### Description

Ultracold atoms in optical lattices are a powerful tool for quantum simulation, precise measurement, and quantum computation. A fundamental problem in applying this quantum system is how to manipulate the higher bands or orbitals in Bloch states effectively. Here we mainly introduce our methods for manipulating high orbital ultracold atoms in optical lattices with different configurations. Based on these methods, we load the ultracold atoms into the P and D bands of the hexagonal optical lattice and the triangular lattice, and then observe the novel quantum phases and study the dynamical evolution of the atoms in the high bands. Furthermore, we construct the atom-orbital qubit under nonadiabatic holonomic quantum control. The effective manipulation of the high orbitals provides strong support for applying ultracold atoms in the optical lattice in many fields.

The first is the shortcut method for transferring the ultracold atoms in a harmonic trap to the D band of a triangular optical lattice. The lattice potential can be expressed as $V(\vec{r})=-V\sum_{i,j}\cos[(\vec{k}_i-\vec{k}_j)\cdot\vec{r}$, where $\vec{k}_1=(\sqrt{3}\pi,-\pi)/\lambda$, $\vec{k}_2=(-\sqrt{3}\pi,-\pi)/\lambda$, $\vec{k}_3=(0,2\pi)/\lambda$, and $V$ is the depth of the triangular lattice. This shortcut method is characterized by short time and high fidelity, which can directly transfer ultracold atoms from the ground state in the harmonic trap to any Bloch state, and accurately manipulate atoms of different orbitals in optical lattices. The shortcut is composed of a series of optical lattice pulse sequences. Each pulse pulse-i consists of two parts. First, the lattice is turned on for $t^{\rm{on}}_j$, and then the interval is $t^{\rm{off}}_j$. The time $\{t^{\rm{on}}_j,t^{\rm{off}}_j\}$ are optimized to achieve the goal of manipulating quantum states. By this method, we load Bose-Einstein condensate of 87Rb atoms into the $\Gamma$ point of the first D band with zero quasimomentum in the triangular optical lattice. Then we investigate the collisional scattering channels for atoms in the excited bands of a triangular optical lattice and demonstrate a dominant scattering channel in the experiment. After some evolution time, the number of atoms scattering into the S-band induced by two-body collisions is around four times the number that scatters into the second most populated band. Our numerical calculation shows that the ss scattering channel is dominant, roughly consistent with the experimental measurement. The appearance of dominant scattering channels in a triangular optical lattice is owing to nonorthogonal lattice vectors. This work is helpful for the research on many-body systems and directional enhancement in optical lattices.

Next, we introduce the band swapping technique for loading the atoms into the second band of a hexagonal optical lattice. The key to realizing this is constructing a controllable composite optical lattice, including deep and shallow wells. In the experiment, we construct the composite hexagonal lattice by combining a triangular lattice and a honeycomb lattice, which can be expressed as $V(\vec{r})=-V_{\epsilon'}\sum_{i,j}\cos[(\vec{k}_i-\vec{k}_j)\cdot\vec{r}+\theta_j-\theta_i]+\frac{1}{2}V_{\epsilon}\sum_{i,j}\cos[(\vec{k}_i-\vec{k}_j)\cdot\vec{r}]$. $V_{\epsilon}$ ($V_{\epsilon'}$) is the depth of the honeycomb (triangular) lattice. This lattice contains two sub-wells, denoted as A and B. At first, well A is deeper than B, and the atoms are located at the A well. By changing the phase $\theta$, well A is shallower than B, and the atoms are pumped into the second band. After the atoms are transferred into the band maximum of the second band, the phase coherence in the state will immediately disappear. After a few milliseconds, the phase coherence reemerges, and the quantum state spontaneously chooses one orientation, giving rise to a three-state Potts nematicity.

Finally, we introduce an atom-orbital qubit using $s$- and $d$-orbitals of a one-dimensional optical lattice. We initial the qubit by the shortcut method, and the average fidelity of the initial states is $99.72(7)\%$. We have measured the orbital relaxation time ($T_1$) and the dephasing time ($T_2$), finding $T_1 = 4.5\pm0.1$ ms (milliseconds), and $T_2 = 2.1\pm0.1$ ms in our experiment. By programming lattice modulation, we reach universal nonadiabatic holonomic quantum gate control over the atom-orbital qubit, which exhibits noise-resilience against laser fluctuations due to geometrical protection. We demonstrate the holonomic quantum control of Hadamard and $\pi/8$ gates, which form a universal gate-set for single-qubit rotation. The lattice modulation pulses are programmed to minimize orbital leakage error, which is the key to reaching high fidelity holonomic quantum control of atom-orbital qubit. We implement quantum process tomography (QPT) on the orbital qubit to measure the full density matrix, from which the obtained average gate fidelity is $98.36(10)\%$. Furthermore, we give a proposal to construct two-qubit gates, by which we can achieve universal quantum computing with the orbit qubit setup. Our work opens up wide opportunities for atom-orbital-based quantum information processing, of vital importance to programmable quantum simulations of multiorbital physics in molecules and quantum materials.

[1] Hongmian Shui, Shengjie Jin (Co-first author), Zhihan Li, Fansu Wei, Xuzong Chen, Xiaopeng Li, and Xiaoji Zhou. Atom-orbital qubit under nonadiabatic holonomic quantum control. Physical Review A 104, L060601 (2021).

[2] Shengjie Jin, Wenjun Zhang, Xinxin Guo, Xuzong Chen, Xiaoji Zhou, and Xiaopeng Li. Evidence of Potts-Nematic Superfluidity in a Hexagonal sp2 Optical Lattice. Physical Review Letters 126, 035301 (2021).

[3] Xinxin Guo, Zhongcheng Yu, Peng Peng, Guoling Yin, Shengjie Jin, Xuzong Chen, and Xiaoji Zhou. Dominant scattering channel induced by two-body collision of D-band atoms in a triangular optical lattice. Physical Review A 104, 033326 (2021).

Presenter name | Xiaoji Zhou |
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