We measure angle- and phase-resolved photoelectron momentum distributions of multiphoton ionization of xenon atoms using bicircular laser fields. In our experiment, the continuum electron ring currents with larger orbital angular momentum are prepared by an intense circular polarized laser field at 400 nm and probed with a spatiotemporally overlapped corotating or counter-rotating weak 800 nm laser pulse. Interestingly, a distinct “carpetlike” interference pattern in the direction of laser propagation is observed for the counter-rotating fields, but not for the corotating fields. By analyzing the momentum-resolved photoelectron yield oscillations with respect to the two-color relative phase (phase-of-the-phase spectrum), we observe a distinct angular dependence in the phase-of-the-phase spectrum in the laser propagation plane when the fields are counter-rotating. In contrast, in the corotating geometry, the phase-of-the-phase spectrum in the laser propagation plane displays an isotropic phase profile. We explain that the carpetlike interference in the propagation plane arises from the constructive and destructive interference of the continuum electron ring currents with different magnetic quantum number, which can be controlled by the light helicity.

Electron vortices emerging in the amplitude of the ionization of an atom by an isolated few-cycle, circularly polarized electromagnetic pulse are analyzed in the multiphoton regime. We demonstrate that the number of vortices, as well as their position and strength, are determined by the relative magnitudes of the dynamical amplitude parameters corresponding to sequential photon absorption. It is shown that the phase maps of the ionization amplitude in the momentum space exhibit spiral structures, which are signatures of the Coulomb scattering phases.

The eigenstate thermalization hypothesis describes how isolated many-body quantum systems reach thermal equilibrium. However, quantum many-body scars and Hilbert space fragmentation violate this hypothesis and cause nonthermal behavior. We demonstrate that Hilbert space fragmentation may arise from lattice geometry in a spin-$\frac{1}{2}$ model that conserves the number of domain walls. We generalize a known, one-dimensional, scarred model to larger dimensions and show that this model displays Hilbert space fragmentation on the Vicsek fractal lattice and the two-dimensional lattice. Using Monte Carlo methods, the model is characterized as strongly fragmented on the Vicsek fractal lattice when the number of domain walls is either small or close to the maximal value. On the two-dimensional lattice, the model is strongly fragmented when the density of domain walls is low and weakly fragmented when the density of domain walls is high. Furthermore, we show that the fragmentation persists at a finite density of domain walls in the thermodynamic limit for the Vicsek fractal lattice and the two-dimensional lattice. We also show that the model displays signatures similar to Hilbert space fragmentation on a section of the second-generation hexaflake fractal lattice and a modified two-dimensional lattice. We study the autocorrelation function of local observables and demonstrate that the model displays nonthermal dynamics.

Photon-mediated interaction can be used for simulating complex many-body phenomena with ultracold atoms coupled to electromagnetic modes of an optical resonator. We study theoretically a method of producing controllable interatomic interaction mediated by forward-diffracted photons circulating inside a ring cavity. One example of such a system is the three-mode cavity, where an on-axis mode can coexist with two diffracted sidebands. We demonstrate how the self-organized stripe states of a Bose-Einstein condensate (BEC) occurring in this cavity geometry can exhibit supersolid properties, due to spontaneous breaking of the Hamiltonian's continuous translational symmetry. A numerical study of the collective excitation spectrum of these states demonstrates the existence of massless and finite-gap excitations, which are identified as phase (Goldstone) and amplitude (Higgs) atomic density modes. We further demonstrate how judicious Fourier filtering of intracavity light can be used to engineer the effective atom-atom interaction profile for many cavity modes. The numerical results in this configuration show the existence of droplet-array and single-droplet BEC states for commensurate and incommensurate cavity modes, respectively. Diffractive coupling in a cavity is thereby introduced as an alternative route towards tailoring the photon-mediated interaction of ultracold atoms. Spatial features of the self-organized optical potentials can here be tuned to scales several times larger than the pump laser wavelength such that the corresponding atomic density distributions could be imaged and manipulated using low-numerical-aperture optics. These calculations and insights pave the way towards quantum simulation of exotic nonequilibrium many-body physics with condensates in a cavity.

