. We focus on half-filling, where on average one fermion occupies each lattice site, and the system displays an intriguing supersolid phase: a superfluid with a checkerboard density modulation. The coexistence of $\text{U}\left(1\right)$ broken symmetry and the density modulations makes this regime very challenging and interesting for the calculation of dynamical properties. We compare our unbiased results with state-of-the-art generalized random phase approximation calculations: both approaches agree on a well-defined low-energy Nambu-Goldstone collective mode in the density correlations, while the higher energy structures appear to differ significantly. We also observe an interesting high-energy spin mode. We argue that our results provide a robust benchmark for generalized random phase approximation techniques, which are widely considered to be the method of choice for dynamical correlations in Fermi gases. Also, our calculations yield new physical insight into the high-energy behavior of the dynamical structure factor of the attractive Hubbard model, which is a well known prototype lattice model for superconductors and is a fertile field to target the observation of collective modes in strongly correlated systems.

We propose that a kind of four-dimensional (4D) Hamiltonians, which host tensor monopoles related to the quantum metric tensor in even dimensions, can be simulated by ultracold atoms in optical lattices. The topological properties and bulk-boundary correspondence of tensor monopoles are investigated in detail. By fixing the momentum along one of the dimensions, it can be reduced to an effective three-dimensional model manifesting with a nontrivial chiral insulator phase. Using the semiclassical Boltzmann equation, we calculate the longitudinal resistance against the magnetic field $B$ and find a negative relative magnetoresistance effect with approximately $-B^2$ dependence when a hyperplane cuts through the tensor monopoles in the parameter space. We also propose an experimental scheme to realize this 4D Hamiltonian by introducing an external cyclical parameter in a 3D optical lattice. Moreover, we show that the quantum metric tensor and Berry curvature can be detected by applying an external drive in the optical lattices.

We report the high-resolution photoassociation (PA) spectroscopy of a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate (BEC) to excited molecular states near the dissociation limit of $5P_{1/2}+5S_{1/2}$ by optical Bragg scattering. Since the detection of optical Bragg scattering in the BEC has a high signal-noise ratio, we obtain the high-resolution PA spectrum of excited molecular states in the range of $\pm 1$ GHz near the dissociation limit of $5P_{1/2}+5S_{1/2}$. We compare the results with the conventional method of trap loss and show that the results agree with each other very well. Many interesting phenomena of excited molecular states are observed, such as light-induced frequency shift and anomalous strong bound molecular lines at the atomic transition from $|F=1\rangle$ to $|F^{\prime }=2\rangle$. The observed excited molecular states in the range of $\pm 1$ GHz near the dissociation limit of $5P_{1/2}+5S_{1/2}$ should help to further improve long-range bound-state models near the dissociation limit.