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Physical systems that display competitive non-linear dynamics have played a key role in the development of mathematical models of Nature. Important examples include predator-prey models in ecology, biology, consumer-resource models in economics, and reaction-diffusion equations in chemical reactions. However, as real world systems are embedded in complex environments, where it is difficult or even impossible to control external parameters, quantitative comparison between measurements and simple models remains challenging. This motivates the search for competitive dynamics in isolated physical systems, with precise control. An ideal candidate is laser excitation in dilute atomic ensembles. For example, atoms in highly-excited Rydberg states display rich many-body dynamics including ergodicity breaking, synchronisation and time crystals. Here, we demonstrate predator-prey dynamics by laser excitation and ionisation of Rydberg atoms in a room temperature vapour cell. Ionisation of excited atoms produce electric fields that suppress further excitation. This starves the ionisation process of resource, giving rise to predator-prey dynamics. By comparing our results to the Lotka-Volterra model, we demonstrate that as well applications in non-linear dynamics, our experiment has applications in metrology, and remote sensing of localised plasmas., Comment: 16 pages, 7 figures

Recent years have witnessed the use of pervasive wireless signals (e.g., Wi-Fi, RFID, and mmWave) for sensing purposes. Due to its non-intrusive characteristic, wireless sensing plays an important role in various intelligent sensing applications. However, limited by the inherent thermal noise of RF transceivers, the sensing granularity of existing wireless sensing systems are still coarse, limiting their adoption for fine-grained sensing applications. In this paper, we introduce the quantum receiver, which does not contain traditional electronic components such as mixers, amplifiers, and analog-to-digital converters (ADCs) to wireless sensing systems, significantly reducing the source of thermal noise. By taking non-intrusive liquid recognition as an application example, we show the superior performance of quantum wireless sensing. By leveraging the unique property of quantum receiver, we propose a novel double-ratio method to address several well-known challenges in liquid recognition, eliminating the effect of liquid volume, device-target distance and container. We implement the quantum sensing prototype and evaluate the liquid recognition performance comprehensively. The results show that our system is able to recognize 17 commonly seen liquids, including very similar ones~(e.g., Pepsi and Coke) at an accuracy higher than 99.9\%. For milk expiration monitoring, our system is able to achieve an accuracy of 99.0\% for pH value measurements at a granularity of 0.1, which is much finer than that required for expiration monitoring., Comment: 7 pages, 6 figures

We demonstrate the continuous broadband microwave receivers based on AC Stark shifts and Floquet States of Rydberg levels in a cesium atomic vapor cell. The resonant transition frequency of two adjacent Rydberg states 78$S_{1/2}$ and 78$P_{1/2}$ is tuned based on AC Stark effect of 70~MHz Radio frequency (RF) field that is applied outside the vapor cell. Meanwhile, the Rydberg states also exhibit Floquet even-order sidebands that are used to extend the bandwidths further. We achieve microwave electric field measurements over 1.172~GHz of continuous frequency range. The sensitivity of the Rydberg receiver with heterodyne technique in the absence of RF field is 280.2~nVcm$^{-1}$Hz$^{-1/2}$, while it is dramatically decreased with tuning the resonant transition frequency in the presence of RF field. Surprisingly, the sensitivity can be greatly improved if the microwave field couples the Floquet sideband transition. The achieving of continuous frequency and high sensitivity microwave detection will promote the application of Rydberg receiver in the radar technique and wireless communication., Comment: 5 pages, 4 figures

Efficient electric manipulation of valley degrees of freedom is critical and challenging for the advancement of valley-based information science and technology. We put forth an electrical scheme, based on a two-band Dirac model, that can switch the fully valley-polarized photocurrent between K and K' valleys using the circular bulk electro-photovoltaic effect. This is accomplished by applying an out-of-plane electric field to the two-dimensional valley materials, which enables continuous tuning of the Berry curvature and its sign flip. We found that the switch of the fully valley-polarized photocurrent is directly tied to the sign change of Berry curvature, which accompanies a topological phase transition, for instance, the quantum spin Hall effect and the quantum valley Hall effect. This scheme has been confirmed in monolayer BiAsI2 and germanene through first-principles calculations. Our paper offers a promising strategy for the development of a volatile valley-addressable memory device and could inspire further research in this area.

