Phase reference calibration is a necessary procedure in practical continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) for the need of Bell-state measurement. However, the phase reference calibration may become imperfect in practical applications. We explored the practical security of CV-MDI-QKD with imperfect phase reference calibration under realistic conditions of lossy and noisy quantum channels. Specifically, a comprehensive framework is developed to model and characterize the imperfection of the practical phase reference calibration operation, which is mainly caused by the nonsynchronization of two remote lasers in senders. Security analysis shows that the imperfect phase reference calibration has significant side effects on the performance and security of the CV-MDI-QKD protocol. A tight security bound to thermal excess noise introduced by imperfect phase reference calibration is derived for reverse reconciliation against one-mode collective Gaussian attack in the asymptotic limit, and the upper threshold of this imperfection tolerated by the system is obtained. This security analysis framework can eliminate the security hazards caused by imperfect phase reference calibration without changing the existing CV-MDI-QKD system structure. In addition, this work will improve the practical security framework of CV-MDI-QKD protocol and provide theoretic instruction for the experimental implementation of CV-MDI-QKD protocol.

We report precision measurements of the Casimir interaction at larger separation distances between the Au-coated surfaces of a sphere and a plate in ultrahigh vacuum using a much softer cantilever of the dynamic atomic-force-microscope-based setup and two-step cleaning procedure of the vacuum chamber and test body surfaces by means of UV light and Ar-ion bombardment. Compared to the previously performed experiment, two more measurement sets for the gradient of the Casimir force are provided, which confirmed and slightly improved the results. Next, additional measurements have been performed with a factor-of-two larger oscillation amplitude of the cantilever. This allowed the obtainment of meaningful results at much larger separation distances. The comparison of the measurement data with theoretical predictions of the Lifshitz theory using the dissipative Drude model to describe the response of Au to the low-frequency electromagnetic field fluctuations shows that this theoretical approach is experimentally excluded over the distances from 250 to 1100 nm (i.e., a major step forward compared to the previous work where it was excluded up to only 820 nm). The theoretical approach using the dissipationless plasma model at low frequencies is shown to be consistent with the data over the entire measurement range from 250 to 1300 nm. The possibilities to explain these puzzling results are discussed.

The double electron loss (DEL) from ${\mathrm{He}}^{-}$ has been investigated in collisions with He atoms at 300-keV impact energy and at electron energies that satisfy the cusp condition; i.e., the corresponding electron velocities match the projectile's velocity. In a time-of-flight experiment the energies of both electrons have been determined by detecting triple coincidences between the two electrons and the outgoing ${\mathrm{He}}^{+}$ ion. The coincidence yield shows a peak as a function of the electron energies at the expected cusp position, providing evidence for the existence of the two-electron cusp [L. Sarkadi and A. Orbán, Phys. Rev. Lett. 100, 133201 (2008)] in DEL. The observed energy distribution of the electron pairs is compared with the results of four-body classical trajectory Monte Carlo calculations carried out applying the soft-Coulomb potential approximation for the inclusion of the electron-electron interaction.

The coherent interaction of Rydberg atoms with microwave fields in the ultrastrong-driving regime, in which the Rabi frequency is of the same order of magnitude as the transition frequency, has been studied for states with principal quantum number $n=105$ in helium. Experiments were performed in pulsed supersonic beams, and the effects of the ultrastrong 1.280 GHz microwave driving field, tuned to near resonance with the $1s105s{}^{3}S_1\to 1s105p{}^{3}P$ transition, were identified from Autler-Townes splittings of the $1s3p{}^{3}P_2\to 1s105s{}^{3}S_1$ transition by cw laser spectroscopy. The microwave field strength was calibrated in situ in the apparatus from Autler-Townes splittings measured in the weak-driving regime in which the rotating-wave approximation holds. The results of the experiments were compared to the energy-level structure of the atoms in the presence of the microwave field calculated using Floquet methods. From this comparison, the microwave-field strengths for which the rotating-wave approximation and the two-level approximation break down have been identified. The feasibility of implementing microwave traps for Rydberg atoms and molecules, which operate in the ultrastrong-driving regime, has been evaluated.

