High-Precision Fiber Noise Detection and Comparison over a 260 km Field Fiber Link.

In this paper, we present a high-precision optical frequency noise detection and comparison technique using a two-way transfer method over a 260 km field fiber link. This method allows for the comparison of optical frequencies between remote optical references without the need for data transfer through communication. We extend a previously established two-way comparison technique to obtain all data at the local site. Two optical carrier signals are injected into the bidirectional fiber from both ends, and one carrier is reflected back from the remote end. This enables the phase comparison of the two carrier signals at a single site without the need to transmit experimental data. The common-mode frequency noise induced by the bidirectional fiber link is detected and effectively suppressed without the need for sophisticated active fiber noise control. Our demonstration system, which uses a 260 km field fiber link and a common laser source, achieves a fractional instability of 2.5×10-17 at 1 s averaging time and scales down to 3.5×10-21 at 8000 s. This scheme offers the distinct advantage of completing the comparison at a single site, eliminating the need for remote data transfer via communication. This method is expected to enhance reliability for high-precision frequency comparisons between remote optical clocks and advanced atomic clocks.

Optomechanics and quantum phase of the Bose-Einstein condensate with the cavity mediated spin-orbit coupling.

We investigated the optomechanical dynamics and explored the quantum phase of a Bose-Einstein condensate in a ring cavity. The interaction between the atoms and the cavity field in the running wave mode induces a semiquantized spin-orbit coupling (SOC) for the atoms. We found that the evolution of the magnetic excitations of the matter field resembles that of an optomechanical oscillator moving in a viscous optical medium, with very good integrability and traceability, regardless of the atomic interaction. Moreover, the light-atom coupling induces a sign-changeable long-range interatomic interaction, which reshapes the typical energy spectrum of the system in a drastic manner. As a result, a new quantum phase featuring a high quantum degeneracy was found in the transitional area for SOC. Our scheme is immediately realizable and the results are measurable in experiments.

Proposal for a hybrid clock system consisting of passive and active optical clocks and a fully stabilized microcomb.

Optical atomic clocks produce highly stable frequency standards and frequency combs bridge clock frequencies with hundreds of terahertz difference. In this paper, we propose a hybrid clock scheme, where a light source pumps an active optical clock through a microresonator-based nonlinear third harmonic process, serves as a passive optical clock via indirectly locking its frequency to an atomic transition, and drives a chip-scale microcomb whose mode spacing is stabilized using the active optical clock. The operation of the whole hybrid system is investigated through simulation analysis. The numerical results show: (i) The short-term frequency stability of the passive optical clock follows an Allan deviation of σy(τ) = 9.3 × 10-14τ-1/2 with the averaging time τ, limited by the population fluctuations of interrogated atoms. (ii) The frequency stability of the active optical clock reaches σy(τ) = 6.2 × 10-15τ-1/2, which is close to the quantum noise limit. (iii) The mode spacing of the stabilized microcomb has a shot-noise-limited Allan deviation of σy(τ) = 1.9 × 10-11τ-1/2. Our hybrid scheme may be realized using recently developed technologies in (micro)photonics and atomic physics, paving the way towards on-chip optical frequency comparison, synthesis, and synchronization.

Implementation of field two-way quantum synchronization of distant clocks across a 7†km deployed fiber link.

The two-way quantum clock synchronization has been shown to provide femtosecond-level synchronization capability and security against symmetric delay attacks, thus becoming a prospective method to compare and synchronize distant clocks with enhanced precision and safety. In this letter, a field test of two-way quantum synchronization between a H-maser and a Rb clock linked by a 7 km-long deployed fiber is implemented by using time-energy entangled photon-pair sources. Limited by the intrinsic frequency stability of the Rb clock, the achieved time stability at 30 s is measured as 32 ps. By applying a fiber-optic microwave frequency transfer technology to build frequency syntonization between the separated clocks, the limit set by the intrinsic frequency stability of the Rb clock is overcome. A significantly improved time stability of 1.9 ps at 30 s is achieved, which is mainly restrained by the low number of acquired photon pairs due to the low sampling rate of the utilized coincidence measurement system. Such implementation demonstrates the high practicability of the two-way quantum clock synchronization method for promoting field applications.

Widely flexible and finely adjustable nonlocal dispersion cancellation with wavelength tuning.

