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.

Probing quantum phase transition point by tuning an external anti trap.

Manipulation of ultracold atoms in optical lattices is one of the optimal ways to observe phase transitions of the Hubbard model which is useful in a variety of condensed-matter systems. Bosonic atoms in this model experience a phase transition from superfluids to Mott insulators by tuning systematic parameters. However, in conventional setups, phase transitions take place over a large range of parameters instead of one critical point due to the background inhomogeneity caused by the Gaussian shape of optical-lattice lasers. To probe the phase transition point more precisely in our lattice system, we apply a blue-detuned laser to compensate for this local Gaussian geometry. By inspecting the change of visibility, we find a sudden jump point at one particular trap depth of optical lattices, corresponding to the first appearance of Mott insulators in inhomogeneous systems. This provides a simple method to detect the phase transition point in such inhomogeneous systems. We believe it will be a useful tool for most cold atom experiments.

Optimal lattice depth on lifetime of D-band ultracold atoms in a triangular optical lattice.

Ultracold atoms in optical lattices are a flexible and effective platform for quantum precision measurement, and the lifetime of high-band atoms is an essential parameter for the performance of quantum sensors. In this work, we investigate the relationship between the lattice depth and the lifetime of D-band atoms in a triangular optical lattice and show that there is an optimal lattice depth for the maximum lifetime. After loading the Bose-Einstein condensate into D band of optical lattice by shortcut method, we observe the atomic distribution in quasi-momentum space for the different evolution time, and measure the atomic lifetime at D band with different lattice depths. The lifetime is maximized at an optimal lattice depth, where the overlaps between the wave function of D band and other bands (mainly S band) are minimized. Additionally, we discuss the influence of atomic temperature on lifetime. These experimental results are in agreement with our numerical simulations. This work paves the way to improve coherence properties of optical lattices, and contributes to the implications for the development of quantum precision measurement, quantum communication, and quantum computing.

All-fiber laser system for all-optical 87Rb Bose Einstein condensate to space application.

In the development of the Cold Atom Physics Research Rack (CAPR) on board the Chinese Space Station, the laser system plays a critical role in preparing the all-optical 87 R b Bose-Einstein condensates (BECs). An all-fiber laser system has been developed for CAPR to provide the required optical fields for atom interaction and to maintain the beam pointing in long-term operation. The laser system integrates a 780 nm fiber laser system and an all-fiber optical control module for sub-Doppler cooling, as well as an all-fiber 1064 nm laser system for evaporative cooling. The high-power, single-frequency 780 nm lasers are achieved through rare-Earth doped fiber amplification, fiber frequency-doubling, and frequency stabilization technology. The all-fiber optical control module divides the output of the 780 nm laser system into 15 channels and regulates them for cooling, trapping, and probing atoms. Moreover, the power consistency of each pair of cooling beams is ensured by three power tracking modules, which is a prerequisite for maintaining stable MOT and molasses. A high-power, compact, controlled-flexible, and highly stable l064 nm all-fiber laser system employing two-stage ytterbium-doped fiber amplifier (YDFA) technology has been designed for evaporative cooling in the optical dipole trap (ODT). Finally, an all-optical 87 R b BEC is realized with this all-fiber laser system, which provides an alternative solution for trapping and manipulating ultra-cold atoms in challenging environmental conditions.

Atomic Ramsey interferometry with S- and D-band in a triangular optical lattice.

Ramsey interferometers have wide applications in science and engineering. Compared with the traditional interferometer based on internal states, the interferometer with external quantum states has advantages in some applications for quantum simulation and precision measurement. Here, we develop a Ramsey interferometry with Bloch states in S- and D-band of a triangular optical lattice for the first time. The key to realizing this interferometer in two-dimensionally coupled lattice is that we use the shortcut method to construct π/2 pulse. We observe clear Ramsey fringes and analyze the decoherence mechanism of fringes. Further, we design an echo π pulse between S- and D-band, which significantly improves the coherence time. This Ramsey interferometer in the dimensionally coupled lattice has potential applications in the quantum simulations of topological physics, frustrated effects, and motional qubits manipulation.

