Objective.We investigated the competition mechanism between topological order and quasiperiodic disorder in one-dimensional double chain systems.Under the uniform limit,the Hamiltonian of the system maintains chiral symmetry,and the topological phase of the system is related to the band gap,which can be characterized by the winding number.We focus on study-ing the competition and localization transition mechanisms between topological order and quasiperiodic disorder. Methods.With numerical analysis methods,we study the energy spectrum,edge states,topological evolution,and localization properties of the system.For example,we identify topological phase transitions and edge state features from the energy spectrum,and calculate the number of windings to characterize the topological phase.Meanwhile,the phase diagram is determined by cal-culating the mean inverse participation ratio(IPR)and the mean normalized participation ratio(NPR)to distinguish the extended,localized,and critical states of the system.In addition,finite size scaling analysis is conducted to verify reentrant behavior. Results and Discussions.Our research results indicate that there is an intermediate regime in the system,where the extended state and localized state coexist,providing evidence for the emergence of a mobility edge.When this intermediate phase reappears under strong quasiperiodic modulation,it indicates the existence of nonmonotonic reentrant localization phenomenon.In addi-tion,through finite size scaling analysis,it was confirmed that this behavior is an inherent property of the system,rather than a finite size artifact.Therefore,the findings show that the competition between topological protection and disorder induced localiza-tion has generated rich phase structures. Conclusions.This work discusses the competitive physical mechanism between topological order and quasiperiodic disorder in one-dimensional double chain systems,and finds that through their interactions,mobility edges and reentrant local behavior can be generated.Our research findings provide theoretical support for understanding and controlling topological states in quasiperi-odic and quasicrystalline systems.
Objective.The Titanium:sapphire-on-insulator(Ti:SaOI)platform provides a brand new route to realize ultra-broadband tunable integrated lasers.To get high efficiency,the amplifier design must be treated carefully to handle the pump and signal light well.Here,we study the optical characteristics of Ti:SaOI waveguide amplifiers and do a systematic geometric opti-mization.The target is to maximize the optical gain and push down the lasing threshold.This work is expected to offer theoretical supports for fabricating high-performance on-chip Ti:sapphire lasers. Methods.We use the multi-physics finite element method to do the numerical simulation.First,mode field analysis is applied.By doing this,the critical bending radius and the single-mode cutoff condition are found to avoid light leakage.After that,a coupled rate equation model is built.We use it to check how the waveguide width affects two competing parameters:the mode confine-ment factor and the effective mode area.Besides,we also look at the waveguide length to see its effect on both the small-signal gain and the large-signal saturation output during the light propagation. Results and discussions.From the mode analysis,we get the safe boundaries for single-mode working.The rate equation simula-tion shows a clear competition.A narrower width makes the effective mode area smaller,which is good for pump intensity,but it drops the confinement factor at the same time.Balancing these things,the device works best when the width is 1.0 μm and the length is 2.0 cm.Using this exact size,we simulated the gain spectrum covering the 700 to 950 nm band.The result points out a very good broadband amplification.The peak gain is increased by about 16 dB compared to the reported experimental data.This increase proves our model works and shows the great potential of the Ti:SaOI platform for wideband applications. Conclusions.Optimizing the geometry is very useful for improving the amplifier performance.We also set up a semi-analytical model to calculate the laser threshold based on the best parameters we found.The calculation tells us that our new waveguide design can reduce the threshold pump power a lot.In short,the findings in this paper give clear design rules and theoretical help for future experiments on ultra-broadband,low-threshold on-chip Ti:sapphire lasers.
Objective.This work aims to build a theoretical framework to simulate one-dimensional Anderson localization within a periodically driven cavity quantum electrodynamics(QED)system.By using the discrete Fock-space structure found in the Jaynes-Cummings model,we attempt to map the Floquet dynamics of this circuit QED setup onto an effective tight-binding model.This mapping then allows us to control and mimic localization and delocalization behavior by adjusting external driving parameters. Methods.We focus on a resonantly coupled atom and single-mode cavity described by the Jaynes-Cummings Hamiltonian.The atom experiences a periodic sequence of pulses;each Floquet period consists of a rotation followed by Jaynes-Cummings evolu-tion lasting a specific time.The single-period Floquet operator is formed by multiplying the rotation operator and the Jaynes-Cummings evolution operator in sequence.We expand the Floquet eigenstates in the photon-number basis,which leads to coupled recurrence relations for the amplitudes of ground and excited states.Applying a nearest-neighbor closure approximation,we remove the excited-state amplitudes and derive an effective difference equation for the ground-state amplitudes alone.This equa-tion has the form of a 1D inhomogeneous tight-binding model,where the photon number plays the role of lattice sites,parameter-dependent coefficients act like hopping amplitudes connecting neighboring sites,and a site-dependent term functions as an effec-tive potential. Results and Discussions.Numerical simulations were done by iterating the Floquet operator repeatedly,starting from the initial condition with the atom in the ground state and no photons.We tracked the photon-number distribution and the mean photon number as indicators of localization.Over a broad range of rotation angles and interaction durations,the mean photon number tended to remain much smaller than the number of evolution steps,suggesting diffusion suppression typical of Anderson localiza-tion.The probability distributions mostly stayed concentrated at low photon numbers,with dominant population in the lowest pho-ton states.Yet,for certain parameter choices,the behavior shifted,showing delocalized transport where probabilities rapidly spread to higher photon-number states and the mean photon number approached the step count.Overall,this demonstrates that the driven cavity QED system can emulate both localized and delocalized regimes,with control over the transition via pulse parameters. Conclusions.We show that a cavity QED system under periodic pulsing offers a practical platform for simulating 1D Anderson localization in Fock space.The Floquet dynamics naturally map onto a generalized Anderson model with parameter-dependent hopping and effective disorder potentials.Numerical evidence indicates localization prevails over most parameters,but delocaliza-tion emerges in certain regions,allowing dynamical switching through external control.This approach provides a clear theoretical picture,good experimental tunability,and aligns well with current quantum technology.Importantly,the framework can be extended to account for detuning,dissipation,quasi-periodic drives,and multi-qubit setups—opening up possibilities for explor-ing richer localization phenomena,nonequilibrium phase transitions,and many-body Floquet quantum simulation.
