Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultracold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various nontrivial condensed-matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultracold atoms are bouncing on a randomly moving mirror.

We theoretically investigate a three-dimensional weakly interacting Bose gas with one-dimensional Raman-type spin-orbit coupling at zero temperature. By employing an improved ansatz, including high-order harmonics in the stripe phase, we show that the critical transition from the stripe to the plane-wave phases is shifted to a relatively larger Rabi frequency compared to the prediction by previous work [Li et al., Phys. Rev. Lett. 108, 225301 (2012)] using a first-order stripe ansatz. We also determine the quantum depletion and superfluid density over a large range of Rabi frequency in different phases. The depletion exhibits an intriguing behavior with a discontinuous jump at the transition between the stripe and plane-wave phases, and a maximum at the transition between the plane-wave and zero-momentum phases. The superfluid density is derived through a phase-twist method. In the plane-wave and zero-momentum phases, it is significantly suppressed along the spin-orbit-coupling direction and vanishes at the transition, consistent with a recent work [Zhang et al., Phys. Rev. A 94, 033635 (2016)], while in the stripe phase, it smoothly decreases with increasing Rabi frequency. Our predictions would be useful for further theoretical and experimental studies of the exotic supersolid stripe phase.

We study photon, phonon statistics, and the cross-correlation between photons and phonons in a quadratically coupled optomechanical system. Photon blockade, phonon blockade, and strong anticorrelation between photons and phonons can be observed in the same parameter regime with the effective nonlinear coupling between the optical and the mechanical modes, enhanced by a strong optical driving field. Interestingly, an optimal value of the effective nonlinear coupling strength for the photon blockade is not within the strong nonlinear coupling regime. This abnormal phenomenon results from the destructive interference between different paths for two-photon excitation in the optical mode with a moderate effective nonlinear coupling strength. Furthermore, we show that phonon (photon) pairs or correlated photons and phonons can be generated in the strong nonlinear coupling regime with a proper detuning between the weak mechanical driving field and mechanical mode. Our results open up a way to generate anticorrelated and correlated photons and phonons, which may have important applications in quantum information processing.

We propose a feasible invisibility approach to suppress the scattering of waves from or to given directions and for particular frequencies, i.e., invisibility on demand. We derive a generalized Hilbert transform for a specific invisibility arrangement relating the two quadratures of the complex permittivity of an object. The scheme allows either designing objects to be invisible, or alternatively modifying the complex susceptibility of a given object to render invisibility. The theoretical proposal is further confirmed by finite-difference time-domain numerical calculations. Moreover, following an iterative chain of generalized Hilbert transforms, we propose the invisibility on demand with additional constraints, i.e., restricting the required modification of the complex refractive index within practical limits by avoiding gain areas. The proposed concept not only opens a venue of real or complex valued index landscapes, but also bridges the gap between Hermitian and non-Hermitian optical systems by unifying these systems under one single generalized design theory.

We have derived and investigated analytical expressions for the spontaneous emission radiative decay rate of an optically active (chiral) molecule placed near a chiral (bi-isotropic) triaxial nanoellipsoid, the size of which is much smaller than the wavelength. Differences in radiative decay rates of optically active molecule enantiomers located near the surface of chiral nanoparticles of spherical, prolate spheroidal, and ellipsoidal shapes have been investigated. It is shown that the change of the nanoparticle's shape from spherical to ellipsoidal results in substantial enhancement of the spontaneous emission radiative decay rate of molecule enantiomers of one type in comparison with the decay rate of the other type of enantiomers.

In this paper we theoretically show that counterpart photonic Cooper pairs can be achieved in nanoscale waveguides with radiation pressure effect. We demonstrate that due to Brillouin scattering a Stokes photon and an anti-Stokes one can exchange virtual phonons, leading to an effective photon-photon interaction. The effective interaction Hamiltonian of the two photons is identical to that for electrons in the BCS theory, and the photonic counterpart of the superconducting energy gap can appear. Quite different from the conventional stimulated Brillouin scattering the number of photon pairs can be amplified. The result could be used as a photon-pair laser and might have a possible application in integrated optics and quantum information processing in the future.

