We conduct a theoretical study of the nonlinear optical response of a two-dimensional semiconductor quantum-dot supercrystal subjected to a quasiresonant continuous-wave excitation. A constituent quantum dot is modeled as a three-level ladderlike system (comprising the ground, the one-exciton, and the biexction states). To study the stationary response of the supercrystal, we propose an exact linear parametric method of solving the nonlinear steady-state problem, while to address the supercrystal optical dynamics qualitatively, we put forward a method to calculate the bifurcation diagram of the system. Analyzing the dynamics, we demonstrate that the supercrystal can exhibit multistability, periodic and aperiodic self-oscillations, and chaotic behavior, depending on parameters of the supercrystal and excitation conditions. The effects originate from the interplay of the intrinsic nonlinearity of quantum dots and the retarded interdot dipole-dipole interaction. The latter provides a positive feedback which results in the exotic supercrystal optical dynamics. These peculiarities of the supercrystal optical response open up a possibility for all-optical applications and devices. In particular, an all-optical switch, a tunable generator of THz pulses (in self-oscillating regime), a noise generator (in chaotic regime), and a tunable bistable mirror can be designed.

One of the theoretical challenges in studying optical trapping is the decomposition of the optical force into the gradient force (conservative component) and scattering force (nonconservative component), which can be achieved either for Raleigh particles or for very large particles in the regime of ray optics. However, for the moderate particles in between these two limits, the scenario is still a mystery. In this paper we present a theoretical approach to bridge this gap and fully split the optical force acting on a spherical particle immersed in a generic monochromatic free-space optical field into two such essentially different components, which is efficient even for large particles with the exact consideration of light polarization, thus offering a benchmark for examining the effective range for application of ray optics. Our approach models general optical fields by a series of homogeneous plane waves. The analytical expressions for the gradient and scattering parts of the optical force exerted on a spherical particle of arbitrary size illuminated by multiple interferential plane waves are then derived. As examples of applications, we investigate the gradient and scattering forces acting on a dielectric particle immersed in the Bessel beam. Our results are in excellent agreement with those obtained based on ray optics methods when the illuminated particle is large enough, while exhibiting effects of Mie resonance that are totally missing in the ray optics for moderate particle sizes. Finally, we study the effect of particle size on the gradient force acting on a spherical particle sitting in multiple interferential plane waves. Our extensively numerical results, up to a size as large as 2000 illuminating wavelengths, suggest an overall decreasing tendency in the ratio of the magnitude of the gradient force to that of the total force as the particle size increases.

We propose a theoretical scheme to deterministically generate Fock states in a Kerr cavity through adiabatic variation of the driving field strength and the cavity detuning. We show that the required time to generate an $n$-photon Fock state scales as the square root of $n$. Requirements for the Kerr coefficient relative to the system decoherence rate are provided as a function of desired state fidelity, indicating that the scheme is potentially realizable with the present state of the art in microwave superconducting circuits.

We show a general relationship between a superposition of macroscopically distinct states and sensitivity in quantum metrology. Generalized cat states are defined by using an index which extracts the coherence between macroscopically distinct states, and a wide variety of states, including a classical mixture of an exponentially large number of states, has been identified as the generalized cat state with this criterion. We find that if we use the generalized cat states for magnetic field sensing without noise, the sensitivity achieves the Heisenberg scaling. More importantly, we even show that sensitivity of generalized cat states achieves the ultimate scaling sensitivity beyond the standard quantum limit under the effect of dephasing. As an example, we investigate the sensitivity of a generalized cat state that is attainable through a single global manipulation on a thermal equilibrium state and find an improvement of a few orders of magnitude from the previous sensors. Clarifying a wide class that includes such a peculiar state as metrologically useful, our results significantly broaden the potential of quantum metrology.