Objective.Photons serve as excellent carriers for quantum information.The generation of single photons with high retrieval efficiency facilitates the entanglement distribution rate in long-distance quantum communication.The Duan-Lukin-Cirac-Zoller(DLCZ)protocol based on atomic ensembles not only enables the generation of single photons but also supports the storage of quantum states,which inherently provides a natural advantage in temporal synchronization.In this work,we employ the cavity-enhanced DLCZ protocol to prepare heralded single-photon sources with high retrieval efficiency in an 87Rb cold atomic ensemble. Methods.We first prepare the atoms in the ground state|5S1/2,F=1,m=-1>,and then apply a write pulse to stimulate the sponta-neous Raman scattering process,generating correlated pairs of Stokes photons and atomic spin waves.The successful detection of Stokes photons heralds the creation of atomic spin waves.After a programmable delay,a read pulse is applied to convert the spin waves into anti-Stokes photons,thereby realizing the experimental preparation of heralded single-photon sources.In the experi-ment,we construct a ring cavity around the atomic ensemble to enhance the conversion efficiency from spin waves to single pho-tons.The dependence of the retrieval efficiency on the storage time is measured,and furthermore,the effects of the storage time t and the write excitation rate x on the autocorrelation function of the anti-Stokes photons α are investigated. Results and Discussions.By utilizing cavity-enhanced technology,we increase the conversion efficiency from spin waves to pho-tons to 48％.The autocorrelation function of the prepared optical field is less than 1 when t＜100 μs(x=1％)orx＜8％(t=1 μs),which maintains the anti-bunching effect of single photon sources.In the next step,we aim to further improve the intrinsic retrieval efficiency of single photons by reducing intracavity losses and optimizing the resonance between the anti-Stokes photons and the cavity.Meanwhile,we also plan to improve the practical retrieval efficiency of single photons by designing a high signal-to-noise ratio filtering system and optimizing the fiber coupling efficiency. Conclusions.The results show that we prepare single-photon sources with the intrinsic retrieval efficiency of 48％and the storage lifetime of 100 μs based on the cavity-enhanced DLCZ protocol.This research provides an experimental foundation for the prepa-ration of high-quality single-photon sources based on the DLCZ protocol.
Objective.Ultraviolet radiation is an important component of solar radiation.Ultraviolet radiation has a variety of important applications,including high-resolution light sources,phototherapy,disinfection,sterilization,deodorization,organic decomposition,photocatalysis,gas sensing,optical dialysis dose monitoring,identification of harmful agents,and more.However,at present,metamaterial absorbers are mainly used in microwave,infrared and visible light frequency bands,and there are relatively few absorbers that can cover the 200～400 nm ultraviolet frequency band.Therefore,it is of great significance to carry out the research on the perfect absorber of broadband metamaterials for the ultraviolet band.In addition,our goal in design-ing this ultraviolet absorber is to create a design that can adapt to various environments,has a simple structure,and achieves high absorption efficiency. Methods.In this paper,Nickel(Ni)metal is selected as the absorbing material,and an ultraviolet(UV)absorber is designed based on a simple metal-insulator-metal(MIM)structure.Figure 1 illustrates the unit structure of the MIM-type ultraviolet absorber based on Ni metal,which is a two-dimensional grating absorber arranged horizontally with P periods.The cell structure consists of a dielectric layer of silicon dioxide(SiO2)with a height of h2,grown on an Ni metal substrate with a thickness of h1.On top of this,a Ni metal pattern layer with a thickness of h3 is formed.This pattern layer is composed of two parts:the outer ring and the inner structure.The outer radius is designated as R,while the inner radius is r1.The internal structure consists of a hollow cylinder with a radius of r2,which is etched inside an Ni metal rectangular cuboid that has a height of h3 and a width of L.Additionally,half air cylinders with a radius of r3 are etched on the four sides of the rectangular cuboid.The finite element method(Comsol Multiphysics™ 5.4)is used to simulate the designed absorber.In the calculation,the minimum grid size used isλ/20,and the maximum grid size is λ/5. Results and Discussions.It is found through a large number of numerical simulations that the optimal parameters of the absorber are as follows:unit period P=400 nm,Ni metal substrate height h1=170 nm,SiO2 dielectric height h2=50 nm,upper Ni pattern height h3=180 nm,upper Ni pattern outer radius R=200 nm,inner ring radius r1=185 nm,inner cavity radius r2=40 nm,pattern layer inner pattern outer semicircle radius r3=85 nm.The side length of the internal original cube is L=255 nm.Under the condition of using the optimal parameters,when the angle of incidence is zero,the average absorption of the absorber can reach more than 90％in the wavelength range of 200～400 nm.Notably,the absorption rate exceeds 95％within the 200～250 nm wavelength range,300～325 nm and 375～400 nm.At 220 nm,the absorption reaches a maximum of 98.8％.Across the 200～400 nm spectral band,the absorption rate remains above 90％.Over a broad range of incident angles(0～50o)and wavelengths(200～400 nm),the average absorption rate maintains above 90％.Due to their rotational symmetry,UV absorbers can achieve polarization-insensitive effects. Conclusions.A novel MIM structured UV absorber consisting of Ni metal,SiO2 dielectric,and Ni metal layers was introduced in this article.Through the finite element method analysis,it is found that the structure can efficiently absorb ultraviolet rays with a wavelength of 200～400 nm,with an absorption efficiency of more than 90％,and the structure is not affected by the angle of incidence and polarization.This design simplifies the manufacturing process and improves absorption efficiency,which is expected to be used in areas such as UV detection,protection,and lithography.
