The concept of the local Chern marker has gained much attention, especially in the field of ultracold quantum gases in optical lattices and artificial gauge fields. We investigate in further detail the microscopic real-space characteristics of the local Chern marker for the two-band Harper-Hofstadter-Hatsugai model and propose a tomographic scheme for the experimental detection of an approximate local Chern marker neglecting higher orders.

Inspired by the renewed experimental activities on $p$-wave resonantly interacting atomic Fermi gases, we investigate theoretically some experimental observables of such systems at zero temperature in two dimensions, using both mean-field theory and Gaussian pair fluctuation theory. These observables include the two $p$-wave contact parameters and the breathing mode frequency, which can be readily measured in current cold-atom setups with ${}^{40}\mathrm{K}$ and ${}^6\mathrm{Li}$ atoms. We find that the many-body component of the two contact parameters exhibits a pronounced peak slightly above the resonance and consequently leads to a dip in the breathing mode frequency. In the resonance limit, we discuss the dependence of the equation of state and the breathing mode frequency on the dimensionless effective range of the interaction $k_F{R}_p\ll 1$, where $k_F$ is the Fermi wave vector and $R_p$ is the effective range. The breathing mode frequency ${\omega }_B$ deviates from the scale-invariant prediction of ${\omega }_c=2{\omega }_0$, where ${\omega }_0$ is the trapping frequency of the harmonic potential. This frequency shift is caused by the necessary existence of the effective range. In the small range limit, we predict that the mode frequency deviation at the leading order is given by $\delta {\omega }_B\simeq -({\omega }_0/4){ln}^{-1}\left(k_F{R}_p\right)$.

The proposal for single-photon generation utilizing quantum interference of two coupled cavity modes with weak Kerr nonlinearity under resonant coherent driving has been successfully put forward in previous work [T. C. H. Liew and V. Savona, Phys. Rev. Lett. 104, 183601 (2010)]. Here we suggest an alternative scheme to explore the statistical properties of the photons and their control in a parametrically amplified photonic molecule that is composed of a pair of coupled cavities, both containing the degenerate optical parametric amplifier (DOPA), by means of extending the model of Liew and Savona. Due to the destructive quantum interference effect between different paths for two-photon excitation, the photons in both cavity modes can exhibit a strong antibunching effect when one of the two cavities is coherently driven by an external laser field. In order to intuitively understand the strong photon antibunching phenomenon occurring in our DOPA photonic molecule, the approximate analytical solutions of the system are provided via the Schrödinger equation and further are compared with the full numerical solutions via the master equation. The in-depth results reveal that the two solutions are in good agreement. For the two cavity modes, we achieve the optimal antibunching conditions in terms of the nonlinear gain and the strength ratio between the two pump laser fields based on analytical calculations, gaining deep insight into the rich physics of photon statistics. We also show that the statistical properties of the photons can be well controlled by regulating the relative phase between the two pump laser fields and the tunneling rate between the two cavity modes. Furthermore, we address the second-order cross-correlation function between the two cavity modes and find that a strong intermodal antibunching can be efficiently generated. Our approach via the DOPA photonic molecule architecture can be useful to generate tunable single-photon sources or controlled photonic quantum gates.

In this paper, the scheme of a force sensor is proposed which has been composed of a hybrid optomechanical cavity containing an interacting cigar-shaped Bose-Einstein condensate (BEC) where the $s$-wave scattering frequency of the BEC atoms as well as the spring coefficient of the cavity moving end-mirror (the mechanical oscillator) are parametrically modulated. It is shown that, in the red-detuned regime and under the so-called impedance-matching condition, the mechanical response of the system to the input signal is enhanced substantially which leads to the amplification of the weak input signal while the added noise of measurement (backaction noise) can be suppressed and lowered much below the standard quantum limit. Furthermore, because of its large mechanical gain, such a modulated hybrid system is a much better amplifier in comparison to the (modulated) bare optomechanical system which can generate a stronger output signal while keeping the sensitivity nearly the same as that of the (modulated) bare one. The other advantages of the presented nonlinear hybrid system accompanied with the mechanical and atomic modulations in comparison to the bare optomechanical cavities are its controllability as well as the extension of the amplification bandwidth.

We investigate the dynamics of a ring cavity made of photonic crystal fiber and driven by a coherent beam working near to the resonant frequency of the cavity. By means of a multiple-scale reduction of the Lugiato-Lefever equation with high-order dispersion, we show that the dynamics of this optical device, when operating close to the critical point associated with bistability, is captured by a real order parameter equation in the form of a generalized Swift-Hohenberg equation. A Swift-Hohenberg equation has been derived for several areas of nonlinear science such as chemistry, biology, ecology, optics, and laser physics. However, the peculiarity of the obtained generalized Swift-Hohenberg equation for photonic crystal fiber resonators is that it possesses a third-order dispersion. Based on a weakly nonlinear analysis in the vicinity of the modulational instability threshold, we characterize the motion of dissipative structures by estimating their propagation speed. Finally, we numerically investigate the formation of moving temporal localized structures often called cavity solitons.