While Bohr's complementarity principle constitutes a bedrock of quantum mechanics with profound implications, coherence, as a defining feature of the quantum realm originating from the superposition principle, pervades almost every quantum consideration. By exploiting the algebraic and geometric structure of state-channel interaction, we show that an information-theoretic measure of coherence and a quantitative symmetry-asymmetry complementarity emerge naturally from the formalism of quantum mechanics. This is achieved by decomposing the state-channel interaction into a symmetric part and an asymmetric part, which satisfy a conservation relation. The symmetric part is represented by the symmetric Jordan product, and the asymmetric part is synthesized by the skew-symmetric Lie product. The latter further leads to a significant extension of the celebrated Wigner–Yanase skew information, and has an operational interpretation as quantum coherence of a state with respect to a channel. This not only presents a basic and alternative framework for addressing complementarity, but also puts the study of coherence in a broad context involving channels. Fundamental properties of the symmetry-asymmetry complementarity are revealed, and applications and implications are illustrated via several prototypical channels as well as the Mach–Zehnder interferometry, in which the fringe visibility is linked to symmetry and the which-path is linked to asymmetry.

We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cramér-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.

Extensive calculations are reported for electron collision strengths, rate coefficients, and transitions probabilities for a wide range of transitions in Fe ii. The collision strengths were calculated in the close-coupling approximation using the B-spline Breit-Pauli R-matrix method. The multiconfiguration Hartree-Fock method in connection with adjustable configuration expansions and a semiempirical fine-tuning procedure is employed for an accurate representation of the target wave functions. The energy correction was also used in the scattering calculations by adding to Hamiltonian matrices prior to transformation to intermediate coupling. The spin-orbit interaction term was added to the final Hamiltonian matrices in scattering calculations. The close-coupling expansion contains 340 fine-structure levels of Fe ii and includes all levels of the $3d^{6}4s$, $3d^{5}4s^2$, $3d^7$, and $3d^{6}4p$ configurations, plus a few lowest levels of the $3d^{5}4s4p$ configuration. The effective collision strengths are obtained by averaging the electron collision strengths over a Maxwellian distribution of velocities at electron temperatures in the range from ${10}^2$ to ${10}^5$ K and are reported for all possible inelastic transitions between the 340 fine-structure levels. The present results are more extensive than the previous calculations and considerably expand the existing data sets for Fe ii, allowing a more detailed treatment of the available measured spectra from different space observatories. Comparison with other calculations for collision rates and available experimental radiative rates is used to place uncertainty bounds on our collision strengths and to assess the likely uncertainties in the existing data sets.

A double-electron-ionization process occurs when an intense laser pulse interacts with atoms or molecules. Exact ab initio numerical simulation of such a situation is extremely computer resource demanding, thus often one is forced to apply reduced dimensionality models to get insight into the physics of the process. The performance of several algorithms for simulating double electron ionization by strong femtosecond laser pulses is studied. The obtained ionization yields and the momentum distributions of the released electrons are compared and the effects of the model dimensionality on the ionization dynamics are discussed.

Derivations for the higher tensor components of the quadrupole polarizabilities are given and their values for the metastable states of the ${\mathrm{Ca}}^{+}$, ${\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$ alkaline-earth-metal ions are estimated. We also give the scalar quadrupole polarizabilities of the ground and metastable states of these ions to compare our results with the previously available theoretical and experimental results. Reasonably good agreement between our calculations with the previous values of scalar quadrupole polarizabilities demonstrate their correctness. The reported scalar and tensor quadrupole polarizabilities could be very useful to estimate the uncertainties due to the gradient of the electric fields in the clock frequencies of the above alkaline-earth-metal ions when the accuracies of these frequency measurements attain a precision level below ${10}^{-19}$.

We investigate higher-order nonlinear inelastic scattering of electrons at an optical standing wave formed by two light waves with the same frequencies in vacuum. Initial conditions necessary for efficient scattering are obtained from the semiclassical energy and momentum conservation laws for all nonlinear orders. The stationary scattering potential in the electrons’ rest frame is derived from the perturbative solution of the classical relativistic equation of motion for the four-photon scattering process. The amplitude of the electron velocity modulation introduced during higher-order scattering processes is calculated numerically. The proposed inelastic interaction leads to a periodic modulation of the electrons’ energy and longitudinal momentum at a higher harmonic frequency of the driving light waves.

Frontiers of attosecond science are constantly shifting, thus addressing more and more intricate effects with increasing resolution. Ultrashort pulses offer a practical way to prepare complex superpositions of quantum states, follow, and steer their dynamics. In this contribution, an ultrafast spin-flip process triggered by subfemtosecond (fs) excitation and strong spin-orbit coupling between $2p$ core-excited states of a transition metal complex is investigated using density matrix-based time-dependent restricted active space configuration interaction theory. The effect of the nuclear vibrations is incorporated making use of an electronic system plus vibrational bath partitioning. The differences between isolated sub-fs pulses and pulse trains as well as the influence of various pulse characteristics on the initiated dynamics are discussed. The effect under study can be potentially used for ultrafast clocking in sub-few-fs experiments.

