Recently, low-order harmonics have gained much attention due to their applications as coherent light sources with a high repetition rate. In addition, the generation process is highly related to the bound electrons and can thus be applied to detect the dynamics of these electrons. In this work, we theoretically investigate the low-order harmonics below the first excited state, produced by a single-cycle optical pulse. We numerically solve the three-dimensional time-dependent Schrödinger equation (TDSE) to calculate the harmonic spectrum. With the help of a perturbation model, we can transparently understand the generation process of the spectrum. The results indicate that the harmonic spectrum can be sensitively influenced by the frequency component of the driving field. We find that the carrier envelope phase (CEP) dependence of low-order-harmonic generation originates from the interference of different harmonic orders. For these harmonics, the CEP effects can only be observed when the spectrum of the driving laser is extremely wide, which corresponds to the very short driving pulse. From the CEP-dependent interference structure, the phase relation of the third and the fifth harmonic can be extracted. The extracted information indicates that the atomic response induces a positive chirp for the emitted low-order harmonics. In addition, we investigated the harmonic phase calculated from the TDSE results. The harmonic phase is different from the phase predicted by the adiabatic model, and this phase difference can be related to the time delay of the electronic response. We extract the time delay from the harmonic phase and explore the CEP and intensity dependence of this time delay.

Many useful properties of dilute Bose gases at ultralow temperature are predicted precisely by the (mean-field) product-state Ansatz, in which all particles are in the same quantum state. Yet, in situations where particle-particle correlations become important, the product Ansatz fails. To include correlations nonperturbatively, we consider a new set of states: the particle-correlated state of $N=l\times n$ bosons is derived by symmetrizing the $n$-fold product of an $l$-particle quantum state. Quantum correlations of the $l$-particle state “spread out” to any subset of the $N$ bosons by symmetrization. The particle-correlated states can be simulated efficiently for large $N$, because their parameter spaces, which depend on $l$, do not grow with $n$. Here we formulate and develop in great detail the pure-state case for $l=2$, where the many-body state is constructed from a two-particle pure state. These paired wave functions, which we call pair-correlated states (PCS), were introduced by A. J. Leggett [Rev. Mod. Phys. 73, 307 (2001)] as a particle-number-conserving version of the Bogoliubov approximation. We present an iterative algorithm that solves for the reduced (marginal) density matrices (RDMs), i.e., the correlation functions, associated with PCS in time $O\left(N\right)$. The RDMs can also be derived from the normalization factor of PCS, which is derived analytically in the large-$N$ limit. To test the efficacy of PCS, we analyze the ground state of the two-site Bose-Hubbard model by minimizing the energy of the PCS state, both in its exact form and in its large-$N$ approximate form, and comparing with the exact ground state. For $N=1000$, the relative errors of the ground-state energy for both cases are within ${10}^{-5}$ over the entire parameter region from a single condensate to a Mott insulator. We present numerical results that suggest that PCS might be useful for describing the dynamics in the strongly interacting regime.

The unification of quantum mechanics and gravity remains as one of the primary challenges of present-day physics. Quantum-gravity-inspired phenomenological models offer a window to explore potential aspects of quantum gravity including qualitatively new behavior that can be experimentally tested. One such phenomenological model is the generalized uncertainty principle, which predicts a modified Heisenberg uncertainty relation and a deformed canonical commutator. It was recently shown that optomechanical systems offer significant promise to put stringent experimental bounds on such models. In this paper, we introduce a scheme to increase the sensitivity of these experiments with an extended sequence of pulsed optomechanical interactions. We also analyze the effects of optical phase noise and optical loss and present a strategy to mitigate such deleterious effects.

The generation of correlated photon pairs is a key to the production of entangled quantum states, which have a variety of applications within the area of quantum information. In spontaneous parametric down-conversion—the primary method of generating correlated photon pairs—the associated photon annihilation and creation events are generally thought of as being colocated: The correlated pair of photons is localized with regards to the pump photon and its positional origin. A detailed quantum electrodynamical analysis highlights a mechanism exhibiting the possibility of a delocalized origin for paired output photons: The spatial extent of the region from which the pair is generated can be much larger than previously thought. The theory of both localized and nonlocalized degenerate down-conversion is presented, followed by a quantitative analysis using discrete-volume computational methods. The results may have significant implications for quantum information and imaging applications, and the design of nonlinear optical metamaterials.

