We describe an approach based on the view of the well-known strong-field approximation (SFA) as an evolution equation. From this point of view the SFA is a nonhomogeneous evolution equation with the inhomogeneous term which determines the departure of the approximate evolution driven by the SFA from the evolution driven by the exact ab initio time-dependent Schrödinger equation (TDSE). A modification of this nonhomogeneous evolution equation making the inhomogeneous term smaller produces results for the photoelectron spectra which agree quantitatively well with the TDSE results for a system with the Coulomb interaction (we use hydrogen as an example).

We consider the problem of expansion of a Bose-Einstein condensate released from a box. Contrary to the standard situation of its release from a harmonic trap, in this case the dynamics is complicated by a process of collision of two rarefaction waves propagating to the center of an initially uniform distribution. A complete analytical solution of this problem is obtained by the Riemann method in the hydrodynamic dispersionless approximation, and the results are compared with the exact numerical solution of the Gross-Pitaevskii equation.

We theoretically investigate the rigid body dynamics of an optically levitated nanodumbbell under parametric feedback cooling and provide a simplified model for describing the motion. Differing from previous studies, the spin of the nanoparticle about its symmetry axis is considered nonnegligible. Simulations reveal that standard parametric feedback cooling can extract energy from two of the five rotational degrees of freedom when the nanoparticle is levitated using a linearly polarized laser beam. The dynamics after feedback cooling are characterized by a normal mode describing precession about the laser polarization axis together with spin about the nanoparticle's symmetry axis. Cooling the remaining mode requires an asymmetry in the two librational frequencies associated with motion about the polarization axis as well as information about the two frequencies of rotation about the polarization axis. Introducing an asymmetric potential allows full cooling of the librational coordinates if the frequencies of both are used in the feedback modulation and is an avenue for entering the librational quantum regime. The asymmetry in the potential needs to be large enough for practical cooling times as the cooling rate of the system depends nonlinearly on the degree of asymmetry, a condition that is easily achieved experimentally.

We describe one-dimensional stationary scattering of a two-component wave field by a non-Hermitian matrix potential which features odd-$\mathcal{P}\mathcal{T}$ symmetry, i.e., symmetry with ${\left(\mathcal{P}\mathcal{T}\right)}^2=-1$. The scattering is characterized by a $4\times 4$ transfer matrix. The main attention is focused on spectral singularities which are classified into two types. Weak spectral singularities are characterized by the zero determinant of a diagonal $2\times 2$ block of the transfer matrix. This situation corresponds to the lasing or coherent perfect absorption of pairs of oppositely polarized modes. Strong spectral singularities are characterized by a zero diagonal block of the transfer matrix. We show that in odd-$\mathcal{P}\mathcal{T}$-symmetric systems any spectral singularity is self-dual, i.e., lasing and coherent perfect absorption occur simultaneously. A detailed analysis is performed for a case example of a $\mathcal{P}\mathcal{T}$-symmetric coupler consisting of two waveguides, one with localized gain and another with localized absorption, which are coupled by a localized antisymmetric medium. For this coupler, we discuss weak self-dual spectral singularities and their splitting into complex-conjugate eigenvalues which represent bound states characterized by propagation constants with real parts lying in the continuum. A rather counterintuitive restoration of the unbroken odd-$\mathcal{P}\mathcal{T}$-symmetric phase subject to the increase of the gain-and-loss strength is also revealed. A comparison between odd- and even-$\mathcal{P}\mathcal{T}$-symmetric couplers, the latter characterized by ${\left(\mathcal{P}\mathcal{T}\right)}^2=1$, is also presented.

We show that a dynamic gain-loss modulation in an optical structure can lead to a direction-dependent parity-time ($\mathcal{PT}$) phase transition. The phase transition can be made thresholdless in the forward direction, and yet remains with a nonzero threshold in the backward direction. As a result, nonreciprocal directional amplification can be realized. Such a dynamic gain-loss modulation can be directly integrated with a semiconductor laser to provide optical isolation for the laser.