Herein, we realize a special class of photonic band gaps (PBGs) called angle-driven PBGs in hybrid one-dimensional (1D) photonic crystals (PhCs) composed of alternating anisotropic metamaterial and dielectric layers. At normal incidence, the effective refractive index of the anisotropic metamaterial is designed to be the same as that of the dielectric. Owing to the lack of refractive index contrast, the angle-driven PBG is closed at normal incidence. Under transverse magnetic (TM) polarization, the effective refractive index of the anisotropic metamaterial is angle-dependent since the isofrequency curve (IFC) is an ellipse or a hyperbola. Therefore, the angle-driven PBG under TM polarization is opened at oblique incidence. However, under transverse electric (TE) polarization, the effective refractive index of the anisotropic metamaterial is angle-independent since the IFC is a circle. Therefore, the angle-driven PBG under TE polarization remains closed. In hybrid 1D PhCs composed of alternating elliptical metamaterial and dielectric layers, we realize blueshift angle-driven PBGs under TM polarization. As the incident angle increases, the angle-driven PBG shifts towards shorter wavelengths. Empowered by the blueshift angle-driven PBG, broadband polarization selection and privacy protection can be achieved. In hybrid 1D PhCs composed of alternating hyperbolic metamaterial and dielectric layers, we realize zero-shift angle-driven PBGs under TM polarization. As the incident angle increases, the angle-driven PBG stays almost unchanged. Empowered by the zero-shift angle-driven PBG, wide-angle polarization selection can be achieved. In addition, blueshift and zero-shift angle-driven Tamm plasmon polaritons (TPPs) are realized by placing a metal layer in front of the hybrid 1D PhCs. Our work not only offers an elegant platform to realize angle-driven PBGs and angle-driven TPPs, but also facilitates the development of high-performance polarizers.

We present a detailed theoretical analysis of a peculiar generation of multiple bound states in the continuum (BICs) in two-dimensional periodic arrays of dielectric spheres. They emerge in high-symmetry lattices with the $C_{6v}$ and $C_{4v}$ point groups and involve doubly degenerate quasiguided modes at the $\mathrm{\Gamma }$ point that can couple to external radiation. By tuning a system parameter, the doubly degenerate modes can exhibit accidental BICs at a critical parameter. In the vicinity of the critical parameter, the two bands originating from the degenerate mode exhibit multiple off-$\mathrm{\Gamma }$ BICs. They move and annihilate across the two bands by changing the parameter around the critical one. A ring-like high-$Q$ channel pinned with multiple BICs emerges particularly for the $C_{6v}$ case. Across the critical coupling, the total vorticity of the multiple BICs is conserved. The $\mathit{k}·\mathit{p}$ perturbation theory explains some features of the phenomena reasonably well.

The Dicke model is a staple of theoretical cavity quantum electrodynamics (cavity QED), describing the interaction between an ensemble of atoms and a single radiation mode of an optical cavity. It is studied both quantum mechanically and semiclassically for two-level atoms, and demonstrates a rich variety of dynamics such as phase transitions, phase multistability, and chaos. In this work we explore an open, spin-1 Dicke model with independent co and counterrotating coupling terms as well as a quadratic Zeeman shift enabling control over the atomic energy-level structure. We investigate the stability of operator and moment equations under two approximations and show the system undergoes phase transitions. To compliment these results, we relax the aforementioned approximations and investigate the system semiclassically. We show evidence of phase transitions to steady-state and oscillatory superradiance in this semiclassical model, as well as the emergence of chaotic dynamics. The varied and complex behaviors admitted by the model highlights the need to more rigorously map its dynamics.

We consider the simultaneous control of the relative phase and populations of two-level quantum systems by an external field. We apply a reverse engineering approach, obtaining an analytical expression for the control field depending upon two user-defined functions that dictate the population and the relative phase dynamics. We show that, in general, the prescribed functions for the dynamics cannot be chosen arbitrarily, but still there is plenty of room for choice. We illustrate the reverse engineering technique for several target states using different kinds of functions to specify the system dynamics. We show that by adjusting these dynamical functions, we produce different kinds of control fields. These controls can be easily built, needing, apart from the dynamical function themselves, only their first derivatives. The methodology presented here will certainly find many applications that go beyond simple two-level systems.

We show that both the efficiency and robustness of the topological excitation transmission can be optimized by the phase factor of the long-range hopping in the dimerized lattice. This phenomenon can be explained as the fact that the phase factor in the hopping can widen the minimal energy space around the gap closing point. By redesigning the configuration of long-range hopping, we implement the perfect topological excitation transmission assisted by the phase factor from the left edge to the right edge. We demonstrate that the present optimized topological excitation transmission essentially originates from the phase transition induced by the phase factor, in which the existence of the phase transition leads to the decreasing of the gap closing points. Furthermore, we also investigate the generalized cases with longer-range hopping and find that the optimized topological excitation transmission is determined by the order of long-range hopping. Our investigation shows the significant effect of the phase factor of hopping strength on the topological excitation transmission, which is usually overlooked in relevant work.

