Electron momentum spectroscopy (EMS) results are presented for the sulfur hexafluoride (${\mathrm{SF}}_6$) molecule using a high-resolution binary ($e$, $2e$) spectrometer at incident energies ($E_i$) of 600, 1200, and 2400 eV plus the binding energy. The valence orbital momentum profiles were measured with a binding energy resolution of 0.68 eV and angular resolutions of $\mathrm{\Delta }\theta =\pm 0.6^{\circ }$, $\mathrm{\Delta }\varphi =\pm 0.{85}^{\circ }$. Whereas the two higher incident energies are in the range where normally EMS measurements do not exhibit an impact-energy dependence, the current experimental data display a dynamic dependence on the impact energies. The measured momentum profiles are compared with predictions from a plane-wave impulse approximation (PWIA) calculation using molecular orbitals obtained from a density-functional-theory quantum-chemistry calculation. The PWIA calculations are in fairly good agreement with experiment only for 2400 eV impact energy, particularly for the summed $1t_{2u}$ and $5t_{1u}$ orbitals. We have also compared the experimental results for the $5a_{1g}$ state with the molecular three-body distorted-wave (M3DW) approach using the orientation-averaged molecular orbital approximation. Unlike the PWIA, the M3DW results are in very good agreement with the experimental data at all three measured incident energies for small momenta, which indicates that dynamical distortion effects are important for this molecule.

We revisit the Floquet-Bloch eigenstates of a one-dimensional electron gas in the presence of the periodic Kronig-Penney potential and an oscillating electric field. Considering the appropriate boundary conditions for the wave function and its derivative, we derive the determining equations for the Floquet-Bloch eigenstates, which are represented by a single-infinite matrix rather than a double-infinite matrix needed for a generic potential. We numerically solve these equations, showing that there appear anticrossings at the crossing points of the different Floquet bands as well as the band gaps at the edges and the center of the Brillouin zone. We also calculate the high-harmonic components of the electric current carried by the Floquet-Bloch eigenstates, showing that the harmonic spectrum shows a plateau for a strong electric field.

We report an alternate formulation of the quantum master equation (QME) to describe the dynamics of a quantum system weakly coupled to a heat bath, in the presence of weak external driving. A key feature of this approach is the introduction of an explicit Hamiltonian to model the thermal fluctuations in the heat bath. We show that the resulting time coarse-grained dynamical equation for the quantum system has dissipators with a natural regulator, which emerges from an ensemble average over the fluctuations. Importantly, such regularized dissipators arise from the second-order contributions of both the external drive as well as the system-environment coupling. We show that the second-order drive terms, regularized to time-scales set by the fluctuations, result in dynamic drive-induced frequency shifts as well as drive-dependent relaxation phenomena. Considering the specific case of an ensemble of two-level systems, subjected to a linearly polarized external drive, we derive the modified Bloch Equations with such drive-dependent shift and damping terms. The resulting drive-induced frequency shifts converge to the known forms of dynamic frequency shifts, such as the Bloch-Siegert shift or the dynamic Stark shift, in appropriate limits. The Kramers-Kronig pairs of these frequency shifts - manifest as drive-dependent damping terms in the modified Bloch Equations and help explain the Redfield limit of free-induction-decay (FID) rates as well as the non-Bloch decay of Rabi oscillations in isotropic medium. Our method predicts correct orders of magnitudes of non-Bloch decay rates in isotropic medium as well as their observed temperature dependence. The QME reported here, correctly describes all known aspects of the driven-dissipative dynamics up to second-order of an open quantum system with appropriate thermal signatures and as such is expected to provide deeper insights into the study of quantum information processing on real systems.

Here we create an effective electric field force for photon in a synthetic frequency lattice to control the spectrum of light. The frequency lattice is created based on an optical waveguide modulator in which the dynamic index modulation can induce photonic transitions between adjacent lattice sites. We show that the wave vector mismatch during photonic transitions and periodic distribution of the modulation phase can be mapped into a linear-varying and a periodically driven gauge potential, which gives rise to a constant and a harmonic oscillating force, respectively. Under different combinations of the constant and oscillating forces, we can realize the effects of frequency Bloch oscillations, anharmonic Bloch oscillations, super-Bloch oscillations, and directional frequency shift. With an appropriate choice of the magnitude of the oscillating force, we also achieve dynamic localization in the frequency domain. The realization of effective force provides a mechanism to control the spectrum of light, which may find applications in frequency perfect imaging, efficient shifting, and precise transduction.

We study terahertz (THz) emission by two-color femtosecond filaments in air using pump wavelengths ${\lambda }_0$ from 0.8 to 10.6 $\mu \mathrm{m}$. Comprehensive three-dimensional numerical simulations show that tens-of-centimeter long filaments created by a 10.6-$\mu \mathrm{m}$ pump pulse can produce mJ energy yields and GV/m field strengths, while the laser-to-THz conversion efficiency exceeds the percent level. Changing temperature and humidity conditions reveals a surprisingly high stability of the THz spectra against different weather conditions. We also examine the role of many-body Coulomb effects on ionization. This additional plasma source promotes longer filaments that act as efficient THz emitters, despite enhanced plasma defocusing.