In fiber-based quantum information processing with energy-time entangled photon pairs, optimized dispersion compensation is vital to preserve the strong temporal correlation of the photon pairs. We propose and experimentally verify that, by simply tuning the wavelength of the entangled photon pairs, nonlocal dispersion cancellation (NDC) can provide a widely flexible and finely adjustable solution for optimizing the dispersion compensation, which cannot be reached with the traditional local dispersion cancellation (LDC) instead. By way of example, when a 50 km-long single-mode fiber (SMF) is dispersion compensated by a 6.2-km-long commercial dispersion compensating fiber (DCF) based on the LDC configuration, it will lead to an almost invariant over-compensation in the wavelength range of 1500-1600 nm which restricts the observed temporal coincidence width of the self-developed energy-time entangled photon-pairs source to a minimum of ∼110 ps. While in the NDC configuration, the dispersion compensation can be readily optimized by tuning the signal wavelength to 1565.7 nm and a minimum coincidence width of 86.1 ± 0.7 ps is observed, which is mainly limited by the jitter of the single-photon detection system. Furthermore, such optimized dispersion compensation can also be achieved as the fiber length varies from 48 km to 60 km demonstrating the wide flexibility of NDC. Thanks to these capabilities, elaborate dispersion compensation modules are no longer required, which makes NDC a more versatile tool in fiber-based quantum information and metrology applications.

Phase gradient protection of stored spatially multimode perfect optical vortex beams in a diffused rubidium vapor.

We experimentally investigate the optical storage of perfect optical vortex (POV) and spatially multimode perfect optical vortex (MPOV) beams via electromagnetically induced transparency (EIT) in a hot vapor cell. In particular, we study the role that phase gradients and phase singularities play in reducing the blurring of the retrieved images due to atomic diffusion. Three kinds of manifestations are enumerated to demonstrate such effect. Firstly, the suppression of the ring width broadening is more prominent for POVs with larger orbital angular momentum (OAM). Secondly, the retrieved double-ring MPOV beams' profiles present regular dark singularity distributions that are related to their vortex charge difference. Thirdly, the storage fidelities of the triple-ring MPOVs are substantially improved by designing line phase singularities between multi-ring MPOVs with the same OAM number but π offset phases between adjacent rings. Our experimental demonstration of MPOV storage opens new opportunities for increasing data capacity in quantum memories by spatial multiplexing, as well as the generation and manipulation of complex optical vortex arrays.

Pulsed vapor cell atomic clock with a differential Faraday rotation angle detection.

Laser intensity noise is one of the main limiting factors in pulsed vapor cell clocks. To reduce the contribution of the laser intensity noise to detection signal in the pulsed optically pumped atomic clock, a scheme based on the differential Faraday rotation angle is proposed. Theoretically, the Ramsey fringes, the sensitivity of clock frequency to laser intensity fluctuation and the signal to noise ratio for absorption, differential, and Faraday rotation angle methods are calculated and compared. Using a Wollaston prism rotated 45°relative to the incident polarization, and two photodetectors, Ramsey fringes of three detection methods are obtained simultaneously. In the proposed scheme, the long-term Faraday rotation angle fluctuation is 0.66% at 30000s, which is much smaller than fluctuation of traditional absorption signal 3.9% at 30000s. And the contribution of laser intensity noise to clock instability is also reduced. Using optimized photodetector with high common mode rejection ratio, a better performance should be expected. This proposed scheme is attractive for the development of high performance vapor clock based on pulsed optically pumped.

The Application of Low-Frequency Transition in the Assessment of the Second-Order Zeeman Frequency Shift.

Second-order Zeeman frequency shift is one of the major systematic factors affecting the frequency uncertainty performance of cesium atomic fountain clock. Second-order Zeeman frequency shift is calculated by experimentally measuring the central frequency of the (1,1) or (-1,-1) magnetically sensitive Ramsey transition. The low-frequency transition method can be used to measure the magnetic field strength and to predict the central fringe of (1,1) or (-1,-1) magnetically sensitive Ramsey transition. In this paper, we deduce the formula for magnetic field measurement using the low-frequency transition method and measured the magnetic field distribution of 4 cm inside the Ramsey cavity and 32 cm along the flight region experimentally. The result shows that the magnetic field fluctuation is less than 1 nT. The influence of low-frequency pulse signal duration on the accuracy of magnetic field measurement is studied and the optimal low-frequency pulse signal duration is determined. The central fringe of (-1,-1) magnetically sensitive Ramsey transition can be predicted by using a numerical integrating of the magnetic field "map". Comparing the predicted central fringe with that identified by Ramsey method, the frequency difference between these two is, at most, a fringe width of 0.3. We apply the experimentally measured central frequency of the (-1,-1) Ramsey transition to the Breit-Rabi formula, and the second-order Zeeman frequency shift is calculated as 131.03 × 10-15, with the uncertainty of 0.10 × 10-15.

Quantification of nonlocal dispersion cancellation for finite frequency entanglement.