We theoretically investigate the simulation of moving cavities in a superconducting circuit setup. In particular, we consider a recently proposed experimental scenario where the phase of the cavity field is used as a moving clock. By computing the error made when simulating the cavity trajectory with superconducting quantum interference devices (SQUIDs), we identify parameter regimes where the correspondence holds, and where time dilation and corrections due to clock size and to particle creation coefficients are observable. These findings may serve as a guideline when performing experiments on simulation of moving cavities in superconducting circuits.

We derive an expression for the two-photon spontaneous emission (TPSE) rate of an excited quantum emitter in the presence of arbitrary bodies in its vicinities. After investigating the influence of a perfectly conducting plate on the TPSE spectral distribution (Purcell effect), we demonstrate the equivalence of our expression with the more usual formula written in terms of the corresponding dyadic Green's function. We establish a convenient relation between the TPSE spectral distribution and the corresponding Purcell factors of the system. Next, we consider an emitter close to a dielectric medium and show that, in the near-field regime, the TPSE spectral distribution is substantially enhanced and changes abruptly at the resonance frequencies. Finally, motivated by the suppression that may occur in the one-photon spontaneous emission of an excited atom between two parallel conducting plates, we discuss the TPSE for this same situation and show that complete suppression can never occur for $s\to s$ transitions.

We study the relations between quantum coherence and quantum nonlocality, genuine quantum entanglement, and genuine quantum nonlocality. We show that the coherence of a qubit state can be converted to the nonlocality of two-qubit states via incoherent operations. The results are also generalized to the qudit case. Furthermore, rigorous relations between the quantum coherence of a single-partite state and the genuine multipartite quantum entanglement, as well as the genuine three-qubit quantum nonlocality, are established.

Vibrational branching ratios in the $B{}^2{\mathrm{\Sigma }}^{+}$–$X{}^2{\mathrm{\Sigma }}^{+}$ and $A{}^2\mathrm{\Pi }$–$X{}^2{\mathrm{\Sigma }}^{+}$ optical-cycling transitions of BaH molecules are investigated using measurements and ab initio calculations. The experimental values are determined using fluorescence and absorption detection. The observed branching ratios have a very sensitive dependence on the difference in the equilibrium bond length between the excited and ground state, $\mathrm{\Delta }{r}_e$: a 1-pm (0.5%) displacement can have a 25% effect on the branching ratios but only a 1% effect on the lifetime. The measurements are combined with theoretical calculations to reveal a preference for a particular set of published spectroscopic values for the $B{}^2{\mathrm{\Sigma }}^{+}$ state ($\mathrm{\Delta }{r}_e^{B–X}=+5.733\mathrm{pm}$), while a larger bond-length difference ($\mathrm{\Delta }{r}_e^{B–X}=6.3–6.7$ pm) would match the branching-ratio data even better. By contrast, the observed branching ratio for the $A{}^2{\mathrm{\Pi }}_{3/2}$–$X{}^2{\mathrm{\Sigma }}^{+}$ transition is in excellent agreement with both the ab initio result and the spectroscopically measured bond lengths. This shows that care must be taken when estimating branching ratios for molecular laser cooling candidates, as small errors in bond-length measurements can have outsize effects on the suitability for laser cooling. Additionally, our calculations agree more closely with experimental values of the $B{}^2{\mathrm{\Sigma }}^{+}$ state lifetime and spin-rotation constant, and revise the predicted lifetime of the $H{}^2\mathrm{\Delta }$ state to 9.5 $\mu \mathrm{s}$.

