It is well known that in a two-slit interference experiment, acquiring which-path information about the particle leads to a degrading of the interference. It is argued that path information has a meaning only when one can unambiguously tell which slit the particle went through. Using this idea, two duality relations are derived for the general case where the two paths may not be equally probable and the two slits may be of unequal widths. These duality relations, which are inequalities in general, saturate for all pure states. Earlier known results are recovered in suitable limit.

Pulses of extreme ultraviolet (XUV) light, with wavelengths between 10 and $100\mathrm{nm}$, can be used to image and excite ultrafast phenomena such as the motion of atomic electrons. Here we show that the illumination of plasma with near-critical electron density may be used as a source of relativistically intense XUV radiation, providing the means for novel XUV-pump–XUV-probe experiments in the nonlinear regime. We describe how the optimal regime may be reached by tailoring the laser-target interaction parameters and by the presence of preplasma. Our results indicate that currently available laser facilities are capable of producing XUV pulses with duration $\sim 10\mathrm{fs}$, brilliance in excess of ${10}^{23}\mathrm{photons}/\mathrm{s}/{\mathrm{mm}}^2/{\mathrm{mrad}}^2$ (0.1% bandwidth), and intensity $I{\lambda }^2\gtrsim {10}^{19}\text{W}{\text{cm}}^{-2}{\mu \mathrm{m}}^2$.

We derive a set of azimuthally polarized hollow beam solutions in free space. These solutions are exact vector solutions to Maxwell's and Poynting's equations with the electric- and magnetic-field components expressed as linear combinations of the partial derivatives of a sinc function. They depict beams the intensity of which vanishes everywhere on the beam axis, forming dark hollow channels. There is one adjustable dimensionless parameter $Q$ in the formulation which governs the degree of focusing of a beam. In the weak focusing limit $\left(Q\gg 1\right)$, a beam shows a doughnut-shaped intensity profile while a multiple-ring intensity distribution is found for the strong focusing case with $Q\le 1$.

We theoretically investigate mid- and long-wavelength infrared laser filamentation in solids, revealing extreme self-steepening and optical shock, multi-octave spanning supercontinuum generation, and, most importantly, subcycle light-bullet generation. Light-bullet generation in solids at long wavelengths depends critically on plasma, which is in sharp contrast to that in air where the arrest of collapse for light-bullet generation is dominated by radiation loss. Our method for subcycle light-bullet generation in solids at long wavelengths may open new possibilities for extreme ultrafast nonlinear optics including high-order-harmonic and attosecond-pulse generation.

We present a qualitative description of the laser-pulse filamentation phenomenon based on light field representation as a self-consistent ensemble of specific localized wave structures known as the diffraction-ray (light) tubes. These light tubes are energetically independent from each other and, at the same time, they are in close field interaction through the phase front of the light wave. The trajectories of light tube centroids represent the evolutionary line of the Poynting vector transverse component. Light tubes do not intersect in space although they can be nested, and the tubes do not exchange light energy with each other. Spatial shape and area of light tubes can vary during pulse propagation, reflecting the influence of different physical processes manifesting themselves upon radiation propagation in a medium. This diffraction-ray approach applies the attributes of the amplitude and phase analysis to the problem of laser radiation self-action and sheds light on the onset and termination conditions of laser-pulse filamentation.

Ray propagation in weakly turbulent media is described by means of a quasilinear (QL) approach in which the dispersion relation and the ray equations are expanded up to, and including, second-order terms in the medium and ray fluctuations, leading to equations for the ensemble-averaged ray and its root-mean-square (rms) spreading. An important feature of the QL formalism is that the average ray does not coincide with the zero-order, unperturbed ray but may exhibit a drift with respect to the latter that is governed by the mean squared fluctuations. The theory is complete in that equations can be set for all quantities necessary to compute the ray trajectory and the rms spreading along its path, yet they obey an infinite downward recurrence in which equations involving lower-order derivatives of the medium fluctuations are recursively generated by the subsequent higher-order derivative, and which must thus be truncated for practical purposes. Using as examples the propagation of rays in homogeneous media with fluctuations arising from the presence of either a single random mode or a multimode isotropic turbulent spectrum, the QL formalism is validated against Monte Carlo (MC) calculations and, whenever possible, its numerical implementation is verified by comparison with analytical predictions. Choosing $4\%$ both for the level of fluctuations and for the maximum ratio between the wavelengths of the propagating ray and of the turbulent modes, so as to remain within the validity of the second-order expansion in the random perturbations and of the eikonal approximation, the overall agreement between QL and MC results is fairly good, particularly for quantities such as the distance traveled by the average ray, its perpendicular rms spread, and the averages of the wave-vector components.

