The Periodic Driving Protocols To Control Quantum Systems

Since the 19th century,along with the new understanding of the microscopic field that quantum mechanics has brought to people,how to use quantum properties to realize a new technological revolution has become the main direction of scientific and technological development.Recent studies have shown that the use of novel non-classical properties of quantum systems,such as quantum entanglement,quantum squeezing,quantum correlation,etc.,can achieve a new generation of quantum technologies that exceed the limits allowed by classical physics.However,the development of these new technologies is inseparable from the preparation,protection and control of novel quantum states.Therefore,how to develop an effective manipulation and control method for quantum systems has become one of the most significant issues in the scientific community today.To achieve this goal,many quantum control schemes have been proposed,such as bath engineering,feedback control and so on.These control schemes have their limitations.For example,the bath engineering's controlling of quantum systems depends on the controlling of the bath's own parameters,which is difficult to achieve experimentally.Due to the wide application of periodic driving in condensed matter,topological physics,quantum optics,quantum chemistry and many other fields in recent years,we hope to realize effective controlling and protection of quantum systems through periodic driving,and then provide new opportunities for new quantum technology in the future.Based on this,in this paper,we study the dissipative quantum battery controlled by periodic driving,the Ramsey interferometer controlled by periodic driving,and the controlling of closed quantum system thermalization-localization transition and quantum chaos-integration transition by periodic driving.In the first part of this thesis,we first studied the periodic driving scheme of dissipative quantum battery reactivation.As an energy storage and conversion device close to the size of an atom,quantum batteries are expected to break through the energy storage capacity of existing classic batteries,and can use quantum resources to improve charging efficiency.However,the widespread decoherence phenomenon in quantum systems can lead to the destruction of the charge-storage-discharge cyclic process.This phenomenon is called the aging of quantum battery.In this thesis,we propose a mechanism to overcome the aging of quantum batteries.Our research shows that when two Floquet bound states are formed in the quasienergy spectrum,the decoherence of the quantum battery is suppressed,but in general,its dynamics are still inconsistent with the ideal charge-discharge cycle.Through the perturbation analysis of the Floquet bound state in this system,we found that only when the quasienergy of the two Floquet bound states are nearly degenerate,or when the quantum battery-charger coupling is strong,the quantum battery in the environment can realize the nearly ideal charge-discharge evolution cycle.Based on the analysis of the Floquet bound state mechanism,we give a complete analysis of the quantum battery charging and discharging scheme under non Markovian dissipative noise.It also points out the parameter range in which the quantum battery can still work well even in the presence of dissipative noise,and gives an explanation of its mechanism.Our results provide a theoretical basis for realizing quantum batteries under realistic conditions by using the Floquet engineering.In the second part of this thesis,we study the controlling of the periodic driving scheme on whether the closed quantum system is thermalized or not.Due to the rapid development of experimental technology in the field of cold atoms in recent years,experimental simulations of closed quantum systems have been realized.Therefore,the thermalization of a closed quantum system has attracted wide attention due to its great significance in both theory and experiment.On the other hand,due to the wide application of periodic driving in various fields,the question of whether the periodic driving non-equilibrium closed quantum system can be thermalized,and what is its long-time steady state has also attracted everyone's attention.In order to answer these questions,this paper studies the heating problem in the periodic-driven two-sites Bose-Hubbard model.Using Floquet's theorem,we analyzed in detail the stroboscopic quantum dynamics of the model in the periodic driving field,and solved its semi-classical dynamics under the thermodynamic limit.The results show that there is a close relationship between the thermalization of the system under the long-time limit and the chaos of the corresponding semi-classical system.When the driving frequency is low,the system heats up.No matter what the initial state is,the local observables will finally relax to the value predicted by the thermal ensemble with T = ?.There,the corresponding Floquet eigenstate satisfies the eigenstate thermalization hypothesis.On the other hand,its Floquet quasienergy level spacing obey Wigner-Dyson distribution,and the semiclassical dynamics appear chaotic.On the contrary,under high-frequency driving,the integrability of the quantum system is restored and no heating occurs.The corresponding Floquet quasienergy level spacing obey the Poisson distribution,and semi-classical dynamics show a large number of periodic orbits.Our results show that even when the driving intensity is strong,all these complex dynamics can be controlled by adjusting the driving frequency.This is beyond the influence of drive strength on the system integrable-chaos pointed out by previous studies.This result not only provides inspiration for the study of the thermalization problem of periodic driving systems,but also provides the possibility to achieve more flexible manipulation of the thermodynamic properties of quantum systems in experiments.In the last part,we studied how to use the periodic driving scheme to achieve highprecision measurement in a dissipative environment.In all fields of modern science,high-precision measurement is of great significance.As an emerging quantum technology,quantum metrology is a technology that uses the non-classical properties of quantum states to achieve measurement accuracy beyond the classical limit.The realization of this technology relies on the effective manipulation of fragile quantum states such as entangled states.However,in actual situations,quantum states always decoherence due to the inevitable interaction between them and the environment,which leads to the loss of quantum advantage.Therefore,how to protect the quantum state from noise during the measurement process is of great significance to the realization of highprecision measurement.Past studies have found that by means of bath engineering,a bound state can be formed in the energy spectrum of the total quantum system and its environment,which can partially maintain the coherence of the quantum system over a long time,thereby achieving higher precision measurement.However,in fact,once the experimental materials are prepared,the parameters of the environment felt by the quantum system will become difficult to adjust.To solve this practical problem,we propose to use periodic driving field to protect the quantum coherence in the measurement process.Through the study of the periodic driving Ramsey process,we found that for the initial GHZ state,the dynamics of the quantum Fisher information of measuring atomic frequency can have two distinct behaviors as the driving parameters change.Either the quantum Fisher information tend to zero in long-time limit,or increase with the increasing of time.Relying on the quasienergy spectrum and quasi-steady state images provided by the Floquet theorem,we found that when the parameters of the periodic driving are adjusted so that the Floquet bound state is formed in the quasienergy spectrum of the driving system,the coherence of the quantum system will be partially maintain in long-time limit.In this case,quantum Fisher information show the second behavior.When there is no bound state formed in the quasienergy spectrum,its quantum Fisher information tend to zero in long-time limit.Thus we know that by controlling the formation of Floquet bound states in the quasienergy spectrum,better measurement accuracy can be obtained.This work provides new ideas for the realization of quantum measurement schemes in dissipative environments.In summary,based on the Floquet theorem,this paper studies three problems: the aging of quantum battery system,the thermalization of two-sites Bose-Hubbard model,and the decoherence in Ramsey interferometer.For the specific problems in each system,the periodic control method and mechanism analysis are given.The research paved the way for the realization of new quantum technologies with periodic driving tool.