Abstract
The Bloch oscillation (BO) and Wannier-Stark localization (WSL) are fundamental concepts about metal-insulator transitions in condensed matter physics. These phenomena have also been observed in semiconductor superlattices and simulated in platforms such as photonic waveguide arrays and cold atoms. Here, we report experimental investigation of BOs and WSL simulated with a 5-qubit programmable superconducting processor, of which the effective Hamiltonian is an isotropic XY spin chain. When applying a linear potential to the system by properly tuning all individual qubits, we observe that the propagation of a single spin on the chain is suppressed. It tends to oscillate near the neighborhood of their initial positions, which demonstrates the characteristics of BOs and WSL. We verify that the WSL length is inversely correlated to the potential gradient. Benefiting from the precise single-shot simultaneous readout of all qubits in our experiments, we can also investigate the thermal transport, which requires the joint measurement of more than one qubits. The experimental results show that, as an essential characteristic for BOs and WSL, the thermal transport is also blocked under a linear potential. Our experiment would be scalable to more superconducting qubits for simulating various of out-of-equilibrium problems in quantum many-body systems.
Highlights
The transport phenomena in solids is one of the central topics in condensed matter physics
Where a^yj a^j is a^yj the (a^j) is the photon number operator, creation operator, n^j gj,j+1 is the nearest-neighbor coupling strength, Uj < 0 is the on-site attractive interaction resulted from the anharmonicity, and hj is the local potential which is tunable by DC biases through Z lines
We have reported the experimental observation of Bloch oscillation (BO) and Wannier-Stark localization (WSL) on a 5-qubit superconducting processor
Summary
The transport phenomena in solids is one of the central topics in condensed matter physics. About 80 years ago, Bloch and Zener predicted that electrons cannot spread uniformly in a crystal lattice under a constant force, and instead, they would oscillate and localize[1,2,3] This oscillation is called Bloch oscillations (BOs), and the corresponding localization is called Wannier-Stark localization (WSL). BOs and WSL are typical quantum effects which reveal the wave properties of electrons They can hardly be observed directly in normal bulk materials due to the requirement of long coherence times. It is not until the 1990s that these phenomena were observed experimentally in semiconductor superlattices[4]. BOs in bosonic systems have been observed in the cold atoms[7,8,9,10,11,12,13,14,15,16] and photonic waveguide arrays[17], etc
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