Evidence of Potts-Nematic Superfluidity in a Hexagonal sp

As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multiorbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry C_{4} broken down to C_{2}. Here, we report an observation of a three-state (Z_{3}) quantum nematic order, dubbed "Potts-nematicity", in a system of cold atoms loaded in an excited band of a hexagonal optical lattice described by an sp^{2}-orbital hybridized model. This Potts-nematic quantum state spontaneously breaks a three-fold rotation symmetry of the lattice, qualitatively distinct from the Ising nematicity. Our field theory analysis shows that the Potts-nematic order is stabilized by intricate renormalization effects enabled by strong interorbital mixing present in the hexagonal lattice. This discovery paves a way to investigate quantum vestigial orders in multiorbital atomic superfluids.

Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime.

In an effort to address integrability breaking in cold gas experiments, we extend the integrable hydrodynamics of the Lieb-Liniger model with two additional components representing the population of atoms in the first and second transverse excited states, thus enabling a description of quasi-1D condensates. Collisions between different components are accounted for through the inclusion of a Boltzmann-type collision integral in the hydrodynamic equation. Contrary to standard generalized hydrodynamics, our extended model captures thermalization of the condensate at a rate consistent with experimental observations from a quantum Newton's cradle setup.

Observation of Many-Body Quantum Phase Transitions beyond the Kibble-Zurek Mechanism.

Quantum critical behavior of many-body phase transitions is one of the most fascinating yet challenging questions in quantum physics. Here, we improved the band-mapping method to investigate the quantum phase transition from superfluid to Mott insulators, and we observed the critical behaviors of quantum phase transitions in both the dynamical steady-state-relaxation region and the phase-oscillation region. Based on various observables, two different values for the same quantum critical parameter are observed. This result is beyond a universal-scaling-law description of quantum phase transitions known as the Kibble-Zurek mechanism, and suggests that multiple quantum critical mechanisms are competing in many-body quantum phase transition experiments in inhomogeneous systems.

Compact optically pumped cesium beam atomic clock with a 5-day frequency stability of 7×10-15.

Compared to other commercial atomic clocks in the time keeping field, the greatest advantage of cesium beam atomic clocks is their superior long-term stability. Compared to magnetic state-selection clocks, optically pumped cesium beam atomic clocks have more interacting atoms, which results in better stability potential. To achieve good long-term stability, we propose methods including stabilization of laser power and reconstruction of circuits. They play a key role in the long-term stability of cesium beam atomic clocks. After 75 days of continuous running and measurement, we released the 5-day stability results (7×10-15 Allan deviation) of our optically pumped cesium beam atomic clock. To the best of our knowledge, this is the best 5-day stability result ever reported for compact optically pumped cesium beam atomic clocks.

The emergence of picokelvin physics.

The frontier of low-temperature physics has advanced to the mid-picokelvin (pK) regime but progress has come to a halt because of the problem of gravity. Ultracold atoms must be confined in some type of potential energy well: if the depth of the well is less than the energy an atom gains by falling through it, the atom escapes. This article reviews ultracold atom research, emphasizing the advances that carried the low-temperature frontier to 450 pK. We review microgravity methods for overcoming the gravitational limit to achieving lower temperatures using free-fall techniques such as a drop tower, sounding rocket, parabolic flight plane and the International Space Station. We describe two techniques that promise further advancement-an atom chip and an all-optical trap-and present recent experimental results. Basic research in new regimes of observation has generally led to scientific discoveries and new technologies that benefit society. We expect this to be the case as the low-temperature frontier advances and we propose some new opportunities for research.

Asymmetric population of momentum distribution by quasi-periodically driving a triangular optical lattice.

Ultracold atoms in periodical-driven optical lattices enable us to investigate novel band structures and explore the topology of the bands. In this work, we investigate the impact of the ramping process of the driving signal and propose a simple but effective method to realize desired asymmetric population in momentum distribution by controlling the initial phase of the driving signal. A quasi-momentum oscillation along the shaking direction in the frame of reference co-moving with the lattice is formed, causing the formation of the mix of ground energy band and first excited band in laboratory frame, within the regime that the driving frequency is far less than the coupling frequency between ground band and higher energy bands. This method avoids the construction of intricate lattices or complex control sequence. With a triangular lattice, we experimentally investigate the influence of the initial phase, frequency, amplitude of the driving signal on the population difference and observe good agreement with our theoretical model. This provides guidance on how to load a driving signal in driven optical lattice experiment and also potentially supplies a useful tool to form a qubit that can be used in quantum computation.

