| Recently the light-matter coupling in experiment has been pushed to an ultra-strongregime that the strength of the coupling is in the same order of frequency of photon orresonance frequency of atom. These breaking-through experiments provide new platformsnot only for exploring new quantum effect in quantum system but also for realizing highfidelity system of quantum information. In this thesis, we reported our studies, based onrecent experimental achievements, on dynamics especially squeezing of two-level atoms(also atom ensembles) and of photon, which should have important application in quantumcomputation. The thesis contains:(1) Superconducting Qubit couples to LC Resonant circuit at an coupling strength of0.1ω with ω frequency of atom, realizing the ultra-strong coupling. The proper descriptionof the system should include the contribution of an anti-rotating wave terms to the Rabimodel. It has been more than70years since the first introducing of Rabi model, however,its analytical solution is yet to be found. Here we put forward a new perturbation solutionfor it and with this method the ground state and excitation states of a system with acoupling strength of0.5ω (which has been recently realized experimentally), are obtained.Our results explain well the observed Bloch-Siegert Shift in experiment, and provideanalytical expressions for new measurable quantities such as the average numbers ofphotons, and correct many long-term misunderstanding on this problem.(2) Our numerical simulation shows the squeezing of light shows a non-monotonousdependence, rather a linear one, on the atom-photon coupling that it reaches its maximumat some critical coupling strength. In the meanwhile, we reveal a particular mechanism ofthe anti-rotating wave terms that is to enhance the squeezing of light. Our results may behelpful to preparation of a maximally-squeezed state in experiment. (3) We investigate the dynamics of the driven Rabi model by a static light field andfound a unique resonance effect which is depended on the strength of driving. Thisresonance is ensures a precise measuring of strength of the driving filed as well as thecoupling of atom and photon. The result here provides a theoretical basis for more precisemeasurement.(4) The group of Esslinger in ETH recently reported their observation ofsuperradiant which has been predicted by Dicke for more than40years ago. Theexperimental protocol they used, taking the advantages of the linear dependence of thecollective coupling of atom-photon on the Rabi frequency of external driving field, ishighly controllable and therefore easy to reach condition of a superradiant phase transition.By introducing a time-dependent atom-photon coupling in this protocol, we can largelyenhance the spin squeezing of atom system. The coefficient of spin squeezing increasesrapidly along with the increasing of driving field. The underlying physics of enhanced spinsqueezing is revealed within a high-frequency approximation as that the time-dependenceof collective coupling of atom-photon will induce a strong repulsive spin interaction. Thepossible maximal spin squeezing coefficient can be as large as-40dB, which is far beyondthe value in previous experimental and theoretical protocols.(5) In a recent experiment, a group of researchers in NIST have realized a strongRashba-Dresselhaus spin-orbital coupling in a cold atoms system by controlling a pair ofRaman laser. Theoretically their system is properly described by a ultra-coupled Dickemodel. In this thesis we proposed a new scheme of spin squeezing by using spin-orbitalcoupling. First we use the spin-orbital coupling to induce a dissipationless and controllablenon-linearly spin interaction with strong coupling strength. Using this spin interaction a-30dB spin squeezing is obtained. Moreover, it is found that the proper phase of initial statecan enhance the spin squeezing greatly. Our result suggests new possible applications ofspin-orbital coupling in quantum metrology. |
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