Objective.The optical platform of an integrating sphere cold atomic clock is key to determing its engineering feasibility and robustness.Traditional designs with free-space optics are having problems like large volume,hard to align,and prone to envi-ronmental perturbations.This paper aims to develop a fully fiber-integrated optical platform,which avoids free-space paths,so it becomes compact,stable,and easy to align. Methods.The master laser is set to be frequency-locked with the hyperfine transition of the Cs D2 line,using modulation transfer spectroscopy.The slave laser is phase-locked to the master via an optical phase-locked loop,which includes a programmable fre-quency synthesizer(ADF4110)).A central processing unit sequentially sets the frequency difference to 235 MHz(cooling light)),0 MHz(pump light)),and 251 MHz(probe light)).All optical functions,like splitting,combing,switching,attenuation,and beat frequency detection,are done via polarization-maintaing fiber devices,so free-space optics is not need. Results and discussions.The locked master laser has a frequency stability of 7.12×10-9 at 1 second.When the slave laser is locked to produce three frequencies,it has a frequency stability that is superior to 1.3×10-8 at 1 second,and a tunable range of±300 MHz.The probe light has a power stability of 5.6×10-4 at 1 second.By using time-sequenced optical fields,a cold atom absorption dip with a depth of 45％is observed,which corresponds to 3.92×106 trapped atoms.Compared to conventional space-based cold atomic clock optical systems,this platform reduces component count by more than 50％,the alignment time is from weeks to less than 2 hours,and the volume is 85％less. Conclusions.All-fiber architecture provides a compact,reliable,and easily adjustable solution for integrating sphere cold atomic clocks,which can be extended to other quantum precision measurement systems.
Objective.At present,most laser frequency stabilization uses Pound-Drever-Hall(PDH)method which obtains error signals through phase modulation and demodulation,while tilt locking,another method without phase modulation,can avoid the low-frequency error drift caused by residual amplitude modulation,has attracted attention in recent years.As we know,the signal-to-noise ratio of the error signal for locking determines the precision of the laser frequency stabilization.The quantum noise originated from quantum proper-ties of the light would limit the ultimate locking precision.The existing theoretical analysis on tilt locking simply reduces the shot noise to the power noise on the detector,this assumption is valid when PDH is used,only a single laser transverse mode TEM00 is considered and a single quadrant detector is used.However,this assumption can't be made in tilt locking scheme.Considering the quantum noise of laser mode and two-quadrant detector,the actual shot noise expression of tilt locking laser frequency stabilization is calculated based on the basic quantum theory.The microscopic source of the shot noise is explained from the quantum mechanical perspective,which theoreti-cally paves a theoretical pathway for subsequent exploration of squeezed light to exceed the limit of shot noise. Methods.This paper presents a theoretical analysis of tilt locking.Unlike conventional laser locking schemes that operate exclusively on the TEM00 transverse mode,we make the direction of the incident laser and the optical axis of the resonator have a non-zero angle,which will excite the higher-order transverse mode in the cavity.In this way,the higher order mode and the fundamental mode will produce beat frequency,thus obtaining an error signal for frequency stabilization.Here,we use the quantum semi-classical method to write the quantum expression of the transverse electric field,and linearize the annihilation operator of the n-order mode.After considering the impedance matching cavity model,we detect the reflected beam with a two-quadrant detector,and calculate the quantum expression of the error sig-nal of the tilt locking,then the interference signal item and the noise item in the error signal are processed respectively. Results and Discussions.The shot noise of tilt locking from the literature comes from the power noise of the reflected sidebands at resonance.However,our results show that the shot noise of tilt locking comes partly from vacuum noise of the fundamental mode introduced from the cavity output mirror(about 64％),and partly from phase quadrature noise of the input beam's higher order mode(about 36％).In theory,injecting vacuum-squeezed light of the fundamental mode into the reflector M2 port can reduce the shot noise in the ring,and achieve the goal of exceeding the standard shot noise limit by using squeezed light.The error signal which depends on several parameters such as tilt angle,Gouy phase,cavity fineness is analyzed and optimized.The error signal reaches the largest value when the tilt angle is 0.71 times the far field divergence angle,the higher the fineness of the cavity,the less the influence of Gouy phase on the error signal. Conclusions.In this paper,the error signal of tilt locking and the shot noise of laser frequency stabilization are calculated by quan-tum semi-classical method,the influencing factors of signal and noise amplitude are discussed,we optimize the parameters of the error signal and obtain the shot noise spectral density under coherent light conditions.The microscopic source of the shot noise is explained from the quantum mechanical view,the shot noise does not depend on the optical power noise of the input optical field,but on the orthogonal phase noise of the even higher-order mode of the input beam and the fundamental mode vacuum noise introduced from the output.The results are helpful to understand the quantum limit of laser frequency stabilization,and provide a theoretical basis beyond the quantum limit of laser frequency stabilization.
Objective.Quantum metrology uses the principles of quantum mechanics and quantum resources to achieve high-precision measurements of physical quantities.However,in real physical systems,quantum systems inevitably couple with their envi-ronment,and the presence of external noise leads to decoherence,causing the achievable measurement precision to be lower than the ideal case.To restore measurement precision and reduce the impact of noise on the system,we propose two optimization strategies. Methods.(ⅰ)First,by deriving the time evolution equation of the system's off-diagonal elements,we obtain the analytical form of quantum Fisher information decaying exponentially with the decoherence factor Γ(t).We find that the decoherence factor contains a controllable spectral density function,and therefore,we can adjust the spectral density through quantum reservoir engineering techniques.(ⅱ)We propose an active approach to restore measurement precision:the pulse control method.This pulse periodi-cally reverses the sign of the system's Hamiltonian,causing the phase accumulation induced by environmental noise over adjacent time intervals to cancel out.This mechanism significantly weakens the damage caused by low-frequency noise to quantum coher-ence,thus suppressing decoherence and maintaining a finite value for quantum Fisher information during long-time evolution. Results and Discussion.(ⅰ)By tuning the parameter s using quantum reservoir engineering,we find that when s is controlled within the range 2＜s＜sc,the system can maintain a certain degree of coherence during long-time evolution.The quantum Fisher information is higher compared to other cases,thereby improving the measurement precision.(ⅱ)By applying bang-bang pulses in the system evolution,we observe that pulses with an appropriate step size can reduce decoherence.Within a certain range,the smaller the pulse step,the higher the quantum Fisher information,thus restoring measurement precision. Conclusions.By utilizing quantum reservoir engineering techniques and applying bang-bang pulses,the lost measurement preci-sion is further restored.The results of this study provide a feasible and controllable theoretical framework for achieving long-term high-precision quantum metrology in real noisy environments and offer references for further research on quantum control and decoherence suppression mechanisms.