Extraction and identification of noise patterns for ultracold atoms in an optical lattice.

To extract useful information about quantum effects in cold atom experiments, one central task is to identify the intrinsic fluctuations from extrinsic system noises of various kinds. As a data processing method, principal component analysis can decompose fluctuations in experimental data into eigenmodes, and give a chance to separate noises originated from different physical sources. In this paper, we demonstrate for Bose-Einstein condensates in one-dimensional optical lattices that the principal component analysis can be applied to time-of-flight images to successfully separate and identify noises from different origins of leading contribution, and can help to reduce or even eliminate noises via corresponding data processing procedures. The attribution of noise modes to their physical origins is also confirmed by numerical analysis within a mean-field theory. As the method does not rely on any a priori knowledge of the system properties, it is potentially applicable to the study of other quantum states and quantum critical regions.

High precision calibration of optical lattice depth based on multiple pulses Kapitza-Dirac diffraction.

The precise calibration of optical lattice depth is an important step in the experiments of ultracold atoms in optical lattices. The Raman-Nath diffraction method, as the most commonly used method of calibrating optical lattice depth, has a limited range of validity and the calibration accuracy is not high enough. Based on multiple pulses Kapitza-Dirac diffraction, we propose and demonstrate a new calibration method by measuring the fully transfer fidelity of the first diffraction order. The high sensitivity of the transfer fidelity to the lattice depth ensures the highly precision calibration of the optical lattice depth. For each lattice depth measured, the calibration uncertainty is further reduced to less than 0.6% by applying the Back-Propagation Neural Network Algorithm. The accuracy of this method is almost one order of magnitude higher than that of the Raman-Nath diffraction method, and it has a wide range of validity applicable to both shallow lattices and deep lattices.

Observation of a Dynamical Sliding Phase Superfluid with P-Band Bosons.

Sliding phases have been long sought after in the context of coupled XY models, as they are of relevance to various many-body systems such as layered superconductors, freestanding liquid-crystal films, and cationic lipid-DNA complexes. Here we report an observation of a dynamical sliding phase superfluid that emerges in a nonequilibrium setting from the quantum dynamics of a three-dimensional ultracold atomic gas loaded into the P band of a one-dimensional optical lattice. A shortcut loading method is used to transfer atoms into the P band at zero quasimomentum within a very short time duration. The system can be viewed as a series of "pancake"-shaped atomic samples. For this far-out-of-equilibrium system, we find an intermediate time window with a lifetime around tens of milliseconds, where the atomic ensemble exhibits robust superfluid phase coherence in the pancake directions, but no coherence in the lattice direction, which implies a dynamical sliding phase superfluid. The emergence of the sliding phase is attributed to a mechanism of cross-dimensional energy transfer in our proposed phenomenological theory, which is consistent with experimental measurements. This experiment potentially opens up a novel venue to search for exotic dynamical phases by creating high-band excitations in optical lattices.

Laser frequency stabilization using a dispersive line shape induced by Doppler Effect.

We report a simple and robust Doppler-free spectroscopic technique to stabilize a laser frequency to the atomic transition. By employing Doppler Effect on the atomic beam, we obtained a very stable dispersive signal with a high signal-to-noise ratio and no Doppler-background, which served as an error signal to electronically stabilize a laser frequency without modulation. For validating the performance of this technique, we locked a DFB laser to the (133)Cs D2 line and observed an efficient suppression of the frequency noise and a long-term reduction of the frequency drifts in a laboratory environment.

Excitation of atoms in an optical lattice driven by polychromatic amplitude modulation.

