光学参量放大器辅助的复合腔磁系统中磁力诱导透明及快慢光效应
0 引言
腔磁系统是由三维微波腔和铁磁材料钇铁石榴石(
随着对腔磁系统不断深入的研究,已有实验证明了腔磁系统中的磁力诱导透明(Magnomechanically Induced Transparency,MMIT)和吸收[10]是磁子与声子耦合产生的量子边带干涉效应。磁力诱导透明与电磁诱导透明(Electromagnetically Induced Transparency,EIT)[11]类似,是一种相干现象。XIONG Hao等[12]从理论上讨论了基于非线性磁振子-声子相互作用的磁力诱导透明和慢光。文献[13]实现了YIG球和原子系综复合腔磁系统中磁力诱导透明现象和可调快慢光效应。可调谐多窗口磁力诱导透明[14]已在耦合单个微波腔模式的两个YIG球组成的系统中提出。对磁力诱导透明的研究促进了基于磁致伸缩力的可控慢光研究[15]。此外,快慢光效应为压缩空间中的光能量和光信号传输提供了可能性,快慢光效应有利于加强光与物质的相互作用,减少设施占用的空间[16-17]。根据快慢光的群延迟特性,能够进行光缓冲、光信号、光开关的时间速度控制[18]。
腔磁系统中还出现许多有趣的现象,例如基于克尔效应的非互易性[19]、高阶奇异点[20]、磁振子阻塞[21]、相干光传输[22]和高阶边带[23-24]。同样,人们对宏观系统中量子效应的产生给予了足够的关注。例如,LI Jie等利用带通约瑟夫逊参量放大器的非线性[25]和磁致伸缩相互作用[26]为实现微腔光子、磁振子和声子模式之间的三体纠缠提供了一个简单可行的理论框架。此外,通过利用微波腔[27]、克尔非线性[28]和磁致伸缩非线性[29]研究了两个宏观YIG球的纠缠特性。在最近的一项研究[30]中发现,与没有光学参量放大器(Optical Parametric Amplifier,OPA)的系统相比,腔磁系统中OPA的存在可以改善微腔光子、磁子和声子之间的纠缠。其中OPA用于产生强机械压缩[31]、两个光学模式之间的纠缠[32]以及光学模式和机械模式之间的纠缠[33]。
基于以上研究,本文提出了一个由非线性介质OPA辅助的复合腔磁力系统。在复合腔磁力系统存在磁振子-声子有效耦合时,输出场吸收谱出现两个透明窗口,透明窗口的特性可以通过调节磁振子-声子之间的耦合强度改变。进一步讨论系统加入OPA后,腔磁耦合强度对系统探测场吸收和色散的影响。腔磁系统中非线性介质OPA的加入也可以增加系统的传输速率,同时可以增强腔磁系统的快慢光传播。与之前的工作[12]相比,引入了非线性OPA介质后,磁力诱导透明和快慢光效应更加灵活可调。实验上已经实现了YIG小球与三维微波腔的耦合[34],其中YIG小球放置在三维微波腔中,通过磁偶极相互作用与微波腔耦合。磁振子通过磁致伸缩相互作用与声子耦合[10]。因此,该系统在实验上可行。
1 模型与系统哈密顿量
1.1 模型
如
图 1. OPA辅助的腔磁系统模型
Fig. 1. Schematic diagram of the hybrid cavity magnetic system assisted by an OPA
1.2 系统哈密顿量
考虑高质量的YIG球体,直径为250 μm,由密度为
式中,
在以驱动场频率为
式中,
2 系统量子动力学和光学涨落谱
2.1 系统量子动力学
基于系统总哈密顿量方程
式中,
假设朗之万噪声项的平均值为零。为了求解非线性方程,使用平均场近似方法
式中,
式中,
式中,
令
式中,
2.2 光学涨落谱
为了研究系统对弱探测场的响应,根据腔磁系统标准输入-输出关系,输出场的振幅可以表示为
式中,
式中,
3 数值分析与结果
在复合腔磁系统中,为了研究非线性介质OPA对于磁力诱导透明、传输速率和群延迟的影响,选用实验上可行的数据[10,17]:
3.1 含有光学参量放大器的复合腔磁系统中的磁力诱导透明现象
首先,研究了无OPA加入
图 2. 在不同的磁振子-声子有效耦合强度 下,输出探测场的吸收 和色散 作为归一化失谐 的函数
Fig. 2. Absorption and dispersion of output detection field as a function of normalized detuning under different magnon-phonon effective coupling strengths
为了研究OPA对于腔磁系统磁力诱导透明的影响,绘制了
图 3. 不同的OPA增益G下,输出探测场的吸收谱 作为归一化失谐 的函数
Fig. 3. The absorption spectrum of the output detection field as a function of normalized detuning under different OPA gains G
为了深入探究腔磁力系统中加入OPA后,腔磁耦合强度对输出探测场的磁力诱导透明现象的影响,绘制了不同微波腔与磁子相互作用强度gma下系统输出场的吸收谱和色散谱。如
图 4. 在不同腔磁耦合强度gma下,输出探测场的吸收谱 (绿色实线)和色散谱 (品红色点虚线)作为归一化失谐 的函数
Fig. 4. Under different cavity-magnon coupling strength gma,the absorption spectrum (green solid line)and dispersion spectrum (magenta dotted line)of the output detection field are used as normalized detuning functions
3.2 光学参量放大器对传输速率和快慢光效应的影响
进一步讨论非线性介质OPA的增益
探测场传输速率可以表示为
通过设置OPA的不同增益G来研究其对腔磁系统探测场传输速率的影响,如
图 5. 在不同的OPA增益G 下,腔磁系统的探测场传输速率 作为归一化失谐 的函数
Fig. 5. Under different OPA gains G ,the transmission rate of the detection field in the cavity magnetic system as a function of normalized detuning
最后,研究了OPA对复合腔磁系统中群延迟的影响。
图 6. 在不同OPA的增益G下,腔磁系统的群延迟 作为归一化失谐 的函数
Fig. 6. Under different OPA gains G,the group delay of the cavity magnetic system as a function of normalized detuning
4 结论
本文研究了光学参量放大器辅助的腔磁系统中磁力诱导透明和快慢光效应。数值模拟结果表明,存在磁振子-声子耦合时,通过改变磁振子-声子耦合强度实现了输出场透明窗口数量、宽度和深度的转换。加入OPA之后对于腔磁系统探测场吸收和色散谱曲线的影响表明,腔场的稳态效应依赖于OPA增益的改变,从而导致腔磁系统内声子数的改变,吸收光谱因此存在不对称现象,且吸收谱的峰值随之增加。另外,腔磁耦合强度也改变了吸收光谱和色散光谱的传输特性。增加OPA的增益提高了系统的传输速率,从而实现了对窗口透射谱的调控。最后,OPA对系统群延迟影响的分析结果显示选择合适的OPA参数实现了增强的慢光效应和快慢光的切换。
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Article Outline
廖庆洪, 宋梦林, 孙建, 邱海燕. 光学参量放大器辅助的复合腔磁系统中磁力诱导透明及快慢光效应[J]. 光子学报, 2024, 53(2): 0227001. Qinghong LIAO, Menglin SONG, Jian SUN, Haiyan QIU. Magnomechanically Induced Transparency and Fast-slow Light Effects in the Hybrid Cavity Magnetic System Assisted by an Optical Parametric Amplifier[J]. ACTA PHOTONICA SINICA, 2024, 53(2): 0227001.