Quantum Simulation Based On Ultracold Atoms And Superconducting Circuits

Recently quantum simulation has raised much attention.Quantum simulation not only can help us to explore many basis properties of the many body system,but also can provide a rout to reveal a lot of novel energy sources and materials.As the experimental techniques improving,the controllability of the quantum coherence has been strong enough to realize the quantum simulators.With the development of quantum coherence technology,many artificial and controllable quantum systems can be used as quantum simulators.There are two kinds of quantum simulations.The quantum simulation based on circuit reconstruction evolution is called digital quantum simulation.On the other hand,using a controllable quantum system to simulate another real complex quantum system is called analog quantum simulation.In this paper,we mainly explore the analog quantum simulation.ultracold atoms and superconducting quantum circuits are two important analog quantum simulators.In the following,we explore a series of important physical problems based on these two quantum simulators.In1995,Bose Einstein condensates was discovered in experiment.the Bose Einstein condensates is also known as ultracold atomic gases which provide a platform to observe the quantum effects on macroscopic scales.When we load the ultracold atom gases in the optical lattice,a pure,independent and controllable quantum simulator with powerful readout tools was contracted.in the 1980 s,scientists discovered the quantum effects in the superconducting circuits induced by the Josephson junctions.In 2007,scientists successfully designed the transmon qubit,which greatly improved the coherence of superconducting quantum circuits system.Moreover,the superconducting quantum circuits system is a macroscopic system,which has much strong controllability.Therefore the superconducting quantum circuits system is an ideal quantum simulator.With the development of experimental technology,superconducting quantum circuits system has developed rapidly.In this paper,our specific studies based on the ultra-cold atoms and superconducting quantum circuits system as follows:1.Two-component lattice bosons with cavity-mediated long-range interaction.We consider a two-component atomic Bose lattice gas inside an optical cavity to explore a competition between the short-range collisional and cavity-mediated long-range interactions.Utilizing a self-consistent mean-field approach,we map out the ground-state phase diagrams showing the superfluid,lattice supersolid,Mott insulator,and spin-density wave phases.Unlike its single-component analog,this lattice supersolid is here characterized by the coexistence of the superfluid and spin-density wave.Moreover,for the relatively small long-range interaction,the phase diagrams exhibit a correspondence between the parity of the lattice filling number and the spin imbalance.Finally,we propose how to detect the different quantum phases under current experimental setups.2.Synthetic gauge field and chiral physics on two-leg superconducting circuitsThe gauge field is essential for exploring novel phenomena in modern physics.However,it has not been realized in the recent breakthrough experiment on two-leg superconducting circuits with transmon qubits.Here we present an experimentally feasible method to achieve the synthetic gauge field by introducing ac microwave driving in each qubit.In particular,the effective magnetic flux per plaquette achieved can be tuned independently by properly choosing the driving phases.Moreover,the ground-state chiral currents for single-and two-qubit excitations are obtained and the Meissnervortex phase transition is found.In the Meissner phase,the ground-state chiral current increases as the magnetic flux increases,while it decreases in the vortex phase.In addition,chiral dynamics,which depends crucially on the initial state of the system,is also revealed.Finally,the possible experimental observations of the chiral current and dynamics are addressed.Our results provide a new route to explore novel many-body properties induced by the interplay of the gauge field,two-leg hoppings,and interaction of photons on superconducting circuits.3.Synthetic Hall tube in superconducting circuitsQuantum Hall effect is an essential phenomenon for exploring topological physics.In this work,we propose a feasible experiment scheme using three legs superconducting circuits with transmon qubits to realize a Hall tube.Then we first investigate its topological properties.Since the time-reversal,particle-hole,and chiral symmetries are all broken for the system,the Hall tube belongs to the A class of the Altland-Zirnbauer classification.We obtain the corresponding topological phase transition both numerically and analytically.Since the chirality is a key character of the quantum Hall effect,we secondly investigate the chiral physics in the Hall tube.In the topological nontrival phase,we find the topological protected chiral edge currents and discuss its robustness with imperfection influence.Finally,we give the possible experimental observations of the topological state and topological protected chiral edge currents in the Hall tube.