We propose a methodical approach to controlling and enhancing deviations from exponential decay in quantum and optical systems by exploiting recent progress surrounding another subtle effect: the bound states in the continuum, which have been observed in optical waveguide array experiments within this past decade. Specifically, we show that by populating an initial state orthogonal to that of the bound state in the continuum, it is possible to engineer system parameters for which the usual exponential decay process is suppressed in favor of inverse power law dynamics and coherent effects that typically would be extremely difficult to detect in experiment. We demonstrate our method using a model based on an optical waveguide array experiment and further show that the method is robust even in the face of significant detuning from the precise location of the bound state in the continuum.

We show that arbitrarily-high-order exceptional points (EPs) can be achieved in a repulsively interacting two-species Bose gas in one dimension. By exactly solving the non-Hermitian two-boson problem, we demonstrate the existence of third-order EPs when the system is driven across the parity-time symmetry-breaking transition. We further address the fourth-order EPs with three bosons and generalize the results to the $N$-body system, where the EP order can be as high as $N+1$. Physically, such high order originates from the intrinsic ferromagnetic correlation in spinor bosons, which causes the entire system to collectively behave as a single huge spin. Moreover, we show how to create an ultrasensitive spectral response around EPs via an interaction anisotropy in different spin channels. Our work puts forward the possibility of atomic sensors made from highly controllable ultracold gases.

The prospect of controlling entanglement in interacting quantum systems offers a myriad of technological and scientific promises, given the progress in experimental studies in systems such as ultracold trapped gases. This control is often challenging because of decoherence, the process by which environmental interactions create spurious entanglements that can destroy the desired entanglement. Considering the collisional decoherence that is relevant for quantum measurements utilizing scattering in one-dimensional trapped gases, here we derive a relationship between particle masses and wave-packet widths that minimizes the entanglement created during scattering. We assess the relevance of our results by directly observing this relationship in the emergent scales of a master equation for a particle undergoing nonthermal scattering. Our relationship is independent of the details of the particle interactions and sheds light on how to design scattering processes that minimize decoherence.

We have embedded two fixed-frequency ${\mathrm{Al}/\mathrm{AlO}}_x$/Al transmons, with ground-to-excited transition frequencies at 6.0714 and 6.7543 GHz, in a single three-dimensional Al cavity with a fundamental mode at 7.7463 GHz. Strong coupling between the cavity and each transmon results in an effective qubit-qubit coupling strength of 26 MHz and a $-1$ MHz dispersive shift in each qubit's transition frequency, depending on the state of the other qubit. Using the all-microwave SWIPHT (speeding up wave forms by inducing phases to harmful transitions) technique [Economou and Barnes, Phys. Rev. B 91, 161405 (2015)], we demonstrate the operation of a generalized controlled-not gate between the two qubits, with a gate time of ${\tau }_g=907$ ns optimized for this device. Using quantum process tomography we find that the gate fidelity is 83–84%, somewhat less than the 87% fidelity expected from relaxation and dephasing in the transmons during the gate time.

We propose a method to verify quantum steering for two-qubit states with an arbitrary amount of null results when both the steering and steered parties cannot be trusted. We converted the steering inequality proposed in a recent article [Phys. Rev. X 2, 031003 (2012)] to a corresponding measurement-device-independent steering criterion that depends on the heralding efficiency of the steering party, number of measurement settings, and imperfection of the state preparation. As a result, for a relative frequency of valid measurement outcomes ${\eta }_h$, the steering can be verified using a number of different measurement settings larger than $1/{\eta }_h$ and maximally entangled states. Furthermore, steerability is guaranteed as long as the measurement efficiency of the steered party is nonzero. Our result is useful for loss-tolerant and measurement-device-independent steering tasks.