Objective.Because of its advantages of high precision,small size and easy integration,fiber FP cavity(Fiber Fabry-Perot cavity)has been paid more and more attention in the study of strong coupling cavity quantum electrodynamics(Cavity QED).The development of fiber cavities not only advances the study of strongly coupled cavity quantum electrodynamics with emitters such as atoms,molecules,ions,color centers,carbon nanotubes,and quantum dots,but also promotes research in cavity optomechanics.Furthermore,fiber cavities play a significant role in applied research areas including precision measure-ment and optical sensing.Research on strongly coupled cavity quantum electrodynamics imposes stricter requirements on the fab-rication and construction of fiber cavities to reduce the influence of the external environment. Methods.Aiming at the requirement of controlling single atom(array)in the fiber FP cavity for strong coupling cavity QED,it is demonstrated that the influence of fiber cavity parameters on the coupling rate and mode matching efficiency when the cavity length is L=100 μm.Based on theoretical calculations,this paper presents the relationship between the two parameters,the coupling rate and mode matching efficiency,and the cavity length with different curvature radius.The coupling rate and mode matching efficiency under different curvature radius of two mirrors in fiber cavity are analyzed respectively,and the curvature radius of mirrors with cavity length of L=100 μm can be determined. Results and Discussions.Considering the tradeoff between the coupling rate and mode matching efficiency,the optimal curva-ture radius of the cavity mirror is R1=54 μm and R2=60 μm.This finding can theoretically guide the processing and selection of optical cavity mirrors and also provide theoretical support for subsequent research work,including strong coupling of light and single atoms,as well as single atom quantum storage.
Objective.Continuous time crystals emerge from the spontaneous breaking of continuous time-translation symmetry,exhibiting stable oscillations with a definite phase.In principle,the phase rigidity of these stable oscillations implies that any early-time phase perturbation is expected to be permanently encoded into the system's dynamics,suggesting an intrinsic memory capability.Nevertheless,the detailed response mechanism of time crystals to phase modulation has not been systematically inves-tigated.This study aims to investigate how phase modulation in the driving field affects the nonlinear dynamics of a continuous time crystal and to uncover the underlying mechanism by which such systems encode and preserve phase information. Methods.We developed a theoretical model based on a continuous time crystal realized in an erbium-doped solid-state system.The dynamics of the system are analyzed by numerically solving the Lindblad master equation within a mean-field approxima-tion.Controlled phase modulations with varying frequencies and depths are introduced into the driving field,and the resulting population dynamics are systematically examined in both the time and Fourier domains to quantify the linear and nonlinear com-ponents of the response. Results and Discussions.The results show that,unlike in the non-time-crystal phase where phase perturbations are rapidly erased by dissipation,the time crystal permanently encodes phase information as a constant shift in the oscillation trajectory.Under peri-odic phase modulation,the system exhibits a wide range of dynamical behaviors.At low modulation depths,the intrinsic time crystal oscillation persists,with the modulation primarily shaping the oscillation envelope.As modulation depth increases,the system transitions into strongly nonlinear regimes,characterized by envelope distortion,emergence of frequency-doubling compo-nents,and suppression of the intrinsic oscillation.Additionally,a frequency-dependent time delay is observed between the phase modulation input and the system's response,indicating bandwidth limitations governed by the system's intrinsic relaxation time and many-body interactions. Conclusions.Continuous time crystals demonstrate a permanent memory of phase perturbations,with the ability to encode tim-ing information into persistent shifts of their oscillatory trajectories.The system's response to phase modulation is highly nonlin-ear and frequency-dependent,revealing a complex interplay between many-body interactions,dissipation,and external driving.These findings deepen the understanding of how continuous time crystals respond to phase modulation in their driving fields and offer theoretical support for their potential applications in precision timing,quantum memory,and sensing technologies.
Objective.The exceptional points(EPs)are important characteristics that distinguish non-Hermitian(NH)systems from Hermitian systems.At the exceptional points(EPs),not only do the system's eigenenergies coalesce,but its eigenstates also become degenerate simultaneously.So far,phenomena related to such exceptional points have been widely studied,but these stud-ies have mainly been limited to classical systems where the eigenstates do not have quantum correlations.The exploration of entanglement phase transitions induced by exceptional points has been restricted to two-body systems.This paper theoretically studies the entanglement behavior of non-Hermition systems composed of multiple qubits in linear arrays.The last qubit among them is dissipated. Methods.We consider a one-dimensional chain consisting of three qubits coupled by their nearest neighbors,where the non-Hermiticity results from dissipation acting on the qubit at one terminal of the array.The system can be described by an effective non-Hermitian Hamiltonian.The energy spectrum structure of the system and the concurrence of two qubits are fitted by numerical analysis. Results and Discussions.The results show that the entanglement behavior in the multibody system is significantly different from that in the common two-qubit case.In the vicinity of the outliers,the degree of concurrence does not change smoothly,but instead exhibits a strong nonlinear dependence on the system's parameters. Conclusions.In conclusion,we analyze a non-Hermitian qubit model and observe features that do not exist in the simpler two-body case.The multi-body system presents a more complex entangled structure,in which the nonlinear effect becomes not negli-gible.These observations enrich the existing knowledge of non-Hermitian multibody systems,and provide a reference for explor-ing entanglement related phenomena in open quantum platforms.
