We identify the contribution of Floquet-Bloch states to the high-order harmonic generation (HHG) in solids by numerically solving the time-dependent Schrödinger equation for both a one-dimensional and a two-dimensional model. Results from the single $k$ point and the full Brillouin zone are compared to each other and the symmetry- breaking effect is discussed. We show that the observed phenomena can be explained under the framework of the Floquet-Bloch theory and the strong-field approximation, respectively. Our results indicate that the total yield of the harmonic radiation increases nonmonotonically with the intensity of the driving pulse. After a rough consideration of the focusing volume effects, we find that the yield of the harmonics shows a steplike structure, which is similar to several recent experimental observations. The present work can contribute to a better understanding of the channel-closing effect in the HHG of solids and may provide a way to detect the Floquet-Bloch bands in a laser field.

We study the probability distribution of an atomic ion being laser cooled in a periodically driven Paul trap using a Floquet approach to the semiclassical photon scattering dynamics. We show that despite the microscopic nonequilibrium forces, a stationary thermal-like exponential distribution can be obtained in the Hamiltonian action, or equivalently in the number of quanta (phonons) of the motion linearized about the zero of the potential. At the presence of additional stray electric fields, the ion is pushed from the origin of the potential and set into a large-amplitude driven oscillation, and above a threshold amplitude of such “excess micromotion,” the action distribution of excitations about the driven oscillation broadens and becomes distinctly nonthermal. We find that by a proper choice of the laser detuning, the distribution can be made exponential again, with a mean phonon number close to that of the Doppler cooling limit. We derive a relation allowing to deduce just from the experimentally observable photon scattering rate both the required detuning for optimal cooling and the final mean phonon number. These results are important for quantum information processing and other applications, and in particular the derived approach can be applied to crystals of trapped ions in planar configurations, where the driven motion of ions is unavoidable.

We investigate a temporal evolution of an impurity atom in a one-dimensional trapped Bose gas following a sudden change of the boson-impurity interaction strength. Our focus is on the effects of inhomogeneity due to the harmonic confinement. These effects can be described by an effective one-body model where both the mass and the spring constant are renormalized. This is in contrast to the classic renormalization, which addresses only the mass. We propose an effective single-particle Hamiltonian and apply the multilayer multiconfiguration time-dependent Hartree method for bosons to explore its validity. Numerical results suggest that the effective mass is smaller than the impurity mass, which means that it cannot straightforwardly be extracted from translationally invariant models.

We consider an optical probe that interacts with an ensemble of rare-earth ions doping a material in the shape of a cantilever. By optical spectral hole burning, the inhomogeneously broadened transition in the ions is prepared to transmit the probe field within a narrow window, but bending of the cantilever causes strain in the material which shifts the ion resonances. The motion of the cantilever may thus be registered by the phase shift of the probe. By continuously measuring the optical field we induce a rapid reduction of the position and momentum uncertainty of the cantilever. Doing so, the probing extracts entropy and thus effectively cools the thermal state of motion towards a known, conditional oscillatory motion with strongly reduced thermal fluctuations. Moreover, as the optical probe provides a force on the resonator proportional to its intensity, it is possible to exploit the phase-shift measurements in order to create an active feedback loop, which eliminates the thermal fluctuations of the resonator. We describe this system theoretically, and provide numerical simulations which demonstrate the rapid reduction in resonator position and momentum uncertainty, as well as the implementation of the active cooling protocol.