We investigate the mutiphoton process between different Bloch states in an amplitude modulated optical lattice. In the experiment, we perform the modulation with more than one frequency components, which includes a high degree of freedom and provides a flexible way to coherently control quantum states. Based on the study of single frequency modulation, we investigate the collaborative effect of different frequency components in two aspects. Through double frequency modulations, the spectrums of excitation rates for different lattice depths are measured. Moreover, interference between two separated excitation paths is shown, emphasizing the influence of modulation phases when two modulation frequencies are commensurate. Finally, we demonstrate the application of the double frequency modulation to design a large-momentum-transfer beam splitter. The beam splitter is easy in practice and would not introduce phase shift between two arms.

Two-stage crossed beam cooling with 6Li and ¹³³Cs atoms in microgravity.

Applying the direct simulation Monte Carlo (DSMC) method developed for ultracold Bose-Fermi mixture gases research, we study the sympathetic cooling process of 6Li and 133Cs atoms in a crossed optical dipole trap. The obstacles to producing 6Li Fermi degenerate gas via direct sympathetic cooling with 133Cs are also analyzed, by which we find that the side-effect of the gravity is one of the main obstacles. Based on the dynamic nature of 6Li and 133Cs atoms, we suggest a two-stage cooling process with two pairs of crossed beams in microgravity environment. According to our simulations, the temperature of 6Li atoms can be cooled to T = 29.5 pK and T/TF = 0.59 with several thousand atoms, which propose a novel way to get ultracold fermion atoms with quantum degeneracy near pico-Kelvin.

Sinusoidal phase-modulating self-mixing interferometer with nanometer resolution and improved measurement velocity range.

A new signal-processing method based on an electronic frequency down-conversion technique has been introduced into a sinusoidal phase-modulating, self-mixing interferometer. The developed interferometer employs an electro-optical crystal placed in the external cavity of a He-Ne laser to generate the sinusoidal phase modulation with high modulation rate and ultralow insertion loss. Phase quadrature signals which have been amplitude-modulated by the sine and cosine functions, respectively, of the measured displacement can be extracted from the high-density optical fringes through the use of dual-channel multiplier/filter circuits. Therefore, the displacement of the external target can be retrieved from the phase quadrature signals with nanometer resolution and high computational efficiency. Moreover, a much-improved measurement speed from 2.5 to 22 mm/s has been realized owing to the simplified signal-processing method. The performance of the proposed interferometer has been experimentally verified by comparison to an Agilent 5529A dual-frequency laser interferometer. The measurement results from the two instruments agree well, and we therefore expect that our new technique offers a powerful instrument for high-speed metrology sciences.

Tunneling dynamics and band structures of three weakly coupled Bose-Einstein condensates.

We study the tunneling dynamics and energy bands of three Bose-Einstein condensates which are coupled weakly with each other. The study is carried out with both the mean-filed model and the second-quantized model. The results from these two models are compared and found to agree with each other when the particle number is large. Without interaction, this system possesses a Dirac point in its energy band. This Dirac point is immediately destroyed and develops into a loop structure with arbitrary small interaction. This loop structure has a strong effect on the tunneling dynamics. We find that the tunneling dynamics in this system is very sensitive to the system parameter, e.g., the interaction strength. This sensitivity is found to be caused by the chaos in the mean-field model and the avoided energy crossings with tiny gaps in the second-quantized model. This result gives a certain indication on how the classical dynamics and quantum dynamics are connected in the semi-classical limit. Our mean-field results are also valid for three mutually coupled optical nonlinear waveguides.

Asymmetric superradiant scattering and abnormal mode amplification induced by atomic density distortion.

The superradiant Rayleigh scattering using a pump laser incident along the short axis of a Bose-Einstein condensate with a density distortion is studied, where the distortion is formed by shocking the condensate utilizing the residual magnetic force after the switching-off of the trapping potential. We find that very small variation of the atomic density distribution would induce remarkable asymmetrically populated scattering modes by the matter-wave superradiance with long time pulse. The optical field in the diluter region of the atomic cloud is more greatly amplified, which is not an ordinary mode amplification with the previous cognition. Our numerical simulations with the density envelop distortion are consistent with the experimental results. This supplies a useful method to reflect the geometric symmetries of the atomic density profile by the superradiance scattering.