Objective.In the sense of the practical application requirements such as efficient identification and detection of weak signals and stronger anti-interference ability of X-band radar receiver,improving the detection and processing ability of X-band microwave signals is of great significance for military-civilian and civilian fields such as space exploration,meteorological moni-toring,earth exploration and satellite communication services.X-band microwave is of great significance in the application fields of radar detection,space detection,weather monitoring,satellite communication,etc. Methods.The sensitivity and accuracy of microwave measurement are in demand by the rich application fields,so we need to improve the detection and identification ability of X-band microwave signals.The X-band microwaves corresponding to nD5/2 →(n+1)P3/2 five transitions(8.5 GHz,9.2 GHz,9.9 GHz,10.72 GHz,11.6 GHz)with principal quantum number n=40～44 are measured.Based on cesium Rydberg atom at room temperature,the X-band microwaves coupled nD5/2→(n+1)P3/2 five transition channels are mea-sured when the principal quantum number n=40～44.The measurement frequency covers the whole X-band.The measurement includes detection sensitivity,dynamic range,out-of-band signal anti-interference capability and noise characteristics.Subse-quently,we studied the measurement results based on Rydberg atomic properties,and analyzed the trend of measurement sensitiv-ity in X-band.Finally,the atomic spectral response data different from the conventional microwave devices are studied,and the future applications of the measured results are predicted. Results and Discussions.Based on Rydberg's physical model of interaction between atoms and microwave electric field,cesium atoms are excited to the principal quantum number n=40～44 at room temperature,and nD5/2→(n+1)P3/2 five transition channels are coupled with microwave signals at five frequency points in the X-band range.In addition,by changing the microwave fre-quency to detect the optical noise,the results show that the noise at the resonance position will drop sharply due to the transient response of atoms.The microwave electric field measurement based on Rydberg atom is expected to enhance the application potential of atomic sensors in civil,meteorological,aviation,military and other fields,and has great significance in many aspects of national defense-related scientific and technological fields. Conclusions.In the X-band range,the field intensity measurement sensitivity of Rydberg atomic electric field meter reaches 0.21 μV·cm-1·Hz-1/2,the dynamic range is greater than 85 dB,it can be seen that with the increase of transition dipole moment,the dynamic range of Rydberg atomic measurement system generally increases(＞85 dB).And the out-of-band rejection ratio of atomic sensor is 75 dB.By evaluating the coupling Rydberg states that may exist in a large frequency range,new experimental ideas can be obtained to enhance the experimental measurement bandwidth.For example,increasing different coupling channels simultaneously can expand the measurement bandwidth of Rydberg atomic sensors.
Objective.All-solid-state single-frequency(SF)continuous-wave(CW)tunable lasers has significant application potential in cutting-edge scientific research areas such as precision measurements,quantum information,and so on.Nowadays,Ti:sapphire lasers have been one of the most commonly used tunable laser sources.However,owing to the short fluorescence lifetime and pump absorption char-acteristic of the Ti:sapphire crystal,it is mainly pumped by a high power all-solid-state continuous-wave green laser,which leads to the large size,high cost,complicated structure and difficult maintenance of the Ti:sapphire laser.In contrast,the Alexandrite crystal(Cr3+:BeAl2O4)has longer fluorescence lifetime and higher saturation energy density,so it is more suitable to be pumped by the increas-ingly mature high-power red laser diode(LD).Moreover,its excellent thermal and mechanical properties give the LD-pumped Alexandrite laser the potential to generate high-power broadband tunable laser with the compact structure.Recently,the red-LD pumped Alexandrite lasers have become one of the mainstream directions of the solid state laser research fields.However,the investigation on the SF CW LD-pumped Alexandrite laser is relatively less,and the output power of this laser is limited within watt level.In this letter,a compact SF CW LD-pumped Alexandrite laser with high output power and broadband tuning range was implemented. Methods.The severe thermal effect induced thermal lens and thermal aberration of the Alexandrite crystal would result in the degradation of the beam quality of high-power LD-pumped Alexandrite laser.Regarding this issue,a dual-crystal structure ring resonator was designed and the pump laser was evenly divided to pump each crystal respectively.On this basis,the focal length of the crystal equivalent lens was increased from 39.1 mm(@36 W pumping)to 99.5 mm(@18 W pumping),which demonstrated that the pump-induced lens effect of the crystal was obviously weakened.Then,two lenses were inserted into the resonator to manipulate the mode matching in the resonator by adjusting the distance between lenses and crystals.For the purpose of realizing the unidirectional operation of the resonator,a self-injection feedback device composed of a lens and a reflection mirror was adopted.A coarse selector birefringent filter with thickness ratio of 0.5 mm,2 mm,8 mm and a fine selector etalon with thickness of 0.5 mm and reflectivity of 20％were also inserted into the resonator to achieve the broadband tuning and single-longitudinal-mode operation of the laser. Results and Discussions.Based on the dual-crystal structure ring resonator,the output power up to 4.39 W of the SF CW Alexan-drite laser was obtained at 760 nm by optimizing the distance between the lenses and crystals as 72.5 mm,with the corresponding slope efficiency of 21％.The measured beam quality at x and y directions was M2x=1.06 and M2y=1.28 respectively.By modifying the tuning angle of the birefringent filter,the broadband wavelength tuning of the attained Alexandrite laser was implemented.With the temperature of the Alexandrite crystals increased from 40 ℃ to 60 ℃,80 ℃ and 100 ℃,the obtained tuning range varied from 732 nm～789.3 nm to 740.2 nm～790.5 nm,743.2 nm～793.5 nm and 748.9 nm～796.3 nm,respectively,and the corre-sponding gain center wavelengths were changed from 756.7 nm to 760.1 nm,764.8 nm and 70.5 nm,which were resulted from the peak wavelength of the Alexandrite crystal emission spectrum shifted towards the infrared direction as its temperature was increased.At last,the broadband wavelength tuning range from 732 nm to 796.3 nm(64.3 nm)of the SF CW Alexandrite laser could be real-ized by jointly adjusting the tuning angle of the birefringent filter and the temperature of the Alexandrite crystal. Conclusions.A compact high-power SF CW tunable LD-pumped Alexandrite laser was presented in this letter.Benefiting from the dual-crystal structure ring resonator and the low insertion loss self-injection unidirectional device,the maximal output power up to 4.39 W of the SF CW laser at 760 nm was successfully achieved,and the broadband wavelength tuning range of 732 nm～796.3 nm(64.3 nm)was implemented by adjusting the intracavity tuner birefringent filter and the temperature of the gain crystal.The demonstrated results provide a feasible reference for further realization of high-power continuously tunable SF CW LD-pumped Alexandrite laser used for quantum precise measurement and cold atom physics.
