Based on relative entropy, we give a unified characterization of quantum correlations for nonlocality, steerability, discord, and entanglement for any bipartite quantum states. For two-qubit states we show that the quantities obtained from quantifying nonlocality, steerability, entanglement, and discord have strictly monotonic relationships. As examples, the Bell diagonal states are studied in detail.

A quantum electrodynamic calculation of the interaction of an excited-state atom with a ground-state atom is performed. For an excited reference state and a lower-lying virtual state, the contribution to the interaction energy naturally splits into a pole term and a Wick-rotated term. The pole term is shown to dominate in the long-range limit, altering the functional form of the interaction from the retarded $1/R^7$ Casimir-Polder form to a long-range tail—provided by the Wick-rotated term—proportional to $cos[2(E_m-E_n)R/\left(\hslash c\right)]/R^2$, where $E_m<E_n$ is the energy of a virtual state, lower than the reference-state energy $E_n$, and $R$ is the interatomic separation. General expressions are obtained which can be applied to atomic reference states of arbitrary angular symmetry. Careful treatment of the pole terms in the Feynman prescription for the atomic polarizability is found to be crucial in obtaining correct results.

The photodetachment of a hydrogen negative ion in the bichromatic oscillating electric field is investigated using the time-dependent closed orbit theory. The photodetachment cross section is specifically calculated in the bichromatic oscillating electric field with a 1:2 frequency ratio and various phase differences. It is found that the oscillatory structure appears in the photodetachment cross section, which depends sensitively on the strength and the phase difference of the bichromatic oscillating electric field. The time-dependent photodetachment cross section is nearly unaffected by a weak bichromatic oscillating electric field. However, with the increase of the oscillating electric field strength, four different types of the detached electron's closed orbits are identified, which makes the photodetachment cross section oscillate in a much more complicated way. In addition, the influence of the phase difference in the bichromatic oscillating electric field on the photodetachment cross section is also investigated quantitatively. The formula we put forward for the time-dependent photodetachment cross section is universal and can be used to calculate the cross section for other frequency ratios in the bichromatic oscillating electric field. On account of its generality, our work provides a clear and intuitive picture for the photodetachment processes of a negative ion in the bichromatic oscillating electric field, and may guide future experimental research on the photodetachment dynamics in the oscillating electric field.

We study interacting bosonic or fermionic atoms in a high synthetic magnetic field in two dimensions spanned by continuous real space and a synthetic dimension. Here the synthetic dimension is provided by hyperfine spin states, and the synthetic field is created by laser-induced transitions between them. While the interaction is short-range in real space, it is long-range in the synthetic dimension in sharp contrast with fractional quantum Hall systems. Introducing an analog of the lowest-Landau-level approximation valid for large transition amplitudes, we derive an effective one-dimensional lattice model, in which density-density interactions turn out to play a dominant role. We show that in the limit of a large number of internal states, the system exhibits a cascade of crystal ground states, which is known as the devil's staircase, in a way analogous to the thin-torus limit of quantum Hall systems.

We report on the stationary and robust propagation of light beams with rather arbitrary and controllable intensity and dissipation transverse patterns in self-focusing Kerr media with nonlinear absorption. When nonlinear absorption is due to multiphoton ionization at high beam powers in transparent media such as glasses and air, these beams can generate multiple plasma channels with tailored geometries. Their nature and spatial characteristics are discussed in detail, as well as the laws determining their spontaneous formation from coherent superpositions of Bessel beams of different amplitudes and topological charges.

We analyze a similar scheme for producing light-mediated entanglement between atomic ensembles, as first realized by Julsgaard, Kozhekin, and Polzik [Nature (London) 413, 400 (2001)]. In the standard approach to modeling the scheme, a Holstein–Primakoff approximation is made, where the atomic ensembles are treated as bosonic modes, and is only valid for short interaction times. In this paper, we solve the time evolution without this approximation, which extends the region of validity of the interaction time. For short entangling times, we find that this produces a state with characteristics similar to those of a two-mode squeezed state, in agreement with standard predictions. For long entangling times, the state evolves into a non-Gaussian form, and the characteristics of the two-mode squeezed state start to diminish. This is attributed to more exotic types of entangled states being generated. We characterize the states by examining the Fock-state probability distributions, Husimi $Q$ distributions, and nonlocal entanglement between the ensembles. We compare and connect several quantities obtained by using the Holstein–Primakoff approach and our exact time evolution methods.

We have directly detected millimeter-wave (mm-wave) free-space superradiant emission from Rydberg states (principal quantum number $n\sim 30$) of barium atoms in single-shot experiments. We trigger the cooperative effects with a weak initial pulse and detect the time-dependent amplitude and phase of the emitted radiation with single-shot sensitivity and 20 ps time resolution. This allows measurement and shot-by-shot analysis of the statistical distribution of decay rates, time delays, and time-dependent frequency shifts. Cooperative line shifts and decay rates are observed that exceed the 250 kHz Doppler width by a factor of 20 and the 50 Hz spontaneous emission rate by a factor of ${10}^5$.