Dual frequency comb generation has been the focus of many recent research efforts owing to its viability in a myriad of applications, ranging from precision measurement to high-speed optical communications. Here, with the state of the art of a single quantum dot (QD) coupled to a pillar microcavity [Nat. Nanotechnol. 12, 663 (2017)], we put forward an alternative setup for the generation of orthogonally polarized dual frequency combs and their corresponding control by using coherent two-tone cavity driving, i.e., a control laser and a probe laser. The present QD-pillar microcavity system operates in the weak-coupling regime, and this makes the experimental realization of the scheme easy. The underlying nonlinear process of the system, thanks to the QD-pillar interaction, for example, degenerate and nondegenerate four-wave mixing, results in efficient frequency comb formation. The dual combs consist of equidistant spectral lines whose spectral spacing coincides with the frequency difference between the control and probe lasers. So, programming this frequency difference between them enables us to tune both the comb-line spacing (i.e., repetition rate) and comb-line number in both vertical ($V$) and horizontal ($H$) polarizations. As compared with the previous approaches for dual microcomb generation, the present scheme has attractive features such as a tunable, slow repetition rate (as slow as a few megahertz), low input power (as low as a few nanowatts), and integrated compact nature in experimentally realistic operating regimes. The achievable low repetition rates are desirable to resolve narrower spectral lines and to enable use of low-power signal processing electronics.

Quantum state tomography aims to determine the quantum state of a system from measured data and is an essential tool for quantum information science. When dealing with continuous variable quantum states of light, tomography is often done by measuring the field amplitudes at different optical phases using homodyne detection. The quadrature-phase homodyne measurement outputs a continuous variable, so to reduce the computational cost of tomography, researchers often discretize the measurements. We show that this can be done without significantly degrading the fidelity between the estimated state and the true state. This paper studies different strategies for determining the histogram bin widths. We show that computation time can be significantly reduced with little loss in the fidelity of the estimated state when the measurement operators corresponding to each histogram bin are integrated over the bin width.

To implement fault-tolerant quantum computation with continuous variables, the Gottesman–Kitaev–Preskill (GKP) qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large-scale quantum computation with the GKP qubit [Phys. Rev. X 8, 021054 (2018)], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large-scale quantum computation, we propose the tracking quantum error correction, where the logical-qubit-level quantum error correction is partially substituted by the single-qubit-level quantum error correction. In the proposed method, the analog quantum error correction is utilized to make the performances of the single-qubit-level quantum error correction almost identical to those of the logical-qubit-level quantum error correction in a practical noise level. The numerical results show that the proposed tracking quantum error correction reduces the number of qubits during a quantum error-correction process by the reduction rate $\left\{2(n-1)4^{l-1}-n+1\right\}/\left(2n\times 4^{l-1}\right)$ for $n$-cycles of the quantum error-correction process using Knill's $C_4/C_6$ code with the concatenation level $l$. Hence, the proposed tracking quantum error correction has great advantage in reducing the required number of physical qubits, and will open a new way to expoloit the advantages of the GKP qubits in practical quantum computation.

Quantum key distribution is rising as an important cryptographic primitive for protecting the communication infrastructure in the digital era. However, its implementation security is often weakened by components whose behavior deviates from what is expected. Here we analyze the response of a self-differencing avalanche photodiode, a key enabler for high speed quantum key distribution, to intense light shone from a continuous-wave laser. Under incorrect settings, the cancellation entailed by the self-differencing circuitry can make the detector insensitive to single photons. However, we experimentally demonstrate that even in such cases intensity modulation can be used as an effective measure to restore the detector's expected response to the input light.

The technique of frequency-stabilized comb-calibrated cavity ring-down spectroscopy was used to observe the weak R(1) transition of the deuturated molecular hydrogen (HD) first overtone band in the near infrared. Like molecular hydrogen, HD is a benchmark system to test quantum electrodynamics, looking for new physics beyond the standard model. The spectral line shape was measured with an extremely high fidelity at relatively low gas pressures. The use of a very refined line-shape model allowed us to retrieve the unperturbed line-center frequency of the R(1) line with a global uncertainty of about 100 kHz ($\delta \nu /\nu =5\times {10}^{-10}$). Our value may solve the ambiguity that recently emerged for this line from a pair of sub-Doppler experiments. We also determined other parameters of interest, such as the line strength, the transition dipole moment, and the pressure-broadening coefficient.

We study electromagnetic trapping in an optical lattice formed by three equiangular in-plane beams. We demonstrate analytically that this optical lattice offers stable trapping sites for particles satisfying specific symmetries, irrespective of the exact nature of their electromagnetic response. Under small displacements, the particles are shown to be subject to equal restoring forces along all directions and the trap is isotropic. Though the intensity distribution of the trap forms a perfect hexagonal lattice, differences in phase variation along opposite directions cause the restoring force to be asymmetric for large displacements, resulting in a force landscape possessing only threefold symmetry. We then show numerically that this asymmetry affects the optical binding force between particles in adjacent trap positions and results in unequal shifts of their equilibrium positions. Universal trapping in the optical lattice combined with this asymmetric mechanical response of trapped particle pairs promises rich optomechanical effects.

