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Physical Review A

Investigation of the Goos-Hänchen shift in an optomechanical cavity via quantum control

Anwar Ali Khan, Muqaddar Abbas, You-Lin Chaung, Iftikhar Ahmed, Ziauddin Ziauddin

Published Nov 18, 2020• 22 citations
Publisher

Abstract

We propose a scheme to study the topic of manipulating the Goos-H\"anchen (GH) shift of the reflected beam in an optomechanical cavity (OMC). Our system consists of two mirrors where one is fixed and the other is movable and a two-level atom is trapped inside the OMC. The fixed mirror is partially reflecting, whereas the movable mirror is perfectly reflecting. We theoretically investigated the behavior of the GH shift in the reflected beam when a Gaussian beam is an incident on the OMC. We find that GH shifts can be greatly enhanced in positive or negative directions via manipulating the quantum parameters such as optomechanical strength ${g}_{\text{mc}}$ and atom-cavity strength ${g}_{\text{ac}}$ under the influence of beam width of a Gaussian beam. Besides, we study the GH shift in the case of the partially coherent light beam as an incident probe field. Giant negative GH shift is achieved for an incident partially coherent beam in the presence of ${g}_{\text{mc}}, {g}_{\text{ac}}$, a measure of global coherence and beam width of a partially coherent beam. The proposed model provides feasibility in practical experiments for studying the behavior of the GH shift.

DOI
10.1103/physreva.102.053718

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We propose a scheme to study the topic of manipulating the Goos-H"anchen (GH) shift of the reflected beam in an optomechanical cavity (OMC). Our system consists of two mirrors where one is fixed and the other is movable and a two-level atom is trapped inside the OMC. The fixed mirror is partially reflecting, whereas the movable mirror is perfectly reflecting. We theoretically investigated the behavior of the GH shift in the reflected beam when a Gaussian beam is an incident on the OMC. We find that GH shifts can be greatly enhanced in positive or negative directions via manipulating the quantum parameters such as optomechanical strength gmc{g}_{\text{mc}}gmc​ and atom-cavity strength gac{g}_{\text{ac}}gac​ under the influence of beam width of a Gaussian beam. Besides, we study the GH shift in the case of the partially coherent light beam as an incident probe field. Giant negative GH shift is achieved for an incident partially coherent beam in the presence of gmc,gac{g}_{\text{mc}}, {g}_{\text{ac}}gmc​,gac​, a measure of global coherence and beam width of a partially coherent beam. The proposed model provides feasibility in practical experiments for studying the behavior of the GH shift.
The behavior of the Goos-H\"anchen (GH) shifts in the reflected and transmitted light beam which is incident on a cavity containing an intracavity medium of three-level or four-level atoms with electromagnetically induced transparency (EIT) is discussed. We report a coherent control of the GH shift in a fixed configuration or device via superluminal and subluminal wave propagation. For superluminal wave propagation, we observe negative GH shifts in the reflected part of the incident light whereas the shifts are positive in the transmitted light beam. This corresponds to the negative group index of the cavity in the former case and positive group index of the cavity in the latter. For subluminal wave propagation, the behavior of the GH shifts in the reflected light changes and positive shifts appear; however, the GH shifts in the transmitted light remains positive. The corresponding group index of the cavity is positive in both cases.
The behavior of the Goos-Hanchen (GH) shifts in the reflected and transmitted light beam which is incident on a cavity containing an intracavity medium of three-level or four-level atoms with electromagnetically induced transparency (EIT) is discussed. We report a coherent control of the GH shift in a fixed configuration or device via superluminal and subluminal wave propagation. For superluminal wave propagation, we observe negative GH shifts in the reflected part of the incident light whereas the shifts are positive in the transmitted light beam. This corresponds to the negative group index of the cavity in the former case and positive group index of the cavity in the latter. For subluminal wave propagation, the behavior of the GH shifts in the reflected light changes and positive shifts appear
The negative and positive Goos-H\"anchen (GH) shifts in reflected light are revisited for a partial coherent light incident on a cavity. A three-level dilute gaseous atomic medium, which follows two-photon Raman transitions, is considered in a cavity. The anomalous (negative group index) and normal (positive group index) dispersions of the intracavity medium lead to negative and positive GH shifts, respectively. The effects of beam width, spatial coherence, and mode index of partial coherent light fields are studied on the negative and positive GH shifts. It is observed that the amplitude of negative and positive GH shifts are relatively large for a small range of beam width and for a small value of spatial coherence of partial coherent light beams. The amplitude of GH shifts becomes small for large beam width and spatial coherence of incident light. Further, the distortion in the reflected light field increases when the amplitude of the GH shifts increases and vice versa.
Abstract In this letter, we propose a novel model for adjusting the Goos–Hänchen shifts (GH) from a fixed cavity. A three-level double quantum dot (QD) molecule is doped in the cavity, which interacts with a probe laser field and an incoherent pumping rate. We initially investigate the refraction index of double QDs utilizing the quantum mechanical density matrix approach in order to achieve negative and positive refractive indexes. The GH shifts of reflected and transmitted light beams in positive and negative refraction indices of the intracavity medium were then studied. The improved negative or positive GH shifts in reflected and transmitted light beams may be accomplished by changing the incoherent pumping rate and tunneling effect. Our findings reveal that the magnitude of the GH shifts is greatly influenced by the absorption of incoming probing light in double QDs. The enormous GH shifts for the perfect tuning cavity have been seen at a given incidence angle.
Control of Goos-H$\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{\text{a}}$nchen (GH) shift in reflected and transmitted light is revisited for a Gaussian light incident on a cavity. The intracavity atomic medium follows duplicated two-level atomic configurations where two fields, i.e., a strong control field and a relatively weak probe field are employed [F. A. Hashmi and M. A. Bouchene, Phys. Rev. Lett. 101, 213601 (2008)]. The coherent control is achieved via phase shift $\ensuremath{\phi}$ between control and probe fields. The effect of incident light width on negative or positive GH shifts and distortion in the reflected and transmitted light is investigated.
We present a proposal to manipulate the Goos-H\"anchen shift of a light beam via a coherent control field, which is injected into a cavity configuration containing the two-level atomic medium. It is found that the lateral shifts of the reflected and transmitted probe beams can be easily controlled by adjusting the intensity and detuning of the control field. Using this scheme, the lateral shift at the fixed incident angle can be enhanced (positive or negative) under the suitable conditions on the control field, without changing the structure of the cavity.