The laser-induced dynamic core-electron polarization (DCEP) was known critical in the ionization of polar molecules such as CO, but less relevant in that of nonpolar ones, such as $\mathrm{CO}{}_2$, $\mathrm{N}{}_2$, or $\mathrm{O}{}_2$. For the harmonic process, the DCEP is proven to play an essential role for the polar molecule CO; it affects the harmonic intensity through the ionization at a specific instant. However, the influence of DCEP on the harmonic process of nonpolar molecules is still questionable. In this paper, we show that DCEP can affect the high-order harmonic generation (HHG) through a different mechanism—suppressing the distortion of the laser field on the highest occupied molecular orbital (HOMO) during the recombination phase, thus partially recovering the HOMO symmetry. Consequently, this shifts and sharpens the minima in the HHG spectra, which arise from the two-center interference. To support our point, we provide reliable numerical simulation by solving the time-dependent Schrödinger equation of the coupled $\mathrm{CO}{}_2$ molecule-laser field within the single active electron framework. From the minima location, we also extract the internuclear separation O–O of $\mathrm{CO}{}_2$, which is more accurate if including the DCEP in the simulation.

Recently, the significant enhancement of ${{\mathrm{N}}_2}^{+}$ lasing realized with the help of a polarization-gated intense 800-nm pump provides crucial clues to optimize both ionization and population coupling processes occurring during ${{\mathrm{N}}_2}^{+}$ lasing generation [Li et al., Phys. Rev. Lett. 122, 013202 (2019)]. In this work, we carried out an experimental and theoretical study on the generation of ${{\mathrm{N}}_2}^{+}$ lasing at 391 nm by the use of two different polarization-modulation schemes for pump pulses. It was found that the probe spectra in the vicinity of 391 nm are readily transformed from absorption to lasing due to population depletion of the ground state of ${{\mathrm{N}}_2}^{+}$ just via changing the pump polarization state. More importantly, ${{\mathrm{N}}_2}^{+}$ lasing intensity can be further increased when the pump polarization is modulated with a half-wave plate and a multiple-order quarter-wave plate compared with that obtained by the polarization-gating technique. All the experimental observations are well explained by the different population inversions between the states $B{}^2\mathrm{\Sigma }_u^{+}$ and $X{}^2\mathrm{\Sigma }_g^{+}$ of ${{\mathrm{N}}_2}^{+}$ in polarization-modulated pump laser fields.

Highly brilliant, coherent, femtosecond x-ray pulses delivered by free-electron lasers (FELs) constitute one of the pillars of modern ultrafast science. Next generation FEL facilities provide up to megahertz repetition rates and pulse durations down to the attosecond regime utilizing self-amplification of spontaneous emission. However, the stochastic nature of this generation mechanism demands single-shot pulse characterization to perform meaningful experiments. Here we demonstrate a fast yet robust online analysis technique capable of megahertz-rate mapping of the temporal intensity structure and arrival time of x-ray FEL pulses with few-femtosecond resolution. We performed angular streaking measurements of both neon photo- and Auger electrons and show their applicability for a direct time-domain feedback system during ongoing experiments. The fidelity of the real-time pulse characterization algorithm is corroborated by resolving isolated x-ray pulses and double pulse trains with few-femtosecond substructure, thus paving the way for x-ray-pump–x-ray-probe FEL science at repetition rates compatible with the demands of LCLS-II and European XFEL.

In this work we present a systematic study of the three-dimensional extension of the ring dark soliton, examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging, such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semianalytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov–de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed.

We study the temporally nonlocal contributions to the gradient expansion of the pair fluctuation propagator for spin- and mass-imbalanced Fermi mixtures. These terms are related to the damping processes of soundlike (Anderson-Bogolyubov) collective modes and are relevant for the structure of the complex pole of the pair fluctuation propagator. We derive conditions under which damping occurs even at zero temperature for a large enough mismatch of the Fermi surfaces. We compare our analytical results with numerically computed damping rates of the Anderson-Bogolyubov mode.

We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle ${\displaystyle \theta }$ of the dipolar bosons. At low tilt angles, ${\displaystyle 0^{\circ }⩽\theta \lesssim {25}^{\circ }}$, the ground states of the system are phases with checkerboard order, which can be either checkerboard supersolids or checkerboard density waves. For high tilt angles, ${\displaystyle {35}^{\circ }\lesssim \theta \lesssim {55}^{\circ }}$, phases with striped order of the supersolid or density wave are preferred. In the intermediate domain, ${\displaystyle {25}^{\circ }\lesssim \theta \lesssim {35}^{\circ }}$, an emulsion or superfluid phase intervenes the transition between the checkerboard and the striped phases. The attractive interaction dominates at ${\displaystyle \theta \gtrsim {55}^{\circ }}$, which renders the system unstable, and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second-order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results. In our study, the incompressible phases have an average occupancy per site ${\displaystyle \rho \le 1}$, but the compressible phases can have ${\displaystyle \rho >1}$.

