Observing a topological phase transition with deep neural networks from experimental images of ultracold atoms.

Although classifying topological quantum phases have attracted great interests, the absence of local order parameter generically makes it challenging to detect a topological phase transition from experimental data. Recent advances in machine learning algorithms enable physicists to analyze experimental data with unprecedented high sensitivities, and identify quantum phases even in the presence of unavoidable noises. Here, we report a successful identification of topological phase transitions using a deep convolutional neural network trained with low signal-to-noise-ratio (SNR) experimental data obtained in a symmetry-protected topological system of spin-orbit-coupled fermions. We apply the trained network to unseen data to map out a whole phase diagram, which predicts the positions of the two topological phase transitions that are consistent with the results obtained by using the conventional method on higher SNR data. By visualizing the filters and post-convolutional results of the convolutional layer, we further find that the CNN uses the same information to make the classification in the system as the conventional analysis, namely spin imbalance, but with an advantage concerning SNR. Our work highlights the potential of machine learning techniques to be used in various quantum systems.

"Designing synthetic topological matter with atoms and lights".

One of the most interesting directions in quantum simulations with ultracold atoms is the expansion of our capability to investigate exotic topological matter. Using sophisticated atom-light couplings in an atomic system, scientists have demonstrated several iconic lattice models that exhibit non-trivial band topology in a controlled manner.

Heuristic machinery for thermodynamic studies of SU(N) fermions with neural networks.

The power of machine learning (ML) provides the possibility of analyzing experimental measurements with a high sensitivity. However, it still remains challenging to probe the subtle effects directly related to physical observables and to understand physics behind from ordinary experimental data using ML. Here, we introduce a heuristic machinery by using machine learning analysis. We use our machinery to guide the thermodynamic studies in the density profile of ultracold fermions interacting within SU(N) spin symmetry prepared in a quantum simulator. Although such spin symmetry should manifest itself in a many-body wavefunction, it is elusive how the momentum distribution of fermions, the most ordinary measurement, reveals the effect of spin symmetry. Using a fully trained convolutional neural network (NN) with a remarkably high accuracy of ~94% for detection of the spin multiplicity, we investigate how the accuracy depends on various less-pronounced effects with filtered experimental images. Guided by our machinery, we directly measure a thermodynamic compressibility from density fluctuations within the single image. Our machine learning framework shows a potential to validate theoretical descriptions of SU(N) Fermi liquids, and to identify less-pronounced effects even for highly complex quantum matter with minimal prior understanding.

Active control of a diode laser with injection locking using a laser line filter.

We present a simple and effective method to implement an active stabilization of a diode laser with injection locking, which requires minimal user intervenes. The injection-locked state of the diode laser is probed by a photodetector, of which sensitivity is enhanced by a narrow laser-line filter. Taking advantage of the characteristic response of laser power to spectral modes from the narrow laser-line filter, we demonstrate that high spectral purity and low-intensity noise of the diode can be simultaneously maintained by active feedback to the injected laser. Our method is intrinsically cost-effective and does not require bulky devices, such as Fabry-Pérot interferometers or wavemeters, to actively stabilize the diode laser. Based on the successful implementation of this method in our quantum gas experiments, it is conceivable that our active stabilization will greatly simplify potential applications of injection locking of diode lasers in modularized or integrated optical systems.

Collective dipole oscillations of a spin-orbit coupled Fermi gas.

The collective dipole mode is induced and measured in a spin-orbit (SO) coupled degenerate Fermi gas of 173Yb atoms. Using a differential optical Stark shift, we split the degeneracy of three hyperfine states in the ground manifold, and independently couple consecutive spin states with the equal Raman transitions. A relatively long-lived spin-orbit-coupled Fermi gas, readily being realized with a narrow optical transition, allows to explore a single-minimum dispersion where three minima of spin-1 system merge into and to monitor collective dipole modes of fermions in the strong coupling regime. The measured oscillation frequency of the dipole mode is compared with the semi-classical calculation in the single-particle regime. Our work should pave the way towards the characterization of spin-orbit-coupled fermions with large spin s >[Formula: see text] in the strong coupling regime.