Topological dislocation modes resulting from the interplay between spatial dislocations and momentum-space topology have recently attracted significant interest. Here, we theoretically and experimentally demonstrate time-dislocation topological modes which are induced by the interplay between temporal dislocations and Floquet-band topology. By utilizing an extra physical dimension to represent the frequency-space lattice, we implement a two-dimensional Floquet higher-order topological phase and observe time-dislocation induced $\pi$-mode topological corner modes in a three-dimensional circuit metamaterial. Intriguingly, the realized time-dislocation topological modes exhibit spatial localization at the temporal dislocation, despite homogeneous in-plane lattice couplings across it. Our study opens a new avenue to explore the topological phenomena enabled by the interplay between real-space, time-space and momentum-space topology., Comment: 9 pages, 4 figures

Local density of states (LDOS) is emerging as powerful means of exploring synthetic topological phases. However, the current LDOS detection method remains rare and merely works for static situations. Here, we introduce a generic dynamical method to detect both the static and Floquet LDOS, based on an elegant connection between dynamics of chiral density and local spectral densities. Moreover, we find that the Floquet LDOS allows to measure out Floquet quasienergy spectra and identify topological $\pi$ modes. As an example, we demonstrate that both the static and Floquet higher-order topological phase can be universally identified via LDOS detection, regardless of whether the topological corner modes are in energy gaps, bands or continue energy spectra without bandgaps. Our study opens a new avenue utilizing dynamics to detect topological spectral densities and provides a universal approach of identifying static and Floquet topological phases.

Topological phases of ultracold atoms recently have been intensively studied both in optical superlattices and Raman lattices. However, the topological features induced by the interplay between such two lattices remain largely unexplored. Here, we present an optical Raman superlattice system that incorporates an optical superlattice and a Raman superlattice. The Raman superlattice presented here supports tunable dimerized spin-orbit couplings and staggered on-site spin flips. We find that such system respects a spin-rotation symmetry and has much richer topological properties. Specifically, we show that various topological phases could emerge in the optical Raman superlattice, such as four different chiral topological insulator phases and two different quantum spin Hall insulator phases, identified by spin winding and spin Chern numbers respectively. We also demonstrate that the spin-dependent topological invariants could be directly measured by quench dynamics.

Ultracold atoms trapped in optical superlattices provide a simple platform for realizing the seminal Aubry-Andr\'{e}-Harper (AAH) model. However, the periodic modulations on the nearest-neighbour hoppings have been ignored in this model. In this paper, we find that optical superlattice system actually can be approximately described by a generalized AAH model in the case of $V_1\gg V_2$, with periodic modulations on both on-site energies and nearest-neighbour hoppings, supporting much richer topological properties that are absent in the standard AAH model. Specifically, by calculating Chern numbers and topological edge states, we show that the generalized AAH model possesses multifarious topological phases and topological phase transitions, as compared to the standard AAH model only supporting a single topological phase. Our findings can open up more opportunities for using optical superlattices to study topological and localization physics.

The laser's frequency noise is crucial to the sensitivity of quantum sensors. Two commonly used methods to suppress the laser's frequency noise are locking the laser to an atomic transition by the lock-in technique or to an ultra-low thermal expansion (ULE) glass cavity by the PDH technique. The former cannot suppress rapidly changing frequency noise and hardly meets the needs; the latter has powerful performance but a heightened cost. The lack of high-performance and low-cost laser noise suppression methods dramatically limits the practical application of quantum sensors. This work demonstrates that, in many quantum sensing applications such as the Rydberg atomic superheterodyne receiver, by cascade locking the laser to both the atomic transition and a low-cost (LC) cavity, the same performance as locking to the ULE cavity can be achieved. This work is significant in promoting the practical application of quantum sensors.

Time crystals, as temporal analogs of space crystals, manifest as stable and periodic behavior that breaks time translation symmetry. In an open quantum system, many-body interaction subjected to dissipation allows one to develop the time crystalline order in an unprecedented way, as refer to dissipative time crystal. Here we report the observation of a time crystal comb in the continuously driven-dissipative and strongly interacting Rydberg thermal gas, in which continuous time crystal and sub-harmonics of limit cycles as well as the high-order harmonic oscillation phases are observed in the same system by manipulating the Rydberg excitation. Our work provides new ways to explore the nonequilibrium phases of matter in open systems. Such time crystals with persistent oscillation rooted in emergent quantum correlations, may emerge as a ubiquitous tool in quantum metrology, for instance, continuous sensing and parameter estimation surpassing the standard quantum limit., Comment: 17 pages, 5 figures

Entanglement plays a crucial role in proposals for quantum metrology, yet demonstrating quantum enhancement in sensing with sustained spin entanglement remains a challenging endeavor. Here, we combine optical pumping and continuous quantum nondemolition measurements to achieve a sustained spin squeezed state with $\bm{4 \times 10^{10}}$ hot atoms. A metrologically relevant steady state squeezing of $\bm{-3.23 \pm 0.24}$ dB using prediction and retrodiction is maintained for about one day. We employ the system to track different types of continuous time-fluctuating magnetic fields, where we construct deep learning models to decode the measurement records from the optical signals. Quantum enhancement due to the steady spin squeezing is verified in our atomic magnetometer. These results represent important progress towards applying long-lived quantum entanglement resources in realistic settings.

