Quantum Control In Ultracold Atomic Gases

Quantum control is a crucial element for the development of quantum computa-tion,quantum communication and quantum simulation.On the one hand,it requires the controlled system be quantum mechanical.For example,a quantum many-body system should obey the Bose-Einstein statistics or Fermi-Dirac statistics,rather than the classical Boltzmann statistics.On the other hand,it also requires that we have con-trol over the quantum states,such as their internal degrees of freedom(internal state),external degrees of freedom(momentum and position),inter-particle interactions and so on.Facilitated by recent progress in experimental techniques,ultracold atomic gases have fully satisfied the above two conditions,and therefore become one of the most promising quantum platforms.Through laser cooling and evaporative cooling techniques,Bose Einstein conden-sation and degenerate Fermi gas were realized in 1995 and 2003,both of which exhibited macroscopic quantum mechanical properties.As far as control methods are concerned,the toolbox for handling ultracold atomic gases has been tremendously enriched in re-cent years.For the atomic internal states,through the artificial gauge field,not only can we control the transition between different energy levels,we can also couple the internal states with the external freedom(momentum)to realize spin-orbit couplings,commonly seen in solid systems.For the interaction between atoms,in addition to conventional magnetic Feshbach where we could adjust the scattering length via the magnetic field in alkali metal atomic gas,researchers have also developed optical Fes-hbach resonance,orbital Feshbach resonance and more,in which we could tune the interaction between different kinds of atoms by different methods.Besides,the rapid development of theoretical and experimental research in open systems has led to the idea of introducing controlled non-Hermicity into ultracold atomic systems.In 2016,people successfully implemented non-Hermitian Hamiltons in ultracold atomic gases,which has further enriched the means of quantum control.Inspired by the development of the latest experimental techniques in quantum control,we study novel quantum phe-nomena in several different ultracold atomic systems and fully analyze their physical implications.In this thesis,the specific research projects are as follows:1.Quench dynamics of a Bose-Einstein condensate under synthetic spin-orbit cou-plingIn this work,we study the quench dynamics of a Bose-Einstein condensate un?der a Raman-assisted synthetic spin-orbit coupling.To model the dynamical process,we adopt a self-consistent Bogoliubov approach,which is equivalent to applying the time-dependent Bogoliubov-de-Gennes equations.We investigate the dynamics of the condensate fraction as well as the momentum distribution of the Bose gas following a sudden change of system parameters.Typically,the system evolves into a steady state in the long-time limit,which features an oscillating momentum distribution and a sta-tionary condensate fraction.We also investigate how different quench parameters such as the inter-and intra-species interactions and the spin-orbit-coupling parameters affect the condensate fraction in the steady state.Furthermore,we find that the time aver-age of the oscillatory momentum distribu-tion in the long-time limit can be described by a generalized Gibbs ensemble with two branches of momentum-dependent Gibbs temperatures.2.Tuning Feshbach resonances in cold atomic gases with interchannel couplingBased on the recent progress of orbital Feshbach resonance in alkaline-earth(-like)atomic gas,we propose a novel light-controlled Feshbach resonance that can control the two-body interaction by adjusting the coupling strength between different scattering channels,and this scheme can be easily implemented in the system of orbital Feshbach resonance.Using 173Yb atoms as an example,we find that both the resonance position and the two-body bound-state energy depend sensitively on the inter-channel coupling strength,which offers control parameters in tuning the inter-atomic interactions.We also demonstrate the dramatic impact of the light-controlled Feshbach resonance on many-body processes such as the polaron to molecule transition and the BCS-BEC crossover.3.Repulsive polarons in alkaline-earth-metal-like atoms across an orbital Fesh-bach resonanceWe characterize properties of the so-called repulsive polaron across the recently discovered orbital Feshbach resonance in alkaline-earth-metal-like atoms.Being a metastable quasiparticle excitation at the positive energy,the repulsive polaron is induced by the interaction between an impurity atom and a Fermi sea.By analyzing in detail the en-ergy,the polaron residue,the effective mass,and the decay rate of the repulsive polaron,we reveal interesting features that are intimately related to the two-channel nature of the orbital Feshbach resonance.In particular,we find that the lifetime of the repulsive po-laron is nonmonotonic in the Zeeman-field detuning between the two channels,and has a maximum on the BEC-side of the resonance.Further,by considering the stability of a mixture of the impurity and the majority atoms against phase separation,we show that the itinerant ferromagnetism may exist near the orbital Feshbach resonance at appro-priate densities.Our results can be readily probed experimentally,and have interesting implications for the observation of itinerant ferromagnetism near an orbital Feshbach resonance.4.Non-Bloch topological invariants in a non-Hermitian domain-wall systemBased on theoretical and experimental advances in simulation of non-Hermitian Hamiltonian and topological phase transitions in cold atomic systems,we study non-Bloch bulk-boundary correspondence in a non-Hermitian Su-Schieffer-Heeger model in a domain-wall configuration where the left and right bulks have different param-eters.Focusing on the case where chiral symmetry is still conserved,we show that non-Hermitian skin effects of bulk states persist in the system,while the definition of the non-Bloch winding number of either bulk depends on parameters on both sides of the boundary.Under these redefined non-Bloch topological invariants,we confirm non-Bloch bulk-boundary correspondence under the domain-wall configuration,which ex-emplifies the impact of boundary conditions in non-Hermitian topological systems.