It is a central question in quantum thermodynamics to determine how irreversible is a process that transforms an initial state $\rho$ to a final state $\sigma$ and whether such irreversibility can be thought of as a useful resource. For example, we might ask how much work can be obtained by thermalizing $\rho$ to a thermal state $\sigma$ at temperature $T$ of an ambient heat bath. Here, we show that, for different sets of resource-theoretic thermodynamic operations, the amount of entropy produced along a transition is characterized by how reversible the process is. More specifically, this entropy production depends on how well we can return the state $\sigma$ to its original form $\rho$ without investing any work. At the same time, the entropy production can be linked to the work that can be extracted along a given transition and we explore the consequences that this fact has for our results. We also exhibit an explicit reversal operation in terms of the Petz recovery channel coming from quantum information theory. Our result establishes a quantitative link between the reversibility of thermodynamical processes and the corresponding work gain.

When a photon passes through an interferometer, quantum mechanics does not provide a clear answer as to its past. Quantum retrodiction is a quantitative theory, which endeavors to make statements about the past of a system based on present knowledge. Quantum retrodiction may be used to analyze the past of a photon, that is, its trajectory. Here we experimentally retrodict the trajectories of single photons in double interferometers by measuring the final state of the photon. A sequence of measurements is made on a photon to determine which path the photon followed, so a series of retrodiction of measurement results can be regarded as a photon trajectory. We obtain information about the partial trajectory and the entire trajectory of the photon. Furthermore, we also observe the effect of different measurements in the extraction of trajectory information. Our experiment highlights the application of retrodiction theory to the study of the photon's past, and provides potential application in quantum communications.

Solving the Toeplitz systems, which involves finding the vector $x$ such that $T_{n}x=b$ given an $n\times n$ Toeplitz matrix $T_n$ and a vector $b$, has a variety of applications in mathematics and engineering. In this paper, we present a quantum algorithm for solving the linear equations of Toeplitz matrices, in which the Toeplitz matrices are generated by discretizing a continuous function. It is shown that our algorithm's complexity is nearly $O(\kappa \mathrm{poly}(logn))$, where $\kappa$ and $n$ are the condition number and the dimension of $T_n$, respectively. This implies our algorithm is exponentially faster than its classical counterpart if $\kappa =O(\mathrm{poly}(logn))$. Since no assumption on the sparseness of $T_n$ is demanded in our algorithm, it can serve as an example of quantum algorithms for solving nonsparse linear systems.

Standard randomized benchmarking protocols entail sampling from a unitary 2-design, which is not always practical. In this article we examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2-designs. We introduce a general method for analyzing such protocols and subsequently apply it to two subgroups, the group generated by controlled-not, Hadamard, and Pauli gates and that generated by only controlled-not and Pauli gates. In both cases the error probability can be estimated to within a factor of 2 or less where the factor can be arranged to be conservative and to decay exponentially in the number of qubits. For randomized benchmarking of logical qubits even better accuracy will typically be obtained. Thus, we show that sampling a distribution which is close to a unitary 2-design, although sufficient, is not necessary for randomized benchmarking to high accuracy.

We show that bipartite entanglement in an one-dimensional quantum spin model undergoing time evolution due to local Markovian environments can be frozen over time. We demonstrate this by using a number of paradigmatic quantum spin models including the anisotropic $XY$ model in the presence of a uniform and an alternating transverse magnetic field (ATXY), the $XXZ$ model, the $XYZ$ model, and the $J_1-J_2$ model involving the next-nearest-neighbor interactions. We show that the length of the freezing interval, for a chosen pair of nearest-neighbor spins, may remain independent of the length of the spin chain, for example, in paramagnetic phases of the ATXY model, indicating a scale invariance. Freezing of entanglement is found to be robust against a change in the environment temperature, the presence of disorder in the system, and whether the noise is dissipative or not dissipative. Moreover, we connect the freezing of entanglement with the propagation of information through a quantum many-body system, as considered in the Lieb-Robinson theorem. We demonstrate that the variation of the freezing duration exhibits a quadratic behavior against the distance of the nearest-neighbor spin pair from the noise source, obtained from exact numerical simulations, in contrast to the linear one as predicted by the Lieb-Robinson theorem.

High-order harmonic generation in graphene driven by the elliptically polarized midinfrared driving pulse is theoretically investigated by solving the two-band semiconductor Bloch equation in the Houston basis under the tight-binding approximation. It is found that the maximal harmonic yield occurs at a specific driver ellipticity whose value is determined by relaxation processes, so that the proper choice of the dephasing time is key to quantitatively reproducing the recent experiment. We show that the ellipticity dependence mainly originates from the interband harmonic emission, and exhibits an almost stable behavior against the crystal orientation. Furthermore, we also demonstrate that both the large magnitude and the circular vortex structure of the transition dipole near the graphene Dirac point are responsible for forming the unique characteristics. These results demonstrate that high-harmonic generation by the elliptically polarized driving field carries significant information on the dephasing time and the electronic structure signature in the graphene.

