Few Body Physics in Synthetic Dimensions with SU(N) Interactions

Chenxi Huang, Tao Chen, Qian Liang +7 more

Topology can imbue lattice systems with special properties, notably the presence of robust eigenstates living at their boundary. Through dimensional reduction, the robust bulk band topology of, e.g., the integer quantum Hall system can be mapped onto similarly robust charge-pumping dynamics of a topological pump living in one lower dimension. Recent studies have uncovered a rich influence of interactions on the dynamics of topological pumps in nonlinear systems, including the robust pumping of self-bound solitons. These striking observations in classical nonlinear photonics have raised a number of questions, chiefly if and how this phenomenology persists in strongly correlated quantum systems and in the few-body limit. Here, using few- and many-atom arrays, we explore how dipolar interactions impact the dynamics of topological population pumping along a Rydberg synthetic dimension. In the few-body limit, we find that dipolar interactions lead to self-bound states that are efficiently pumped along the synthetic dimension, described by an emergent pair-state topological pump. We find that this interaction-assisted pumping persists in many-atom arrays, with a sharpened dependence on the dipolar interaction strength that stems from the enhanced spatial connectivity. These Rydberg-based studies on interaction-assisted topological pumping help connect observations from classical nonlinear photonics to the few-body quantum limit and pave the way for studies of new strongly correlated quantum pumping phenomena.

Sergio A Albeverio, S.-M. Fei, Pavel Kurasov

Yusuke Nishida

Junlin Wang, Luojia Wang, Jin-Lou Ma +3 more

Generation and control of entanglement are fundamental tasks in quantum information. In this paper, we propose a novel approach to generating controllable frequency-entangled photons using the concept of synthetic frequency dimension in an optical system. This system consists of a ring resonator made of tailored third-order nonlinear media to induce photon-photon interactions and a periodic modulator to manipulate coupling between different frequency modes. We show that this system provides a unique platform for the exploration of distinct few- or many-body quantum phases including chaos, localization, and integrability in a highly integrable photonics platform. In particular, we develop a proposal to calculate the spectral form factor, which characterizes the degree of chaos in the system and differentiates between these phases based on observable measurements. Then, the switching of the quench dynamics from an intermediate phase between integrable and chaotic to the Stark many-body phase can generate and sustain stable frequency-entangled multiphoton states. This work is the first to explore rich and controllable quantum phases beyond single-particle physics in a synthetic dimension.

V. Polkanov, Orest Hryhorchak, V. Pastukhov

Thomas Bilitewski

This thesis considers novel phenomena arising in the few and many-body physics of ultracold atomic gases. The specific models considered are motivated by recent experimental developments. A main focus will be the theoretical description of systems used in the simulation of artificial gauge fields via time-modulated tuning of system parameters and via the coupling of internal atomic states by Raman lasers. A second aspect will be the study of systems with synthetic dimensions and the effects of the unconventional infinite range interactions that arise in this description. It explores time-dependent effects in the single and few particle setting and the collective many-body phases arising in these models. Using the framework of Floquet theory it studies the interplay of time-dependence and particle-interactions both in continuum and lattice systems. In particular, it provides a general explanation for how heating effects can arise in interacting periodically time-dependent quantum systems, identifying an underlying mechanism for heating via two-particle collisions and the relevant scaling of the associated rates with system parameters. Furthermore, the general framework is applied to specific experimental set-ups. This yields heating rates and population dynamics in agreement with the experimental data. Finally, it also proposes improvements to the experiment that allow to limit the heating rates which is required to access the strongly interacting regime. In the case of synthetic dimensions the focus lies on the intriguing interplay of artificial gauge fields and strong particle interactions of atoms confined in optical lattices. In these systems a suitable coupling of internal spin-states of the atoms allows to simulate an additional finite dimension. In contrast to the typically encountered situation of short-range interactions the particle interactions are infinite-range in this synthetic dimension. In the strong coupling limit an effective description for this system is derived and its ground state phase diagram is studied using numerical tools.