We measure the laser-intensity-dependent photoelectron momentum and energy spectra and identify the emerged resonant $(4s,3d$, and $4f)$ states of multiphoton ionization of Ne at 400 nm. We employ parallelly polarized two-color fields involving a strong ionizing 400-nm field and a weak 800-nm field to probe the relative time delay of resonant states. By analyzing phase-resolved three-dimensional photoelectron momentum distributions, we find the time delay of resonant states has an anisotropic angle dependence. Using an intuitive model, we show that the angle-dependent time delay carries the information of subcycle evolution of quantum states and reflects the temporal coherent properties of multiphoton resonant states during absorption and emission of photons. We find that the relative time delays among the resonant ionization via $4s,3d$, and $4f$ states along the polarization depend on the number of photons absorbed. This study has implications for coherent imaging of electron wave packets in the multiphoton ionization regime.

We consider general three-mode interferometers using a spin-1 atomic Bose-Einstein condensate with macroscopic magnetization. We show that these interferometers, combined with the measurement of the number of particles in each output port, provide an ultrahigh phase sensitivity. We construct effective two-mode interferometers which involve two Zeeman modes showing that they also provide an ultrahigh phase sensitivity but of a bit reduced factor in the corresponding Fisher information. A special case of zero magnetization is shown to persist the efficiency of the two-mode interferometry.

We present the general analytical theory for Dyakonov surface waves at the interface of a biaxial anisotropic dielectric with an isotropic medium. We demonstrate that these surface waves can be divided into two distinct classes, with qualitatively different spatial behavior. We obtain explicit expressions for the Dyakonov waves' dispersion and the parameter ranges for their existence.

We investigate time-dependent spectra of the intermittent resonance fluorescence of a single, laser-driven, three-level atom due to electron shelving. After a quasistationary state of the strong transition, a slow decay due to shelving leads to the steady state of the three-level system. The long-term stationary spectrum consists of a coherent peak, an incoherent Mollow-like structure, and a very narrow incoherent peak at the laser frequency. We find that in the ensemble-average dynamics, the narrow peak emerges during the slow decay regime, after the Mollow spectrum has stabilized but well before an average dark time has passed. The coherent peak, being a steady-state feature, is absent during the time evolution of the spectrum.

Large dynamical fluctuations—atypical realizations of the dynamics sustained over long periods of time—can play a fundamental role in determining the properties of collective behavior of both classical and quantum nonequilibrium systems. Rare dynamical fluctuations, however, occur with a probability that often decays exponentially in their time extent, thus making them difficult to be directly observed and exploited in experiments. Here, using methods from dynamical large deviations, we explain how rare dynamics of a given (Markovian) open quantum system can always be obtained from the typical realizations of an alternative (also Markovian) system. The correspondence between these two sets of realizations can be used to engineer and control open quantum systems with a desired statistics “on demand.” We illustrate these ideas by studying the photon emission behavior of a three-qubit system which displays a sharp dynamical crossover between active and inactive dynamical phases.

Generation and manipulation of the quantum state of a single photon is at the heart of many quantum information protocols. There has been growing interest in using phase modulators as quantum optics devices that preserve coherence. In this Rapid Communication, we have used an electro-optic phase modulator to shape the state vector of single photons emitted by a quantum dot to generate new frequency components (modes) and explicitly demonstrate that the phase modulation process agrees with the theoretical prediction at a single-photon level. Through two-photon interference measurements we show that for an output consisting of three modes (the original mode and two sidebands), the indistinguishability of the mode engineered photon, measured through the second-order intensity correlation $\left[g^2\left(0\right)\right]$ is preserved. This work demonstrates a robust means to generate a photonic qubit or more complex state (e.g., a qutrit) for quantum communication applications by encoding information in the sidebands without the loss of coherence.

We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical harmonics. The Wigner representation of a propagator can be experimentally recovered by measuring expectation values of rotated axial spherical tensor operators in an augmented system with an additional ancilla qubit. The methodology is experimentally demonstrated for standard one-qubit quantum gates using nuclear magnetic resonance spectroscopy. In particular, this approach provides a direct and compelling visualization of the spinor property of the propagators corresponding to the rotation of a spin-1/2 particle.