Zhang Ren, associate professor of the School of Physics of Xi'an Jiaotong University (XJTU), and the research group of Professor Zhou Qi of Purdue University in the United States have made progress in the quantum simulation of ultra-cold atomic physics. Related results were published in top physics journals Physical Reviews Letter and Science Bulletin.

Based on the ultra-cold atomic physics platform, people can carry out novel quantum physics research and deepen people's understanding of curved space and its symmetry applications.

On one hand, with the flexible maneuverability of ultra-cold atomic physics, people can study physical phenomena in high-dimensional space. Therefore, the study of artificial dimensions is one of the frontier research directions that people have attached great importance to in recent years.

For example, by using the interaction between lasers and atoms, people have realized geometric structures such as Hall cylinders and Hall bands, and therefore been able to study the novel physical phenomena in them.

The research group of Zhou and Associate Professor Zhang Ren studied the localization phenomenon of the Hall cylinder, and theoretically pointed out that the boundary conditions in the artificial dimension are crucial to the appearance of the localization state.

The conclusions are consistent with the experimental results of Professor Ian Spielman's group of the National Bureau of Standards. The research results were published in the Physical Review Letters (2021) under the title of "Localization on a synthetic Hall cylinder".

On the other hand, the research of ultra-cold atom physics has gradually intersected with other research fields. The Efimov state, with discrete scale invariance, has attracted the interest of physicists for decades. Recent studies have found that the Efimov effect not only exists in the three-body problem, but also in condensed matter, such as topological materials and graphene.

The quantum state studied on the hyperbolic plane has similar properties to the Efimov state. Specifically, the non-zero energy eigenstates on the Poincaré half-plane and the Poincaré disk are infinitely degenerate. There is a discrete scale invariance similar to the Efimov state between the degenerate states. Therefore, they call these degenerate eigenstates Efimov-like states.

By manipulating the non-uniform transition intensity between the grid points and the energy occupied by the grid points, the author pointed out that the grid point model in a flat, two-dimensional space can simulate Poincaré half-planes, Poincaré disks and other arbitrary two-dimensional Riemann surfaces, and provide a new platform for studying novel quantum effects in curved space.

For example, there is a funnel mouth in hyperbolic space. In the hyperbolic coordinate system, the eigenstate index of the system is distributed near the mouth of the funnel. Therefore, in the process of dynamical evolution, any initial wave packets will gather towards the funnel mouth. This phenomenon is called the quantum funnel phenomenon. This is the first time that physicists have discovered the quantum funnel phenomenon in the Hermitian system.

The research results were published online in the "Chinese Science Bulletin" under the title "Efimov-like states and quantum funneling effects on synthetic hyperbolic surfaces". Zhang is the first author of the above two papers, and XJTU is the first signatory unit.

Symmetry is one of the most important tools for people to carry out physics research. With the aid of symmetry analysis, people can get the most thorough understanding of related physical phenomena.

Based on the SU (1,1) symmetry of the two-dimensional interaction condensate, the research group of Zhang and Zhou studied the dynamics of two-dimensional Bose gas, and proposed an SU (1,1) echo method that can modulate the dynamic evolution of the breathing mode. Based on this method, they provided an intuitive physical image of the behavior of breathing patterns with special geometric structures.

An experiment conducted by the Research University of Paris (Ecole Normale Superieure), one of France's best post-secondary institutions, in 2019 found that the oscillation period of certain shapes of breathing modes is consistent with the traditional theory, while other shapes have longer periods, and even produce irregular, non-periodical motions.

These novel behaviors of breathing modes have aroused great interest in the entire field, but there has been a lack of theoretical explanations. As the breathing mode of the eigenstate of any harmonic potential well, its dynamic evolution can be visualized on a single Poincaré disk, corresponding to closed or open orbits under attractive or repulsive potential wells, respectively.

The SU (1,1) echo method can reverse these dynamic processes and close these orbits. As the eigenstate of an inharmonic potential well, the breathing mode needs to rely on multiple disks to describe its dynamics. The periodic behavior is derived from the quantum interference between different disks.

If the dynamic phase in quantum interference is incommensurate, the motion of the breathing mode will not show any periodic behavior. Different from the breathing mode generated by passive dynamics, the SU (1,1) echo periodically modulates the frequency of the potential well. 

On one hand, the dynamic process including free expansion can be reversed, and on the other hand, the degree of freedom in the dynamic evolution of the breathing mode is expanded, which makes the breathing mode SU(1,1) echo method have certain advantages in detecting the detuning of the harmonic potential well.

The spin echo based on the symmetry of SU (2) has been widely used in medical and scientific research, and has a profound impact on people's daily lives. Researchers believe that the SU (1,1) echo method is also expected to have an important impact in the future.

The research results are titled "SU (1,1) Echoes for Breathers in Quantum Gases" and was published in Physical Review Letters (2020) in December 2020. Zhang is the co-first author of the paper. 

This series of research was funded by the National Key R&D Program of China and the National Natural Science Foundation of China. Zhang's main research interests focus on the few-body problem of ultra-cold atomic physics, the evolution of many-body dynamics, and the quantum simulation of curved space.

Link to the paper: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.253002

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.193001

https://www.sciencedirect.com/science/article/pii/S2095927321004400#f0025