The $1s\to np$ Rydberg transitions below the $1s$ ionization thresholds of Kr and Xe are obscured in x-ray absorption spectra due to core-hole lifetime broadening. However, the $np$ spectator electrons associated with those resonances can affect the core-hole decay spectra. We report on ion charge-state distributions of Kr and Xe measured in coincidence with ${KL}_{2,3}$ ($K{\alpha }_{1,2}$), ${KM}_{2,3}$ ($K{\beta }_{1,3}$), and ${\mathrm{KN}}_{2,3}$ ($K{\beta }_2$) x-ray fluorescence as the incident x-ray energy is scanned through pre-edge resonances and ionization thresholds. The coincidence measurements select vacancy cascades that begin with a radiative transition that transfers $1s$ holes to the $2p$, $3p$, and $4p$ shells followed by emission of Auger electrons. We observe shifts of ion yields from higher to lower charge states that we attribute to $np$ spectator electrons. For the special case of ${\mathrm{Kr}}^{1+}$ that is produced in coincidence with $K{\beta }_2$ x rays, the ion yield decreases in the pre-edge region. This is attributed to production of neutral, metastable Kr $4p^{-1}np$ states that reduce the ${\mathrm{Kr}}^{1+}$ yield. Model fits to the x-ray absorption spectra are presented to show the lifetime broadened pre-edge resonances and ionization thresholds. High-level relativistic coupled-cluster calculations that treat relativistic, electron correlation, and wave function relaxation effects on the same footing obtain agreement with the experimental $1s$ ionization energies of Kr and Xe to $<2$ eV. The Xe $K$-edge x-ray absorption spectrum and ion charge-state distributions of ${\mathrm{XeF}}_2$ were also recorded. Excitation of the $7{\sigma }_u$ lowest unoccupied molecular orbital (LUMO) in ${\mathrm{XeF}}_2$ is observed in the pre-edge region. Our ab initio calculations find that the $6p_z$ Rydberg state is strongly perturbed by the presence of the $7{\sigma }_u$ LUMO. A fit to the measured LUMO, $6p_x$, $6p_y$, $6p_z$ Rydberg states, and ionization threshold is guided by the relativistic coupled-cluster calculations. The F ligands modify the valence electron charge distribution and result in a $\sim 2.3$ eV chemical shift of the Xe $1s$ ionization energy relative to atomic Xe. Xe $1s^{-1}$ core-hole decay in ${\mathrm{XeF}}_2$ results in ionization of the F ligands and energetic fragmentation into atomic ions. Ion charge-state spectra of ${\mathrm{XeF}}_2$ were recorded in coincidence with x-ray fluorescence for excitation on the LUMO resonance and above the Xe $1s$ ionization threshold. For the ion time of flight spectra recorded on the LUMO resonance, the ${\mathrm{F}}^{q+}$ ($q=1$–4) peaks are split into two peaks along the linear polarization direction of the incident x-ray beam. This effect is attributed to spatial alignment of ${\mathrm{XeF}}_2$ molecules by resonant x-ray absorption, and the peak splittings are used to measure the F ion fragmentation energies following $K{\alpha }_{1,2}$, $K{\beta }_{1,3}$, and $K{\beta }_2$ x-ray fluorescence. We observe variations of the F ion charge state yields and fragmentation energies for the three fluorescence pathways that leave the molecule in different outer-shell hole states.

Electron motion in molecules can be initiated by a laser pulse and, through the induced charge migration, can, in turn, trigger a response from the nuclei. The generated electron-nuclear wave packets can quickly decohere, but also lead to recurrence of coherences. Presented here is a quantum dynamics study of ${\mathrm{H}}_2$ and LiH in strong fields. No separation of electronic and nuclear motion is assumed, and no precomputed potential energy surface is required. It is shown that electron and nuclear motion are strongly coupled through the laser-pulse excitation, and already moderate nuclear excitation can substantially impact the electron dynamics. Through the full quantum dynamical treatment, coherence properties of electronic and nuclear wave function can be investigated. The nuclear motion leads to decoherences while it can also introduce recurrence of coherences.

We calculate two-dimensional photoelectron momentum distributions and energy spectra after multiphoton ionization of Li atoms subject to intense laser fields in the one-photon Rabi-flopping regime. The time-dependent Schrödinger equation is solved within the single-active-electron approximation using a model potential which reproduces accurately the binding energies and dipole matrix elements of the Li atom. Interaction with the external electromagnetic field is treated within the dipole approximation. We show that the Rabi oscillations of the population between the ground $2s$ state and the excited $2p$ state in the one-photon resonance regime are reflected in the energy spectra of emitted photoelectrons, which manifest interference structures with minima. Transformations of the interference structures in the photoelectron energy spectra caused by the variation of the laser peak intensity and pulse duration are analyzed.

We calculate the spectra of electrons emitted upon Auger decay of the $2p$ vacancy in chlorine. The vacant atomic and ionic states are populated by a single-photon absorption from the ground state of the chlorine atom and are tested by comparing the calculated photoabsorption spectrum with the existing theoretical and experimental photoionization data. The agreement is reasonably good, although the calculated Auger decay rates and oscillator strengths of the low-lying states are overestimated due to neglect of the core polarization effects. In the absence of any published experimental result, the nonresonant $L-M_{23}^2$ Auger spectrum of Cl at 220 eV photon energy is compared with the Cl $L-V^2$ Auger spectrum of HCl, measured at 235 eV photon energy. The calculated spectator and participator resonant Auger spectra of some strongly photoexcited Cl $2p^{-1}$ states are presented for future reference.

