Heavy polar diatomic molecules are currently among the most promising probes of fundamental physics. Constraining the electric dipole moment of the electron ($e\mathrm{EDM}$), in order to explore physics beyond the standard model, requires a synergy of molecular experiment and theory. Recent advances in experiment in this field have motivated us to implement a finite-field coupled-cluster (FFCC) approach. This work has distinct advantages over the theoretical methods that we had used earlier in the analysis of $e\mathrm{EDM}$ searches. We used relativistic FFCC to calculate molecular properties of interest to $e\mathrm{EDM}$ experiments, that is, the effective electric field ($E_{\mathrm{eff}}$) and the permanent electric dipole moment (PDM). We theoretically determine these quantities for the alkaline-earth monofluorides (AEMs), the mercury monohalides ($\mathrm{Hg}X$), and PbF. The latter two systems, as well as BaF from the AEMs, are of interest to $e\mathrm{EDM}$ searches. We also report the calculation of the properties using a relativistic finite-field coupled-cluster approach with single, double, and partial triples’ excitations, which is considered to be the gold standard of electronic structure calculations. We also present a detailed error estimate, including errors that stem from our choice of basis sets, and higher-order correlation effects.

We have designed, constructed, and commissioned a cryogenic helium buffer-gas source for producing a cryogenically cooled molecular beam and evaluated the effect of different cell geometries on the intensity of the produced molecular beam, using ammonia as a test molecule. Planar and conical entrance and exit geometries are tested. We observe a threefold enhancement in the ${\mathrm{NH}}_3$ signal for a cell with planar entrance and conical-exit geometry, compared to that for a typically used “boxlike” geometry with planar entrance and exit. These observations are rationalized by flow field simulations for the different buffer-gas cell geometries. The full thermalization of molecules with the helium buffer gas is confirmed through rotationally resolved resonance-enhanced multiphoton ionization spectra yielding a rotational temperature of 5 K.

We study theoretically the collective mode spectrum of a strongly imbalanced two-component unitary Fermi gas in a cigar-shaped trap, where the minority species forms a gas of polarons. We describe the collective breathing mode of the gas in terms of the Fermi-liquid kinetic equation taking collisions into account using the method of moments. Our results for the frequency and damping of the longitudinal in-phase breathing mode are in good quantitative agreement with an experiment by Nascimbène et al. [Phys. Rev. Lett. 103, 170402 (2009)] and interpolate between a hydrodynamic and a collisionless regime as the polarization is increased. A separate out-of phase breathing mode, which for a collisionless gas is sensitive to the effective mass of the polaron, however, is strongly damped at finite temperature, whereas the experiment observes a well-defined oscillation.

We report on the transport properties of a single-mode quantum pump that operates by the simultaneous translation and oscillation of a potential well. We examine the dynamics comparatively using quantum, classical, and semiclassical simulations. The use of an attractive or well potential is found to present several striking features absent if a barrier potential is used instead, as usually favored. The trapping of particles by the well for variable durations and subsequent release leads to a fractal-like structure in the distribution of the classical scattering trajectories. Interference among them leads to a rich dynamical structure in the quantum current, conspicuously missing in the classical current. Specifically, we observe sharp steps, spikes, and dips in the current as a function of the incident energy of the carriers and determine that a dynamical version of Fano resonance has a role that depends on the direction of incidence and on multiple scattering by the potential.

We present a detailed analysis of dynamical processes involving two or three particles in a double-well potential. Motivated by experimental realizations of such a system with optically trapped cold atoms, we focus on spin-1 bosons with special attention on the effects of a spin-dependent interaction in addition to the usual Hubbard-like repulsive one. For a sufficiently weak tunneling amplitude in comparison to the dominant Hubbard coupling, particle motion is strongly correlated, occurring only under fine-tuned relationships between well-depth asymmetry and interactions. We highlight processes involving tunneling of coupled particle pairs and triads, emphasizing the role of the spin-dependent interaction in resonance conditions.

We present an analytical study of the frequency comb coherence due to random noise in the pulses phases. We derive a simple expression for the comb lineshape, which depends on a single parameter $N_{\text{eff}}$ with the physical meaning of number of coherent comb pulses, inversely proportional to the variance of the phase jumps between subsequent comb pulses. A comparison to the case of a cw-monomode laser with white noise frequency fluctuations is also presented.

Demonstrating quantum advantage with less powerful but more realistic devices is of great importance in modern quantum information science. Recently, a significant quantum speedup was achieved in the problem of learning a hidden parity function with noise. However, if all data qubits at the query output are completely depolarized, the algorithm fails. In this work, we present a quantum parity learning algorithm that exhibits quantum advantage as long as one qubit is provided with nonzero polarization in each query. In this scenario, the quantum parity learning naturally becomes deterministic quantum computation with one qubit. Then the hidden parity function can be revealed by performing a set of operations that can be interpreted as measuring nonlocal observables on the auxiliary result qubit having nonzero polarization and each data qubit. We also discuss the source of the quantum advantage in our algorithm from the resource-theoretic point of view.