We present enhanced sensing of radio frequency (RF) electric fields (E-fields) by the combined polarizability of Rydberg atoms and the optimized local oscillator (LO) fields of supergheterodyne receiving. Our modified theoretical model reveals the dependencies of sensitivity of E-field amplitude measurement on the polarizability of Rydberg states and the strength of the LO RF field. The enhanced sensitivity of megahertz(MHz) E-field are demonstrated at an optimal LO field for three different Rydberg states $\rm 43D_{5/2}$, $\rm 60S_{1/2}$, and $\rm 90S_{1/2}$. The sensitivity of 63 MHz for the $\rm 90S_{1/2}$ state reaches 0.96 $\mu \rm V/cm/\sqrt{Hz}$ that is about an order of magnitude higher than those already published. This result closely approaches the theoretical sensitivity limit of RF dipole antennas, and indicates the potential for breaking the limit in measuring sub-MHz E-fields. This atomic sensor based on Rydberg Stark effect with heterodyne technique is expected to boost an alternative solution to electric dipole antennas.

Microwave electric field sensing is of importance for a wide range of applications in areas of remote sensing, radar astronomy and communications. Over the past decade, Rydberg atoms, owing to their exaggerated response to microwave electric fields, plentiful optional energy levels and integratable preparation methods, have been used in ultra-sensitive, wide broadband, traceable, stealthy microwave electric field sensing. This review first introduces the basic concept of quantum sensing, properties of Rydberg atoms and principles of quantum sensing of microwave electric fields with Rydberg atoms. Then an overview of this very active research direction is gradually expanded, covering progresses of sensitivity and bandwidth in Rydberg atoms based icrowavesensing,uperheterodyne quantum sensing with microwave-dressed Rydberg atoms, quantum-enhanced sensing of microwave electric field, recent advanced quantum measurement systems and approaches to further improve the performance of microwave electric field sensing. Finally, a brief outlook on future development directions is discussed.

We investigate the magnetic order and related strongly-correlated effects in an one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix-renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our work enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds., Comment: 9 pages, 12 figures

We investigate the response bandwidth of a superheterodyne Rydberg receiver at a room-temperature vapor cell, and present an architecture of multi-channel lasers excitation to increase the response bandwidth and keep sensitivity, simultaneously. Two microwave fields, denoted as a local oscillator (LO) $E_{LO}$ and a signal field $E_{Sig}$, couple two Rydberg states transition of $|52D_{5/2}\rangle\to |53P_{3/2}\rangle$. In the presence of the LO field, the frequency difference between two fields can be read out as an intermediate frequency (IF) signal using Rydberg electromagnetically induced transparency (EIT) spectroscopy. The bandwidth of the Rydberg receiver is obtained by measuring the output power of IF signal versus the frequency difference between two fields. The bandwidth dependence on the Rabi frequency of excitation lasers is presented, which shows the bandwidth decrease with the probe Rabi frequency, while it is quadratic dependence on the coupling Rabi frequency. Meanwhile, we investigate the effect of probe laser waist on the bandwidth, showing that the bandwidth is inversely proportional to the laser waist. We achieve a maximum response bandwidth of the receiver about 6.8~MHz. Finally, we design an architecture of multi-channel lasers excitation for increasing the response and keeping the sensitivity, simultaneously. Our work has the potential to extend the applications of Rydberg atoms in communications.

Long-range $(n+2)D_{5/2} \, nF_J$ Rydberg macro-dimers are observed in an ultracold cesium Rydberg gas for $39\leq n\leq48$. Strong dipolar "flip" ($\langle D_{5/2} F_{5/2} \vert \hat{V}_{dd} \vert F_{5/2} D_{5/2} \rangle$, $\langle D_{5/2} F_{7/2} \vert \hat{V}_{dd} \vert F_{7/2} D_{5/2} \rangle$) and "cross" ($\langle D_{5/2} F_{7/2} \vert \hat{V}_{dd} \vert F_{5/2} D_{5/2} \rangle$) couplings lead to bound, fine-structure-mixed $(n+2)D_{5/2}nF_J$ macro-dimers at energies between the $F_J$ fine-structure levels. The $DF$ macro-dimers are measured by microwave photo-association from optically prepared $[(n+2)D_{5/2}]_2$ Rydberg pair states. Calculated adiabatic potential curves are used to elucidate the underlying physics and to model the $DF$ macro-dimer spectra, with good overall agreement. Microwave photo-association allows Franck-Condon tuning, which we have studied by varying the detuning of a Rydberg-atom excitation laser. Further, in Stark spectroscopy we have measured molecular DC electric polarizabilities that are considerably larger than those of the atomic states. The large molecular polarizabilities may be caused by high-$\ell$ mixing. The observed linewidths of the Stark-shifted molecular lines provide initial evidence for intra-molecular induced-dipole-dipole interaction.