The bound states of atoms play important roles during the interaction with a strong laser pulse. In the present work, we observe a set of harmonics which are not located at the usual odd harmonics. These harmonics can be clearly identified when the driving frequency is resonant with the excited states. The observed set of harmonics become stronger than the usual odd harmonics for a rather long laser pulse at a moderate intensity. From ab initio calculations, we find that an atom can be resonantly pumped to the excited states during the interaction with lasers at some wavelengths. After the excitation, the electrons can be ionized from these excited states and then recombine to the ground state, which leads to another set of harmonic peaks near the atomic ionization potential. We investigate the role of different laser wavelengths as well as atomic potentials. In addition, we find that the phases of these harmonics are far more sensitive than the usual harmonics when we change the parameters of the driving pulse, which can cause a large divergent angle. The parameter dependence of the phases of these harmonics is interpreted through an intuitive model.

Electrometry is performed using Rydberg states to evaluate the quadratic Stark shift of the $5s^2{}^{1}S_0-5s5p{}^{3}P_0$ clock transition in strontium. By measuring the Stark shift of the highly excited $5s75d{}^{1}D_2$ state using electromagnetically induced transparency, we characterize the electric field with sufficient precision to provide tight constraints on the systematic shift to the clock transition. Using the theoretically derived, and experimentally verified, polarizability for this Rydberg state, we can measure the residual field with an uncertainty well below 1 $\mathrm{V}{\mathrm{m}}^{-1}$. This resolution allows us to constrain the fractional frequency uncertainty of the quadratic Stark shift of the clock transition to $2\times {10}^{-20}$.

Using the recently developed Coulomb quantum orbit strong-field approximation, we perform a systematic analysis of several features encountered in above-threshold ionization photoelectron angle-resolved distributions, such as side lobes and intra- and intercycle interference patterns. The latter include not only the well-known intracycle rings and the near-threshold fan-shaped structure, but also previously overlooked patterns. We provide a direct account of how the Coulomb potential distorts different types of interfering trajectories and changes the corresponding phase differences, and show that these patterns may be viewed as generalized holographic structures formed by up to three types of trajectories. We also derive analytical interference conditions and estimates valid in the presence or absence of the residual potential, and assess the range of validity of Coulomb-corrected interference conditions provided in the literature.

The Feshbach resonance provides precise control over the scattering length and effective range of interactions between ultracold atoms. We propose the ultratransferable pseudopotential to model effective interaction ranges $-1.5\le k_{\mathrm{F}}^2{R}_{\mathrm{eff}}^2\le 0$, where $R_{\mathrm{eff}}$ is the effective range and $k_{\text{F}}$ is the Fermi wave vector, describing narrow to broad Feshbach resonances. We develop a mean-field treatment and exploit the pseudopotential to perform a variational and diffusion Monte Carlo study of the ground state of the two-dimensional Fermi gas, reporting on the ground-state energy, contact, condensate fraction, momentum distribution, and pair-correlation functions as a function of the effective interaction range across the BEC-BCS crossover. The limit $k_{\mathrm{F}}^2{R}_{\mathrm{eff}}^2\to -\infty$ is a gas of bosons with zero binding energy, whereas $ln\left(k_{\mathrm{F}}a\right)\to -\infty$ corresponds to noninteracting bosons with infinite binding energy.

We report experimental studies of quantum interference of multiphoton states impinging on a two-port balanced beam splitter. When the distinguishability between the two input paths is increased, we observe a reduction followed by a resurgence of the interference visibility in multiphoton coincidence detection. We ascribe this unusual behavior to the competition among contributions from distinct number state components of the interfering fields. Our results suggest that wave-particle duality gives rise to a wide range of largely unexplored phenomena in multiparticle interference.

In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of $\pm 1$ and $\pm 2$ formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at $f=5.6$ MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about $L/r\approx 190$ and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, “diffraction-free” propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by $\pi$, the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 $\mu \mathrm{m}$ in our case), the BPAs can form the beams at incident radiation with any wavelength, albeit with a reduced diffraction efficiency, and their cross section is the same for any wavelength.

In this paper, we develop a simple model describing inherent photon-number noise in Rarity-Tapster-Loudon-type interferometers. This noise is caused by generating photon pairs in the process of spontaneous parametric down-conversion and adding a third photon by attenuating the fundamental laser mode to the single-photon level. We experimentally verify our model and present resulting signal-to-noise ratios as well as obtained three-photon generation rates as functions of various setup parameters. Subsequently we evaluate the impact of this particular source of noise on quantum teleportation which is a key quantum information protocol using this interferometric configuration.

We study the frequency splitting of nearly degenerate optical modes in weakly deformed microdisks. The analysis is restricted to even- and odd-parity modes in cavities with a mirror-reflection symmetry. The frequency splitting is explained in a semiclassical approach by dynamical tunneling (resonance-assisted tunneling) between clockwise- and counterclockwise-propagating waves. We derive semiclassical predictions for the frequency splittings which are in good agreement with full numerical calculations. Two deformations are studied in detail, the ellipse and the quadrupole, representing a deformation with integrable and nonintegrable ray dynamics. Furthermore, the differences between Dirichlet and dielectric boundary conditions are discussed.

