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Optics Express

Nonreciprocal and enhanced Goos-Hänchen shifts in the cavity-assisted atomic lattice of parity-time antisymmetry

Xiao Liu, Yixin Wang, Jin‐Hui Wu

Published Feb 18, 2025• 5 citations
Publisher

Abstract

We propose a scheme for realizing nonreciprocal and largely enhanced Goos-Hänchen (GH) shifts in a lattice of cold atoms exhibiting the parity-time ( P T ) antisymmetric susceptibility when driven by a probe beam and a coupling beam. This atomic lattice in the free space allows to attain unidirectionally detectable nonreciprocal GH shifts for reflected probe beams provided a Bragg bright resonance is tuned to overlap with an exceptional point. Placing this atomic lattice in an optical cavity, we can further attain bidirectionally detectable nonreciprocal GH shifts for reflected probe beams, benefiting from the interplay between a Bragg bright resonance and a cavity dark resonance. Nonreciprocal GH shifts in our cavity-assisted P T -antisymmetric atomic lattice exhibit the advantages of dynamic tunability and reversibility, while enhanced up to hundreds of probe wavelengths, in the case of nonzero detectable reflections.

DOI
10.1364/oe.556001

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We propose a scheme for realizing nonreciprocal and largely enhanced Goos-Hänchen (GH) shifts in a lattice of cold atoms exhibiting the parity-time ( P T ) antisymmetric susceptibility when driven by a probe beam and a coupling beam. This atomic lattice in the free space allows to attain unidirectionally detectable nonreciprocal GH shifts for reflected probe beams provided a Bragg bright resonance is tuned to overlap with an exceptional point. Placing this atomic lattice in an optical cavity, we can further attain bidirectionally detectable nonreciprocal GH shifts for reflected probe beams, benefiting from the interplay between a Bragg bright resonance and a cavity dark resonance. Nonreciprocal GH shifts in our cavity-assisted P T -antisymmetric atomic lattice exhibit the advantages of dynamic tunability and reversibility, while enhanced up to hundreds of probe wavelengths, in the case of nonzero detectable reflections.
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Abstract This article investigates the Goos-Hӓnchen(GH) shift of the reflected light of an ensemble of optical lattices in a cavity. We consider a lambda-type ensemble of three-level atoms to form the optical lattice and apply three fields, two weak fields (probe and microwave) and one strong field. The microwave field transforms the medium into a gain medium, resulting in the optical lattice containing both loss and gain. The co-existence of gain and loss leads to parity-time symmetry in the system. By satisfying the parity-time symmetry condition, we can modify the magnitude of the GH shift. Our results suggest that the GH shift can be controlled in systems exhibiting parity-time symmetry.
Influence of PT\mathcal{PT}PT symmetry on the Goos-H\"anchen (GH) shift in the reflected light is presented for an ensemble of atomic medium in a cavity, in the configuration of four-level NNN-type (87Rb^{87}\mathrm{Rb}87Rb atoms) systems driving by two copropagating strong laser fields and a weak probe field. The atom-field interaction follows the realization of PT\mathcal{PT}PT symmetry by adjusting the coupling field detunings [J. Sheng et al., Phys. Rev. A 88, 041803(R) (2013)]. A giant enhancement for the GH shift in the reflected light is revealed when the PT\mathcal{PT}PT-symmetry condition is satisfied.
Goos-Hänchen Shift in PT\mathcal{PT}PT-Symmetric and Passive Cavity Optomechanical Systems
We theoretically investigate the control of the Goos-Hänchen shift (GHS) of a reflected weak probe field in both parity-time (PT\mathcal{PT}PT)-symmetric and conventional optomechanical systems. The proposed scheme consists of a single optomechanical platform where a passive optical cavity is coupled to an active mechanical resonator, in contrast to standard passive-passive configurations. Analysis of the eigenfrequency spectrum reveals the emergence of an exceptional point under balanced gain-loss conditions at a tunable effective optomechanical coupling strength. Using the transfer-matrix method combined with stationary-phase analysis, we examine the GHS across broken and unbroken PT\mathcal{PT}PT phases and compare it with that in the conventional system. The lateral shift exhibits strong phase dependence: it is markedly enhanced in the unbroken regime relative to both the broken phase and the passive configuration. We further show that the GHS can be actively tuned through the cavity detuning and the intracavity medium length. These results provide a controlled means for manipulating beam shifts in optomechanical systems and suggest pathways toward tunable photonic components and precision optical sensing.
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.