Squeezed spin states and squeezed light are both key resources for quantum metrology and quantum information science, but have largely been separately investigated experimentally so far. Simultaneous generation of these two types of quantum states in one experiment setup is an intriguing goal, and could also enable the study of the analogies and distinctions between atoms and light from a new perspective. Here we report an experimental demonstration of concurrent spin squeezing and light squeezing in a hot atomic ensemble, by judiciously engineering a symmetric atom-light interaction Hamiltonian. The squeezing process is deterministic, yielding fixed squeezing directions for the light field and the collective atomic spin. Furthermore, the squeezed light modes lie in the multiple frequency sidebands of a single spatial mode. This novel type of dual squeezed state may be a promising resource for quantum information science and technologies. Our method can be extended to other quantum platforms such as optomechanical and cold atom systems., Comment: manuscript with 7 pages, 4 figures, supplemental material with 8 pages, 4 figures

In multistate non-Hermitian systems, higher-order exceptional points and exotic phenomena with no analogues in two-level systems arise. A paradigm is the exceptional nexus (EX), a third-order EP as the cusp singularity of exceptional arcs (EAs), that has a hybrid topological nature. Using atomic Bose-Einstein condensates to implement a dissipative three-state system, we experimentally realize an EX within a two-parameter space, despite the absence of symmetry. The engineered dissipation exhibits density dependence due to the collective atomic response to resonant light. Based on extensive analysis of the system's decay dynamics, we demonstrate the formation of an EX from the coalescence of two EAs with distinct geometries. These structures arise from the different roles played by dissipation in the strong coupling limit and quantum Zeno regime. Our work paves the way for exploring higher-order exceptional physics in the many-body setting of ultracold atoms., Comment: accepted by PRL

Governed by the hairy ball theorem, classical antennas with isotropic responses to linearly polarized radio waves are unrealizable. This work shows that the antenna based on Rydberg atoms can theoretically achieve an ideal isotropic response to linearly polarized radio waves; that is, it has zero isotropic deviation. Experimental results of isotropic deviation within 5 dB, and 0.3 dB achievable after optimization, in microwave and terahertz wave measurements support the theory and are at least 15 dB improvement than the classical omnidirectional antenna. Combined with the SI traceable and ultrawideband property, the ideal isotropic response will make radio wave measurement based on atomic antenna much more accurate and reliable than the traditional method. This isotropic atomic antenna is an excellent example of what a tailored quantum sensor can realize, but a classical sensor cannot. It has crucial applications in fields such as radio wave electrometry.

We report on high-resolution microwave spectroscopy of cesium Rydberg $(n+2)D_{5/2}\rightarrow nF_{J}$ transitions in a cold atomic gas. Atoms laser-cooled and trapped in a magnetic-optical trap are prepared in the $D$ Rydberg state using a two-photon laser excitation scheme. A microwave field transmitted into the chamber with a microwave horn drives the Rydberg transitions, which are probed via state selective field ionization. Varying duration and power of the microwave pulse, we observe Fourier side-band spectra as well as damped, on-resonant Rabi oscillations with pulse areas up to $\gtrsim 3 \pi$. Furthermore, we investigate the Zeeman effect of the clearly resolved $nF_J$ fine-structure levels in fields up to 120~mG, where the transition into $nF_{7/2}$ displays a thee-peak Zeeman pattern, while $nF_{5/2}$ shows a two-peak pattern. Our theoretical models explain all observed spectral characteristics, showing good agreement with the experiment. Our measurements provide a pathway for the study of high-angular-momentum Rydberg states, initialization and coherent manipulation of such states, Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the presented methods are suitable for calibration of microwave radiation as well as for nulling and calibration of DC magnetic fields in experimental chambers for cold atoms.

