Nonlinear localization of ultracold atomic Fermi gas in moiré optical lattices

Moirésuperlattices,a twisted functional structure crossing the periodic and nonperiodic potentials,have recently attracted great interest in multidisciplinary fields,including optics and ultracold atoms,because of their unique band structures,physical properties,and potential implications.Driven by recent experiments on quantum phenomena of bosonic gases,the atomic Bose–Einstein condensates in moiréoptical lattices,by which other quantum gases such as ultracold fermionic atoms are trapped,could be readily achieved in ultracold atom laboratories,whereas the associated nonlinear localization mechanism remains unexploited.Here,we report the nonlinear localization theory of ultracold atomic Fermi gases in two-dimensional moiréoptical lattices.The linear Bloch-wave spectrum of such a twisted structure exhibits rich nontrivial flat bands,which are separated by different finite bandgaps wherein the existence,properties,and dynamics of localized superfluid Fermi gas structures of two types,gap solitons and gap vortices(topological modes)with vortex charge S¼1,are studied numerically.Our results demonstrate the wide stability regions and robustness of these localized structures,opening up a new avenue for studying soliton physics and moiréphysics in ultracold atoms beyond bosonic gases.

Strontium optical lattice clock at the National Time Service Center

We report the 87Sr optical lattice clock developed at the National Time Service Center. We achieved a closed-loop operation of the optical lattice clock based on 87Sr atoms. The linewidth of the spin-polarized clock peak is 3.9 Hz with a clock laser pulse length of 300 ms, which corresponds to a Fourier-limited linewidth of 3 Hz. The fitting of the in-loop error signal data shows that the instability is approximately 5 × 10 15τ-1/2, affected primarily by the white noise. The fractional frequency difference averages down to 5.7 × 10 ^-17 for an averaging time of 3000 s.

A transportable optical lattice clock at the National Time Service Center

We report a transportable one-dimensional optical lattice clock based on 87Sr at the National Time Service Center.The transportable apparatus consists of a compact vacuum system and compact optical subsystems.The vacuum system with a size of 90 cm×20 cm×42 cm and the beam distributors are assembled on a double-layer optical breadboard.The modularized optical subsystems are integrated on independent optical breadboards.By using a 230 ms clock laser pulse,spin-polarized spectroscopy with a linewidth of 4.8 Hz is obtained which is close to the 3.9 Hz Fourier-limit linewidth.The time interleaved self-comparison frequency instability is determined to be 6.3 × 10^-17 at an averaging time of 2000 s.

First Evaluation and Frequency Measurement of the Strontium Optical Lattice Clock at NIM

An optical lattice clock based on 87Sr is built at National Institute of Metrology （NIM） of China. The systematic frequency shifts of the clock are evaluated with a total uncertainty of 2.3×10-16. To measure its absolute frequency with respect to NIM＇s cesium fountain clock NIM5, the frequency of a flywheel H-maser of NIM5 is transferred to the Sr laboratory through a 50-kin-long fiber. reference frequency of this H-maser, is used for the optical this Sr clock is measured to be 429228004229873.7（1.4）Hz. A fiber optical frequency comb, phase-locked to the frequency measurement. The absolute frequency of

Magic Wavelength Measurement of the ^(87)Sr Optical Lattice Clock at NIM

We report on the magic wavelength measurement of our optical lattice clock based on fermion strontium atoms at the National Institute of Metrology （NIM）. A Ti：sapphire solid state laser locked to a reference cavity inside a temperature-stabilized vacuum chamber is employed to generate the optical lattice. The laser frequency is measured by an erbium fiber frequency comb. The trap depth is modulated by varying the lattice laser power via an acousto-optic modulator. We obtain the frequency shift coefficient at this lattice wavelength by measuring the diffbrential frequency shift of the clock transition of the strontium atoms at different trap depths, and the frequency shift coefficient at this lattice wavelength is obtained. We measure the frequency shift coefficients at different lattice frequencies around the magic wavelength and linearly fit the measurement data, and the magic wavelength is calculated to be 368554672（44）MHz.

Clock-transition spectrum of ^(171)Yb atoms in a one-dimensional optical lattice

An optical atomic clock with 171yb atoms is devised and tested. By using a two-stage Doppler cooling technique, the 171Yb atoms are cooled down to a temperature of 6 ± 3 μK, which is close to the Doppler limit. Then, the cold 171Yb atoms are loaded into a one-dimensional optical lattice with a wavelength of 759 nm in the Lamb-Dicke regime. Furthermore, these cold 171yb atoms are excited from the ground-state 1S0 to the excited-state 3P0 by a clock laser with a wavelength of 578 nm. Finally, the 1S0-3P0 clock-transition spectrum of these 171yb atoms is obtained by measuring the dependence of the population of the ground-state 1 S0 upon the clock-laser detuning.

Elliptic Function Waves of Spinor Bose-Einstein Condensates in an Optical Lattice

An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.

Tunneling dynamics of Bose-Einstein condensates with higher-order interactions in optical lattice

The nonlinear Landau Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate （BEC） with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters （i.e., the modulation amplitude and frequency） and the strength of periodic potential.

Chaotic Ratchet Effect for Bose-Einstein Condensed Atoms in 1D Optical Lattices

The chaotic ratchet effect for Bos-Einstein condensed atoms in an optical lattice is investigated. By using the direct perturbation method we obtain the chaotic solution of the condensed system. Theoretical analysis reveals that the transport of the condensed atoms in the ratchet potential is a chaotic one, and corresponding numerical results agree well with the theoretical results.