We study the splitting dynamics of giant vortices in dilute Bose-Einstein condensates by numerically integrating the three-dimensional Gross-Pitaevskii equation in time. By taking advantage of tetrahedral tiling in the spatial discretization, we decrease the error and increase the reliability of the numerical method. An extensive survey of vortex splitting patterns is presented for different aspect ratios of the harmonic trapping potential. The discrete rotational symmetries of the splitting patterns that emerge in the time evolution are in good agreement with predictions obtained by solving the prevailing dynamical instabilities from the Bogoliubov equations. Furthermore, we observe intertwining of the split vortices in prolate condensates and a split-and-revival phenomenon in a spherical condensate.

Atom matterwave interferometry requires mirror and beam splitter pulses that are robust to inhomogeneities in field intensity, magnetic environment, atom velocity, and Zeeman substate. We present theoretical results which show that pulse shapes determined using quantum control methods can significantly improve interferometer performance by allowing broader atom distributions, larger interferometer areas, and higher contrast. We have applied gradient ascent pulse engineering (grape) to optimize the design of phase-modulated mirror pulses for a Mach-Zehnder light-pulse atom interferometer, with the aim of increasing fringe contrast when averaged over atoms with an experimentally relevant range of velocities, beam intensities, and Zeeman states. Pulses were found to be highly robust to variations in detuning and coupling strength and offer a clear improvement in robustness over the best established composite pulses. The peak mirror fidelity in a cloud of $\sim 80\mu \mathrm{K}{}^{85}\mathrm{Rb}$ atoms is predicted to be improved by a factor of 2 compared with standard rectangular $\pi$ pulses.

We present an experimental method for complete identification of the nonclassicality of Gaussian states in the whole phase space. Our method relies on nonclassicality witnesses written in terms of measured integrated intensity moments up to the third order, provided that appropriate local coherent displacements are applied to the state under consideration. The introduced approach, thus, only requires linear detectors for measuring intensities of optical fields, that is, very convenient and powerful from the experimental point of view. Additionally, we demonstrate that the proposed technique not only allows to completely identify the nonclassicality of the Gaussian states, but also to quantify it.

The resonant-state expansion, a rigorous perturbation theory recently developed in electrodynamics, is applied to nonrelativistic quantum-mechanical systems in one dimension. The method is used here for finding the resonant states in various potentials approximated by combinations of Dirac $\delta$ functions. The resonant-state expansion is first verified for a triple-quantum-well system, showing convergence to the available analytic solution as the number of resonant states in the basis increases. The method is then applied to multiple-quantum-well and barrier structures, including finite periodic systems. Results are compared with the eigenstates in triple quantum wells and infinite periodic potentials, revealing the nature of the resonant states in the studied systems.

The balance of gain and loss in an open system may maintain certain Hermitian dynamical behaviors which can be hardly observed in a popular Hermitian system. In this paper, we systematically study a 1D $\mathcal{PT}$-symmetry non-Hermitian Su-Schrieffer-Heeger model with open boundary condition based on an exact approximate solution. We show that the long-wavelength standing-wave modes can be achieved within the linear dispersion region when the system is tuned at the exceptional point. The whole Hilbert space can be decomposed into two quasi-Hermitian subspaces, which are consisted of positive and negative energy levels, respectively. Within each subspace, the system maintains all the features of a Hermitian system. We construct a coherentlike state in a subspace and find that it exhibits perfect simple harmonic motion (SHM). In contrast to a canonical coherent state, the shape of the wave packet deforms periodically rather than entirely by translation, and the amplitude of the SHM is not determined by the initial condition but by the shape of the wave packet. Our result indicates that novel Hermitian dynamics can be realized by a non-Hermitian system.

In closed quantum systems, dynamical phase transitions are identified by the nonanalytic behavior of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a non-Hermitian lattice realizable by optical resonators. Dynamical quantum phase transitions with topological signatures are found when an isolated exceptional point is crossed during the quench. A winding number defined by a real, noncyclic geometric phase is introduced, whose value features quantized jumps at critical times of these phase transitions and remains constant elsewhere, playing the role of a topological order parameter. This work provides a simple framework to study dynamical and topological quantum phase transitions in non-Hermitian systems.

We present two verification protocols where the correctness of a “target” computation is checked by means of “trap” computations that can be efficiently simulated on a classical computer. Our protocols rely on a minimal set of noise-free operations (preparation of eight single-qubit states or measurement of four observables, both on a single plane of the Bloch sphere) and achieve linear overhead. To the best of our knowledge, our protocols are the least demanding techniques able to achieve linear overhead. They represent a step toward further reducing the quantum requirements for verification.

Laser excitation pulses that lead to perfect adiabatic state transfer in an ensemble of three-level ladder atoms lead to highly entangled states of many atoms if their highest excited state is subject to Rydberg blockade. Solution of the Schrödinger equation shows that it is increasingly difficult to ensure the adiabatic evolution as the number of atoms increases. A diminishing energy gap, significant variations in collective observables, and increased work fluctuations link the critical slowing down of the adiabatic evolution with a quantum-phase-transition-like behavior of the system.