Bloch oscillations (BOs) are oscillations of electrons under external constant forces in a lattice, revealing the wavelike behavior of electrons. BOs lead to the localization of the wave packet that is called Wannier-Stark localization (WSL), resulting in the inhibition of conductivity. We simulate BOs experimentally in a one-dimensional superconducting circuit with nine qubits. The nine qubits form a one-dimensional lattice and an electron is mapped to a photon. We experimentally realize the coherent control of BOs by applying a well-controlled driving force with a frequency close to BOs. We observe the competition between localization and delocalization of the wave pocket by changing the drive parameters. Our study demonstrates the visualized wave behavior of electrons and proves a way to modulate electron transport in a perfect lattice. Published by the American Physical Society 2024
Bloch oscillations (BOs) are oscillations of electrons under external constant forces in a lattice, revealing the wavelike behavior of electrons. BOs lead to the localization of the wave packet that is called Wannier-Stark localization (WSL), resulting in the inhibition of conductivity. We simulate BOs experimentally in a one-dimensional superconducting circuit with nine qubits. The nine qubits form a one-dimensional lattice and an electron is mapped to a photon. We experimentally realize the coherent control of BOs by applying a well-controlled driving force with a frequency close to BOs. We observe the competition between localization and delocalization of the wave pocket by changing the drive parameters. Our study demonstrates the visualized wave behavior of electrons and proves a way to modulate electron transport in a perfect lattice. Published by the American Physical Society 2024
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.
Atoms undergoing Bloch oscillations (BOs) in an accelerating optical lattice acquire momentum of two photon recoils per BO. This technique provides a large momentum transfer tool for atom optics, but its full exploitation for atom interferometric sensors requires both experimental and theoretical characterization of associated phases. Each BO involves a Landau-Zener crossing with multiple crossings inducing interference known as Stückelberg interference. We develop a multipath Stückelberg interferometer and investigate atomic phase evolution during BOs, up to 100 photon recoil momentum transfer. We compare to numerically calculated single-particle Schrödinger evolution, demonstrate highly coherent BO sequences, and assess phase stability requirements for BO-enhanced precision interferometry in fundamental physics and sensing applications. Published by the American Physical Society 2024
Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to the external force in a lattice, where the system possessing single- or multipleparticles could exhibit distinct oscillation behaviors. In particular, it has been pointed out that quantum statistics could dramatically affected the Bloch oscillation even in the absence of particle interactions, where the oscillation frequency of two pseudofermions with the anyonic statistical angle being pi becomes half of that for two bosons. However, these statisticdependent Bloch oscillations have never been observed in experiments up to now. Here, we report the first experimental simulation of anyonic Bloch oscillations using electric circuits. By mapping eigenstates of two anyons to modes of designed circuit simulators, the Bloch oscillation of two bosons and two pseudofermions are verified by measuring the voltage dynamics. It is found that the oscillation period in the two-boson simulator is almost twice of that in the two-pseudofermion simulator, which is consistent with the theoretical prediction. Our proposal provides a flexible platform to investigate and visualize many interesting phenomena related to particle statistics, and could have potential applications in the field of the novelty signal control.
Abstract Particle transport and localization phenomena in condensed-matter systems can be modeled using a tight-binding lattice Hamiltonian. The ideal experimental emulation of such a model utilizes simultaneous, high-fidelity control and readout of each lattice site in a highly coherent quantum system. Here, we experimentally study quantum transport in one-dimensional and two-dimensional tight-binding lattices, emulated by a fully controllable 3 × 3 array of superconducting qubits. We probe the propagation of entanglement throughout the lattice and extract the degree of localization in the Anderson and Wannier-Stark regimes in the presence of site-tunable disorder strengths and gradients. Our results are in quantitative agreement with numerical simulations and match theoretical predictions based on the tight-binding model. The demonstrated level of experimental control and accuracy in extracting the system observables of interest will enable the exploration of larger, interacting lattices where numerical simulations become intractable.
Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to an external force in a lattice, where a system possessing single or multiple particles could exhibit distinct oscillation behaviors. In particular, it has been pointed out that quantum statistics could dramatically affect the Bloch oscillation even in the absence of particle interactions, where the oscillation frequency of two pseudofermions with an anyonic statistical angle of [Formula: see text] becomes half of that for two bosons. However, these statistically dependent Bloch oscillations have never been observed in experiments until now. Here, we report the experimental simulation of anyonic Bloch oscillations using electric circuits. By mapping the eigenstates of two anyons to the modes of the designed circuit simulators, the Bloch oscillations of two bosons and two pseudofermions are verified by measuring the voltage dynamics. The oscillation period in the two-boson simulator is almost twice of that in the two-pseudofermion simulator, that is consistent with the theoretical prediction. Our proposal provides a flexible platform to investigate and visualize many interesting phenomena related to particle statistics and could have potential applications in the field of the signal control.
Bloch oscillation (BO), i.e., the oscillatory motion of a quantum particle in a periodic potential, is one of the most striking effects of coherent quantum transport in matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called acceleration theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e., not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only on average, and that the periodic wave-packet motion of the particle in real space is described by a trajectory in the complex plane, i.e., it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates.