The Fourier transform proves indispensable in the processing of classical information as well as in the quantum domain, where it finds many applications ranging from state reconstruction to prime factorization. An implementation scheme of the $d$-dimensional Fourier transform acting on single photons is known that uses path encoding and requires $O\left(d{log}_{2}d\right)$ optical elements. In this paper, we present an alternative design that uses orbital angular momentum as a carrier of information and needs only $O\left(\sqrt{d}{log}_{2}d\right)$ elements, rendering the path-encoded design inefficient. The advantageous scaling and the fact that our approach uses only conventional optical elements allows for the implementation of a 256-dimensional Fourier transform with existing technology. Improvements of our design as well as explicit setups for low dimensions are also presented.

Twists are defects in a lattice that can be used to perform encoded computations. Three basic types of twists can be introduced in color codes: twists that permute color, charge of anyons, and domino twists that permute the charge label of an anyon with a color label. In this paper, we study a subset these twists from a coding theoretic viewpoint. Specifically, we discuss systematic construction of charge permuting and color permuting twists in color codes. We show that by braiding alone, Clifford gates can be realized in color codes with charge permuting twists. We also discuss implementing single-qubit Clifford gates by a Pauli frame update and CNOT gate by braiding holes around twists in color codes with color permuting twists. Finally, we also discuss implementing a non-Clifford gate by state injection, thus completing the realization of a universal gate set.

An approach to the full wave analysis of the time evolution of the polarization induced in the electromagnetic scattering from dispersive nonmagnetic particles is presented. It is based on the combination of the Hopfield model for the polarization field, the expansion of the polarization field in terms of static longitudinal and transverse modes of the particle, the expansion of the radiation field in terms of transverse wave modes of free space, and the principle of least action. The polarization field is linearly coupled to the electromagnetic field. The losses of the matter are described thorough a linear coupling of the polarization field to a bath of harmonic oscillators with a continuous range of natural frequencies. The set of linear ordinary differential integral equations of convolution type of the overall system is reduced by eliminating both the radiation degrees of freedom and the bath degrees of freedom, and the reduced system of equations is studied. The role played by the radiation field in the coupling between the longitudinal and transverse mode amplitudes of the polarization is described. The principal characteristics of the temporal evolution of the mode amplitudes are found as the particle size varies, including the impulse response. Results are presented for the analytically solvable spherical particle. The proposed approach leads to a general method for the analysis of the temporal evolution of the polarization field induced in dispersive particles of any shape, as well as for the computation of transients and steady states.

We propose a computational ghost imaging (CGI) scheme using customized pink noise speckle pattern illumination. By modulating the power spectrum distribution of the speckles, we generate speckle patterns with a significant positive spatial intensity fluctuation correlation. We experimentally reconstruct images using our synthesized speckle patterns in the presence of a variety of noise sources and pattern distortion and show it is robust to noise environment. The results are compared with the use of standard white noise speckle patterns. We show that our method gives much better image qualities under different types of noise than the traditional way. The proposed scheme promises potential applications in underwater, dynamic, and moving target CGI.

We consider an oscillating micromirror replacing one of the two fixed mirrors of a Mach-Zehnder interferometer. In this ideal optical set-up the quantum oscillator is subjected to the radiation pressure interaction of traveling light waves, no cavity is involved. The aim of this configuration is to show that squeezed light can be generated by pure scattering on a quantum system, without involving a cavity. The squeezing can be detected at the output ports of the interferometer either by direct detection or by measuring the spectrum of the difference current. We use the quantum-stochastic Schrödinger equation (Hudson-Parthasarathy equation) to model the global evolution. Indeed, it can describe the scattering of photons and the resulting radiation pressure interaction on the quantum oscillator. Moreover, it allows us to consider also the interaction with a thermal bath, so that it can describe also the damping of the harmonic oscillator and non-Markovian thermal effects. In this way we have a unitary dynamics giving the evolution of oscillator and fields. The Bose fields of quantum stochastic calculus and the related generalized Weyl operators allow us to describe the whole optical circuit. By working in the Heisenberg picture, the quantum Langevin equations for position and momentum and the output fields arise, which are used to describe the monitoring in continuous time of the light at the output ports. In the case of strong laser and weak radiation pressure interaction highly nonclassical light is produced, and this can be revealed either by direct detection (a negative Mandel $Q$-parameter is found) or by the intensity spectrum of the difference current of two photodetector; in the second case a nearly complete cancellation of the shot noise can be reached. In this last case it appears that the Mach-Zehnder configuration together with the detection of the difference current corresponds to an homodyne detection scheme, so that we can say that the apparatus is measuring the “spectrum of squeezing.”

Based on a recently developed quantum theory for a two-level quantum well screen with a mesoscopic hole [J. Jung and O. Keller, Phys. Rev. A 98, 053825 (2018)] a quantum electrodynamical (QED) theory for diffraction of light from mesoscopic holes is presented. A propagator formalism is used to calculate the super $\mathbf{S}$ matrix, relating the scattered field operators to the incident field operators in the Heisenberg picture. The developed QED formalism accounts for electric dipole (ED), magnetic dipole (MD), and electric quadrupole (EQ) diffraction and it opens up for the analysis of mesoscopic hole diffraction of, e.g., squeezed, entangled, and coherent quantum states of light. The theory is exemplified via a study of Young diffraction from two mesoscopic holes paying particular attention to MD and EQ scattering. The scattering of a single-photon state composed of just two plane-wave components both with wave vectors directed perpendicular to the screen is obtained. It is shown from a detailed calculation of the polarization selection rules that the relative importance of the MD and EQ scattering varies with the scattering angle. The single-photon counting signal is determined as a function of one of the two incoming frequencies, keeping the other fixed near the two-level quantum well (Bohr) resonance.

Recent work [G. David, M. Filoche, and S. Mayboroda, arXiv:1909.10558 [Adv. Math. (to be published)]] has proved the existence of bounds from above and below for the integrated density of states (IDOS) of the Schrödinger operator throughout the spectrum, called the landscape law. These bounds involve dimensional constants whose optimal values are yet to be determined. Here, we investigate the accuracy of the landscape law in 1D and 2D tight-binding Anderson models, with binary or uniform random distributions. We show, in particular, that in 1D, the IDOS can be approximated with high accuracy through a single formula involving a remarkably simple multiplicative energy shift. In 2D, the same idea applies but the prefactor has to be changed between the bottom and top parts of the spectrum.

Recent work has shown that the stress tensor components, such as energy density or pressure, of a quantum field can be subject to large vacuum fluctuations. The energy density or pressure must be averaged in time before the fluctuations can be finite, and the probability of a large fluctuation depends upon the details of the averaging and can be much larger than that predicted by a Gaussian distribution. This paper explores vacuum radiation pressure fluctuation on Rydberg atoms and their possible observable effects. The excitation and de-excitation of a Rydberg atom provide an explicit model for the time averaging of the radiation pressure, as the atomic polarizability becomes time dependent, first increasing and then decreasing again by several orders of magnitude. This switched polarizability can induce large vacuum pressure fluctuations, which can in turn temporarily transfer linear momentum to the atom and cause a transient recoil which might be observable.

We show that a topological pump in a one-dimensional insulator can induce a strictly quantized transport in an auxiliary chain of noninteracting fermions weakly coupled to the first. The transported charge is determined by an integer topological invariant of the fictitious Hamiltonian of the insulator, given by the covariance matrix of single-particle correlations. If the original system consists of noninteracting fermions, this number is identical to the Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) invariant of the original system and thus the coupling induces a transfer of topology to the auxiliary chain. When extended to particles with interactions, for which the TKNN number does not exist, the transported charge in the auxiliary chain defines a topological invariant for the interacting system. In certain cases this invariant agrees with the many-body generalization of the TKNN number introduced by Niu, Thouless, and Wu. We illustrate the topology transfer to the auxiliary system for the Rice-Mele model of noninteracting fermions at half filling and the extended superlattice Bose-Hubbard model at quarter filling. In the latter case the induced charge pump is fractional.

