Nanophotonic Quantum Phase Switch With A Single Atom Pdf Free

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To further understand our scheme, we give a discussion of the physical mechanism of the conditional phase shift. As mentioned above, we have the conditional phase shift and, where the subscripts and denote the cavity and atom, respectively. It is clear that the conditional phase shift is only related to the atomic state and the input-output properties of the cavity. As shown in Ref. [28], the driving process of the cavity is described by the following LÃ¼ckenberger-type interaction Hamiltonian where is the cavity field operator, is the coupling strength, and is the coupling operator. is the atom-cavity coupling operator and is the atomic state operator. Here we expand the operators in the Heisenberg picture as and, where the superscripts and denote the initial cavity state and the initial atomic state, and the operator has a form of the operator in the SchrÃ¶dinger picture. To derive the evolution equation of the cavity field, we consider the input-output process of the cavity field. In the Heisenberg picture, the input-output relation reads the following form of, where is the input operator, and is the output operator. The operator has a form of the operator in the SchrÃ¶dinger picture. It is clear that the input operator is the cavity field operator and the output operator is the cavity field operator. Under the condition, the output operator from the cavity has a form of, where and. From Eqs. (2) and (5), we find that the Hamiltonian in the Heisenberg picture does not change the input-output relation of the cavity field, therefore, the photon pulse in the cavity will also have a conditional phase shift via the input-output process of the cavity field. It is well known that the atoms in cavity can be described by a effective two-level system. In the Heisenberg picture, the evolution of the atom-cavity system is described by the following Hamiltonian Ref. [28], here is the atomic state operator and is the atomic coupling operator. In the condition, we have the steady state and. The operator has a form of the operator in the SchrÃ¶dinger picture. In the condition, the evolution of the atom-cavity system is described by the following Hamiltonian Ref. [28], here is the coupling operator. The operator has a form of the operator in the SchrÃ¶dinger picture. In the condition, we have the steady state and.

In our scheme, the cavity mode is weakly driven by a classical field with Rabi frequency, thus the system is driven adiabatically. The field is resonant with the transition, where the driving field gives a bias to the system. If the pulse length is shorter than the photon lifetime in the system, then the state decays into the initial state, which drives the atom back to state. If the pulse duration is longer than the photon lifetime in the system, then the state is stable. This is the conventional EIT scheme. Therefore, we conclude that the dark state, which is defined as a state that is decoupled from state by the quantum interference, is the dark state that is crucially important to our scheme. This dark state is mapped to the state of no atom coupled to the cavity. The temporal shape of the pulse is the result of the interference between the cavity photon and the photon in the atomic ensemble1. 827ec27edc