The spin-orbit (SO) coupling matrix elements between the excited states of the lightest heteronuclear alkali metal dimers AB(A, B = Li, Na, K, Rb) converging to the first three dissociation limits were evaluated by employing the quasirelativistic electronic wave functions in a wide range of interatomic distances, $R$. The inner-shell electrons of alkali atoms were described using nonempirical shape-consistent effective core potentials. To take the core-valence correlation effects into account, core polarization potentials for each atom were implemented. Dynamical correlation was introduced through the multireference configuration interaction method, which was applied to two valence electrons keeping all subvalence electrons frozen. The reliability of the derived SO functions is accessed through comparison, wherever possible, with their preceding theoretical and experimental counterparts. The ab initio SO matrix elements were approximated beyond the LeRoy radius using the formula: ${\xi }_{if}^{\text{SO}}\left(R\right)=\alpha +{\beta }_{if}^{\left[k\right]}/R^k$, where (1) $k=6$ and $\alpha ={\xi }_{n{}^2\mathrm{P}}^{\text{SO}}$ is the SO splitting of the atom $\mathrm{A}(n{}^2\mathrm{P}$) for the states of the AB molecule converging to the same $\mathrm{A}(n_{\mathrm{A}}{}^2\mathrm{P}$) + $\mathrm{B}(n_{\mathrm{B}}{}^2\mathrm{S}$) dissociation limit, and (2) $k=3$ and $\alpha =0$ for the molecular $i$ and $f$ states converging to the $\mathrm{A}\left(n_{\mathrm{A}}{}^2\mathrm{P}\right)+\mathrm{B}\left(n_{\mathrm{B}}{}^2\mathrm{S}\right)$ and $\mathrm{A}\left(n_{\mathrm{A}}{}^2\mathrm{S}\right)+\mathrm{B}(n_{\mathrm{B}}{}^2\mathrm{P}$) atomic thresholds, respectively. A theoretical justification of these formulas was derived from the multipole expansion of the molecular SO operator in terms of the inverse powers of the internuclear distance and of products of operators acting on the electronic coordinates of the atoms A and B.

We present a comprehensive study of electron collisions with calcium atoms by using the convergent $B$-spline $R$-matrix method. Elastic, excitation, and ionization cross sections were obtained for all transitions between the lowest 39 physical states of calcium (except for $3p^{6}4s5g{}^{3,1}G$) up to the $3p^{6}4s8s{}^{1}S$ state, for incident electron energies ranging from threshold to 100 eV. A multiconfiguration Hartree-Fock method with nonorthogonal term-dependent orbitals was employed to generate accurate wave functions for the pseudo target states. Close-coupling expansions including the 39 physical states plus 444 pseudo target states of calcium were used to check the sensitivity of the results to coupling to the target continuum. The cross-section dataset obtained from the large-scale calculations is expected to be sufficiently accurate and comprehensive for most current modeling applications involving neutral calcium.

We study the signature of two-center interferences in molecular high-order harmonic spectra, with an emphasis on the spectral phase. With the help of both ab initio computations based on the time-dependent Schrödinger equation and the molecular strong-field approximation (SFA) as developed by Chirilă et al. [Phys. Rev. A 73, 023410 (2006)] and Faria [Phys. Rev. A 76, 043407 (2007)], we observe that the phase behavior is radically different for the short and the long trajectory contributions. By means of Taylor expansions of the molecular SFA, we link this effect to the dynamics of the electron in the continuum. More precisely, we find that the value of the electric field at recombination time plays a crucial role in the shape of the destructive interference phase jump.

We study the spatial interference effects appearing during the ionization of atoms (H, He, Ne, and Ar) by few-cycle laser pulses using single-electron ab initio calculations. The spatial interference is the result of the coherent superposition of the electronic wave packets created during one half cycle of the driving field following different spatial paths. This spatial interference pattern may be interpreted as the hologram of the target atom. With the help of a wave-function analysis (splitting) technique and approximate (strong-field and Coulomb-Volkov) calculations, we directly show that the hologram is the result of the electronic-wave-packet scattering on the parent ion. On the He target we demonstrate the usefulness of the wave-function splitting technique in the disentanglement of different interference patterns. Further, by performing calculations for the different targets, we show that the pattern of the hologram does not depend on the angular symmetry of the initial state and it is strongly influenced by the atomic species of the target: A deeper bounding potential leads to a denser pattern.