We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. The $n$-rotor Clifford group, $\text{U}{\left(1\right)}^{n(n+1)/2}⋊{\text{GL}}_n\left(\mathbb{Z}\right)$, is represented by continuous $\text{U}\left(1\right)$ gates generated by polynomials quadratic in angular momenta, as well as discrete ${\text{GL}}_n\left(\mathbb{Z}\right)$ gates generated by momentum sign-flip and sum gates. Our understanding of this group allows us to establish connections between homological rotor error-correcting codes [Vuillot, Ciani, and Terhal, Commun. Math. Phys. 405, 53 (2024)] and oscillator quantum codes, including Gottesman-Kitaev-Preskill codes and rotation-symmetric bosonic codes. Inspired by homological rotor codes, we provide a systematic construction of multimode rotation-symmetric bosonic codes by making a parallel between oscillator Fock states and rotor states with fixed non-negative angular momentum. This family of homological number-phase codes protects against dephasing and changes in occupation number. Encoding and decoding circuits for these codes can be derived from the corresponding rotor Clifford operations. As a result of independent interest, we show how to nondestructively measure the oscillator phase using conditional occupation-number addition and postselection. We also outline several rotor and oscillator varieties of the Gottesman-Kitaev-Preskill-stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020).].

Variational quantum algorithms, inspired by neural networks, have become a novel approach in quantum computing. However, designing efficient parameterized quantum circuits remains a challenge. Quantum architecture search tackles this by adjusting circuit structures along with gate parameters to automatically discover high-performance circuit structures. In this study, we propose an end-to-end distributed quantum architecture search framework, where we aim to automatically design distributed quantum circuit structures for interconnected quantum processing units with specific qubit connectivity. We devise a circuit generation algorithm which incorporates TeleGate and TeleData methods to enable nonlocal gate implementation across quantum processing units. While taking into account qubit connectivity, we also incorporate qubit assignment from logical to physical qubits within our quantum architecture search framework. A two-stage progressive training-free strategy is employed to evaluate extensive circuit structures without circuit training costs. Through numerical experiments on three VQE tasks, the efficacy and efficiency of our scheme is demonstrated. Our research into discovering efficient structures for distributed quantum circuits is crucial for near-term quantum computing where a single quantum processing unit has a limited number of qubits. Distributed quantum circuits allow for breaking down complex computations into manageable parts that can be processed across multiple quantum processing units.

Ground-based interferometric gravitational-wave detectors are highly precise sensors for weak forces, limited in sensitivity across their detection band by quantum fluctuations of light. Current and future instruments address this limitation by injecting frequency-dependent squeezed vacuum into the detection port, utilizing narrow-band, low-loss optical filter cavities for optimal rotation of the squeezing ellipse at each signal frequency. This study introduces a scheme of such vacuum injection employing the principles of quantum teleportation which works the same as an arbitrary number of filter cavities without additional kilometer-scale infrastructure. We applied this scheme to a detuned signal-recycled Fabry-Pérot–Michelson interferometer, which is the baseline design of the low-frequency detector within the Einstein Telescope xylophone detector. It is shown that our scheme achieves broadband suppression of quantum noise without requiring additional filter cavities or modifications to the core optics of the main interferometer.

We studied the nonradiative double-electron capture in collisions of 95, 146, and 197 MeV/u $\mathrm{X}{\mathrm{e}}^{54+}$ ions with Kr and Xe atoms by measuring the x-ray intensity ratios $I\left(1s\mathcal{n}p\to 1s^2\right)/I\left(\mathcal{n}p\to 1s\right)$ ($\mathcal{n}=2$, 3, and 4) of the resulting $\mathrm{X}{\mathrm{e}}^{52+*}$ and $\mathrm{X}{\mathrm{e}}^{53+*}$ ions. It was found that the double-electron capture becomes more important with decreasing projectile energy, although the single-electron capture is always dominant. At the lower energies of 95 and 146 MeV/u the intensity ratios $I\left(1s2p\to 1s^2\right):I\left(1s3p\to 1s^2\right):I\left(1s4p\to 1s^2\right)$ of $\mathrm{X}{\mathrm{e}}^{52+*}$ ions were found to be nearly identical to the ratios $I\left(2p\to 1s\right):I\left(3p\to 1s\right):I\left(4p\to 1s\right)$ of $\mathrm{X}{\mathrm{e}}^{53+*}$ ions for the Kr target, which implies that the double-electron capture can be regarded as two uncorrelated one-electron capture processes, whereas this feature disappears for the heavier Xe target. It was also found that at 95 and 146 MeV/u the relative double-electron capture intensity for $\mathrm{X}{\mathrm{e}}^{54+}+\mathrm{Xe}$ collisions is significantly larger than that for $\mathrm{X}{\mathrm{e}}^{54+}+\mathrm{Kr}$ collisions. We speculate that the resonant electron transfer plays an important role in the symmetric $\mathrm{X}{\mathrm{e}}^{54+}+\mathrm{Xe}$ collisions and the double-electron capture therein cannot be regarded as two independent one-electron capture events.