We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide a necessary and sufficient condition for such “quantum-state synchronization,” prove tight lower bounds on the dimension of the ancilla's Hilbert space in two main classes of quantum-state synchronizers, and give an analytical solution for their construction. The functioning of the found quantum-state synchronizer of two qubits is demonstrated experimentally on an IBM quantum computer and we show that the remaining asynchronicity is a sensitive measure of the quantum computer's imperfection.

We investigate the effect of degenerate atomic states on the exciton delocalization of dipole-dipole interacting Rydberg assemblies. Using a frozen gas and regular one-, two-, and three-dimensional lattice arrangements as examples, we see that degeneracies can enhance the delocalization compared to the situation when there is no degeneracy. This enhancement is particularly large in the case of the three-dimensional (3D) random gas, but is absent for 1D arrangements. Using the Zeeman splitting provided by a magnetic field, we controllably lift the degeneracy to study in detail the transition between degenerate and nondegenerate regimes. These observations, although specific to the experimentally clean Rydberg gas, have generic implications for various dipole-interacting systems.

A cold-atom gyroscope as an intrinsic high-precision sensor has, however, one inevitable limitation for its dynamic application lying in the vanishing fringe contrast beyond the rotation-rate limit. Here, we realize the measurement beyond the rotation-rate limit via the tip-tilt mirror compensation technique in a three-pulse cold-atom gyroscope. The contrasts of both fringes at an external rotation rate of ${15}^{\circ }$/s or below are fully recovered to about 35%, nearly the same as that in the static condition. We elucidate theoretically that intact rotation information can still be extracted from the phase output even though the mirror completely counteracts its rotation. Before reaching 50% contrast loss, detailed numerical verification shows a two-orders-of-magnitude extension in the dynamic range for the compensated case compared with that without compensation. Further analysis shows that no reduction of sensitivity up to ${60}^{\circ }$/s is found for our scheme, whereas other schemes have a trade-off between sensitivity and dynamic range. Whereas other schemes have a trade-off between sensitivity and dynamic range, the simulation shows that no reduction to the sensitivity is found for the measurement beyond the rotation-rate limit in our scheme for up to ${60}^{\circ }$/s. These features are especially of major relevance in applications such as inertial sensing and navigation.

We show that nonparaxial polarized light beams propagating in a bulk nonlinear Kerr medium naturally exhibit a coupling between the motional and the polarization degrees of freedom, realizing a spin-orbit-coupled mixture of fluids of light. We investigate the impact of this mechanism on the Bogoliubov modes of the fluid, using a suitable density-phase formalism built upon a linearization of the exact Helmholtz equation. The Bogoliubov spectrum is found to be anisotropic, and features both low-frequency gapless branches and high-frequency gapped ones. We compute the amplitudes of these modes and propose a couple of experimental protocols to study their excitation mechanisms. This allows us to highlight a phenomenon of hybridization between density and spin modes, which is absent in the paraxial description and represents a typical fingerprint of spin-orbit coupling.

We investigate the formation and control of stationary optical patterns in a cold Rydberg atomic gas via double electromagnetically induced transparency. We show that, through the modulational instability of the plane-wave state of a laser field with two polarization components, the system undergoes a spontaneous symmetry breaking and hence the emergence of plentiful self-organized spatial optical structures, which can be manipulated by the ratio between the cross- and self-Kerr nonlinearities, the nonlocality degree of the Kerr nonlinearities, and the populations initially prepared in the two atomic ground states. Interestingly, a crossover from mixture to separation in space (optical phase separation) of the two polarization components occurs when the ratio between the cross- and self-Kerr nonlinearities exceeds a critical value. We also show that the system supports nonlocal two-component spatial optical solitons and vortices when the parameters of the system are selected suitably. The rich diversity and active controllability of the self-organized optical structures reported here provide a way for realizing novel optical patterns and solitons and their structural phase transitions based on Rydberg atomic gases.