Objective.Optical parametric oscillator(OPO)has been widely used to generate long wavelength laser light and quantum resources in quantum information science.However,it is challenging to design an OPO with both low threshold and wide continuous tunning range.We have demonstrated a triply resonant continuous-wave optical parametric oscillator(OPO)that uses separated optical cavities to independently resonate the pump,signal and idler beams.A continuous tuning range over 2 GHz,which is almost three times the free spectral range of resonant cavity,was obtained.The intensity quantum correlation between the signal and idler beams,which have a tuning range of 940～1 024 nm and 1 104～1 222 nm respectively,was also observed with a correlation matrix.This opens up a new avenue for the generation of tunable triple entanglement with OPO in quantum optics. Methods.The OPO consists of three separated cavities,which are constituted by three curved mirrors and one flat mirror.All the optical components of the OPO system are arranged on a 30 cm×20 cm breadboard and the three cavities are in a"T"configura-tion.The finesse of the pump cavity is about 20,while the finesses for the signal and idler cavities are 80～110 depending on the operating wavelength.The nonlinear crystal is a 15-mm-long type Ⅱ periodically poled KTiOPO4(PPKTP)crystal set at the com-mon region of the three-cavity OPO.The OPO is pumped by a frequency doubled monolithic Nd:YAG laser.To operate the OPO,the pump and signal cavities are locked by the PDH technique and the dither-locking technique.Then,the cavity length of the idler cavity is changed by applying DC volts on its PZT.The outputs of the dual-port OPO are characterized by a power meter and a wavelength meter.Furthermore,the intensity correlation between the signal and idler beams was also investigated. Results and Discussions.A signal tuning range of 1 024 nm to 940 nm corresponding to the idler range of 1 104～1 222 nm was obtained when the crystal temperature was varied from 40 ℃ to 105 ℃.The OPO operates with an oscillation threshold of less than 50 mW for different temperatures,and a minimum threshold of 30 mW was obtained at the temperature of 58 ℃.The maxi-mum conversion efficiency is about 65％.We further demonstrate fine tuning range at a fixed temperature.A smooth continuous tuning range of about 2.2 GHz,which is almost three times the FSR,is observed by driving the PZT on the idler cavity.Further-more,the intensity correlation with a coefficient of 0.82 was obtained between the signal and idler beams. Conclusions.We have demonstrated a triple-resonant continuous-wave optical parametric oscillator.It uses separated optical cavi-ties to independently resonate the pump,signal,and idler beams.A continuous tuning range of over 2 GHz was obtained thanks to the separated configuration.The intensity correlation between the signal and idler beams,which have a tuning range of 940～1 024 nm and 1 104～1 222 nm respectively,was also observed with a correlation matrix.
Objective.The presence of exceptional points(EPs)can be used to distinguish non-Hermitian systems from Hermitian systems.In EPs,the eigenvalues and the eigenstates in non-Hermitian systems merge simultaneously.In non-Hermitian systems with parity-time(PT)symmetry,EPs are the boundary points from the symmetric phase to the symmetric breaking phase,and PT-symmetric Hamiltonian can construct a new CPT inner product.In PT-symmetric optomechanical system,the phonon laser can be generated in the close equilibrium between gain and loss.In a non-Hermitian optomechanical system,which contains loss and coupled to a gain cavity,we calculate a phonon laser two-level model with phonon mode dissipation and the corresponding super-mode spectrum.In addition,CPT inner product of quantum state are constructed.Finally,by comparing trace distance,we con-clude that CPT inner product is more superior than traditional inner product in distinguishing quantum state in the phonon laser two-level model.This results maybe have certain theoretical significance in quantum information and computation. Methods.Phonon lasers have garnered widespread attention and have long been realized in optomechanical systems.Subse-quently,phonon lasers with ultralow thresholds were achieved in PT-symmetric optomechanical systems.In recent years,continu-ous advancements have led to the realization of magnomechanical phonon lasers,nonreciprocal phonon lasers in rotating micro-wave optomechanical systems with highly tunable resonator spin velocity and direction,and ultrasensitive phonon laser force sen-sors.In coupled optomechanical systems,two coupled optical modes can be diagonalized into two optical supermodes,thereby forming a phonon laser two-level system.When the acoustic field output power suddenly increases and the linewidth abruptly nar-rows,coherent acoustic output amplification occurs,resulting in phonon lasing. Results and Discussions.This article discusses the distinguishability of quantum states in two-level non-Hermitian phonon lasers under a new inner product.A cavity optomechanical system based on PT symmetry,where two coupled optical modes generate two optical supermodels in the PT symmetry phase;When the input optical field power reaches a certain threshold,coherent acoustic output amplification is formed within the microcavity;At this point,it forms a phonon laser two-level with two optical supermodels.This article mainly considers the dissipation of phonon modes and the different physical properties of the energy spectrum before and after the singularity point in this phonon laser two-level;Then,by introducing appropriate PT symmetric Hamiltonian to construct the CPT framework,the results show that the discrimination of quantum states under CPT inner product is better than that under traditional inner product.This result has certain theoretical significance for the application of phonon lasers in quantum information and transmission,and also has certain reference value for distinguishing quantum states in quantum information and computation.