Standard protocols for quantum key distribution (QKD) require that the sender be able to transmit in two or more mutually unbiased bases. Here, we analyze the extent to which the performance of QKD is degraded by diffraction effects that become relevant for long propagation distances and limited sizes of apertures. In such a scenario, different states experience different amounts of diffraction, leading to state-dependent loss and phase acquisition, causing an increased error rate and security loophole at the receiver. To solve this problem, we propose a precompensation protocol based on preshaping the transverse structure of quantum states. We demonstrate, both theoretically and experimentally, that when performing QKD over a link with known, state-dependent loss and phase shift, the performance of QKD will be better if we intentionally increase the loss of certain states to make the loss and phase shift of all states equal. Our results show that the precompensated protocol can significantly reduce the error rate induced by state-dependent diffraction and thereby improve the secure key rate of QKD systems without sacrificing the security.

Rydberg states of atoms and molecules are very sensitive to electric fields. This property makes them ideal electric-field sensors but is detrimental to applications of Rydberg states in quantum optics, quantum-information processing, and quantum simulation because of inhomogeneous Stark broadening and the resulting loss of quantum coherence. We demonstrate, with the example of Rydberg states of ${}^{39}\mathrm{K}$, the existence of Rydberg-Rydberg transitions with extremely small differential dc Stark shifts, which we call dc-field-magic Rydberg-Rydberg transitions. These transitions hardly exhibit any Stark broadening, even when the electric-field strength varies by as much as $10\mathrm{V}{\mathrm{cm}}^{-1}$ over the experimental volume. We present a systematic study of dc-field-magic Rydberg-Rydberg transitions combining experiment and calculations and classify them in three main types, which should also be encountered in the other alkali-metal atoms, in alkaline-earth-metal atoms, and even in molecules. The observed insensitivity to dc electric fields does not reduce the interactions between Rydberg atoms, even if they are dominantly electric dipole-dipole in nature. Rydberg states coupled by dc-field-magic Rydberg-Rydberg transitions, therefore, have great potential as qubits.

The polarization of high-order harmonic generation in ${\mathrm{H}}_2{}^{+}$ driven by a counterrotating bichromatic $\omega /3\omega$ circularly polarized laser field is investigated theoretically. The elliptically polarized harmonics are characterized by ellipticity and rotation angle, where the latter is expanded to $[-\pi /2,\pi /2]$ by an optimized definition. We find a critical alignment angle where the ellipticity of high-energy harmonics is almost the same, so an attosecond pulse train with a high degree of polarization can be synthesized. In addition, we find that the rotation angle is always different from the alignment angle by ${90}^{\circ }$ with a small deflection. Thus, we propose a scheme to control the harmonic polarization state by the molecular alignment angle.

Determination of enantiomeric excess is important and remains challenging. We propose theoretically a spectroscopic method for this issue based on the chirality-dependent ac Stark effects in cyclic three-level models under the three-photon resonance condition. The enantiomeric excess of the chiral mixture is determined by comparing the amplitudes of the two ac Stark peaks chosen in the Fourier transform spectrum of the induced polarizations, which are (approximately) proportional to the number of molecules of the two enantiomers, respectively. In contrast to current spectroscopic methods based on the interference between the electric and (usually weak) magnetic dipole transition moments and/or with the need for enantiopure samples, our method involves only electric dipole transitions and does not require the enantiopure samples. Therefore, it will give strong chiral signals and can be applied to the determination of enantiomeric excess for chiral molecules whose enantiopure samples are still challenging to achieve.

Photon-pair sources from atomic ensembles are considered essential to the development of quantum science and technology based on atom-photon interfaces. The measurement of spectral-temporal biphoton wave forms is important for the characterization of frequency-time entangled photon pairs. Here, we demonstrate a stimulated measurement of the biphoton spectral wave form (BSW) of narrow-band photon pairs emitted from a Doppler-broadened cascade-type atomic ensemble. A BSW with submegahertz resolution is obtained as a function of the absolute optical frequency determined by atomic transitions, which reveals a spectral shift of approximately 510 MHz from the expected resonance frequency of the $5P_{3/2}-5D_{5/2}$ and $5S_{1/2}-5P_{3/2}$ transitions of ${}^{87}\mathrm{Rb}$ atoms.