Structured electron beams carrying orbital angular momentum are currently of considerable interest, both from a fundamental point of view and for application in electron microscopy and spectroscopy. Until recently, most studies have focused on the azimuthal structure of electron vortex beams with well-defined orbital angular momentum. To unambiguously define real electron-beam states and realize them in the laboratory, the radial structure must also be specified. Here we use a specific set of orthonormal modes of electron (vortex) beams to describe both the radial and azimuthal structures of arbitrary electron wavefronts. The specific beam states are based on truncated Bessel beams localized within the lens aperture plane of an electron microscope. We show that their Fourier transform set of beams can be realized at the focal planes of the probe-forming lens using a binary computer-generated electron hologram. Using astigmatic transformation optics, we demonstrate that the azimuthal indices of the diffracted beams scale with the order of the diffraction through phase amplification. However, their radial indices remain the same as those of the encoding beams for all the odd diffraction orders or are reduced to the zeroth order for the even-order diffracted beams. This simple even-odd rule can also be explained in terms of the phase amplification of the radial profiles. We envisage that the orthonormal cylindrical basis set of states could lead to new possibilities in phase contrast electron microscopy and spectroscopy using structured electron beams.

We propose a method to prepare the spin singlet in an ensemble of integer-spin atoms confined within a high-finesse optical cavity. Using a cavity-assisted Raman transition to produce an effective Tavis-Cummings model, we show that a high-fidelity spin singlet can be produced probabilistically, although with low efficiency, heralded by the absence of photons escaping the cavity. In a different limit, a similar configuration of laser and cavity fields can be used to engineer a model that emulates spinor collisional dynamics. Borrowing from techniques used in spinor Bose-Einstein condensates, we show that adiabatic transformation of the system Hamiltonian (via a time-dependent, effective quadratic Zeeman shift) can be used to produce a low-fidelity spin singlet. Then, by following this method with the aforementioned heralding technique, we show that it is possible to prepare the singlet state with both high fidelity and good efficiency for a large ensemble.

Experimental demonstrations of coherent dynamics for the driven quantum system are usually limited by their shorter coherent times (due to the inevitable environment noises). Given the Maxwell equation for the electromagnetic waves (EMWs) prorogating in the optical waveguides takes the similar form of the Schrödinger equation for the driven quantum system, the quantum dynamics in time domain can be simulated by the light propagating along the waveguide in spatial domain. To simulate the fast time evolutions of quantum states during the Landau-Zener (LZ) transitions and Landau-Zenner-Stückelberg (LZS) interferences for the periodically driven two-level systems, we develop an invariant method to design the compacted curved wavguides and demonstrate the LZ transitions and LZS interferometery in the spatial domain. Due to significantly long coherent lengths of the EMWs propagating along the waveguides, the proposed optical-quantum analogies should be feasible with the current integrated optical devices.

The continuous monitoring of a quantum system strongly influences the emergence of chaotic dynamics near the transition from the quantum regime to the classical regime. Here we present a feedback control scheme that uses adaptive measurement techniques to control the degree of chaos in the driven-damped quantum Duffing oscillator. This control relies purely on the measurement backaction on the system, making it a uniquely quantum control, and is only possible due to the sensitivity of chaos to measurement. We quantify the effectiveness of our control by numerically computing the quantum Lyapunov exponent over a wide range of parameters. We demonstrate that adaptive measurement techniques can control the onset of chaos in the system, pushing the quantum-classical boundary further into the quantum regime.

It is well known that certain quantum correlations like quantum steering exhibit a monogamous relationship. In this paper, we exploit the asymmetric nature of quantum steering and show that there exist states which exhibit a polygamous correlation, known as collective correlation [He and Reid, Phys. Rev. Lett. 111, 250403 (2013)], where the state of one party, Alice, can be steered only by the joint effort of the other two parties, Bob and Charlie. As an example, we explicitly single out a particular set of three qubit states which exhibit this polygamous relationship, known as collective steerability. We provide a recipe to identify the complete set of such states. We also provide a possible application of such states to an information theoretic task, termed as quantum key authentication (QKA) protocol. QKA can also be used in conjunction with other well-known cryptography protocols to improve their security, and we provide one such example with quantum private comparison.