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Physical Review A

Multiphoton transition in the Tavis-Cummings model

M. Sebawe Abdalla, S S Hassan, A.‐S. F. Obada

Published Dec 1, 1986• 40 citations
Publisher

Abstract

The Holstein-Primakoff transformation is used to transform the model of N (>1) two-level atoms collectively interacting with multiphotons of a single quantized mode of the field (the Tavis-Cummings model) into a boson-boson model. Formal solutions are obtained in the strong-coupling limit and/or the large-number-of-atoms limit. The analogy is drawn with a simple model of frequency conversion. The characteristic function in the p representation for the transformed model is calculated.

DOI
10.1103/physreva.34.4869

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The Holstein-Primakoff transformation is used to transform the model of N (>1) two-level atoms collectively interacting with multiphotons of a single quantized mode of the field (the Tavis-Cummings model) into a boson-boson model. Formal solutions are obtained in the strong-coupling limit and/or the large-number-of-atoms limit. The analogy is drawn with a simple model of frequency conversion. The characteristic function in the p representation for the transformed model is calculated.
In the strong coupling regime of cavity QED where the characteristic damping rates are orders of magnitude below the coherent coupling, resolved multi-photon resonances can be observed for strong enough driving strength. In a certain frequency range, the external coherent drive field hits multi-photon resonances which correspond to very high order transitions that cannot be excited at the given power of the driving field. We found that in this range the cavity field evolves into a robust semiclassical solution which is the mixture of the vacuum and an excited quasi-classical state. The system is reminiscent of optical bistability, however, here a single atom produces a telegraph signal for the outgoing intensity by switching between two states with large photon number difference. We calculate this behavior also for the Tavis-Cummings model representing three qubits in an existing circuit QED experimental setting.
用 multipohton Tavis-Cummings 模型，在贝尔联合二水平的原子说与一块单个模式的真空地交往的二的纠纷进化被使用否定性调查。在二的纠纷进化上联合在原子，原子起始的状态和转变的光子数字之间的常数联合二水平的原子的影响被讨论。用二个原子的纠纷与联合在原子，原子起始的状态和光子之间的常数是相关的数字方法表演获得的结果转变数。当起始的状态是 11 时，二原子的纠纷状态将永远呆在最大的纠纷状态。当二个原子的起始的状态是 01 时，二个原子的纠纷显示周期的摆动行为。并且它有联合在原子或光子之间的常数增加的摆动时期减少转变数。在另一方面，当起始的状态是 00 或 10 时，二个原子的纠纷与联合在原子或转变的光子数字之间的常数增加显示 quasiperiodic 摆动行为和它的摆动时期减少。
Using Tavis-Cummings model,the evolution of the atom's occupancy in interaction of two coupling two-level atoms with the single mode coherent field through multiphoton transition is studied.The influences of coupling coefficient between atoms,the initial mean photon number of field and the degree of entanglement of two atoms on the evolution of the atom's occupancy are discussed.The results obtained by numerical calculations show that the initial mean photon number of field influences violently the evolution properties of the atom's occupancy,the influence of coupling coefficient between atoms may be neglected,and the degree of entanglement of two atoms influences the reverse of atoms.
A modification of the Holstein-Primakoff transformation is proposed such that creation and annihilation operators for a bosonic field are rewritten as operators of a SU(2)SU(2)SU(2) algebra. Once it is applied to a quantum Hamiltonian, a subsequent application of the prescription by Lieb to obtain the classical limit for spin operators allows one to write efficiently a classical Hamiltonian for the system. This process is illustrated for the MMM-atom Jaynes-Cummings model.
By utilizing our previous operator solution [17], we have investigated the squeezing in the radiation field of the Tavis-Cummings model (collective N ≫ 1 two-level atoms interacting with a resonant single cavity quantized mode). With field and atoms initially in coherent field state strong or weak and atomic coherent state (of few excited atoms), periodic time-dependent squeezing in the field and the macroscopic polarization is expressed in terms of Jacobian elliptic functions of the first kind. The statistical investigations are carried out for the quasiprobability distribution functions (Wigner function and Q function). The distribution function of the field quadrature has a variance less (greater) than that for a coherent state if this quadrature is squeezed (unsqueezed).