Dissipative Kerr soliton frequency combs generated in high-Q microresonators may unlock novel perspectives in a variety of applications and crucially rely on quantitative models for systematic device design. Here, we present a global bifurcation study of the Lugiato-Lefever equation which describes Kerr comb formation. Our study allows systematic investigation of stationary comb states over a wide range of technically relevant parameters. Quantifying key performance parameters of bright and dark-soliton combs, our findings may serve as a design guideline for Kerr comb generators.

In estimating an unknown parameter of a quantum state the quantum Fisher information (QFI) is a pivotal quantity, which depends on the state and its derivate with respect to the unknown parameter. We prove the continuity property for the QFI in the sense that two close states with close first derivatives have close QFIs. This property is completely general and irrespective of dynamics or how states acquire their parameter dependence and also the form of parameter dependence—indeed this continuity is basically a feature of the classical Fisher information that in the case of the QFI naturally carries over from the manifold of probability distributions onto the manifold of density matrices. We demonstrate that, in the special case where the dependence of the states on the unknown parameter comes from one dynamical map (quantum channel), the continuity holds in its reduced form with respect to the initial states. In addition, we show that, when one initial state evolves through two different quantum channels, the continuity relation applies in its general form. A situation in which such a scenario can occur is an open-system metrology where one of the maps represents the ideal dynamics, whereas the other map represents the real (noisy) dynamics. In the making of our main result, we also introduce a regularized representation for the symmetric logarithmic derivative which works for general states even with incomplete rank, and it features continuity similar to the QFI.

It is usually assumed that the field isotope shift (FIS) is completely determined by the change of the averaged squared values of the nuclear charge radius $\langle r^2\rangle$. Relativistic corrections modify the expression for FIS, which is actually described by the change of $\langle r^{2\gamma }\rangle$, where $\gamma =\sqrt{1-Z^2{\alpha }^2}$. In the present paper we consider corrections to FIS which are due to the nuclear deformation and due to the predicted reduced charge density in the middle of the superheavy nuclei produced by a very strong proton repulsion (hole in the nuclear center). Specifically, we investigate effects which cannot be completely reduced to the change of $\langle r^2\rangle$ or $\langle r^{2\gamma }\rangle$.

We study the inelastic scattering of two-dimensional massless Dirac fermions by an inhomogeneous time-dependent driving field. As a physical realization, we consider a monolayer graphene normally illuminated with a circularly polarized laser of frequency $\mathrm{\Omega }$ in a given region. The interaction Hamiltonian introduced by the laser, being periodic in time, can be treated with the Floquet method, which naturally leads to a multichannel scattering problem. We analyze planar and circular geometries of the interface separating the irradiated and nonirradiated regions and find that there is an anomalous Goos-Hänchen shift in the inelastic channel. The latter is weakly dependent on the amplitude of the driving (for small amplitudes) while its sign is determined by the polarization of the laser field. We related this shift with the appearance of topological edge states between two illuminated regions of opposite chiralities.

We develop a method to extract the dissipation for a heavy moving impurity immersed in superfluid Fermi gases, which may serve as a theoretical model to explain relevant experiments. The drag force is derived analytically. As a reward, we are able to extract the density-density correlation function, from which density excitations of the system are carefully examined. We show that dissipations through drag force is associated with two types of excitations, one being single-particle and the other being collective. We map out the critical velocity for dissipation across the Bose-Einstein condensate-Bardeen-Cooper-Schrieffer (BEC-BCS) crossover, consistent with existing experiments. For a magnetic impurity, we show that the dissipation is immune to collective excitations. Our study clearly manifests that dissipation and associated excitations can be controlled by coupling superfluid Fermi gases with a moving impurity, and paves the way for further exploring the intriguing realm of nonequilibrium phenomena and dissipation dynamics.

Photon antibunching based on a single two-level atom strongly coupled to a single-mode optical cavity has been demonstrated in experiments. Here, we put forward an improved version of such an antibunching by introducing a pump field and a microwave field in the coupled atom-cavity system to form both a three-level $\mathrm{\Delta }$-type transition and closed-loop coupling. Via calculating the zero-time-delay second-order correlation function $g^{\left(2\right)}\left(0\right)$ of the single-mode cavity field, we find that a complete photon blockade, namely, $g^{\left(2\right)}\left(0\right)=0$, can be well achieved without detuning the driving and cavity resonance. In addition, it is clearly shown that this strong photon antibunching effect appears in the weak-coupling regime of light-atom interactions. The enhanced photon antibunching is ascribed to quantum interference between the two transition paths from the three-level $\mathrm{\Delta }$ atom weakly coupled to the three involved fields (cavity, pump, and microwave). Our proposal is useful for the single-photon generation by photon blockade, which has applications in quantum information processing.