We investigate the quantum phases of bosons in a two-chain-coupled ladder. This bosonic ladder is generally in a biased configuration, meaning that the two chains of the ladder can have dramatically different on-site interactions and potential energies. Adopting the numerical density-matrix renormalization-group method, we analyze the phase transitions in various parameter spaces. We find signatures of both insulating-to-superfluid and superfluid-to-insulating quantum phase transitions as the interchain tunnelling is increased. Interestingly, tunning the interaction to some intermediate values, the system can exhibit a reentrant quantum phase transition between insulating and superfluid phases. We show that for infinite interaction bias, the model is amenable to some analytical treatments, whose prediction about the phase boundary is in great agreement with the numerical results. We finally clarify some critical parameters which separate the system into regimes with distinct phase behaviours, and briefly compare typical properties of the biased and unbiased bosonic ladder systems. Our work enriches the Bose-Hubbard physics., Comment: 10 pages, 7 figures

The topological phase in amorphous systems adds a new dimension to the topological states of matter. Here, we present an interesting phenomenon dubbed the topological Anderson amorphous insulator (TAAI). Anderson disorder can drive topologically trivial amorphous systems with structural disorders into noncrystalline topological insulators. The gap closing and reopening, spin Bott index, robust edge states, and quantized conductance characterize the Anderson disorder-induced nontrivial topology in amorphous systems. More importantly, phase diagrams are given for the topological phase transition (TPT). It is found that amorphous structural disorder and Anderson disorder are synergistic to drive the s-p band inversion of the system and hence the TPT, which is further confirmed by the effective medium theory. Our findings report a disorder-induced topological phenomenon in noncrystalline systems and shed light on the physical understanding of the interplay between the coexistence of two types of disorder effects and topology., Comment: 4 figures

Measurement sensitivity is one of the critical indicators for Rydberg atomic radio receivers. This work quantitatively studies the relationship between the atomic superheterodyne receiver's sensitivity and the number of atoms involved in the measurement. The atom number is changed by adjusting the length of the interaction area. The results show that for the ideal case, the sensitivity of the atomic superheterodyne receiver exhibits a quantum scaling: the amplitude of its output signal is proportional to the atom number, and the amplitude of its read-out noise is proportional to the square root of the atom number. Hence, its sensitivity is inversely proportional to the square root of the atom number. This work also gives a detailed discussion of the properties of transit noise in atomic receivers and the influence of some non-ideal factors on sensitivity scaling. This work is significant in the field of atom-based quantum precision measurements.

Recently, the exciting reentrant localization transition phenomenon was found in a one-dimensional dimerized lattice with staggered quasiperiodic potentials. Usually, long-range hopping is typically important in actual physical systems. In this work, we study the effect of next-nearest neighbor hopping (NNNH) on the reentrant localization phenomenon. Due to the presence of NNNH, the broken chiral symmetry is further enhanced and the localization properties of electron states in the upper and lower bands become quite different. It is found that the reentrant localization can still persist within a range of NNNH both in Hermitian and non-Hermitian cases. Eventually, the reentrant localization disappears as the strength of NNNH increases to some extent, since the increasing NNNH weakens the dimerization of the system and destroys its competition with the quasiperiodic disorder. Our work thus reveals the effect of long-range hopping in the reentrant localization phenomenon and deepens its physical understanding., Comment: 10 figures

Driven by various physical origins, the interesting reentrant phenomena in quantum Hall effect (QHE), quantum anomalous Hall effect (QAHE) and non-Hermitian systems have been discussed recently. Here, we present that the reentrant phenomena of quantum spin Hall effect (QSHE) can be achieved by introducing a uniform exchange field into a topological insulator with a four-band model Hamiltonian. Furthermore, it is found that both time-reversal (TR) symmetry broken QSHE and spin-polarized QAHE can simultaneously be generated in the system with proper exchange field strength by inspecting the corresponding edge states. Through analyzing the energy dependent spin-Chern number $\nu_s$ and transmission in the presence of random disorders, we verify the topological protection and the robustness of induced QSHE and QAHE. Finally, the theoretical realization of reentrant QSHE in a topolectrical circuit is demonstrated. Our work not only extends the reentrant phenomena into the QSHE but also stimulates interest in their realization in different systems., Comment: 4 figures

Topological corner states are exotic topological boundary states that are bounded to zero-dimensional geometry even the dimension of systems is large than one. As an elegant physical correspondence, their numbers are dictated by the bulk topological invariants. So far, all previous realizations of HOTIs are hallmarked by $\mathbb{Z}_2$ topological invariants and therefore have only one corner state at each corner. Here we report an experimental demonstration of $\mathbb{Z}$-class HOTI phases in electric circuits, hosting $N$ corner modes at each single corner structure. By measuring the impedance spectra and distributions, we clearly demonstrate the $\mathbb{Z}$-class HOTI phases, including the zero-energy corner modes and their density distributions. Moreover, we reveal that the local density of states (LDOS) at each corner for $N=4$ are equally distributed at four corner unit cells, prominently differing from $\mathbb{Z}_2$-class case where the LDOS only dominates over one corner unit cell. Our results extend the observation of HOTIs from $\mathbb{Z}_2$ class to $\mathbb{Z}$ class and the coexistence of spatially overlapped large number of corner modes which may enable exotic topological devices that require high degeneracy boundary states., Comment: 8 pages, 4 figures