Observation of symmetry-protected topological band with ultracold fermions.

Symmetry plays a fundamental role in understanding complex quantum matter, particularly in classifying topological quantum phases, which have attracted great interests in the recent decade. An outstanding example is the time-reversal invariant topological insulator, a symmetry-protected topological (SPT) phase in the symplectic class of the Altland-Zirnbauer classification. We report the observation for ultracold atoms of a noninteracting SPT band in a one-dimensional optical lattice and study quench dynamics between topologically distinct regimes. The observed SPT band can be protected by a magnetic group and a nonlocal chiral symmetry, with the band topology being measured via Bloch states at symmetric momenta. The topology also resides in far-from-equilibrium spin dynamics, which are predicted and observed in experiment to exhibit qualitatively distinct behaviors in quenching to trivial and nontrivial regimes, revealing two fundamental types of spin-relaxation dynamics related to bulk topology. This work opens the way to expanding the scope of SPT physics with ultracold atoms and studying nonequilibrium quantum dynamics in these exotic systems.

Mean-Field Scaling of the Superfluid to Mott Insulator Transition in a 2D Optical Superlattice.

The mean-field treatment of the Bose-Hubbard model predicts properties of lattice-trapped gases to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number z. We test this scaling directly by comparing coherence properties of ^{87}Rb gases that are driven across the superfluid to Mott insulator transition within optical lattices of either the kagome (z=4) or the triangular (z=6) geometries. The coherent fraction measured for atoms in the kagome lattice is lower than for those in a triangular lattice with the same interaction and tunneling energies. A comparison of measurements from both lattices agrees quantitatively with the scaling prediction. We also study the response of the gas to a change in lattice geometry, and observe the dynamics as a strongly interacting kagome-lattice gas is suddenly "hole doped" by introducing the additional sites of the triangular lattice.

One-dimensional sawtooth and zigzag lattices for ultracold atoms.

We describe tunable optical sawtooth and zigzag lattices for ultracold atoms. Making use of the superlattice generated by commensurate wavelengths of light beams, tunable geometries including zigzag and sawtooth configurations can be realised. We provide an experimentally feasible method to fully control inter- (t) and intra- (t') unit-cell tunnelling in zigzag and sawtooth lattices. We analyse the conversion of the lattice geometry from zigzag to sawtooth, and show that a nearly flat band is attainable in the sawtooth configuration by means of tuning the lattice parameters. The bandwidth of the first excited band can be reduced up to 2% of the ground bandwidth for a wide range of lattice setting. A nearly flat band available in a tunable sawtooth lattice would offer a versatile platform for the study of interaction-driven quantum many-body states with ultracold atoms.

Ultracold atoms in a tunable optical kagome lattice.

We realize a two-dimensional kagome lattice for ultracold atoms by overlaying two commensurate triangular optical lattices generated by light at the wavelengths of 532 and 1064 nm. Stabilizing and tuning the relative position of the two lattices, we explore different lattice geometries including a kagome, a one-dimensional stripe, and a decorated triangular lattice. We characterize these geometries using Kapitza-Dirac diffraction and by analyzing the Bloch-state composition of a superfluid released suddenly from the lattice. The Bloch-state analysis also allows us to determine the ground-state distribution within the superlattice unit cell. The lattices implemented in this work offer a near-ideal realization of a paradigmatic model of many-body quantum physics, which can serve as a platform for future studies of geometric frustration.

Itinerant ferromagnetism in a Fermi gas of ultracold atoms.

Can a gas of spin-up and spin-down fermions become ferromagnetic because of repulsive interactions? We addressed this question, for which there is not yet a definitive theoretical answer, in an experiment with an ultracold two-component Fermi gas. The observation of nonmonotonic behavior of lifetime, kinetic energy, and size for increasing repulsive interactions provides strong evidence for a phase transition to a ferromagnetic state. Our observations imply that itinerant ferromagnetism of delocalized fermions is possible without lattice and band structure, and our data validate the most basic model for ferromagnetism introduced by Stoner.