We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the dynamics of atoms along the lattice is effectively governed by a periodically driven Su-Schrieffer-Heeger model, which is equivalent to a discrete-time topological quantum walk. We directly measure the underlying topological invariants through time-averaged mean chiral displacements, which are consistent with our experimental observation of topological phase transitions. We then observe interaction-induced localization in the quantum-walk dynamics, where atoms tend to populate a single momentum-lattice site under interactions that are nonlocal in momentum space. Our experiment opens up the avenue of investigating discrete-time topological quantum walks using cold atoms, where the many-body environment and tunable interactions offer exciting new possibilities.
We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the dynamics of atoms along the lattice is effectively governed by a periodically driven Su-Schrieffer-Heeger model, which is equivalent to a discrete-time topological quantum walk. We directly measure the underlying topological invariants through time-averaged mean chiral displacements, which are consistent with our experimental observation of topological phase transitions. We then observe interaction-induced localization in the quantum-walk dynamics, where atoms tend to populate a single momentum-lattice site under interactions that are nonlocal in momentum space. Our experiment opens up the avenue of investigating discrete-time topological quantum walks using cold atoms, where the many-body environment and tunable interactions offer exciting new possibilities.
Recent experiments demonstrated that single-particle quantum walks can reveal the topological properties of single-particle states. Here, we generalize this picture to the many-body realm by focusing on multiparticle quantum walks of strongly interacting fermions. After injecting N particles with multiple flavors in the interacting SU(N) Su-Schrieffer-Heeger chain, their multiparticle continuous-time quantum walk is monitored by a variety of methods. We find that the many-body Berry phase in the N-body part of the spectrum signals a topological transition upon varying the dimerization, similarly to the single-particle case. This topological transition is captured by the single- and many-body mean chiral displacement during the quantum walk and remains present for strong interaction as well as for moderate disorder. Our predictions are well within experimental reach for cold atomic gases and can be used to detect the topological properties of many-body excitations through dynamical probes.
"As the progress of science pushes the frontiers of studying nature to both the extremely large scale and the incredibly small scale, experiments can become increasingly difficult to perform. Therefore, a scale model experiment for these kinds of physics can be useful as long as it is relatively easy to access and control. This is the idea of quantum simulation, where one system exactly mimics another when they are subjected to equivalent physical scenarios. Topological systems, those with a property that is stabilized by their specific configuration, are often quite challenging to experimentally probe. Therefore, test bed systems have been widely and successfully applied to studying topology in an effort to advance the field, which promises enticing applications such as robust quantum technology. Our particular scheme uses a novel type of ""synthetic"" dimension for atoms of a Bose–Einstein condensate, which we call a momentum-space lattice, to emulate one-dimensional lattice models. The idea of a synthetic dimension or synthetic lattices is a useful construct to describe how the particle dynamics can evolve in degrees of freedom that are not directly related to transport in real space. This can relate to population dynamics in an internal degree of freedom, such as spin, or, in our case, in the dynamics of free-particle-like atomic momentum states. We expose a Bose–Einstein condensate to two laser fields that are capable of driving transitions between different momentum states of the condensate atoms through a two-photon Bragg diffraction process. Neighboring states in the free-particle dispersion relation are characterized by a unique momenta and energy spacing such that we can independently control every aspect of their coupling. In this thesis, we report on the design and construction of an apparatus for the production of 87Rb Bose–Einstein condensates as well as the partial construction of an apparatus for the production of 39K Bose–Einstein condensates. We also discuss the experimental realization of, and theoretical background for, our momentum-space lattice. Using the momentum-space lattice, we perform experiments on not only topological systems, but also on driven artificial spins featuring chaotic dynamics, as well as faster-than-adiabatic quantum state control and preparation. Our measurements of topological systems are based in the 1D Su–Schrieffer–Heeger model, where we report on the direct observation of the localized, solitonic edge state created by the topology inherent in the system. Through the addition of exactly tunable tunneling disorder, we observe the destruction of the band topology due to disorder at a random-singlet transition. Furthermore, we drive a trivial system into a topological phase through the addition of disorder, observing a counter-intuitive phenomenon known as the topological Anderson insulator for the first time. We go on to report on our driven, tunable spin experiment, where we probe effective spin ""squeezing"" (in the absence of any entanglement in our noninteracting system), the out-of-time-ordered correlation function, and chaos. And finally, we use our momentum-space lattice to demonstrate a technique which allows a system to be transformed faster than the adiabatic limit with no diabatic transitions in a highly non-trivial regime. Due to the versatility of the momentum-space lattice, the results detailed here have a broad impact. Our observations of topological phenomena in elementary and canonical 1D systems are some of the first experimental verifications of long-standing predictions. Further, our studies of the interplay between classical chaos and quantum systems may help shed light on this complex and rich problem. And from a more ""applied science"" perspective, our demonstrations of generalized counter-diabatic techniques are widely beneficial and applicable to many systems where adiabaticity is challenged."