When an optical beam passes through a thin slice of a homogeneous material, the change of its phase and amplitude is characterized by the material's linear and nonlinear susceptibility, the latter also known as the hyperpolarizability. The standard method for measuring the nonlinear susceptibility is the $Z$ scan. This widely used method is sometimes applied outside of its range of validity, leading to systematic errors. These errors are illustrated for a two-level system with parameters taken from atomic rubidium. The present paper proposes a method called the phase retrieval of modes to determine the nonlinear susceptibility without an assumption about its functional form, in contrast to both the $Z$-scan method and variants intended to apply in cases of saturation. In brief, a Gaussian beam passes through a thin sample and is detected on three planes in a focal scan. Phase retrieval methods are used to find coefficients of the modes which in turn determine the optical nonlinear susceptibility. Nearly exact recovery of the nonlinear susceptibility is shown numerically in the no-noise case. Additionally, two types of noise are considered: shot noise on the detector and intensity fluctuations of the input.

We propose a scheme for achieving twofold nonreciprocal optomechanically induced transparency (OMIT) in a three-cavity optomechanical system. In this system, an optical microring resonator is evanescently coupled to two microring optomechanical resonators simultaneously, and a beam splitter is utilized to establish two distinct optical paths. By utilizing a strong control laser and a weak probe laser to drive the resonators, a twofold nonreciprocal OMIT phenomenon can be observed. Specifically, the distinct propagation direction of the control laser will result in nonreciprocal OMIT in the two different paths, respectively. In contrast to two-cavity optomechanical systems, the OMIT can be significantly enhanced through indirect coupling, resulting in an $\sim 23.4\%$ increase at the frequency resonance. This unique structure of a three-cavity system renders it an ideal optical single-pole double-throw (SPDT) switch or an ideal optical SPDT-like isolator, which can play an pivotal role in optical communication networks and present exciting opportunities in quantum technologies.

Subtracting accidental coincidences is a common practice in quantum optics experiments. For zero mean Gaussian states, such as a squeezed vacuum, we show that if one removes accidental coincidences, the measurement results are quantitatively the same for both photon coincidences at very low flux and intensity covariances. Consequently, pure quantum effects at the photon level, like interference of photon wave functions or photon bunching, are reproduced in the correlation of fluctuations of macroscopic beams issued from spontaneous down-conversion. This is true both in experiment if the detection resolution is smaller than the coherence cell (size of the mode) and in stochastic simulations based on sampling the Wigner function. We also discuss the limitations of this correspondence, such as Bell inequalities (for which one cannot subtract accidental coincidences), highly multimode situations such as quantum imaging, and higher-order correlations.

We propose a quantum Rabi square model where both the nearest-neighbor and the next-nearest-neighbor photon hopping are allowed among four quantum Rabi systems located at the vertices of a square. By tuning the next-nearest hopping strength, we realize a first-order phase transition between the antiferromagnetic superradiant phase and the frustrated superradiant phase, as well as a second-order phase transition between the normal and the superradiant phases. To understand the emergence of such phases, we show analytically that the effect induced by next-nearest hopping is equivalent to that of an artificial gauge phase. Our findings suggest that the next-nearest-neighbor hopping can serve as an alternative for the gauge phase to realize quantum control in applications of quantum simulation and quantum materials and that our model represents a basic building block for the frustrated $J_1\text{−}{J}_2$ quantum spin model on square lattices.

Optical cat states, the nonclassical superposition of two quasi-classical coherent states, serve as a basis for gedankenexperiments testing quantum physics on mesoscopic scales and are increasingly recognized as a resource for quantum information processing. Here, we report the first experimental realization of optical cat states by adding a photon to a squeezed vacuum state; so far only photon-subtraction protocols have been realized. Photon addition gives us the advantage of using heralded signal photons as experimental triggers, and we can generate cat states at rates exceeding $2.3\times {10}^5$ counts per second. Our most highly squeezed vacuum input state shows −8.9 dB squeezing, but such squeezing entails some degradation—in this case, 15.1 dB antisqueezing. Even so, our approach enables us to synthesize a state with a maximum cat amplitude of $\left|\alpha \right|\approx 1.77$ whose Wigner distribution still shows pronounced negative parts. Our experimental implementation with controlled photon addition demonstrates a powerful and robust building block for advanced quantum state engineering and shows that heralded photon addition can be controlled well and performed at high rates.

Quantum state production and characterization are fundamental elements for many quantum technological applications. In this paper, we studied the generation of polarization quantum states by interacting light with a Kerr medium and the dependency of the outcome on orthogonal polarization seeding. Starting from coherent states produced by Ti:sapphire laser, interaction with a ${}^{87}\mathrm{Rb}$ warm vapor cell led to noise compression of $-5.2\pm 0.5\mathrm{dB}(6.4\pm 0.6\mathrm{dB}$ after correction of the detection quantum efficiency). Experimental characterization of the effect of an orthogonal polarization light seed on squeezing is shown to agree with the theoretical model.