A domain wall of relative phase in a flattened harmonically trapped Bose-Einstein condensed mixture of two atomic hyperfine states, subject to a stationary Rabi coupling of intensity $\mathrm{\Omega }$, is predicted to decay through two different mechanisms. For small values of $\mathrm{\Omega }$ the instability has an energetic nature and is associated with the formation of a vortex-antivortex pair of the same atomic hyperfine states, the motion of which inside the trap causes the emergence of magnetization, the bending of the domain wall, and its consequent fragmentation. For large values of $\mathrm{\Omega }$ the domain wall instead undergoes a dynamic snake instability, caused by the negative value of its effective mass, and results in the fast fragmentation of the wall into smaller domain walls confining vortex pairs of different atomic species. Numerical predictions are given by solving the time-dependent Gross-Pitaevskii equation in experimentally available configurations of mixtures of sodium atomic gases.

We study the repulsive polaron problem in a two-component two-dimensional system of fermionic atoms. We use two different interaction models: a short-range (hard-disk) potential and a dipolar potential. In our approach, all the atoms have the same mass and we consider the system to be composed of a uniform bath of a single species and a single atomic impurity. We use the diffusion Monte Carlo method to evaluate polaron properties such as its chemical potential and pair distribution functions, together with a discussion on the deficit of volume induced by the impurity. We also evaluate observables that allow us to determine the validity of the quasiparticle picture: the quasiparticle residue and the effective mass of the polaron. Employing two different potentials allows us to identify the universality regime, where the properties depend only on the gas parameter $n{a}_s^2$ fixed by the bath density and the two-dimensional scattering length.

Bound states in the continuum (BICs) are observed experimentally in a one-dimensional dimerized chain consisting of identical dipole resonators. The existence of BICs can be identified by the singularities of effective mode polarizability. These singularities can emerge both at and off the $\mathrm{\Gamma }$ point and lead to a phase jump of $\pi$ of the coupling strength between these modes and external waves. For the off-$\mathrm{\Gamma }$ BICs, a reversal of Fano line shape is revealed in the scattering spectra. This type of BICs is exemplified by the dimerized chain made of plasmonic particles and high-dielectric resonators in the subwavelength scale. Our results may have applications in subwavelength waveguiding, high-$Q$ cavity sensing, and enhanced light-matter interaction.

We establish a classical electrodynamic theory for the nonradiative transfer of field helicity [resonance helicity transfer (RHELT)] and energy [resonance energy transfer (RET)] between a donor and an acceptor, both being dipolar, magnetoelectric, and bi-isotropic, chiral in particular, with rotating excited dipoles. We introduce orientational factors that control this process. Also, a RHELT and RET interaction radius is put forward. The detection of RHELT adds a wealth of information contained in the helicity of the transferred fields. The nature of these dipolar magnetoelectric bi-isotropic particles and/or molecules with induced dipoles possessing angular momentum enriches the number of variables and associated effects. Hence, the landscape involved in this transfer phenomenon is significantly broader than in conventional Förster resonance energy transfer (FRET). In this way, chiral interacting objects convey terms in the equations of transfer rate of helicity and energy that are discriminatory, so that one can extract information on their structural chirality handedness and polarization rotation. As such, not only the rate of electromagnetic helicity transfer, but also that of energy transfer may be negative, which for the latter means an enhanced emission from the donor in presence of acceptor, a phenomenon which does not exist in conventional FRET. Importantly, both the RHELT and RET rates, as well as the RHELT interaction radius, are very sensitive to changes in the helicity, or state of polarization, of the illumination, as well as to the polarization of the excited electric and magnetic dipole moments of donor and acceptor. Finally, we introduce the observable quantities in terms of which one can obtain the transfer rates and interaction radii.

We describe how stimulated Raman adiabatic passage (STIRAP) can be applied to create spectral holes in an inhomogeneously broadened system. Due to the robustness of STIRAP, our proposal guarantees a high flexibility and accuracy, and at variance with traditional spectral hole burning techniques, it may require substantially fewer time resources since it does not rely upon the spontaneous decay of an intermediate excited state. We investigate the effects on the scheme of dephasing and dissipation as well as of unintentional driving of undesired transitions due to a finite splitting of the initial and target states. Finally, we show that the pulses can be reversed to create narrow absorption structures inside a broad spectral hole, which can be used as qubits for precise quantum operations on inhomogeneously broadened few-level systems.