Optical frequency combs (OFCs) are of extreme importance for modern photonics. A great number of OFC generation methods and practical application ideas have been suggested. In this paper we propose and theoretically analyze an OFC generation method based on frequency-shifting loop utilizing collinear acousto-optic (AO) diffraction. This method offers two OFC generation schemes. The first one applies the closed-loop optical system with collinear AO cell driven by external radio-frequency (rf) generator. The second scheme applies a principle of an optoelectronic oscillator. This system includes not only the optical feedback but also the optoelectronic feedback connecting the optical output of the system with the piezoelectric transducer of the AO cell and operates above the self-excitation threshold without external rf generator. In both cases OFCs may be obtained in several ways: two different types of single side band modulation and amplitude modulation. The switching between the methods is realized by mutual reorientation of a pair of polarizers placed in front of and behind the AO cell and achromatic half-wave plate included in the optical feedback loop. It is shown that the parameters OFCs obtained in the system with only optical feedback are determined by AO cell material, rf generator signal frequency and magnitude, optical loss and amplification. The system with both optic and electronic feedback gives the unique opportunity to obtain chirped OFCs even without using any rf generator. In this case the OFC parameters depend on the AO cell material, electric feedback gain, optical loss, and optical gain.

The Doppler effect of relative motion-induced frequency shift as an interesting fundamental wave phenomenon draws significant research interest in many applied aspects of physics and engineering. Photonic settings represent an important class of platforms to observe and manipulate this effect. Here, an anomalous Doppler effect via dynamic index tuning in a photonic crystal (PhC) is proposed and investigated theoretically by considering the guided reflection of light from a moving front at near the speed of light. A virtual waveguide constructed in a square lattice PhC slab utilizing the self-collimation effect is proposed, and the moving equivalent reflector is realized by photonic band shift induced by a pump light for changing the refractive index dynamically. The anomalous Doppler shift occurs at multiple wavelengths, which depends on the Bloch nature of this photonic crystal and its band structure. Moreover, another kind of small spectral shift caused by adiabatic wavelength conversion is also observed. This nonstationary procedure is studied combining the full-wave numerical simulation and wavelet transform analysis. This work sheds light on the emergence of anomalous Doppler effect and wavelength conversion via dynamic index tuning in photonic crystals and can be important for manipulating such effects in practical photonic devices.

We study the dissipative preparation of pure non-Gaussian states of a target mode which is coupled both linearly and quadratically to an auxiliary damped mode. We show that any pure state achieved independently of the initial condition is either (i) a cubic phase state, namely, a state given by the action of a non-Gaussian (cubic) unitary on a squeezed vacuum or (ii) a (squeezed and displaced) finite superposition of Fock states. Which of the two states is realized depends on whether the transformation induced by the engineered reservoir on the target mode is canonical (i) or not (ii). We discuss how to prepare these states in an optomechanical cavity driven with multiple control lasers, by tuning the relative strengths and phases of the drives. Relevant examples in (ii) include the stabilization of mechanical Schrödinger-cat-like states or Fock-type states of any order. Our analysis is entirely analytical: it extends reservoir engineering to the non-Gaussian regime and enables the preparation of novel mechanical states with negative Wigner function.

Analysis indicates that tunable spin-orbit coupling (SOC) can be introduced into the paraxial Schrödinger-type equation for a spinor image traveling through a rotating electromagnetically induced transparency (EIT) medium. As a fundamental example, we show that, due to a radial gradient of large group refractive index, the SOC can lead to spatial separation of the oppositely oriented spinor states in the probe image, mimicking the fine-structure splitting of a spin-$\frac{1}{2}$ quantum harmonic oscillator described by the Pauli equation. Such a result enables a direct manipulation and visualization of spin-orbit physics by all-optical means based on EIT slow-light media. Possible experimental implementations of our model with ultracold atoms are discussed.

A heralded single-photon source (HSPS) with competitive single-photon purity and indistinguishability has become an essential resource for photonic quantum information processing. Here we propose a theoretical regime to enhance heralded single-photon generation by multiplexing the degree of freedom of orbital angular momentum (OAM) of down-converted entangled photon pairs emitted from a nonlinear crystal. Experimentally, a proof-of-principle experiment is performed through multiplexing three OAM modes. We achieve a $47\%$ enhancement in the single-photon rate. A second-order autocorrelation function $g^{\left(2\right)}\left(0\right)<0.5$ ensures our multiplexed heralded single photons with good single-photon purity. We further indicate that an OAM-multiplexed HSPS with high quality can be constructed by generating higher-dimensional entangled states and sorting them with high efficiency in OAM space. Our method may approach a good HSPS with the deterministic property.