The radiation-pressure interaction between one or more laser fields and a mechanical oscillator gives rise to a wide range of phenomena: From sideband cooling and backaction-evading measurements to ponderomotive and mechanical squeezing to entanglement and motional sideband asymmetry. In many protocols, such as dissipative mechanical squeezing, multiple lasers are utilized, giving rise to periodically driven optomechanical systems. Here we show that in this case Floquet dynamics can arise due to presence of Kerr-type nonlinearities, which are ubiquitous in optomechanical systems. Specifically, employing multiple probe tones, we perform sideband asymmetry measurements, a macroscopic quantum effect, on a silicon optomechanical crystal sideband cooled to 40% ground-state occupation. We show that the Floquet dynamics, resulting from the presence of multiple pump tones, gives rise to an artificially modified motional sideband asymmetry by redistributing thermal and quantum fluctuations among the initially independently scattered thermomechanical sidebands. For pump tones exhibiting large frequency separation, the dynamics is suppressed and accurate quantum noise thermometry demonstrated. We develop a theoretical model based on Floquet theory that accurately describes our observations. The resulting dynamics can be understood as resulting from a synthetic gauge field among the Fourier modes, which is created by the phase lag of the Kerr-type response. This phenomenon has wide-ranging implications for schemes utilizing several pumping tones, as commonly employed in backaction-evading measurements, dissipative optical squeezing, dissipative mechanical squeezing, and quantum noise thermometry. Our observation may equally well be used for optomechanical Floquet engineering, e.g., generation of topological phases of sound by periodic time modulation.

We explore numerically and analytically the pattern formation and symmetry breaking of beams propagating through left-handed (negative) nonlinear metamaterials. When the input beam is a vortex with topological charge (winding number) $Q$, the initially circular (isotropic) beam acquires the symmetry of a polygon with $Q$, $2Q$, or $3Q$ sides, depending on the details of the response functions of the material. Within an effective field-theory model, this phenomenon turns out to be a case of spontaneous dynamical symmetry breaking described by a Landau-Ginzburg functional. Complex nonlinear dependence of the magnetic permittivity on the magnetic field of the beam plays a central role, as it introduces branch cuts in the mean-field solution, and permutations among different branches give rise to discrete symmetries of the patterns. By considering loop corrections in the effective Landau-Ginzburg field theory we obtain reasonably accurate predictions of the numerical results.

We present the explicit analytic formulas for the electromagnetic (optical) eigenmodes propagating in a lamellar grating. Then, we analytically calculate a mutual transformation of the wave's spatial harmonics due to diffraction in the course of propagation through the grating as well as the matrices of the eigenmode reflectance and transmittance at the grating boundaries. Finally, we develop a theory of the nonadiabatic transformation of the eigenmodes in the inhomogeneous gratings. It allows one to disclose the effects which go beyond the geometrical optics of eigenmodes. We show that in a transition layer of a thick nonlamellar grating such effects occur due to mode coupling of just a few lower-band eigenmodes. This approach allows one to find the overall optical response of the nonlamellar gratings fully and efficiently. The results are given for both transverse electric and transverse magnetic polarizations, as well as for any absorptive permittivity.

In most optomechanical systems, a movable mirror is a part of an optical cavity, and its oscillation modulates either the resonance frequency of the cavity or its coupling to the environment. There exists the third option—which we call a “coherent coupling”—when the mechanical oscillation couples several nondegenerate optical modes supported by the cavity. Identifying the nature of the coupling can be an important step in designing the setup for a specific application. In order to unambiguously distinguish between different optomechanical couplings, we develop a general framework based on the Hamiltonian of the system. Using this framework, we give examples of different couplings and discuss in details one particular case of a purely coherent coupling in a ring cavity with a movable mirror inside. We demonstrate that in certain cases coherent coupling can be beneficial for cooling the motion of the mechanical oscillator. Our general framework allows us to approach the design of optomechanical experiments in a methodological way, for precise exploitation of the strengths of particular optomechanical couplings.

Mainly with respect to the mathematical part of the article by Kruglov and Harvey [Phys. Rev. A 98, 063811 (2018)] some (supplementary) remarks on the solution method, on the conditions of existence, and on the parameter dependence are presented. For elucidation, numerical examples are included.