We present precise measurements of the quantum defects of cesium $n$F$_J$ Rydberg levels. We employ high-precision microwave spectroscopy of $(n+2)\mathrm{D}_{5/2}\rightarrow n\mathrm{F}_{5/2,7/2}$ transitions for $n=45$ to 50 in a cold-atom setup. Cold cesium $(n+2)$D$_{5/2}$ atoms, prepared via two-photon laser excitation, are probed by scanning weak microwave fields interacting with the atoms across the $n\mathrm{F}_{5/2,7/2}$ resonances. Transition spectra are acquired using state-selective electric-field ionization and time-gated ion detection. Transition-frequency intervals are obtained by Lorentzian fits to the measured spectral lines, which have linewidths ranging between 70~kHz and 190~kHz, corresponding to about one to three times the Fourier limit. A comprehensive analysis of relevant line-shift uncertainties and line-broadening effects is conducted. We find quantum defect parameters $\delta_{0}(\mathrm{F}_{5/2})=0.03341537(70)$ and $\delta_{2}(\mathrm{F}_{5/2})=-0.2014(16)$, as well as $\delta_{0}(\mathrm{F}_{7/2})=0.0335646(13)$ and $\delta_{2}(\mathrm{F}_{7/2})=-0.2052(29)$, for $J=5/2$ and $J=7/2$, respectively. Fine structure parameters $A_{FS}$ and $B_{FS}$ for Cs $n{\rm{F}}_J$ are also obtained. Results are discussed in context with previous works, and the significance of the results is discussed.

Since its theoretical sensitivity is limited by quantum noise, radio wave sensing based on Rydberg atoms has the potential to replace its traditional counterparts with higher sensitivity and has developed rapidly in recent years. However, as the most sensitive atomic radio wave sensor, the atomic superheterodyne receiver lacks a detailed noise analysis to pave its way to achieve theoretical sensitivity. In this work, we quantitatively study the noise power spectrum of the atomic receiver versus the number of atoms, where the number of atoms is precisely controlled by changing the diameters of flat-top excitation laser beams. The results show that under the experimental conditions that the diameters of excitation beams are less than or equal to 2 mm and the read-out frequency is larger than 70 kHz, the sensitivity of the atomic receiver is limited only by the quantum noise and, in the other conditions, limited by classical noises. However, the experimental quantum-projection-noise-limited sensitivity this atomic receiver reaches is far from the theoretical sensitivity. This is because all atoms involved in light-atom interaction will contribute to noise, but only a fraction of them participating in the radio wave transition can provide valuable signals. At the same time, the calculation of the theoretical sensitivity considers both the noise and signal are contributed by the same amount of atoms. This work is essential in making the sensitivity of the atomic receiver reach its ultimate limit and is significant in quantum precision measurement.

We study Rydberg electromagnetically induced transparency (EIT) of a cascade three-level atom involving 80$D_{5/2}$ state in a strong interaction regime employing a cesium ultracold cloud. In our experiment, a strong coupling laser couples 6$P_{3/2}$ to 80$D_{5/2}$ transition, while a weak probe, driving 6$S_{1/2}$ to 6$P_{3/2}$ transition, probes the coupling induced EIT signal. At the two-photon resonance, we observe that the EIT transmission decreases slowly with time, which is a signature of interaction induced metastability. The dephasing rate $\gamma_{\rm OD}$ is extracted with optical depth OD = $\gamma_{\rm OD}t$. We find that the optical depth linearly increases with time at onset for a fixed probe incident photon number $R_{\rm in}$ before saturation. The dephasing rate shows a nonlinear dependence on $R_{\rm in}$. The dephasing mechanism is mainly attributed to the strong dipole-dipole interactions, which leads to state transfer from $nD_{5/2}$ to other Rydberg states. We demonstrate that the typical transfer time $\tau_{0(80D)}$ obtained by the state selective field ionization technique is comparable with the decay time of EIT transmission $\tau_{0({\rm EIT})}$. The presented experiment provides a useful tool for investigating the strong nonlinear optical effects and metastable state in Rydberg many-body systems., Comment: 7 pages, 5 figures