Hertz-Level Clock Spectroscopy of ^(171)Yb Atoms in a One-Dimensional Optical Lattice

An ultra-narrow spectroscopy of clock transition with high signal-to-noise ratio is crucial for a high-performance atomic optical clock. We present a detailed study about how to obtain a Hertz-level clock transition spectrum of 171 Yb atoms. About 4 × 10^4 atoms are loaded into a one-dimensional optical lattice with a magic wavelength of 759 nm, and a long lifetime of 3 s is realized with the lattice power of I W. Through normalized shelving detection and spin polarization, 171 Yb clock spectroscopy with a fourier-limited linewidth of 5.9 Hz is obtained. Our work represents a key step toward an ytterbium optical clock with high frequency stability.

Stability of trapped Bose-Einstein condensates in one-dimensional tilted optical lattice potential

Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.

Impurity-induced localization of Bose-Einstein condensates in one-dimensional optical lattices

The impurity-induced localization of two-component Bose-Einstein condensates loaded into deep one-dimensional optical lattices is studied both analytically and numerically. It is shown that, the analytical criteria for self-trapping and moving soliton/breather of the primary-component condensate are modified significantly by an admixture of an impurity component （the second component）. The realization of the self-trapped state and the moving soliton/breather states of the primary-component becomes more easy with the minor admixture of the impurity-component, even if the two components are partly overlapped.

Energy Spectrum of Two-Component Bose-Einstein Condensates in Optical Lattices

With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We End that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.

Controllable optical multi-well trap and its optical lattices using compounded cosine patterns

This paper proposes a flexible scheme to form various optical multi-well traps for cold atoms or molecules by using a simple optical system composed of an compounded amplitude cosine-only grating and a single lens illuminated by a plane light wave or a Gaussian beam. Dynamic manipulation and evolution of multi-well trap can be easily implemented by controlling the modulation frequency of the cosine patterns. It also discusses how to expand this multi-well trap to two-dimensional lattices with single- or multi-well trap by using an orthogonally or non-orthogonally modulated grating, as well as using incoherent multi-beam illumination, and these results show that all the symmetric structures of two-dimensional Bravais lattices can be obtained facilely by using proposed scheme.

Interrogation of optical Ramsey spectrum and stability study of an ^(87)Sr optical lattice clock

The optical Ramsey spectrum is experimentally realized in an ^(87)Sr optical lattice clock, and the measured linewidth agrees well with theoretical expectation. The coherence time between the clock laser and the atoms, which indicates the maximum free evolution period of using Ramsey detection to measure the atom-laser phase information, is determined as 340(23) ms by measuring the fringe contrasts of the Ramsey spectrum as a function of the free evolution period. Furthermore, with the same clock duty cycle of about 0.1, the clock stability is measured by using the Ramsey and Rabi spectra,respectively. The experimental and theoretical results show approximately the same stability as the two detection methods, which indicates that Ramsey detection cannot obviously improve the clock stability until the clock duty cycle is large enough. Thus, it is of great significance to choose the detection method of a specific clock.

Observation of V-type electromagnetically induced transparency and optical switch in cold Cs atoms by using nanofiber optical lattice

Optical nanofiber(ONF)is a special tool to achieve the interaction between light and matter with ultralow power.In this paper,we demonstrate V-type electromagnetically induced transparency(EIT)in cold atoms trapped by an ONFbased two-color optical lattice.At an optical depth of 7.35,90%transmission can be achieved by only 7.7 pW coupling power.The EIT peak and linewidth are investigated as a function of the coupling optical power.By modulating the pWlevel control beam of the ONF-EIT system in sequence,we further achieve efficient and high contrast control of the probe transmission,as well as its potential application in the field of quantum communication and quantum information science by using one-dimensional atomic chains.

Dynamics of Airy beams in parity–time symmetric optical lattices

We investigate the dynamics of airy beams propagating in the parity–time(PT) symmetric optical lattices in linear and nonlinear regimes, respectively. For the linear propagation, the position of the channel guided by the PT lattice can be shifted by tuning the lattice frequency. The underlying physical mechanism of this phenomenon is also discussed. An interesting phenomenon is found in the nonlinear regime in that the airy beam becomes a tilt channel with several Rayleigh lengths. These findings create new opportunities for optical steering and manipulations.

Tunable ground-state solitons in spin–orbit coupling Bose–Einstein condensates in the presence of optical lattices

Properties of the ground-state solitons, which exist in the spin-orbit coupling （SOC） Bose-Einstein condensates （BEC） in the presence of optical lattices, are presented. Results show that several system parameters, such as SOC strength, lattice depth, and lattice frequency, have important influences on properties of ground state solitons in SOC BEC. By controlling these parameters, structure and spin polarization of the ground-state solitons can be effectively tuned, so ma- nipulation of atoms may be realized.

Effect of interaction strength on gap solitons of Bose-Einstein condensates in optical lattices

We have developed a systematic analytical approach to the study on the dynamic properties of the linear and the nonlinear excitations for quasi-one-dimensional Bose-Einstein condensate trapped in optical lattices. A novel linear dispersion relation and an algebraic soliton solution of the condensate are derived analytically under consideration of Bose-Einstein condensate with a periodic potential. By analysing the soliton solution, we find that the interatomic interaction strength has an important effect on soliton dynamic properties of Bose-Einstein condensate.

A Longitudinal Zeeman Slower Based on Ring-Shaped Permanent Magnets for a Strontium Optical Lattice Clock

We report a longitudinal Zeeman slower based on ring-shaped permanent magnetic dipoles used for the strontium optical lattice clock. The Zeeman slower is composed of 40 permanent magnets with the same outer diameter but different inner diameters. The maximum variation of the axial field from its target values is less than 2%. In most parts of the Zeeman slower, the intensity variations of the field in radial spatial distribution are less than 0.1 roT. With this Zeeman slower, the strontium atoms are slowed down to 95m/s, and approximately 2% of the total atoms are slowed down to less than 50m/s.