We show that the authors of the preceding Comment [Schürmann and Serov, preceding Comment, Phys. Rev. A 100, 057801 (2019)] have not found a more general family of solutions of the generalized nonlinear Schrödinger equation (NLSE) with higher-order dispersions. Moreover, the necessary and sufficient conditions for the existence of the bounded traveling solutions presented by Kruglov (arXiv:1905.00960v1; arXiv:1905.00960v2) differ from the appropriate conditions in the preceding Comment. We have found (see the work by Kruglov) a regular method which yields the traveling-wave solutions of the generalized NLSE. This method differ from the approach presented in the preceding Comment. Moreover, our method yields a periodic bounded solution which is expressed in terms of elliptic Jacobi functions.

We extend the systematic calculation of an approximately relativistic Hamiltonian for center of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [Phys. Rev. A 98, 042106 (2018)] to the case including a weak post-Newtonian gravitational background field, described by the Eddington-Robertson parametrized post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows us to systematically derive the coupling of the model system to gravity, instead of “guessing” it by means of classical notions of relativistic effects. We embed this technical result into a critical discussion concerning the problem of implementing and interpreting general couplings to the gravitational field and the connected problem of how to properly address the question concerning the validity of the Equivalence Principle in Quantum Mechanics.

The quantum Cheshire cat (QCC) thought experiment proposes that a quantum object's property (e.g., polarization, spin, etc.) can be separated from its physical body. This conclusion arose from an argument that interprets a zero weak value (WV) of polarization as no polarization. We show that this argument is incomplete in the sense that a zero WV reading could equally be interpreted as linear polarization. Nevertheless, through a generalization of the QCC, we complete their argument by excluding the possibility of linear polarization as a consistent interpretation. We go further and introduce the dual of the generalized QCC. The dual QCC exhibits an intriguing effect, where a horizontally polarized interferometer with just one arm can give rise to interference which is vertically polarized. The interference appears to arise as the result of the phase difference between the physical arm and a phantom arm. This peculiar effect arises from the interplay between the preselected and postselected states, which characterize WVs. The QCC has not yet been unambiguously experimentally demonstrated. The QCC dual offers an alternative pathway to experimental realization.

The $0_0^0\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}-\tilde{X}{}^2{\mathrm{\Sigma }}^{+}$, $1_1^0\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}-\tilde{X}{}^2{\mathrm{\Sigma }}^{+}$, and $1_0^1\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}-\tilde{X}{}^2{\mathrm{\Sigma }}^{+}$ bands of an internally cold molecular beam sample of ytterbium monohydroxide, YbOH, have been recorded at the near natural linewidth limit and analyzed to determine the fine structure parameters. Numerous lines in the $0_0^0\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}-\tilde{X}{}^2{\mathrm{\Sigma }}^{+}$ band associated with the lowest rotational levels were recorded in the presence of a static electric field and analyzed to determine the magnitude of the molecular frame permanent electric dipole moment, $|{\vec{\mu }}_{el}|$, for the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}(0,0,0)$ and $\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}(0,0,0)$ states of 1.9(2) and 0.43(10) D, respectively. An electrostatic polarizability model is used to predict the ${\vec{\mu }}_{el}$ for the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}(0,0,0)$ state. The $0_0^0\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}-\tilde{X}{}^2{\mathrm{\Sigma }}^{+}$ band is recorded in the presence of a weak static magnetic field to observe the electric dipole allowed transitions having $\mathrm{\Delta }J=-2$, which are used to assist in the rotational quantum number assignment and confirm the identity of the excited state. An expression for the $\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}(0,0,0)$ magnetic $g$ factor is derived and shown to correctly model the observed magnetic tuning. A comparison with YbF is made and implications for the use of YbOH as a venue for symmetry violation measurements are discussed.

Multistep laser-resonance-ionization spectroscopy of tellurium (Te) has been performed at TRIUMF's off-line laser ion source test stand. Six clean and regular even-parity Rydberg series $5p^3$ $\left({{}^{4}S}_{3/2}^{\circ }\right)$ $np{}^{3}P_{0,1,2}$, $np{}^{5}P_{1,2}$, and $nf{}^{3}F_2/{}^{5}F_{1,2}$ were observed. The ionization potential of Te was extracted from the measured series as $72669.114{\left(56\right)}_{\mathrm{stat}}{\left(45\right)}_{\mathrm{sys}}{\mathrm{cm}}^{-1}$. Excited from two different intermediate levels, seven odd-parity autoionization Rydberg series converging to the $5s^{2}5p^3$ $\left({{}^{2}D}_{3/2}^{\circ }\right)$ core state of Te were obtained.