We outline a general method of constructing finite-range cloaking potentials which render a given finite-range real or complex potential, $v\left(x\right)$, unidirectionally reflectionless or invisible at a wave number, $k_0$, of our choice. We give explicit analytic expressions for three classes of cloaking potentials which achieve this goal while preserving some or all of the other scattering properties of $v\left(x\right)$. The cloaking potentials we construct are the sum of up to three constituent unidirectionally invisible potentials. We discuss their utility in making $v\left(x\right)$ bidirectionally invisible at $k_0$ and demonstrate the application of our method to obtain antireflection and invisibility cloaks for a Bragg reflector.

Strong-field manipulation of autoionizing states is a crucial aspect of electronic quantum control. Recent measurements of the attosecond transient absorption spectrum (ATAS) of helium dressed by a few-cycle visible pulse [C. Ott et al., Nature (London) 516, 374 (2014)] provide evidence of the inversion of Fano profiles. With the support of accurate ab initio calculations that reproduce the results of the latter experiment, here we investigate the new physics that arise from ATAS when the laser intensity is increased. In particular, we show that (i) previously unnoticed signatures of the dark $2p^2{}^{1}S$ doubly excited state are observed in the experimental spectrum, (ii) inversion of Fano profiles is predicted to be periodic in the laser intensity, and (iii) the ac Stark shift of the higher terms in the $s{p}_{2,n}^{+}$ autoionizing series exceeds the ponderomotive energy, which is the result of a genuine two-electron contribution to the polarization of the excited atom.

We show how nitrogen-vacancy centers can be used to detect the presence of weak magnetic fields, that is, to find out whether a magnetic field, about which we may not have complete information, is actually present or not. The solution to this problem comes from quantum state discrimination theory. The effect of decoherence is taken into account to optimize the time over which the nitrogen-vacancy center is allowed to interact with the magnetic field before making a measurement. We also find the optimum measurement that should be performed. We then show how multiple measurements reduce the error in detecting the magnetic field. Finally, a major limitation of the measurement process, namely, limited photon detection efficiency, is taken into account. Our proposals should be implementable with current experimental technology.

Decoherence-free states have been found in Markovian open system dynamics and in the framework of non-Markovian fermionic environments. In the latter scenario we determine an energy range where quantum coherence is maintained over long times for every initial coherent configuration. In particular, for a two-state fermionic system interacting with a non-Markovian fermionic environment, undamped oscillating or stable coherence between the two energy eigenstates appears if the degenerate energy level is below a critical energy. If these energies coincide, the same behavior is observed in the superohmic regime and, under special conditions, the initial coherence is approached asymptotically. Equivalently, coherence persists if a defined dressed energy of the system is less than the band-gap energy of the reservoir. Same properties are found in the framework of bosonic environments.

In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and formulate two quantum uncertainty equalities, which hold for all pairs of incompatible observables and indicate the new uncertainty relations recently introduced by L. Maccone and A. K. Pati [Phys. Rev. Lett. 113, 260401 (2014)]. In fact, we obtain a series of inequalities with hierarchical structure, including the Maccone-Pati's inequalities as a special (weakest) case. Furthermore, we present an explicit interpretation lying behind the derivations and relate these relations to the so-called intelligent states. As an illustration, we investigate the properties of these uncertainty inequalities in the qubit system and a state-independent bound is obtained for the sum of variances. Finally, we apply these inequalities to the spin squeezing scenario and its implication in interferometric sensitivity is also discussed.

Intrinsic entanglement (IE) is a quantity which aims at quantifying bipartite entanglement carried by a quantum state as an optimal amount of the intrinsic information that can be extracted from the state by measurement. We investigate in detail the properties of a Gaussian version of IE, the so-called Gaussian intrinsic entanglement (GIE). We show explicitly how GIE simplifies to the mutual information of a distribution of outcomes of measurements on a conditional state obtained by a measurement on a purifying subsystem of the analyzed state, which is first minimized over all measurements on the purifying subsystem and then maximized over all measurements on the conditional state. By constructing for any separable Gaussian state a purification and a measurement on the purifying subsystem which projects the purification onto a product state, we prove that GIE vanishes on all Gaussian separable states. Via realization of quantum operations by teleportation, we further show that GIE is nonincreasing under Gaussian local trace-preserving operations and classical communication. For pure Gaussian states and a reduction of the continuous-variable GHZ state, we calculate GIE analytically and we show that it is always equal to the Gaussian Rényi-2 entanglement. We also extend the analysis of IE to a non-Gaussian case by deriving an analytical lower bound on IE for a particular form of the non-Gaussian continuous-variable Werner state. Our results indicate that mapping of entanglement onto intrinsic information is capable of transmitting also quantitative properties of entanglement and that this property can be used for introduction of a quantifier of Gaussian entanglement which is a compromise between computable and physically meaningful entanglement quantifiers.