Based on Lyapunov control, a scheme is proposed to accelerate dissipation dynamics for the generation of high-fidelity entanglement between two Rydberg atoms in the context of cavity QED. We first use quantum Zeno dynamics and the Rydberg antiblockade to find a unique steady state (two-atom singlet state) for the system. Then, we apply additional coherent control (ACC) fields to improve the evolution speed of the dissipative system. The ACC fields are designed based on the target state and they vanish gradually along with increasing of the fidelity; thus, the system is guaranteed to be finally stable. Additionally, the current accelerated scheme is checked to be robust against systematic and amplitude-noise errors.

Scattering coefficients can diverge at spectral singularities. In such situation, the stationary solution becomes a laser solution with outgoing waves only. We explore a parity-time $\left(\mathcal{PT}\right)$-symmetric non-Hermitian two-arm Aharonov-Bohm interferometer consisting of three coupled resonators enclosing synthetic magnetic flux. The synthetic magnetic flux does not break the $\mathcal{PT}$ symmetry, which protects the symmetric transmission. The features and conditions of symmetric, asymmetric, and unidirectional lasing at spectral singularities are discussed. We elucidate that lasing affected by the interference is asymmetric; asymmetric lasing is induced by the interplay between the synthetic magnetic flux and the system's non-Hermiticity. The product of the left and right transmissions is equal to that of the reflections. Our findings reveal that the synthetic magnetic flux affects light propagation, and the results can be applied in the design of lasing devices.

Temporally and spatially overlapping but field-orthogonal photonic temporal modes (TMs) that intrinsically span a high-dimensional Hilbert space are recently suggested as a promising means of encoding information on photons. Presently, the realization of photonic TM technology, particularly to retrieve the information it carries, i.e., demultiplexing of photonic TMs, is mostly dependent on nonlinear medium and frequency conversion. Meanwhile, its miniaturization, simplification, and optimization remain the focus of research. In this paper, we propose a scheme of TM demultiplexing using linear systems consisting of resonators with linear couplings. Specifically, we examine a unidirectional array of identical resonators with short environment correlations. For both situations with and without tunable couplers, propagation formulas are derived to demonstrate photonic TM demultiplexing capabilities. The proposed scheme, being entirely feasible with current technologies, might find potential applications in quantum information processing.

The two-qubit maximally steerable mixed state (MSMS), defined as one that violates to the most degree a steering inequality for any fixed linear entropy, is derived mathematically here based on the two-setting (three-setting) linear steering inequality and the two-setting Clauser-Horne-Shimony-Holt–like steering inequality. Interestingly, the form of the MSMS based on such different steering inequalities obtained here is identical to the two-qubit maximally nonlocal mixed state (MNMS). It is clearly shown that finding any two-qubit state, of which the state mixedness exceeds $2/3$, thus violating the three-setting steering inequalities, is impossible. The violation of the inequalities with the Werner state and with the maximally entangled mixed state, respectively, as well as the relations between their optimal violation and the linear entropy, is also discussed comprehensively. In particular, within the range $\varepsilon \left(\rho \right)\in [0,2/3]$ of the fixed linear entropy, the Werner state reaches the same violation as the MSMS does of the three-setting linear steering inequality, but not of the two-setting steering inequalities (for the latter inequalities the violation with the Werner state is generally less than that with the MSMS). For the MEMS, the optimal violation is always lower than that of the MSMS for any fixed linear entropy.

There is usually a limitation of weak interaction on the application of weak-value measurement. This limitation dominates the performance of the quantum state tomography toward a typical target in the finite and high-dimensional complex-valued superposition of its basis states, especially when the compressive sensing technique is also employed. Here we propose an alternative method of quantum state tomography, presented as a general model, toward such typical target via weak-value measurement to overcome such limitation. In this model the pointer for the weak-value measurement is a qubit, and the target-pointer coupling interaction is no longer needed within the weak interaction limitation, meanwhile this interaction under the compressive sensing can be described with the Taylor series of the unitary evolution operator. The postselection state at the target is the equal superposition of all basis states, and the pointer readouts are gathered under multiple Pauli operator measurements. The reconstructed quantum state is generated from an optimization algorithm of total variation augmented Lagrangian alternating direction algorithm. Furthermore, we demonstrate an example of this general model for the quantum state tomography toward the planar laser-energy distribution and discuss the relations among some parameters at both our general model and the original first-order approximate model for this tomography.