We investigate the Meissner currents of interacting bosons subjected to a staggered artificial gauge field in a three-leg ribbon geometry, realized by spin-tensor--momentum coupled spin-1 atoms in a 1D optical lattice. By calculating the current distributions using the state-of-the-art density-matrix renormalization-group method, we find a rich phase diagram containing interesting Meissner and vortex phases, where the currents are mirror symmetric with respect to the {\color{red}middle leg} (i.e., they flow in the same direction on the two boundary legs opposite to that on the middle leg), leading to the spin-tensor type Meissner currents, which is very different from previously observed chiral edge currents under uniform gauge field. The currents are uniform along each leg in the Meissner phase and form vortex-antivortex pairs in the vortex phase. Besides, the system also support a polarized phase that spontaneously breaks the mirror symmetry, whose ground states are degenerate with currents either uniform or forming vortex-antivortex pairs. We also discuss the experimental schemes for probing these phases. Our work provides useful guidance to ongoing experimental research on synthetic flux ribbons and paves the way for exploring novel many-body phenomena therein., Comment: 10 pages, 9 figures

We propose a novel paradigm to vector magnetometry based on machine learning. Unlike conventional schemes where one measured signal explicitly connects to one parameter, here we encode the three-dimensional magnetic-field information in the set of four simultaneously acquired signals, i.e., the oscillating optical rotation signal's harmonics of a frequency modulated laser beam traversing the atomic sample. The map between the recorded signals and the vectorial field information is established through a pre-trained deep neural network. We demonstrate experimentally a single-shot all optical vector atomic magnetometer, with a simple scalar-magnetometer design employing only one elliptically-polarized laser beam and no additional coils. Magnetic field amplitude sensitivities of about 100 $\textrm{fT}/\sqrt{\textrm{Hz}}$ and angular sensitivities of about 100 $\mu rad/\sqrt{\textrm{Hz}}$ (for a magnetic field of about 140 nT) are derived from the neural network. Our approach can reduce the complexity of the architecture of vector magnetometers, and may shed light on the general design of multiparameter sensing., Comment: 8 pages,4 figures

We study a three-level Dicke model in V-configuration under both closed and open conditions. With independently tunable co- and counter-rotating coupling strength of the interaction Hamiltonian, this model is a generalization of the standard Dicke model that features multiple distinct parameter regimes. Based on a mean-field approach and third quantization analysis, it is found that the system exhibits rich quantum phase behaviours, including distinct superradiant fixed points, multi-phase coexistence and limit cycle oscillation. In particular, the cavity dissipation stabilizes a family of inverted spin coherent steady states, whose stability region can be enlarged or reduced by properly tuning the imbalance between the co- and counter-rotating interactions. This property provide a conceptually new scenario to prepare coherent atomic state with high fidelity., Comment: 17 pages, 7 figures

Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of SSH model into four sublattices and thus is dubbed SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from topological insulator to charge density wave (CDW) phase can be identified by analyzing the variations of entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator and CDW phases, respectively. In contrast to interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial/nontrivial phases are shown to be continuous phase transitions. Finally, we {also} show the phase diagram of interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices., Comment: 9 pages, 5 figures

Exploring non-Hermitian phenomenology is an exciting frontier of modern physics. However, the demonstration of a non-Hermitian phenomenon that is quantum in nature has remained elusive. Here, we predict quantum non-Hermitian phenomena: the fractional quantum Zeno (FQZ) effect and FQZ-induced photon antibunching. We consider a quantum optics platform with reservoir engineering, where nonlinear emitters are coupled to a bath of decaying bosonic modes whose own decay rates form band structures. By engineering the dissipation band, the spontaneous emission of emitters can be suppressed by strong dissipation through an algebraic scaling with fractional exponents - the FQZ effect. This fractional scaling originates uniquely from the divergent dissipative density of states near the dissipation band edge, different from the traditional closed-bath context. We find FQZ-induced strong photon antibunching in the steady state of a driven emitter even for weak nonlinearities. Remarkably, we identify that the sub-Poissonian quantum statistics of photons, which has no classical analogs, stems here from the key role of non-Hermiticity. Our setup is experimentally feasible with the techniques used to design lattice models with dissipative couplings., Comment: 16+15 pages, 8+6 figures

Mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. Aubry-Andr\'{e} (AA) model, a paradigm for exploring quantum localization, does not naturally allow mobility edges due to self-duality. Using the momentum-state lattice of quantum gas of Cs atoms to synthesize a nonlinear AA model, we provide experimental evidence for mobility edge induced by interactions. By identifying the extended-to-localized transition of different energy eigenstates, we construct a mobility-edge phase diagram. The location of mobility edge in the low- or high-energy region is tunable via repulsive or attractive interactions. Our observation is in good agreement with the theory, and supports an interpretation of such interaction-induced mobility edge via a generalized AA model. Our work also offers new possibilities to engineer quantum transport and phase transitions in disordered systems., Comment: 7+4 pages, 8 figures

