| The 21 st century is the era of quantum information.In the fields of quantum computing,quantum communication,quantum network and quantum information processing,the core issue is the interaction of light and matter.The ideal substance is of course an isolated single alkali metal atom,but due to the difficulty of controlling and detecting technology,atomic ensemble,qubits and quantum dots are mostly used in practice.Cavity quantum electrodynamics(QED)system is one of the ideal platforms for studying the interaction between quantized light field and matter in confined space,and it is also a good non-classical light source and quantum network node,so it has received extensive attention and research.In this thesis,optical parametric amplification(OPA)technology is used to control the superradiant quantum phase transition in cavity QED system,to observe the dynamics evolution of the system at avoid energy level crossing,and to prepare the quantum states with high fidelity.The specific research content and main conclusions are summarized as follows:First,the second order nonlinear crystal in the pumped cavity generates a squeezed cavity mode,which can be used to induce the symmetry of the system to be broken,thus realizing the superradiant quantum phase transition.The boundary conditions of the superradiant quantum phase transition are analytically derived by means of mean field approximation,and the quantum fluctuations are calculated by using the quantum Langevin equation and Holstein-Primakoff(HP)transformation.Different from others’ work,in our model,the second order quantum phase transition from normal phase to super-radiative phase and the first order quantum phase transition from normal phase to coexisting phase can be realized by changing the pump field strength G without changing the atom-cavity coupling strength λ.We also calculate the system Wigner function to judge the state of the system in the phase space.In the normal phase,the Wigner function of the system is one sphere.In the super-radiative phase,the Wigner function of the system is two spheres.And if the system is in the coexistence phase(the normal phase and the super-radiative phase coexist),the Wigner function is three spheres.The Wigner function can also reflect whether the state of the system is compressed or not,such as changing from a sphere to an ellipsoid.At the critical point of the phase transition,the quantum fluctuations of the second-order phase transition are continuous,while that of the first-order phase transition are abrupt.Secondly,in the JC model,we found that when the relationship between the qubitcavity coupling strength 2)and the system detuning Δ satisfies certain conditions,the energy levels of the dressed state of the system will be degenerate.At this time,if driven by an external field,these degenerate dressed states will split and form avoided dressed state crossing.Based on this principle,we applied OPA to the JC model.The OPA process compresses the cavity mode,and the compressed cavity mode can reduce the time consumption in the quantum state transfer process and thus reduce the system decoherence.At the point of avoided dressed state crossing,we can not only observed the quantum beat phenomenon,but also prepared high-fidelity non-classical states,superposition of two odd or even Fock states with equal amplitude but with arbitrary phase.Our findings can be applied to quantum metrology,quantum entanglement,quantum state preparation,and so on.Finally,using adiabatic switching of the pump field amplitude,a non-classical quantum state with high fidelity and large photon number is prepared in the JC model driven by parameter interaction.Theoretically,as long as the accuracy is high enough,we can also prepare quantum states with a larger number of photons.At the same time,an application method of our model in external magnetic field measurement is proposed.In addition,our research also has potential applications in quantum entanglement and quantum communication. |
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