We show that in the exact solution describing the resonant scattering of a plane monochromatic electromagnetic wave by a lossless spherical or cylindrical particle of radius $R$, the scattering coefficients in the multipolar expansion have the generic singularities at vanishing $R$ and certain values of the particle permittivity. At these singularities, the linewidths of the corresponding resonances turn to zero, while the partial cross sections do not have definite limits and may take any value from a certain domain. The value depends on the trajectory along which one approaches the singularities in the plane of the problem parameters. To resolve the singularity it is required to go beyond the commonly used monochromatic approximation, to take into account the finite linewidth of the incident wave, and then to perform the correct sequence of limit transitions, while the straightforward application of the monochromatic approximation may give rise to erroneous results. The effects of finite dissipation are discussed too. Our study may be important for a broad class of resonant wave scattering phenomena associated with high-$Q$ resonances, in particular to the problem of the incident wave interaction with the bound states in the continuum.

In a recent paper [I. Brevik, Phys. Rev. A 98, 043847 (2018)], Brevik analyzed the experiment by Kundu et al. [A. Kundu et al., Sci. Rep. 7, 42538 (2017)] reporting deformation of a graphene oxide (GO) film after it has been irradiated by a laser beam. The two-dimensional atomic force microscope (AFM) line scanning of the deformation of the GO film after switching off the laser beam takes by far too much time for any elastic changes to remain in the AFM scans. Thus, the changes in the GO film are irreversible and the optoelastic model used by Brevik is not applicable. The rough estimates of the kinetic energy and displacement of atoms by the optical force of a light pulse calculated by Brevik are correct, but in making a comparison with the corresponding high-precision results for the kinetic energy and displacement of atoms in our work [M. Partanen et al., Phys. Rev. A 95, 063850 (2017)], the kinetic energy of atoms is confused with their rest energy. The atoms and their masses are displaced forward by the field and their displaced rest energies give rise to an energy flux. The difference of arguments between ours and Brevik's culminates on the question whether the flux of rest energy caused by the displacement of the medium moving with light should be included in the total energy flux. We also show that the four-divergence of the stress-energy-momentum tensor of the mass polariton theory of light is zero.

The Comment of Partanen and Tulkki [Partanen and Tulkki, Phys. Rev. A 100, 017801 (2019)] claims that my criticism [Brevik, Phys. Rev. A 98, 043847 (2018)] of the earlier paper of Partanen et al. [Partanen et al., Phys. Rev. A 95, 063850 (2017)] was incorrect. Now, there are essentially three points involved here: (i) The first one regards the physical interpretation of the radiation pressure experiment of Kundu et al. [Kundu et al., Sci. Rep. 7, 42538 (2017)]. My mathematical analysis of this situation was certainly simplistic, but yet it was able to illustrate the main property of the experiment, namely that it showed the action from the radiation forces on the dielectric boundaries, and from the Lorentz force in the interior, but it did not have any relationship to the Abraham-Minkowski momentum problem as was originally stated by the investigators. (ii) The second and most important point was my emphasis on the fact that in an electromagnetic pulse in a medium, there cannot be an accompanying mechanical energy density of the same order of magnitude as the electromagnetic energy density itself. The electromagnetic wave carries with it a mechanical momentum, but not a mechanical energy (the latter being of second order in the particle velocity). Here, I illustrate this point by a simple numerical analysis. (iii) When going to a relativistic formulation of the electromagnetic theory in matter, care must be taken to secure that fundamental conditions from field theory are satisfied. In particular, one cannot in general take the electromagnetic total energy and momentum of a radiation pulse to constitute a four-vector; such a property holds only if the electromagnetic energy-momentum tensor is divergence free. For the Minkowski tensor, this condition is satisfied, whereas for the Abraham tensor, it is not. As a conclusion, my earlier standpoint on the Abraham-Minkowski problem remains unchanged.