Objective.Four-wave mixing represents one of the promising schemes for the experimental generation of intensity-dif-ference squeezed light fields.Improving its squeezing degree is of great significance for its applications in quantum communica-tion and quantum metrology.This study discusses a cascaded phase-sensitive amplifier(PSA)based on four-wave mixing.Consid-ering the influence of losses,the input-output expressions of the optical fields in this cascaded system are derived theoretically.On this basis,the dependence of the intensity-difference squeezing of the light field on loss,intensity gain,and phase is numeri-cally simulated.In practical scenarios with losses,the intensity-difference squeezing of PSA has achieved a certain degree of improvement compared to PIA,while cascaded PSA further enhance the squeezing effect on the basis of PSA.Furthermore,the performance of the cascaded PSA,single-stage PSA and phase-insensitive amplifier(PIA)is compared.More importantly,the cascaded system has lower demands on phase-locking precision compared with the single-stage PSA system.This feature pro-vides more relaxed technical conditions for the engineering implementation of practical quantum squeezed light sources.The research results can lay a theoretical foundation for the preparation of high-quality quantum light sources. Methods.This paper focuses on the cascaded PSA based on the four-wave mixing process of rubidium atoms.The cascaded PSA is a system in which the output signal and conjugated light from the first four-wave mixing process are send to the input ports of the second four-wave mixing process.Considering the loss and phase delay,the noise formula of the output intensity-difference squeezed light is finally obtained based on the input-output relationship of PIA and PSA.Hence,the dependence of the squeezing characteristics on actual physical system parameters is explored. Results and Discussions.In the paper,based on the noise formulas,the dependence of the intensity-difference squeezing from the cascaded PSA on phase delay,intensity gain,and the absorption loss of the atomic vapor is numerically simulated and pre-sented.Considering actual experimental parameters,the squeezing property of the PIA,PSA,and cascaded PSA is compared.With 10％loss in the atomic vapor cell and intensity gain ranging from 1 to 5,PSA can achieve a 2 dB improvement in squeezing degree compared with the PIA,while the cascaded PSA system can further enhance the squeezing by approximately 3 dB relative to the single-stage PSA.When the loss is reduced,the above squeezing enhancement effect is significantly strengthened. Conclusions.Studies have shown that the cascaded PSA system is a highly effective system for enhancing intensity-difference squeezing.It further improves the squeezing degree on the basis of PSA,and the squeezing enhancement effect is particularly sig-nificant under low-loss conditions.Meanwhile,it has lower requirements for the phase-locking system.This study holds certain guiding significance for improving the quality of quantum light sources in practical experiments.
Objective.Nonlinear interferometers utilize optical parametric process to achieve beam splitting and combining of opti-cal fields,exhibit great potential in fields such as quantum precision measurement and sensing.The quantum properties of low-gain nonlinear interferometers originate from the non-local correlations of photon pairs,and the relationship between inter-stage loss and visibility can be harnessed for quantum sensing.In this paper,we employ the four-wave mixing in optical fibers to build a nonlinear interferometer.By independently controlling the gain and inter-stage loss during nonlinear beam splitting and combin-ing,we analyze the relationship between visibility and the gain ratio of two fiber optical parametric amplifiers(FOPAs).The rela-tionship between visibility and inter-stage transmission efficiency is further measured at the gain ratio under optimized condi-tions.The experiment results indicate that the interference visibility for signal(idler)output fields of nonlinear interferometers operating in the low-gain regime turns out to be linearly proportional to the idler(signal)inter-stage transmission efficiency.This study lays the foundation for the further development of all-fiber nonlinear interferometers operating in the low-gain regime and the exploration of their applications in quantum sensing. Methods and Results.The beam splitting and combining of the nonlinear interferometer are both achieved based on the third-order nonlinear optical effect in FOPAs,and each stage of the FOPA consists of dispersion shifted fiber(DSF)and coarse wave-length division multiplexer(CWDM),realizing the four-wave mixing process under the condition of phase-matching.We use a mode-locked laser as the pump source.It has a repetition rate of 50 MHz,a central wavelength of 1561 nm,and a bandwidth of around 20 nm.The zero-dispersion wavelength of the DSFs used is approximately 1 553 nm.To satisfy the phase-matching condi-tion for the four-wave mixing process in the DSF,the laser output is filtered to obtain pulsed pump with a central wavelength of 1 553.3 nm and a FWHM of 0.6 nm.The pulsed pump is split into P1 and P2 for the two FOPAs respectively,maintaining coher-ence and enabling independent control.The inter-stage transmission efficiencies of the signal and idler can be adjusted indepen-dently via variable optical attenuators(VOA1 and VOA2)with tuning ranges of 0～60％and 0～50％,respectively.By varying the voltage applied to the piezoelectric transducer(PZT)in the P2 pump path,the relative phase between P1 and P2 is varied in time.The time-dependent photon count rates of the output signal and idler are then measured using single-photon detectors(SPDs),from which the interference fringes are obtained.The measured results demonstrate a clear linear relationship between the output idler visibility and the square root of signal inter-stage efficiency. Conclusions.We demonstrate a nonlinear interferometer with two independently pumped DSFs,analyzing the influence of the gain ratio and inter-stage efficiency on the interference visibility of nonlinear interferometers operating in the low-gain regime.The results show that when other parameters are fixed and only inter-stage transmission efficiency of idler(signal)ηi(s) is varied,the interference visibility of signal(idler)exhibits a strong linear relationship with the square root of inter-stage efficiency √ηi(s).This study verifies the dependence of visibility on system parameters in the low-gain region for nonlinear interferometers,laying a foundation for its further application in quantum sensing.
