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Journal of the Optical Society of America B

Phase diffusion model of a one-dimensional superradiance lattice and its application as a controllable high-frequency light reflector

Atif Shabbir, Sajid Qamar

Published Dec 15, 2021• 3 citations
Publisher

Abstract

We study the effect of quantum phase fluctuation (QPF) on a one-dimensional superradiance lattice (1DSL) and its application as a controllable high-frequency light reflector. In electromagnetically induced transparency (EIT)-based 1DSL [ Phys. Rev. Lett. 114 , 043602 ( 2015 ) PRLTAO 0031-9007 10.1103/PhysRevLett.114.043602 ], counter-propagating control laser fields are responsible for the hopping of electrons from the i th to the j th atom, where n 1 and n 2 coupling photons are required for forward and backward modes, respectively. In the limit of n 1 , n 2 ≫ 1 , the role of QPF becomes significant, and, therefore, the phase diffusion model of 1DSL needs to be considered. We show that in the presence of QPF a perfect 1DSL can be realized due to the fact that EIT vanishes at the resonance condition when probe detuning is zero. It leads to a reasonably high (around 60%) reflectivity of the incident probe field at resonance condition. For the off resonant case, the reflectivity reduces due to the phase diffusion; however, it can be overcome via manipulation of the control fields.

DOI
10.1364/josab.444022

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We study the effect of quantum phase fluctuation (QPF) on a one-dimensional superradiance lattice (1DSL) and its application as a controllable high-frequency light reflector. In electromagnetically induced transparency (EIT)-based 1DSL [ Phys. Rev. Lett. 114 , 043602 ( 2015 ) PRLTAO 0031-9007 10.1103/PhysRevLett.114.043602 ], counter-propagating control laser fields are responsible for the hopping of electrons from the i th to the j th atom, where n 1 and n 2 coupling photons are required for forward and backward modes, respectively. In the limit of n 1 , n 2 ≫ 1 , the role of QPF becomes significant, and, therefore, the phase diffusion model of 1DSL needs to be considered. We show that in the presence of QPF a perfect 1DSL can be realized due to the fact that EIT vanishes at the resonance condition when probe detuning is zero. It leads to a reasonably high (around 60%) reflectivity of the incident probe field at resonance condition. For the off resonant case, the reflectivity reduces due to the phase diffusion; however, it can be overcome via manipulation of the control fields.
Abstract We propose a scheme for generating frequency combs in an electromagnetically induced transparency—based superradiance lattice. When the probe frequency satisfies the m th-order resonance condition with the control field, 2 m + 1 discrete spectral components emerge, forming a frequency comb. The comb spacing and reflectivity are dynamically tunable via the control-field strength. The proposed scheme is experimentally feasible and enables the generation of low-frequency (infrared) combs using 87 Rb atoms. Moreover, high-frequency combs in the ultraviolet and x-ray regimes can be realized using 85 Rb atoms and Be 2 + ions, exhibiting appreciable reflectivity. These results establish a versatile platform for frequency-comb generation with potential applications in quantum optics and quantum information processing.
We show that the momentum of light can be reversed via the atomic coherence created by another light with one or two orders of magnitude lower frequency. Both the backward retrieval of single photons from a timed Dicke state and the reflection of continuous waves by high-order photonic band gaps are analyzed. The required control field strength scales linearly with the nonlinearity order, which is explained by the dynamics of superradiance lattices. Experiments are proposed with 85Rb^{85}\mathrm{Rb}85Rb atoms and Be2+{\mathrm{Be}}^{2+}Be2+ ions. This holds promise for light-controllable x-ray reflectors.
Abstract We report that modified superradiance lattice (2023, Phys. Scr. 98 015 105) can be used to obtain high-frequency photonic band gaps which are controllable using low-frequency light. Here, we also notice that the maximum reflectivity of these photonic band gaps can be achieved via low-frequency light control. This maximum reflectivity remains constant for a certain range of probe detuning depending upon the strength of the control field. We also report that this can lead to experimental realization of the soft x-ray regime (high-frequency) via 61st-order low-frequency light using Be2+ ions, the corresponding reflectivity in this case is 96%. Therefore, one can construct controllable x-ray photonic band gaps which can further be used to devise optical switches, beam splitters, and frequency combs. Moreover, this scheme holds the promise of working efficiently in all types of other configurations where reflection of high-frequency light is needed using nth order low-frequency light.
We investigate the manipulation of the quantum interference (QI) in an electromagnetically induced transparency (EIT) system via phase fluctuations and their correlation of interacting fields. We show that the field fluctuation correlation and atomic dephasing rate have a similar effect to atomic coherence, and furthermore that QI is dependent on the fluctuation and correlation. Using the theoretical model in a dressed-state representation, the contribution of QI and Autler-Townes splitting (ATS) to probe absorption can be expressed in separate terms, such that the obvious enhancement of QI is found with highly correlated fields while ATS remains unchanged. In particular, when the relative large Rabi frequency of coupling field is applied, in which case the ATS plays a more prominent role than QI, we can still modulate the QI to be higher than ATS with correlated fields. This result could allow the strict EIT condition to be relaxed and be easily realized, or it may be a method to get a narrow EIT window for applications in efficient light storage and quantum interface.
We study the all-optical control of the quantum fluctuations of a light beam via a combination of single-atom cavity quantum electrodynamics (CQED) and electromagnetically induced transparency (EIT). Specifically, the EIT control field is used to tune the CQED transition frequencies in and out of resonance with the probe light. In this way, photon blockade and antiblockade effects are employed to produce sub-Poissonian and super-Poissonian light fields, respectively. The achievable quantum control paves the way towards the realization of a prototype of a novel quantum transistor which amplifies or attenuates the relative intensity noise of a light beam. Its feasibility is demonstrated by calculations using realistic parameters from recent experiments.
The one-atom laser based on electromagnetically induced transparency, suggested recently [ Phys. Rev. Lett. 124 , 093603 ( 2020 ) PRLTAO 0031-9007 10.1103/PhysRevLett.124.093603 ], is capable of generating Schrödinger cat states in the regime of strong ground-state coupling. In this regime, we find the exact solution for the Schrödinger equation with a time-dependent effective Hamiltonian by considering the Magnus expansion of the time-ordered exponential and calculating analytically the time-ordering terms, omitted in the previous study. We show that the time-ordering term affects the relative phase of two coherent components of the generated Schrödinger cat state. We show this influence by calculating various nonclassicality indicators for the cavity field, such as total noise, average parity, and relative total noise. We find that time-ordering becomes important at the average photon number in the cavity below 1, in striking contrast to the case of single-pass parametric downconversion, where it becomes important at average photon number in one optical mode above 4.