We investigate the multiple-Fano-resonance-induced fast and slow light in a hybrid nanomechanical-resonator (NR) system, where a doubly clamped suspended NR with an embedded quantum dot driven by two-tone fields is coupled to another two NRs with different frequencies via the Coulomb interaction. We display the absorption spectra of the weak probe field under different exciton-pump field detuning, and the sharp peaks in the absorption spectra are determined by the interaction between the NRs under the resonance. In the off-resonance, the absorption spectra can exhibit multiple Fano resonance, and the positions of the multiple Fano resonances are related to the interaction between the NRs and the frequencies of the different NRs. Furthermore, the multiple Fano resonances are accompanied by the rapid normal phase dispersion, which indicates the slow- and fast-light effect. We obtain that the group velocity index is tunable by the interaction between the NRs and the detuning, which can reach the conversion between the fast and slow light.

We introduce a two-level atom into a cavity as an ancilla to control the hysteresis of the system where the cavity is described by a driven-dissipative nonlinear Kerr model. We find that the dynamic optical hysteresis can be modulated by changing the atom-cavity coupling strength, and the nonlinearity induced by atom-cavity coupling weakens the Kerr nonlinearity in the weak coupling regime. This leads to the change in the critical point corresponding to the decrease in the hysteresis area. The physics behind the modulation is closely related to the effect of the atom-cavity coupling on the discontinuity of the first nonzero Liouvillian eigenvalue. A relative deviation of the metastable state and target steady state is defined to characterize the relation between the hysteresis and adiabaticity of the system. Taking only two Liouvillian eigenvectors into account in the composite system, we derive an expression for the dependence of the hysteresis area on the sweeping speed and discuss its feature in the slow sweeping limit.

Thermal states of light are widely used in quantum optics for testing of various quantum phenomena. Particularly, they can be utilized for characterization of photon creation and photon annihilation operations. During the last decade the problem of photon subtraction from multimode quantum states has become of much significance. Therefore in this paper we present a technique for statistical parameter estimation of multimode multiphoton-subtracted thermal states of light, which can be used for the multimode photon annihilation test.

We present a theoretical model of a four-photon excitation process to the Rydberg state in thermal atomic vapor where the motion-induced dephasing in the system is eliminated. This is achieved by arranging the four laser beams in a suitable geometry such that the residual wave vector is reduced to zero. The method of adiabatic elimination has been used to reduce the complex five-level system to an effective three-level system to study electromagnetically induced transparency (EIT) where the transition from ground state to second excited state can be considered as the effective probe and second excited state to the Rydberg state as the effective coupling transition. The effect of the blockade phenomenon is observed in the strong interaction regime, where the two atoms are considered to be moving with independent velocities and the system is Doppler averaged using Monte Carlo simulation technique. Also, the dephasing mechanisms in the system are investigated in detail. Though the system is not frozen during the excitation process, a strong blockade effect is still observed similar to the cold atom system. We conclude the paper with a proposal for experimentally investigating the four-photon excitation process to the Rydberg state in thermal rubidium vapor.

Two twin beams with a shared signal beam and separated idler beams are used together with the photon-number-resolving postselection in the signal beam to arrive at two coupled beams with anticorrelations in photon-number fluctuations. Moreover, the beams exhibit the sub-Poissonian photon-number statistics in their marginal distributions under suitable conditions. The postselected fields with the increasing mean photon numbers are reconstructed from the experimental photocount histograms by the maximum likelihood approach. Also a suitable Gaussian fit of both original twin beams and simulation of the postselection process are applied to arrive at the corresponding photon-number distributions. Their nonclassical properties are analyzed by suitable nonclassicality criteria and quantified by the corresponding nonclassicality depths. Determining the appropriate quasidistributions of integrated intensities with negative values, the performance of different non-classicality criteria is judged. Properties of the postselected fields reached both by the used and ideal photon-number-resolved detectors are mutually compared.