Qi Zhou

Though it was believed that breathers of Bose-Einstein condensates oscillate at a frequency fixed by the external traps, a recent ENS experiment has shown that breathers of different initial shapes could have distinct frequencies. Some of them even do not have regular periods at all. We have solved this puzzle (PRL,2020). Whereas the quantum dynamics of a previously studied breather can be described by a single Poincare disk, a generic breather requires multiple Poincare disks. The interference between trajectories on multiple disks leads to extra dynamical factors and thus the observed period multiplication. When incommensurate frequencies are involved, breathers will not be able to recover the initial states.

Chemical reactions are known for their complexities. Taking into account quantum effects imposes an even bigger challenge to physicists and chemists. Unprecedentedly, universality exists in chemical reactions of dilute molecules, as we recently found (Science Advances, 2020). We established universal relations between the two-body losses of reactive molecules and quantum many-body correlations , which are valid for arbitrary particle numbers, arbitrary temperatures, and arbitrary interaction strengths. This work opens the door to an unexplored area intertwining quantum chemistry, atomic, molecular and optical physics, and condensed matter physics.

In quantum dynamics of Bose-Einstein condensates, it is well-known that there are both stable and unstable modes, the latter of which are referred as to the so-called dynamical instability. We have found that such dynamics have an underlying geometry of a Poincare disk (PRL, 2020). Stable and unstable modes are actually closed and open trajectories on the Poincare disk, respectively. This connection between dynamics and geometry has deep roots in symmetry -- the same SU(1,1) symmetry controls both the dynamics and geometry. Our work suggests a new geometric framework to coherently control quantum systems using SU(1,1) echoes, which could reverse dynamics of interacting bosons without changing the sign of a Hamiltonian.

Despite that fermions are governed by the Pauli exclusion principle, they could behave like bosons under certain conditions. In a joint project with Prof. G. Jo's group at HKUST, we found for the first time the evidence for bosonizations of 3D fermions (PRX, 2020). Using the scaling of the contact with the number of components, we have unambiguously shown that a fermionic system with the SU(N) symmetry approaches spinless bosons in the large N limit, since the contact is the central quantity controlling all thermodynamic observables. These results do not rely on exact solutions in 1D as previously studied.

Whereas periodical drivings lead to many interesting phenomena, such as discrete time crystals, they inevitably cause thermalization. We show that an all-to-all interaction allows discrete time crystals to evade thermalization and maintain quantum synchronization regardless of spatial inhomogeneities (PRR, 2020). In particular, such a perfect synchronization provides discrete time crystals with a powerful application in precision measurement of the driving frequency or the interaction strength beyond the Heisenberg limit.

A synthetic torus consists of a ring trap in the real space and internal states of atoms cyclically coupled by Laguerre-Gaussian Raman beams (PRL, 2019). A net effective magnetic flux could be threaded through its surface—an impossible mission for a torus in the real space. Due to the periodic boundary condition in the synthetic dimension, a periodic lattice emerges in the real dimension. This scheme allows physicists to bypass constraints imposed by certain physical laws in experiments and to create exotic synthetic spaces.

Though it is in general believed that photoassociation leads to two-body loss, our collaborators, Prof. Y. Chen's group, and we have found that a coherent superposition of internal states of atoms (colored spheres) gives rise to a complete suppression of this type of two-body loss, due to a destructive interference of two photoassociation pathways (PRL, 2018). This is a concrete example of quantum control of photochemical reaction.

A single boson with four internal or external states (colored spheres) sees a Yang monopole of charge 1 in a five-dimensional parameter space. What will a collection of interacting bosons see ? We show that they see something very different, including multiple Yang monopoles scattered in the parameter space or a giant Yang monopole, whose charge is the total particle number squared. More interestingly, many bosons together may even see continuous topological defects (PRL, 2018).

Recent years have seen fascinating progress in the study of synthetic gauge fields for charge-neutral ultracold atoms. This topical review (Journal of Physics B, 2017) surveys recent developments in using synthetic gauge fields to manipulate novel quantum phenomena that are not easy to access in other systems, ranging from unconventional single-particle dispersions to novel quantum many-body states induced by the interplay between interactions and synthetic gauge fields.

Spin–orbit coupling (SOC) is central to many physical phenomena. Whereas laser–atom interaction provides physicists a unique means to create synthetic SOC in ultracold atoms, a two-dimensional (2D) synthetic SOC eluded experiments for quite a while. In this work (Nature Physics, 2016), a 2D synthetic SOC was created for the first time in a laboratory by our experimental collaborators, Prof. Jing Zhang's group at Shanxi University.

In ultracold atoms, the average inter-particle spacing is much larger than the range of interactions. Such separation of length scales allows us to define contact matrix, which governs not only universal thermodynamic relations of dilute systems, but also correlations in many-body systems, for instance, atomic quantum Hall states (Physical Review Letters, 2016) and some intriguing superfluids (Physical Review A, 2017).

It is notably difficult to realize a chiral d-wave superfluid, a preliminary example of interacting topological superfluid, as a strong d-wave interaction is often required. This work (Physical Review Letters, 2015) presents a new principle for creating a chiral d-wave superfluid using a periodically driven lattice. Because of an imprinted 2D pseudospin-orbit coupling, s-wave interaction naturally creates a synthetic d-wave interaction and a chiral d-wave superfluid.

Half particles in the universe have a natural instinct to condense at zero temperature. We show that this textbook result will be changed by unconventional single-particle dispersions created by synthetic gauge fields (Nature communications, 2015). When quartic dispersions show up at the Lifshitz point, a 2D algebraic quantum liquid rises at the ground state. A similar phenomenon occurs in 1D when a non-Luttinger liquid emerges at the Lifshitz point (Physical Review A, Rapid Communication, 2014).

Physical systems near a critical point are entirely governed by the universality class of the phase transitions. Dilute systems are governed by universal relations through contacts. Whereas these two types of universality describe distinct phenomena, this work (Nature Communications, 2014) establishes an intrinsic connection between them by revealing critical behaviors of the s-wave contact near continuous phase transition points.