Recent experimental advance in creating dissipative couplings provides a new route for engineering exotic lattice systems and exploring topological dissipation. Using the spatial lattice of atomic spinwaves in a vacuum vapor cell, where purely dissipative couplings arise from diffusion of atoms, we experimentally realize a dissipative version of the Su-Schrieffer-Heeger (SSH) model. We construct the dissipation spectrum of the topological or trivial lattices via electromagnetically-induced-transparency (EIT) spectroscopy. The topological dissipation spectrum is found to exhibit edge modes within a dissipative gap. We validate chiral symmetry of the dissipative SSH couplings, and also probe topological features of the generalized dissipative SSH model. This work paves the way for realizing non-Hermitian topological quantum optics via dissipative couplings., Comment: 6 pages, 4 figures

We demonstrate a continuous frequency electric field measurement based on the far off-resonant AC stark effect in a Rydberg atomic vapor cell. In this configuration, a strong far off-resonant field, denoted as a local oscillator (LO) field, acts as a gain shifting the Rydberg level to a high sensitivity region. An incident weak signal field with a few hundreds of kHz difference from the LO field is mixed with the LO field in Rydberg system to generate an intermediate frequency (IF) signal, which is read out by the Rydberg electromagnetically induced transparency (Rydberg-EIT) spectroscopy. Not like resonant EIT-AT spectra, we realize the electric field measurement of the signal frequency from 2 GHz to 5 GHz using a single Rydberg state. A minimum detectable filed strength is down to 2.31~$\mu$V/cm and a linear dynamic range is over 65~dB. The minimum detectable filed is comparable with a resonant microwave-dressed Rydberg heterodyne receiver using the same system, which is 1.45~$\mu$V/cm. We also show the system has an inherent polarization selectivity feature. Our method can provide a high sensitivity of electric field measurement and be extended to arbitrary frequency measurements., Comment: 5 pages, 4 figures

Realization and manipulation of parity-time (PT) symmetry in multidimensional systems are highly desirable for exploring nontrivial physics and uncovering exotic phenomena in non-Hermitian systems. Here, we report the first experimental observation of partial PT (pPT) symmetry in a cesium atomic gas coupled with laser fields, where a two-dimensional pPT-symmetric optical potential for probe laser beam is created. A transition of the pPT symmetry from an unbroken phase to a broken one is observed through changing the beam-waist ratio of the control and probe laser beams, and the domains of unbroken, broken, and non-pPT phases are also discriminated unambiguously. Moreover, we develop a technique to precisely determine the location of the exceptional point of the pPT symmetry breaking by measuring the asymmetry degree of the probe-beam intensity distribution. The findings reported here pave the way for controlling multidimensional laser beams in non-Hermitian systems via laser-induced atomic coherence, and have potential applications for designing new types of light amplifiers and attenuators, Comment: 6 pages (including references), 4 figures

Different from the chiral edge states, antichiral edge states propagating in the same direction on the opposite edges are theoretically proposed based on the modified Haldane model, which is recently experimentally realized in photonic crystal and electric lattice systems. Here, we instead present that the antichiral edge states in the two-dimensional system can also be achieved based on the original Haldane model by combining two subsystems with the opposite chirality. Most importantly, by stacking these two-dimensional systems into three-dimension, it is found that the copropagating antichiral hinge states localized on the two opposite diagonal hinge cases of the system can be implemented. Interestingly, the location of antichiral hinge states can be tuned via hopping parameters along the third dimension. By investigating the local Chern number/layer Chern number and transmission against random disorders, we confirm that the proposed antichiral edge states and hinge states are topologically protected and robust against disorders. Our proposed model systems are expected to be realized in photonic crystal and electric lattice systems., Comment: 4 figures

The discovery of topologically protected boundary states in topological insulators opens a new avenue toward exploring novel transport phenomena. The one-way feature of boundary states against disorders and impurities prospects great potential in applications of electronic and classical wave devices. Particularly, for the 3D higher-order topological insulators, it can host hinge states, which allow the energy to transport along the hinge channels. However, the hinge states haveonly been observed along a single hinge, and a natural question arises: whether the hinge states can exist simultaneously on all the three independent directions of one sample? Here we theoretically predict and experimentally observe the hinge states on three different directions of a higher-order topological phononic crystal, and demonstrate their robust one-way transport from hinge to hinge. Therefore, 3D topological hinge transport is successfully achieved. The novel sound transport may serve as the basis for acoustic devices of unconventional functions.