It is demonstrated here that local dynamics have the ability to strongly modify the entangling power of unitary quantum gates acting on a composite system. The scenario is common to numerous physical systems, in which the time evolution involves local operators and nonlocal interactions. To distinguish between distinct classes of gates with zero entangling power we introduce a complementary quantity called gate typicality and study its properties. Analyzing multiple, say $n$, applications of any entangling operator, $U$, interlaced with random local gates we prove that both investigated quantities approach their asymptotic values in a simple exponential form. These values coincide with the averages for random nonlocal operators on the full composite space and could be significantly larger than that of $U^n$. This rapid convergence to equilibrium, valid for subsystems of arbitrary size, is illustrated by studying multiple actions of diagonal unitary gates and controlled unitary gates.

Recently, several studies have investigated synchronization in quantum-mechanical limit-cycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillator's phase was overdamped and therefore incoherent. We show that there exist regimes of underdamped and even quantum-coherent phase motion, opening up new possibilities to study quantum synchronization dynamics. To this end, we investigate the Van der Pol oscillator (a paradigm for a self-oscillating system) synchronized to an external drive. We derive an effective quantum model which fully describes the regime of underdamped phase motion and additionally allows us to identify the quality of quantum coherence. Finally, we identify quantum limit cycles of the phase itself.

An approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and nonlocal setting. It combines heralded gates previously studied for atom or atomlike qubits with logical encoding from linear optical quantum computation in order to perform high-fidelity quantum gates across a quantum network. The error-detecting properties of the heralded operations ensure high fidelity while the encoding makes it possible to correct for failed attempts such that deterministic and high-quality gates can be achieved. Importantly, this is robust to photon loss, which is typically the main obstacle to photonic-based quantum information processing. Overall this approach opens a path toward quantum networks with atomic nodes and photonic links.

The ground state of a pair of ultrastrongly coupled bosonic modes is predicted to be a two-mode squeezed vacuum. However, the corresponding quantum correlations are currently unobservable in condensed matter where such a coupling can be reached, since it cannot be extracted from these systems. Here, we show that superconducting circuits can be used to perform an analog simulation of a system of two bosonic modes in regimes ranging from strong to ultrastrong coupling. More importantly, our quantum simulation setup enables us to detect output excitations that are related to the ground-state properties of the bosonic modes. We compute the emission spectra of this physical system and show that the produced state presents single- and two-mode squeezing simultaneously.

Recently the lifetime of the excited $3d^{9}4s^2{}^2{D}_{3/2}$ in ${\mathrm{Ni}}^{-}$ was measured to be $15.1\pm 0.4$ s [Phys. Rev. A 93, 012512 (2016)]. This deviates from results from nonrelativistic, within the $LS$-approximation, calculations for this forbidden magnetic-dipole transition of 18.88 s [J. Phys. B 50, 025001 (2017)]. We here present elaborate and fully relativistic multiconfiguration Dirac–Hartree–Fock calculations, to explore this difference. Our calculated transition energy $1485.65{\mathrm{cm}}^{-1}$ is in excellent agreement with the experimental $1485\pm 3{\mathrm{cm}}^{-1}$ [Phys. Rev. A 58, 2051 (1998)]. However the lifetime of 18.86 s, while agreeing well with the nonrelativistic analytical value, deviates from experiment by 25%. The uncertainties of our calculated wavelength and lifetime are estimated to be better than 0.1% and 1%, respectively. In spite of including a careful investigation of contributions from correlation as well as higher-order relativistic effects, we cannot find any explanation from the structure theory for this deviation.

We consider an analytically solvable model of two interacting electrons that allows for the calculation of the exact exchange-correlation kernel of time-dependent density functional theory. This kernel, as well as the corresponding density response function, is studied in the limit of large repulsive interactions between the electrons and we give analytical results for these quantities as an asymptotic expansion in powers of the square root of the interaction strength. We find that in the strong interaction limit the three leading terms in the expansion of the kernel act instantaneously while memory terms only appear in the next orders. We further derive an alternative expansion for the kernel in the strong interaction limit on the basis of the theory developed previously [Phys. Chem. Chem. Phys. 18, 21092 (2016)] using the formalism of strictly correlated electrons in the adiabatic approximation. We find that the first two leading terms in this series, corresponding to the strictly correlated limit and its zero-point vibration correction, coincide with the two leading terms of the exact expansion. We finally analyze the spatial nonlocality of these terms and show when the adiabatic approximation breaks down. The ability to reproduce the exact kernel in the strong interaction limit indicates that the adiabatic strictly correlated electron formalism is useful for studying the density response and excitation properties of other systems with strong electronic interactions.