We present analytical results for the nonlocal pair correlations in one-dimensional bosonic systems with repulsive contact interactions that are uniformly valid from the classical regime of high temperatures down to weak quantum degeneracy entering the regime of ultralow temperatures. By using the information contained in the short-time approximations of the full many-body propagator, we derive results that are nonperturbative in the interaction parameter while covering a wide range of temperatures and densities. For the case of three particles we give a simple formula for arbitrary couplings that is exact in the dilute limit while remaining valid up to the regime where the thermal de Broglie wavelength ${\lambda }_T$ is of the order of the characteristic length $L$ of the system. We then show how to use this result to find analytical expressions for the nonlocal correlations for arbitrary but fixed particle numbers $N$ including finite-size corrections. Neglecting the latter in the thermodynamic limit provides an expansion in the quantum degeneracy parameter $N{\lambda }_T/L$. We compare our analytical results with numerical Bethe ansatz calculations, finding excellent agreement.

When the spectrum of magnetic excitations of a quantum mixture is much softer than the density spectrum, the system becomes effectively incompressible and can host magnetic defects. These are characterized by the presence of a topological defect in one of the two species and by a local modification of the density in the second one, the total density being practically unaffected. For miscible mixtures interacting with equal intraspecies coupling constants, the width of these magnetic defects is fixed by the difference $\delta g$ between the intraspecies and interspecies coupling constants and becomes increasingly larger as one approaches the demixing transition at $\delta g=0$. When the density of the filling component decreases, the incompressibility condition breaks down, and we predict the existence of a critical filling, below which all the atoms of the minority component remain bound in the core of the topological defect. Applications to the sodium atomic spin species $|F=1,m_F=\pm 1\rangle$ in both uniform and harmonically trapped configurations are considered, and a protocol to produce experimentally these defects is discussed. The case of binary mixtures interacting with unequal intraspecies forces and experiencing buoyancy is also addressed.

We consider the system of dimers formed in a one-dimensional mass-balanced Bose-Bose mixture of species $\sigma =\uparrow ,\downarrow$ with attractive interspecies and repulsive intraspecies contact interactions. In the plane parametrized by the ratios of the coupling constants $g_{\uparrow \uparrow }/\left|g_{\uparrow \downarrow }\right|$ and $g_{\downarrow \downarrow }/\left|g_{\uparrow \downarrow }\right|$ we trace out the curve where the dimer-dimer interaction switches from attractive to repulsive. We find this curve to be significantly (by more than a factor of 2) shifted towards larger $g_{\sigma \sigma }$ (or smaller $|g_{\uparrow \downarrow }|$) compared to the mean-field stability boundary $g_{\uparrow \uparrow }{g}_{\downarrow \downarrow }=g_{\uparrow \downarrow }^2$. For a weak dimer-dimer attraction we predict a dilute dimerized liquid phase stabilized against collapse by a repulsive three-dimer force.

It has been recently proposed that single molecule spectroscopy could be employed to detect the motion of nanomechanical resonators. Estimates of the coupling constant ($g$) between the molecular two-level system and the oscillator indicate that it can reach values much larger than the mechanical resonating pulsation (${\omega }_m$) and the two-level system linewidth ($\mathrm{\Gamma }$). Other experimental realizations of the same system are also approaching this strong-coupling regime. In this paper we investigate the behavior of the system in the limit for slow mechanical oscillator ${\omega }_m\ll \mathrm{\Gamma }$. We find that, for sufficiently large coupling, the system undergoes a bistability reminiscent of that observed in optical cavities coupled to mechanical resonators.

Emission of electromagnetic radiation by accelerated particles with electric, toroidal, and anapole dipole moments is analyzed. It is shown that ellipticity of the emitted light can be used to differentiate between electric and toroidal dipole sources and that anapoles, elementary neutral nonradiating configurations, which consist of electric and toroidal dipoles, can emit light under uniform acceleration. The existence of nonradiating configurations in electrodynamics implies that it is impossible to fully determine the internal makeup of the emitter given only the distribution of the emitted light. Here we demonstrate that there is a loop hole in this “inverse source problem.” Our results imply that there may be a whole range of new phenomena to be discovered by studying the electromagnetic response of matter under acceleration.

Spectral broadening of ultrashort laser pulses is simultaneously described by either self-phase modulation (SPM) or four-wave mixing (FWM). The latter implies the instantaneous conservation of both the photon number and energy, while the former describes a time-dependent frequency shift, implying a violation of the energy conservation if the number of photons is to be conserved in each time slice. We resolve this paradox by considering the transient energy storage in the propagation medium, which can be calculated in the SPM formalism via the dephasing between the incident pulse and the medium polarization leading to an effective imaginary part in the third-order susceptibility. In parallel, considering the temporal variation of the incident intensity in FWM offsets the instantaneous frequency.