We study the time evolution of the entanglement entropy in bosonic systems with time-independent, or time-periodic, Hamiltonians. In the first part, we focus on quadratic Hamiltonians and Gaussian initial states. We show that all quadratic Hamiltonians can be decomposed into three parts: (a) unstable, (b) stable, and (c) metastable. If present, each part contributes in a characteristic way to the time dependence of the entanglement entropy: (a) linear production, (b) bounded oscillations, and (c) logarithmic production. In the second part, we use numerical calculations to go beyond Gaussian states and quadratic Hamiltonians. We provide numerical evidence for the conjecture that entanglement production through quadratic Hamiltonians has the same asymptotic behavior for non-Gaussian initial states as for Gaussian ones. Moreover, even for nonquadratic Hamiltonians, we find a similar behavior at intermediate times. Our results are of relevance to understanding entanglement production for quantum fields in dynamical backgrounds and ultracold atoms in optical lattices.

We consider the problem of establishing entangled states of optimal singlet fraction and negativity between two remote parties for every use of a noisy quantum channel and trace-preserving local operations and classical communication (LOCC) under the assumption that the parties do not share prior correlations. We show that for a family of quantum channels in every finite dimension $d\ge 3$, one-shot optimal singlet fraction and entanglement negativity are attained only with appropriate nonmaximally entangled states. A consequence of our results is that the ordering of entangled states in all finite dimensions may not be preserved under trace-preserving LOCC.

When two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).

The arithmetic problem of factoring an integer $N$ can be translated into the physics of a quantum device, a result that supports Pólya's and Hilbert's conjecture to demonstrate Riemann's hypothesis. The energies of this system, being univocally related to the factors of $N$, are the eigenvalues of a bounded Hamiltonian. Here we solve the quantum conditions and show that the histogram of the discrete energies, provided by the spectrum of the system, should be interpreted in number theory as the relative probability for a prime to be a factor candidate of $N$. This is equivalent to a quantum sieve that is shown to require only $o{(ln\sqrt{N})}^3$ energy measurements to solve the problem, recovering Shor's complexity result. Hence the outcome can be seen as a probability map that a pair of primes solve the given factorization problem. Furthermore, we show that a possible embodiment of this quantum simulator corresponds to two entangled particles in a Penning trap. The possibility to build the simulator experimentally is studied in detail. The results show that factoring numbers, many orders of magnitude larger than those computed with experimentally available quantum computers, is achievable using typical parameters in Penning traps.

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys. Rev. A 86, 022342 (2012)], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord for pure quantum states.

We derive a mean-field relativistic formula for the isotope shift of an electronic energy level for arbitrary angular momentum; we then use it to predict the spectra of superheavy metastable neutron-rich isotopes belonging to the hypothetical island of stability. Our results may be applied to the search for superheavy atoms in astrophysical spectra using the known values of the transition frequencies for the neutron-deficient isotopes produced in the laboratory. An example of a relevant astrophysical system may be the spectra of the Przybylski's star where superheavy elements up to $Z=99$ have been possibly identified. In addition, it has been recently suggested to use the measurements of King plot nonlinearity in a search for hypothetical new light bosons. On the other hand, one can find the nonlinear corrections to the King plot arising already in the standard model framework. We investigate contributions to the nonlinearity arising from relativistic effects in the isotope field shift, the nuclear polarizability, and many-body effects. It is found that the nuclear polarizability contribution can lead to the significant deviation of the King plot from linearity. Therefore, the measurements of the nonlinearity of King plots may be applied to obtain the nuclear polarizability change between individual isotopes. We then proceed with providing a rough analytical estimate of the nonlinearity arising solely from the effect of a hypothetical scalar boson. Our predictions give theoretical limitations on the sensitivity of the search for new interactions and should help to identify the most suitable atoms for corresponding experiments.

We report on spectroscopic results on the ${}^{2}S_{1/2}\to {}^{2}P_{3/2}$ transition in single trapped ${\mathrm{Yb}}^{+}$ ions. We measure the isotope shifts for all stable ${\mathrm{Yb}}^{+}$ isotopes except ${}^{173}\mathrm{Yb}^{+}$, as well as the hyperfine splitting of the ${}^{2}P_{3/2}$ state in ${}^{171}\mathrm{Yb}^{+}$. Our results are in agreement with previous measurements but are a factor of 5–9 more precise. For the hyperfine constant $A\left({}^{2}P_{3/2}\right)=875.4\left(10\right)\mathrm{MHz}$ our results also agree with previous measurements but deviate significantly from theoretical predictions. We present experimental results on the branching ratios for the decay of the ${}^{2}P_{3/2}$ state. We find branching fractions for the decay to the ${}^{2}D_{3/2}$ state and ${}^{2}D_{5/2}$ state of 0.17(1)% and 1.08(5)%, respectively, in rough agreement with theoretical predictions. Furthermore, we measured the isotope shifts of the ${}^{2}F_{7/2}\to {}^{1}D{[5/2]}_{5/2}$ transition and determine the hyperfine structure constant for the ${}^{1}D{[5/2]}_{5/2}$ state in ${}^{171}\mathrm{Yb}^{+}$ to be $A\left({}^{1}D{[5/2]}_{5/2}\right)=-107\left(6\right)\mathrm{MHz}$.