The production of events in quantum theory, that is, of outcomes to which a probability can be associated, is inconsistent with a unitary evolution for systems in arbitrary initial states. In particular, within unitary quantum mechanics, there exist global protocols that allow verifying that no definite event occurs. Instead, states that start in a coherent superposition over possible outcomes always remain as a superposition. We show that when taking into account fundamental errors in measuring length and time intervals, which have been put forward as a consequence of a conjunction of quantum mechanical and general relativity arguments, there are instances in which such global protocols no longer allow one to distinguish whether or not the state is in a superposition. All predictions become identical as if one of the outcomes occurs, with probability determined by the state. We use this as a criteria to define events, as put forward in the Montevideo interpretation of quantum mechanics. We analyze in detail the occurrence of events in the paradigmatic case of a particle in a superposition of two different locations. We argue that our approach provides a consistent (C) single-world (S) picture of the universe, thus allowing an economical way out of the limitations imposed by a recent theorem by Frauchiger and Renner showing that having a self-consistent single-world description of the universe is incompatible with quantum theory. In fact, the main observation of this paper may be stated as follows: If quantum mechanics is extended to include gravitational effects to a quantum-gravitational (QG) theory, then QG, S, and C are satisfied.

Wheeler's delayed-choice experiment investigates the indeterminacy of wave-particle duality and the role played by the measurement apparatus in quantum theory. Due to the inconsistency with classical physics, it has been generally believed that it is not possible to reproduce the delayed-choice experiment using a hidden-variable theory. Recently, it was shown that Wheeler's delayed-choice experiment can be explained by a causal two-dimensional hidden-variable theory [R. Chaves, G. B. Lemos, and J. Pienaar, Phys. Rev. Lett. 120, 190401 (2018)]. Here, we carry out a delayed-choice experiment by using photon states that are spacelike separated and demonstrate that the experiment is consistent with quantum theory but inconsistent with any causal two-dimensional hidden-variable theory in a device-independent manner. This demonstrates that causality can be used to test quantum theory in a complementary way to the Bell and Leggett-Garg tests.

Wave-particle duality constitutes one of the most intriguing features in quantum physics. A well-known gedanken experiment that provides evidence for this is Wheeler's delayed-choice experiment based on a Mach-Zehnder interferometer [J. A. Wheeler, in Mathematical Foundations of Quantum Theory, edited by A. R. Marlow (Academic, New York, 1978), pp. 9–48; in Quantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, 1984), pp. 182–213]. Many different versions of delayed-choice experiments have been conducted with both classical and quantum detecting devices. Recently, it was proposed that the delayed-choice experiment could be devised from the perspective of a device-independent prepare-and-measure scenario [R. Chaves et al., Causal Modeling the Delayed-Choice Experiment, Phys. Rev. Lett. 120, 190401 (2018)]. In our work, we experimentally realize this modified version with a deterministic single-photon source and examine the wave-particle objective in a causal-modeled scheme without the assistance of entanglement, which is achieved by violating the dimension-witness inequalities. Our experiment also provides an intriguing perspective and exhibits the benefits of studying quantum theory from the casual model point of view.

We investigate the discrimination of two candidates for an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing to distinguishing two Hamiltonians [A. H. Kiilerich and K. Mølmer, Phys. Rev. A 98, 022103 (2018)]. Based on the measurement output and stochastic master equation, temporal evolutions of posterior probabilities of two hypotheses are given by Bayes' formula. The Bayes criterion is presented by the likelihood ratio conditioned on the outcome of measurements. Differently from the calculation method based on the maximum a posteriori criterion, the Bayes-criterion-based method for calculating the average probability of making errors is more suitable and efficient in the general situation of binary discrimination. Finally, an example of distinguishing two candidate Hamiltonians is given and the running times for calculating the average probability of error under the Bayes criterion and the maximum a posteriori criterion are compared to illustrate the feasibility of hypothesis testing for quickly distinguishing two candidates for the parameter to be estimated.