Control strategies for dissipative preparation of target quantum states, both pure and mixed, and subspaces are obtained by switching between a set of available semigroup generators. We show that the class of problems of interest can be recast, from a control-theoretic perspective, into a switched-stabilization problem for linear dynamics. This is attained by a suitable affine transformation of the coherence-vector representation. In particular, we propose and compare stabilizing time-based and state-based switching rules for entangled state preparation, showing that the latter not only ensure faster convergence with respect to nonswitching methods, but can be designed so that they retain robustness with respect to initialization, as long as the target is a pure state or a subspace.

In the context of bipartite bosonic systems, two notions of classicality of correlations can be defined: $P$ classicality, based on the properties of the Glauber-Sudarshan $P$ function; and $C$ classicality, based on the entropic quantum discord. It has been shown that these two notions are maximally inequivalent in a static (metric) sense, as they coincide only on a set of states of zero measure. We extend and reinforce quantitatively this inequivalence by addressing the dynamical relation between these types of nonclassicality in a paradigmatic quantum-optical setting: the linear mixing at a beam splitter of a single-mode Gaussian state with a thermal reference state. Specifically, we show that almost all $P$-classical input states generate outputs that are not $C$ classical. Indeed, for the case of zero thermal reference photons, the more $P$-classical resources at the input the less $C$ classicality at the output. In addition, we show that the $P$ classicality at the input—as quantified by the nonclassical depth—does instead determine quantitatively the potential of generating output entanglement. This endows the nonclassical depth with a new operational interpretation: it gives the maximum number of thermal reference photons that can be mixed at a beam splitter without destroying the output entanglement.

Random numbers play a key role in information science, especially in cryptography. Based on the probabilistic nature of quantum mechanics, quantum random number generators can produce genuine randomness. In particular, random numbers can be produced from laser phase fluctuations with a very high speed, typically in the Gbps regime. In this work, by developing a physical model, we investigate the origin of the randomness in quantum random number generators based on laser phase fluctuations. We show how the randomness essentially stems from spontaneous emissions. The laser phase fluctuation can be quantitatively evaluated from basic principles and qualitatively explained by the Brownian motion model. After taking account of practical device precision, we show that the randomness generation speed is limited by the finite resolution of detection devices. Our result also provides the optimal experiment design in order to achieve the maximum generation speed.

Spin effects in the tunneling regime of strong-field ionization of hydrogenlike highly charged ions in linearly as well as circularly polarized laser fields are investigated. The impact of the polarization of a laser field on the spin effects is analyzed. Spin-resolved differential ionization rates are calculated employing the relativistic Coulomb-corrected strong-field approximation developed in the previous paper of the series. Analytical expressions for spin asymmetries and the spin-flip probability, depending on the laser's polarization, are obtained for the photoelectron momentum corresponding to the maximum of the tunneling probability. A simple intuitive model is developed for the description of spin dynamics in tunnel ionization. The spin flip is shown to be experimentally observable by using moderate highly charged ions with a charge of the order of 20 and a laser field with an intensity of $I\sim {10}^{22}{\mathrm{W}/\mathrm{cm}}^2$.

Engineering topological quantum order has become a major field of physics. Many advances have been made by synthesizing gauge fields in cold atomic systems. Here we carry over these developments to other platforms which are extremely well suited for quantum engineering, namely, trapped ions and nano-trapped atoms. Since these systems are typically one-dimensional, the action of artificial magnetic fields has so far received little attention. However, exploiting the long-range nature of interactions, loops with nonvanishing magnetic fluxes become possible even in one-dimensional settings. This gives rise to intriguing phenomena, such as fractal energy spectra, flat bands with localized edge states, and topological many-body states. We elaborate on a simple scheme for generating the required artificial fluxes by periodically driving an XY spin chain. Concrete estimates demonstrating the experimental feasibility for trapped ions and atoms in wave guides are given.