Benefiting from the unique quantum feature of nonlocal dispersion cancellation (NDC), the strong temporal correlation of frequency-entangled photon pair source can be maintained from the unavoidable dispersive propagation. It has thus played a major role in many fiber-based quantum information applications. However, the limit of NDC due to finite frequency entanglement has not been quantified. In this study, we provide a full theoretical analysis of the NDC characteristics for the photon pairs with finite frequency entanglement. Experimental examinations were conducted by using two spontaneous parametric down-conversion photon pair sources with frequency correlation and anticorrelation properties. The excellent agreement demonstrates the fundamental limit on the minimum temporal correlation width by the nonzero two-photon spectral correlation width of the paired photons, which introduces an inevitable broadening by interaction with the dispersion in the signal path. This study provides an easily accessible tool for assessing and optimizing the NDC in various quantum information applications.

Inherent resolution limit on nonlocal wavelength-to-time mapping with entangled photon pairs.

Nonlocal wavelength-to-time mapping between frequency-entangled photon pairs generated with the process of spontaneous parametric down-conversion is theoretically analyzed and experimentally demonstrated. The spectral filtering pattern experienced by one photon in the photon pair will be non-locally mapped into the time domain when the other photon propagates inside a dispersion-compensation fiber with large group velocity dispersion. Our work, for the first time, points out that the spectral bandwidth of the pump laser will become the dominated factor preventing the improvement of the spectral resolution when the involved group velocity dispersion is large enough, which provides an excellent tool for characterizing the resolution of a nonlocal wavelength-to-time mapping for further quantum information applications.

Hybrid frequency-time spectrograph for the spectral measurement of the two-photon state.

In this Letter, a hybrid frequency-time spectrograph combining a tunable optical filter and a dispersive element is presented for measurement of the spectral properties of the two-photon state. In comparison with the previous single-photon spectrograph utilizing the dispersive Fourier transformation (DFT) technique, this method is advanced since it avoids the need for additional wavelength calibration and the electronic laser trigger for coincidence measurement; therefore, its application is extended to continuous wave (CW) pumped two-photon sources. The achievable precision of the spectrum measurement has also been discussed in theory and demonstrated experimentally with a CW pumped periodically poled lithium niobate (PPLN) waveguide-based spontaneous parametric down-conversion photon source. Such a device is expected to be a versatile tool for the characterization of the frequency entangled two-photon state.

Simulation and realization of a second-order quantum-interference-based quantum clock synchronization at the femtosecond level.

Quantum clock synchronization schemes utilizing frequency-entangled pulses have flourished for their potentially superior precision to the classical protocols. In this Letter, a new experimental record based on the second-order quantum interference algorithm is reported, to the best of our knowledge. The synchronization accuracy between two parties separated by a 6 km fiber coiling link, which is evaluated by the time offset shift relative to that with the fibers removed, has been measured to be 13±1 ps. The stability in terms of time deviation (TDEV) of 0.81 ps at an averaging time of 100 s has been achieved. The long-term synchronization stability is seen determined by the measurement device, and a minimum stability of 60 fs has been reached at 25,600 s. Furthermore, for the first time to the best of our knowledge, we quantify the performance of this quantum synchronization scheme, and very good agreements with the experimental results have been achieved. According to the quantum simulation, further improvements for both the synchronizing stability and accuracy can be expected.

Chiral Supersolid in Spin-Orbit-Coupled Bose Gases with Soft-Core Long-Range Interactions.

Chirality represents a kind of symmetry breaking characterized by the noncoincidence of an object with its mirror image and has been attracting intense attention in a broad range of scientific areas. The recent realization of spin-orbit coupling in ultracold atomic gases provides a new perspective to study quantum states with chirality. In this Letter, we demonstrate that the combined effects of spin-orbit coupling and interatomic soft-core long-range interaction can induce an exotic supersolid phase in which the chiral symmetry is broken with spontaneous emergence of circulating particle current. This implies that a finite angular momentum can be generated with neither rotation nor effective magnetic field. The direction of the angular momentum can be altered by adjusting the strength of spin-orbit coupling or interatomic interaction. The predicted chiral supersolid phase can be experimentally observed in Rydberg-dressed Bose-Einstein condensates with spin-orbit coupling.

Design of an atom source collimator for a compact frequency-stabilized laser.