We present a technique for hyperentangled Bell-state analysis that only relies on linear optics and is assisted by auxiliary entangled states. This technique can be used to implement hyperdense coding with an experimentally realizable two-photon state hyperentangled in polarization and two longitudinal-momentum degrees of freedom. The 16 hyperentangled states in the first two degrees of freedom are classified into 12 groups with the help of the third degree of freedom. This allows the transmission of 3.58 bits/photon via our hyperdense coding scheme. We also generalize our technique to $n$-qubit hyperentangled Bell-state analysis assisted by additional auxiliary entangled states. We show that given $n$ degrees of freedom, the $4^n$ hyperentangled Bell states can be separated via linear optics into $x_k=2^{n+k+1}-2^{2k}$ groups with the help of $k(k\le n)$ ancillary entangled states. When $k=n$, all $4^n$ hyperentangled states can be distinguished. Our results are useful for quantum information processing based on hyperentanglement.

This work explores the notion of inter-convertibility between a cryptographic primitive: the random access code (RAC) and bipartite no-signaling nonlocal resources. To this end we introduce two generalizations of the Popescu-Rohrlich box (PR) and investigate their relation with the corresponding RACs. The first generalization is based on the number of Alice's input bits; we refer to it as the $B_n$-box. We show that the no-signaling condition imposes an equivalence between the $B_n$-box and the $(n\to 1)$ RAC (encoding of $n$ input bits to 1 bit of message). As an application we show that $(n-1)$ PRs supplemented with one bit communication are necessary and sufficient to win a $(n\to 1)$ RAC with certainty. Furthermore, we present a signaling instant of a perfectly working $(n\to 1)$ RAC which cannot simulate the $B_n$-box, thus showing that it is weaker than its no-signaling counterpart. For the second generalization we replace Alice's input bits with $d\mathrm{its}$ ($d$-leveled classical systems); we call this the $B_n^d$-box. In this case the no-signaling condition is not enough to enforce an equivalence between the $B_n^d$-box and $(n\to 1,d)$ RAC (encoding of $n$ input $d\mathrm{its}$ to $1d\mathrm{it}$ of message); i.e., while the $B_n^d$-box can win a $(n\to 1,d)$ RAC with certainty, not all no-signaling instances of a $(n\to 1,d)$ RAC can simulate the $B_n^d$-box. We use resource inequalities to quantitatively capture these results.

We analyze Vaidman's three-path interferometer with weak path marking [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, “the particle's path” has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] with unambiguous path discrimination. We present a detailed proposal for such an experiment.

The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla-system couplings, that is applicable to arbitrary (pseudo)spin systems and arbitrary equilibrium or nonequilibrium initial states. Different choices of the coupling operator give access to the real and imaginary parts of the dynamic correlation function. This protocol reduces disturbances due to the early-time measurements to a minimum, and we quantify the deviation of the measured correlation functions from the theoretical, unitarily evolved ones. Implementations of the protocol in trapped ions and other experimental platforms are discussed. For spin-$1/2$ models and single-site observables we prove that measurement backaction can be avoided altogether, allowing for the use of ancilla-free protocols.

In quantum information, $W$ states are a central class of multipartite entangled states because of their robustness against noise and their use in many quantum processes. Their generation, however, remains a demanding task whose difficulty increases with the number of particles. We report a simple scalable conceptual scheme where a single particle in an ancilla mode works as an entanglement catalyst of the $W$ state for other $N$ separated identical particles. A crucial aspect of the scheme, which exploits basically spatial indistinguishability, is its universality, being applicable without essential changes to both bosons and fermions. Our proposal represents a paradigm within the experimental preparation of many-particle entanglement based on quantum indistinguishability.

The survival of Gaussian quantum states in a turbulent atmospheric channel is of crucial importance in free-space continuous-variable (CV) quantum key distribution (QKD), in which the transmission coefficient will fluctuate in time, thus resulting in non-Gaussian quantum states. Different from quantum hacking of the imperfections of practical devices, here we propose a different type of attack by exploiting the security loopholes that occur in a real lossy channel. Under a turbulent atmospheric environment, the Gaussian states are inevitably afflicted by decoherence, which would cause a degradation of the transmitted entanglement. Therefore, an eavesdropper can perform an intercept-resend attack by applying an entanglement-distillation operation on the transmitted non-Gaussian mixed states, which allows the eavesdropper to bias the estimation of the parameters and renders the final keys shared between the legitimate parties insecure. Our proposal highlights the practical CV QKD vulnerabilities with free-space quantum channels, including the satellite-to-earth links, ground-to-ground links, and a link from moving objects to ground stations.