We propose a scheme for microscopy with resolution far beyond the diffraction limit by using coherent Rabi oscillations. When the sample is illuminated by a gradient laser field, Rabi oscillations will be induced which can lead to a sinusoidal excitation in the sample. This is similar to the structured illumination microscopy (SIM) which can recover high-spatial-frequency components in the far field. However, different from linear SIM, the sinusoidal pattern here can have a spatial frequency much higher than that of the linear standing wave. Due to this property, we can achieve extremely high resolution, as in the nonlinear saturated SIM, but keep the reconstruction algorithm as simple as the linear one.

Resonant scattering of a photon by an electron in the presence of the field of the low intensity circularly polarized pulsed laser wave is studied theoretically. The approximation used the case in which a laser-pulse duration is significantly greater than the characteristic oscillation time. The resonance conditions of the exchange diagrams by electron and positron intermediate states were determined. The probability of such a process is calculated. It is demonstrated that the resonant probability may be six to ten orders of magnitude higher than the probability of the Compton effect in the absence of the external field. Obtained results can be verified experimentally in the framework of modern research projects (SLAC, FAIR, XFEL, and ELI).

We present quantum-beat spectroscopy of excited states of helium atoms populated selectively with high-order-harmonic emission below the atomic ionization potential by means of low-pass filtering of the pump radiation. The created electron wave packet is ionized by few-cycle infrared (IR) pulses leading to characteristic peaks in the photoelectron yield, which beat with a frequency proportional to the energy gap between the states involved in the two-color photoionization process. Minimizing the direct ionization by the extreme ultraviolet (XUV) radiation, we can follow the evolution of the electron wave packet also in the region of temporal pump-probe overlap. A detailed time-frequency analysis of the quantum beats and direct comparison with the solution of the time-dependent Schrödinger equation reveal the existence of quantum beats characterized by a final state of mixed parity. Finally, we show that by varying the carrier-envelope offset phase of the probe pulse, one can optically control the preferred direction of photoelectron emission and the contrast of such beats.

We study a Floquet realization of the Harper-Hofstadter model that has recently been implemented in a gas of cold bosonic atoms. We study in detail the scattering processes in this system in the weakly interacting regime due to the interplay of particle interactions and the explicit time dependence of the Floquet states that lead to band transitions and heating. We focus on the experimentally used parameters and explicitly model the transverse confining direction. Based on transition rates computed within the Floquet-Fermi golden rule we obtain band population dynamics which are in agreement with the dynamics observed in experiment. Finally, we discuss whether and how photon-assisted collisions that may be the source of heating and band population dynamics might be suppressed in the experimental setup by appropriate design of the transverse confining potential. The suppression of such processes will become increasingly important as experiments progress into simulating strongly interacting systems in the presence of artificial gauge fields.

We report on the Bose-Einstein condensation of metastable ${}^4\mathrm{He}$ atoms using a hybrid approach, consisting of a magnetic quadrupole and an optical dipole trap. In our setup we cross the phase transition with $2\times {10}^6$ atoms, and we obtain pure condensates of $5\times {10}^5$ atoms in the optical trap. This approach to cooling ${}^4\mathrm{He}$ provides enhanced cycle stability, large optical access to the atoms and results in the production of a condensate every 6 s—a factor 2 faster than the state of the art. This speed-up will significantly reduce the data acquisition time needed for the measurement of many particle correlations, made possible by the ability of metastable helium atoms to be detected individually.

We propose to use the resonant enhancement of the parametric instability in an optomechanical system of two optical modes coupled to a mechanical oscillator to prepare mechanical limit cycles with sub-Poissonian phonon statistics. Strong single-photon coupling is not required. The requirements regarding sideband resolution, circulating cavity power, and environmental temperature are in reach with state of the art parameters of optomechanical crystals. Phonon antibunching can be verfied in a Hanburry Brown–Twiss measurement on the output field of the optomechanical cavity.

We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions. Both these definitions seem to be physically consistent while becoming equivalent only in certain cases. Moreover, when autocorrelation functions are considered, one can introduce another function defined as the relative difference between the two definitions. We conjecture that such a function can be used to assess the positive semidefiniteness of the density operator without computing its eigenvalues. We illustrate these points by studying analytically a number of models with two energy levels.