The dipole blockade of very-high-$n, n\sim 300$, strontium $5snf{}^1{F}_3$ Rydberg atoms in a hot atomic beam is studied. For such high $n$, the blockade radius can exceed the linear dimensions of the excitation volume. Rydberg atoms formed inside the excitation volume can, upon leaving the region, continue to suppress excitation until they have moved farther away than the blockade radius. Moreover, the high density of states originating from the many magnetic sublevels associated with the $F$ states results in a small but finite probability of excitation of $L=3n{}^1{F}_3$ atom pairs at small internuclear separations below the blockade radius. We demonstrate that these effects can be distinguished from one another by the distinct features they imprint on the Mandel $Q$ parameter as a function of the duration of the exciting laser.

We study, within a framework of the classical fields approximation, the static structure factor of a weakly interacting Bose gas at thermal equilibrium. As in a recent experiment [R. Schley et al., Phys. Rev. Lett. 111, 055301 (2013)], we find that the thermal distribution of phonons in a three-dimensional Bose gas follows the Planck distribution. On the other hand we find a disagreement between the Planck and phonon (calculated just as for the bulk gas) distributions in the case of elongated quasi-one-dimensional systems. We attribute this discrepancy to the existence of spontaneous dark solitons [i.e., thermal solitons as reported in T. Karpiuk et al., Phys. Rev. Lett. 109, 205302 (2012)] in an elongated Bose gas at thermal equilibrium.

A quantum state is fully characterized by its density matrix or equivalently by its quasiprobabilities in phase space. A scheme to identify the quasiprobabilities of a quantum state is an important tool in the recent development of quantum technologies. One of the most fundamental interaction models in quantum optics is the so-called Jaynes-Cummings model (JCM), which has been massively studied theoretically and experimentally. However, the expected essential dynamics of the field states under the resonant JCM has not been observed experimentally due to the lack of a proper reconstruction scheme. In this paper, we further develop a highly efficient vacuum measurement scheme and study the JCM dynamics in a trapped ion system with the capability of the vacuum measurement to reconstruct its quasiprobability $Q$ function, which is a preferred choice to study the core of the dynamics of a quantum state in phase space. During the JCM dynamics, the Gaussian peak of the initial coherent state bifurcates and rotates around the origin of phase space. They merge at the so-called revival time at the other side of phase space. The measured $Q$ function agrees with the theoretical prediction. Moreover, we reconstruct the Wigner function by deconvoluting the $Q$ function and observe the quantum interference in the Wigner function at half of the revival time, where the vibrational state becomes nearly disentangled from the internal energy states and forms a superposition of two composite states. The scheme can be applied to other physical setups including cavity or circuit-QED and optomechanical systems.

We develop a Floquet scattering formalism for the description of quasistationary states of microwave photons in a one-dimensional waveguide interacting with a nonlinear cavity by means of a periodically modulated coupling. This model is inspired by the recent progress in engineering of tunable coupling schemes with superconducting qubits. We argue that our model can realize the quantum analog of an optical chopper. We find strong periodic modulations of the transmission and reflection envelopes in the scattered few-photon pulses, including photon compression and blockade, as well as dramatic changes in statistics. Our theoretical analysis allows us to explain these nontrivial phenomena as arising from nonadiabatic memory effects.

We theoretically study the unique applications of optomechanics based on traveling-wave microresonators, where the optomechanical coupling of degenerate modes (clockwise and counterclockwise) can be enhanced selectively by optically pumping in different propagation directions. We show that the unique features of degenerate optical modes can be applied for the entangled photon generation. Specifically, the coherent coupling between the degenerate optical modes and two acoustic modes is also studied, in which the relative phase of the optomechanical couplings plays a key role in the optical nonreciprocal conversion. In addition, we have studied another mechanical vibration based on the Brillouin scattering in the microresonators. The parity-time symmetry of acoustic modes can be observed in the slightly deformed microresonators because of the interaction of forward and backward stimulated Brillouin scattering in the triple-resonance system. The degenerate modes are in the decoherence-free subspace, which is robust against environmental noises. Based on parameters realized in recent experiments, these optomechanical devices should be readily achievable.

We show that spin-squeezing criteria commonly used for entanglement detection can be erroneous if the probe is not symmetric. We then derive a lower bound on squeezing for separable states in spin systems probed asymmetrically. Using this we further develop a procedure that allows us to verify the degree of entanglement of a quantum state in the spin system. Finally, we apply our method for entanglement verification to existing experimental data, and use it to prove the existence of tripartite entanglement in a spin-squeezed atomic ensemble.

The transition-path-time distribution is formalized for quantum systems and applied to a number of examples. Using a symmetrized thermal density, transition times are studied for the free particle, a $\delta$-function potential, a square-barrier potential, and symmetric-double-well dynamics at very low temperature. These studies exemplify extreme nonlocality for motion in $\delta$-function potentials, vanishing tunneling times for the square-barrier potential, and varying transit times in the symmetric-double-well potential. In all cases, there are regions where the longer the distance traversed, the shorter the mean transit time is. For the thermal density correlation functions studied here, the Hartman effect exemplifies itself through the independence of the transit time on the barrier height. However, due to the thermal distribution, the transit time does depend on the barrier width, initially decreasing with increasing width but then increasing again.