In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven notoriously difficult due to the noncommutativity of observables. Motivated by recent progress in the experimental control of quantum systems, we propose a framework for the implementation of quantum constraints based on the idea of work protocols, which are dynamically engineered to enforce the constraints. As a proof of principle, we consider the dynamical mean-field approach of the many-body quantum spherical model, which takes the form of a quantum harmonic oscillator plus constraints on the first and second moments of one of its quadratures. The constraints of the model are implemented by the combination of two work protocols, coupling together the first and second moments of the quadrature operators. We find that such constraints affect the equations of motion in a highly nontrivial way, inducing nonlinear behavior and even classical chaos. Interestingly, Gaussianity is preserved at all times. A discussion concerning the robustness of this approach to possible experimental errors is also presented.

We propose a method for synchronous measurement of inertial rotation and magnetic field based on the nuclear spin magnetization of the ${}^{21}\mathrm{Ne}$ self-compensation magnetic field and enhancement of the rotation signal in a $\mathrm{K}\text{−}\mathrm{Rb}{\text{−}}^{21}\mathrm{Ne}$ comagnetometer. Under different working temperature conditions, we study the operation of the system as a self-compensation comagnetometer. Using the formulated Bloch equations, the magnetic field and inertial rotation are simultaneously measured by the transient and steady responses in a single probe beam configuration. The measurement of earth rotation projection on the horizontal plane from $-5.59\times {10}^{-5}$ to $5.59\times {10}^{-5}\mathrm{rad}/\mathrm{s}$ based on the steady signal and measurement of the magnetic field ranging from 0.016 to 1.760 nT based on the transient signal have been presented. Furthermore, the simultaneous measurements of angular velocity varying from $-4.01\times {10}^{-5}$ to $5.37\times {10}^{-5}\mathrm{rad}/\mathrm{s}$ with an accuracy of $2\times {10}^{-5}\mathrm{rad}/\mathrm{s}$ and a magnetic field changing from 0.048 to 0.128 nT with an accuracy of 0.01 nT have also been demonstrated.

We introduce and study the $l_1$-norm coherence of assistance both theoretically and operationally. We first provide an upper bound for the $l_1$-norm coherence of assistance and show a necessary and sufficient condition for the saturation of the upper bound. For two- and three-dimensional quantum states, the analytical expression of the $l_1$-norm coherence of assistance is given. Operationally, the mixed quantum coherence can always be increased with the help of another party's local measurement and one way classical communication since the $l_1$-norm coherence of assistance, as well as the relative-entropy coherence of assistance, are shown to be strictly larger than the original coherence. The relation between the $l_1$-norm coherence of assistance and entanglement is revealed. Finally, a comparison between the $l_1$-norm coherence of assistance and the relative-entropy coherence of assistance is made.

The transmission coefficient of the free-space channel is fluctuating due to the occurrence of random fluctuations of the refractive index and noise. The Gaussian-modulated quantum states of light may degrade into a non-Gaussian mixture at a certain probability after being transmitted through the free-space channel. In such a situation, Eve can apply an entanglement-distillation attack to steal secret information without it being revealed if Alice and Bob regard the practical fluctuation losses as constant. However, the entanglement-distillation attack is available only when the transmitting states are a non-Gaussian mixture; otherwise, Eve will expose herself. Exploiting this loophole and considering the limitations of the attack, we enhance Eve's eavesdropping ability by integrating a machine-learning technique with the entanglement-distillation attack. With the help of convolutional neural network (CNN, one of the most popular machine leaning tools), Eve can choose the best opportunity to launch the entanglement-distillation attack. Therefore, Eve has a chance to bias the estimation of the parameters by improving the entanglement resource of the mixed states, which allows Eve to render the final keys shared between the legitimate parties insecure. Our proposed CNN-based entanglement-distillation attack does not require additional resources and can be implemented using simple means based on the present technologies.