The dynamical Casimir effect (DCE) is the production of photons by the amplification of vacuum fluctuations. In this paper, we demonstrate resonance conditions in DCE that potentially allow the production of optical photons when the mechanical frequency is smaller than the lowest frequency of the cavity field. We consider a cavity with one mirror fixed and the other allowed to oscillate. In order to identify the region where production of photons takes place, we do a stability analysis of the Heisenberg–Langevin equations of motion and investigate the dynamic stability of the system under small fluctuations. By using a numerical solution of the master equation, the time evolution of the mean number of photons produced in the unstable region is studied.

We outline the nonperturbative theory of multiple scattering of resonant, intense laser light off a dilute cloud of cold atoms. A combination of master equation and diagrammatic techniques allows a quantitative description of nonlinear diffusive transport as well as of coherent backscattering of the injected electromagnetic field, notwithstanding the exponential growth of Hilbert space with the number of atomic scatterers. As an exemplary application, we monitor the laser light's intensity profile within the medium, the spectrum of the backscattered light, and the coherent backscattering peak's height with increasing pump intensity. Our theory establishes a general, microscopic, scalable approach to nonlinear transport phenomena in complex quantum materials.

We study the effect of polarization on optical micromanipulation in a hexagonal optical lattice formed by three equiamplitude plane waves that have their wave vectors lying equiangularly in a plane, taking into account the vectorial characteristic of the electromagnetic waves. It is demonstrated that different polarizations generate different optical force landscapes, resulting in a trapping versus detrapping phenomenon tunable by tailoring the polarization of the incident beams. The physical origin of the polarization effect on the force landscapes is then traced to the ratio between the conservative (gradient) and nonconservative (scattering) optical forces acting on a particle immersed in the three-wave optical lattice. The trapping-detrapping transition phenomenon due to the change of polarization in small particles, where the gradient force dominates, is revealed to originate from the reverse of the conservative optical force, which manifests itself by a transition of the optical potential energy landscape from one exhibiting a periodic distribution of pits to one showing a distribution of humps over space. Our results suggest an alternative handle to manipulate small particle by tuning the polarization.

We study the zero-temperature phase diagram of the Lechner-Hauke-Zoller model. An analytic expression for the free energy and critical coefficients for finite-size systems and in the thermodynamic limit are derived and numerically verified. With the aim to improve standard quantum annealing, we introduce an inhomogeneously driven transverse field with an additional time-dependent parameter that allows one to evade the first-order quantum phase transition and, thus, improve the efficiency of the ground-state preparation considerably.

Electronic stopping cross sections (SCSs) of nickel, silicon, and nickel-silicon alloys for protons and helium (He) ions are studied in the regime of medium- and low-energy ion scattering, i.e., for ion energies in the range from $500\mathrm{eV}$ to $200\mathrm{keV}$. For protons, at velocities below the Bohr velocity the deduced SCS is proportional to the ion velocity for all investigated materials. In contrast, for He ions nonlinear velocity scaling is observed in all investigated materials. Static calculations using density functional theory (DFT) available from the literature accurately predict the SCS of Ni and Ni-Si alloy in the regime with observed velocity proportionality. At higher energies, the energy dependence of the deduced SCS of Ni for protons and He ions agrees with the prediction by recent time-dependent DFT calculations. The measured SCS of the Ni-Si alloy was compared to the SCS obtained from Bragg's rule based on SCS for Ni and Si deduced in this study, yielding good agreement for protons, but systematic deviations for He projectiles, by almost 20%. Overall, the obtained data indicate the importance of nonadiabatic processes such as charge exchange for proper modeling of electronic stopping of, in particular, medium-energy ions heavier than protons in solids.