A concise laser system for optically pumped cesium beam clocks is presented. The laser's frequency is locked by a fluorescence signal, produced by the interaction between a cesium atomic beam and laser. A cesium oven with a longer atom source collimator, formed by an array of channels, was used to reduce the divergence angle of the cesium atomic beam. The size of the cesium source collimator is 4 mm×0.6 mm, and the cesium expenditure rate is 2.4×10-1 g per year. A dense cesium atomic flux was used to interact with the laser to generate a fluorescence signal when the oven heating temperature is not too high. The cesium beam tube could have a longer lifetime. The optical structure of the laser system is compact. The measured frequency stability of the laser is ∼4×10-11 at 10,000 s when the laser frequency is locked in the F=4→F'=5 transition of the cesium D2 line. The design of an atom oven and atom source may be used in other atomic beam clocks to improve their performance.

A Quantum-Based Microwave Magnetic Field Sensor.

In this paper, a quantum-based method for measuring the microwave magnetic field in free space is presented by exploring atomic Rabi resonance in the clock transition of 133Cs. A compact cesium glass cell serving as the microwave magnetic field sensing head was used to measure the spatial distribution of microwave radiation from an open-ended waveguide antenna. The measured microwave magnetic field was not restricted by other microwave devices. The longitudinal distribution of the magnetic field was measured. The experimental results measured by the sensor were in agreement with the simulation. In addition, a slightly electromagnetic perturbation caused by the glass cell was investigated through simulation calculations.

Realization of multiform time derivatives of pulses using a Fourier pulse shaping system.

The technique of multiform time derivatives of pulse has been shown necessary to achieve various time-space metrology goals with a precision at or beyond the standard quantum limit. However, the efficient generation of the desired time derivatives remains challenging. In this paper, we report on the efficient realization of multiform time derivatives with a programmable 4-f pulse shaping system. The first-order time derivative of the pulse electric field has been achieved with a generation efficiency of 72.12%, which is more than 20 times higher than that of previous methods. Moreover, the first- and second-order time derivatives of the pulse envelope have been achieved with the generation efficiencies being 11.10% and 3.53%, respectively. In comparison, these efficiencies are three times higher than those for previously reported methods. Meanwhile, the measured fidelities of the three time-derived pulses are reasonably high, with values of 99.53%, 98.37% and 97.32% respectively.

Robust optical-frequency-comb based on the hybrid mode-locked Er:fiber femtosecond laser.

We demonstrate an optical frequency comb in which an Er:fiber-based femtosecond laser employs nonlinear amplifier loop mirror (NALM) and nonlinear polarization evolution (NPE) mode-locking mechanisms. The laser combines advantages of good robustness of NALM and low noise feature of NPE. Our experimental results show that the hybrid mode-locked laser has high power, low relative intensity noise and self-started property, enabling the construction of a robust optical frequency comb system. In-loop relative instabilities of both stabilized repetition rate and carrier-envelope-offset frequency are well below 1 × 10-17 at 1 second integration time.

Steering optical comb frequencies by rotating the polarization state.

We demonstrate a new approach to steer the frequencies of a nonlinear polarization-rotation mode-locked laser, where a specially designed intrcavity electro-optic modulator tunes the polarization state of the laser signal. This approach not only results in the broadband associated with high performance, but also results in a large dynamic range associated with good robustness. Our experimental results show that frequency control dynamic ranges are at least one order of magnitude larger than those of the previous ultra-fast frequency control techniques, reaching hundreds of hertz and hundreds of megahertz for repetition rate (fr) and carrier-envelope-offset frequency (fceo), respectively.

Electro-optic modulator with ultra-low residual amplitude modulation for frequency modulation and laser stabilization.

The reduction of the residual amplitude modulation (RAM) induced by electro-optic modulation is essential for many applications of frequency modulation spectroscopy requiring a lower system noise floor. Here, we demonstrate a simple passive approach employing an electro-optic modulator (EOM) cut at Brewster's angle. The proposed EOM exhibits a RAM of a few parts per million, which is comparable with that achieved by a common EOM under critical active temperature and bias voltage controls. The frequency instability of a 10 cm cavity-stabilized laser induced by the RAM effect of the proposed EOM is below 3×10-17 for integration times from 1 to 1000 s, and below 4×10-16 for comprehensive noise contributions for integration times from 1 to 100 s.

Demonstration of CNOT gate with Laguerre Gaussian beams via four-wave mixing in atom vapor.

We present an experimental study of controlled-NOT (CNOT) gate through four-wave mixing (FWM) process in a Rubidium vapor cell. A degenerate FWM process in a two level atomic system is directly excited by a single diode laser, where backward pump beam and probe beam are Laguerre Gaussian mode. By means of photons carrying orbital angular momentum, we demonstrate the ability to realize CNOT gate with topological charges transformation in this nonlinear process. The fidelity of CNOT gate for a superposition state with different topological charge reaches about 97% in our experiment.