Simulating higher-order topological materials in synthetic quantum matter is an active research frontier for its theoretical significance in fundamental physics and promising applications in quantum technologies. Here we experimentally implement two-dimensional (2D) momentum lattices with highly programmable ability using ultracold 87Rb atoms. Through precise control of experimental parameters, we simulate a 2D Su-Schrieffer-Heeger model with this technique, and observe the characteristic dynamics of corner and edge-bound states, where the corner state is identified as a higher-order topological bound state in the continuum. We further study the adiabatic preparation of the corner state by engineering evolutions with time-dependent Hamiltonians. We also demonstrate the higher-order topological phase transition by measuring both the bulk topological invariant and the topological corner state. Our new platform opens the avenue for exploring the exotic dynamics and topology in higher synthetic dimensions, making use of the rich degrees of freedom of cold atoms systems.
Simulating higher-order topological materials in synthetic quantum matter is an active research frontier for its theoretical significance in fundamental physics and promising applications in quantum technologies. Here we experimentally implement two-dimensional (2D) momentum lattices with highly programmable ability using ultracold 87Rb atoms. Through precise control of experimental parameters, we simulate a 2D Su-Schrieffer-Heeger model with this technique, and observe the characteristic dynamics of corner and edge-bound states, where the corner state is identified as a higher-order topological bound state in the continuum. We further study the adiabatic preparation of the corner state by engineering evolutions with time-dependent Hamiltonians. We also demonstrate the higher-order topological phase transition by measuring both the bulk topological invariant and the topological corner state. Our new platform opens the avenue for exploring the exotic dynamics and topology in higher synthetic dimensions, making use of the rich degrees of freedom of cold atoms systems.
We present a discrete-time, one-dimensional quantum walk based on the entanglement between the momentum of ultracold rubidium atoms (the walk space) and two internal atomic states (the "coin" degree of freedom). Our scheme is highly flexible and can provide a platform for a wide range of applications such as quantum search algorithms, the observation of topological phases, and the realization of walks with higher dimensionality. Along with the investigation of the quantum-to-classical transition, we demonstrate the distinctive features of a quantum walk and contrast them to those of its classical counterpart. Also, by manipulating either the walk or coin operator, we show how the walk dynamics can be steered or even reversed.
Symmetry plays a crucial role in understanding topological phases in materials. In one-dimensional systems, such as the Su-Schrieffer-Heeger (SSH) model, chiral symmetry is thought to ensure the quantization of the Zak phase and the nontrivial topological phase. However, our work demonstrates that the one-dimensional lattice system with broken chiral symmetry can still possess quantized Zak phase and nontrivial topological phase. Specifically, we use a Bose-Einstein condensate of 87Rb atoms in a momentum space lattice of ultracold atoms to effectively simulate a one-dimensional Zigzag model of 26 sites, which intrinsically breaks the chiral symmetry by additional next-nearest-neighbor coupling. To ensure the existence of the nontrivial topological phase, where the Zak phase can be measured from the time-averaged displacement during the system’s evolution, we need to preserve the inversion symmetry by modulating laser power so that all next-nearest-neighbor coupling strengths are equal. Furthermore, by changing the ratio of nearest-neighbor coupling strengths, we observe a topological phase transition from a nontrivial topological phase to a trivial topological phase at the point where the ratio equals 1. Our work demonstrates that the ultracold atom system provides a controllable platform for studying the symmetrical phase and topological phase, with the potential to explore nonlinear topological phenomena by increasing the interactions among atoms. In addition, our system can be used to investigate other interesting topological phenomena with more complex models, such as critical phenomena at the phase transitions and flat band structures in the extended SSH model with long-range coupling. By controlling the coupling strengths, we can also explore the influence of different symmetries on the topological properties of extended SSH models in the future. Moreover, our platform makes it possible to studythe models with more energy bands, such as the Aharonov-Bohm caging model with a three-level structure, which shows peculiar flat-band properties. This work provides opportunities for various studies in the fields of symmetry, topology, and the interaction of controllable quantum systems.