Objective.Quantum batteries(QBs)represent a promising paradigm for energy storage,leveraging quantum resources such as entanglement and coherence to achieve faster charging and higher work extraction compared to classical counterparts.However,the practical realization of QBs is severely impeded by open-system dynamics,where interaction with the environment leads to decoherence and energy dissipation,thereby degrading storage capacity and retention time.The non-reciprocal scheme based on reservoir engineering([Physical Review Letters,2024,132(21):210402])offers a potential solution.However,this scheme requires precise control of system parameters to eliminate reverse coupling.The core goal of this study is to realize direc-tional energy transfer and stable,long-term energy storage by utilizing the dark state physical properties and spontaneous emis-sion effects in the atomic ensemble-cavity coupling system.Different from the reservoir engineering method,this scheme can achieve one-way energy transmission relying on the naturally existing spontaneous emission channels in atoms. Methods.The theoretical model we put forword consists of an atomic ensemble containing N four-level atoms trapped within a single-mode dissipative optical cavity.The atoms possess two ground states(|s>,|f>)and two excited states(|l>,|r>).To analyze the system dynamics,we employ the Lindblad master equation to simulate the time evolution of the system's density matrix,accounting for cavity decay and atomic spontaneous emission.By performing a unitary transformation and diagonalizing the Hamiltonian,we identify the system's bright and dark modes.We apply the adiabatic elimination approximation to derive an effective Hamiltonian,which describes the effective energy transfer.Crucially,the non-reciprocity is introduced via the specific dissipation channel where the excited state|r>spontaneously decays into the target battery ground state|f>.This irreversible pro-cess breaks the time-reversal symmetry of the system.Additionally,we derive the Heisenberg equations of motion for the system operators to obtain analytical solutions for the steady-state populations and energy scaling. Results and Discussions.Numerical simulations demonstrate that the proposed non-reciprocal scheme substantially surpasses standard reciprocal charging protocols.The energy is efficiently transferred from the charger(cavity mode)to the intermediate dark mode,and subsequently rectified into the battery mode(atomic ground state|f>)via spontaneous emission.Comparison shows that the charging efficiency of the non-reciprocal model is orders of magnitude higher than that of the reciprocal one.In the steady-state limit,the storage capacity is shown to scale favorably with the driving field intensity and the effective coupling strength.The approximate analytical solutions show excellent agreement with the numerical simulations,verifying the reliability of the analytical solution.The mechanism essentially functions as a"quantum diode"for energy,ensuring directional flow and preventing discharge back into the driving field. Conclusions.This study successfully constructed a theoretical framework for a non-reciprocal quantum battery based on an atomic ensemble-cavity platform.It utilizes atomic spontaneous emission to achieve non-reciprocal energy transfer,with the bat-tery's energy stored in the ground state,thereby enabling the battery to have a longer coherence time and more stable energy stor-age.Furthermore,this architecture employs the natural spontaneous emission channel and does not require precise parameter con-trol through reservoir engineering schemes.These findings not only provide a promising option for stable quantum batteries but also offer new insights into the design of non-reciprocal light-matter interfaces and quantum network nodes that require stable energy or information retention.
Objective.Rydberg atoms are highly excited state atoms with unique physical properties,making them widely used in fields such as quantum science and precision measurement.The transitions between Rydberg states have longer wavelengths and larger transition dipole moments,which easily satisfy the Dicke limit,making Rydberg atoms become an ideal medium for study-ing superradiance effect.Superradiance effect is a collective dynamic evolution process in dense atomic sample.Rydberg atoms superradiance has broad application prospects in quantum optics,lasers,atomic clocks,and so on,and has promoted the research on multi-body entanglement and collective effect in quantum information science.In this article,the influence of electric field on the superradiance of ultracold Rydberg atoms is discussed. Methods.In this paper,the ground state atoms are excited to the Rydberg state through two-photon resonance excitation in an ultracold dense cesium atomic ensemble metal magneto-optical trap.The Rydberg atom number evolution process as function of the delay time t was detected using the state selective field ionization technique.We observe the|60D5/2>→|61P3/2>superradiant spectrum in the experiment.By applying an external electric field to align the polarization direction of the Rydberg atom with the electric field,the influence of dipole-dipole interaction on superradiance effect is studied. Results and Discussions.We have observed the evolution process of cesium Rydberg|60D5/2>state atom signals corresponding to the different Rydberg atom density in metal magneto-optical trap.As the atom density increases,the evolution process acceler-ates.Under appropriate atomic density conditions,the|60D5/2>Rydberg atoms will transfer to adjacent|61P3/2>Rydberg states,which is known as the superradiance effect.On this basis,the density of Rydberg atoms is fixed,and an electrostatic field is applied to study the effect of the electric field on the superradiance effect.The superradiance effect is suppressed as the electric field value increases.To further illustrate,the e-exponential function is used to fit the dynamic evolution process of the Rydberg|60D5/2>state,and obtain the decay rates corresponding to the different electric fields.With the increase of electric field,the decay rates shows slowly decrease,and as the electric field continues to increase,the decay rates decreases accelerates until it approaches zero.The existence of an electric field can suppress the evolution process of Rydberg state atoms,thereby suppressing the superradiance effect. Conclusions.We have studied the|60D5/2>Rydberg atom signal as the function of delay time t for the different Rydberg atom density in magneto-optical trap and observed superradiance of Rydberg atom|60D5/2>to|61P3/2>.The influence of dipole-dipole interaction on the superradiance effect was studied by applying an electric field.Research has shown that the larger the electric field value,the less obvious the superradiance effect,and the dipole-dipole interaction suppresses the superradiance effect.The study utilizes the experimental platform of the Rydberg atomic ensemble,which can help people to better understand and explore the mechanism of superradiance effects and the evolution process of atomic ensemble.
