Efficient simulation of ultrafast quantum nonlinear optics with matrix product states
Efficient simulation of ultrafast quantum nonlinear optics with matrix product states
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DOI：
10.1364/optica.423044
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发表时间：
2021-02
期刊：
影响因子：
10.4
通讯作者：
Ryotatsu Yanagimoto;Edwin Ng;Logan G. Wright;Tatsuhiro Onodera;H. Mabuchi
中科院分区：
文献类型：
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作者：
Ryotatsu Yanagimoto;Edwin Ng;Logan G. Wright;Tatsuhiro Onodera;H. Mabuchi
在非线性纳米光子波导中传播的超短脉冲可以同时利用时间和空间场限制，有望在全光子平台中实现单光子非线性。然而，在这种多模量子体系中，对脉冲动力学的精确数值模拟天真地要求在指数级大的希尔伯特空间中表示状态。在这里，我们采用了时域，矩阵乘积状态（MPS）表示，使有效的模拟，利用纠缠结构的系统。为了从这些模拟中提取物理见解，我们开发了一种算法来将MPS量子态分解为组成时间超模，例如，获得任意脉冲波形的相空间图。作为演示，我们进行精确的数值模拟克尔孤子的量子制度。我们观察到非经典的魏格纳函数的发展，在孤子模式以及量子修正的半经典动力学的脉冲。对$\chi^{（2）}$ simultons的类似分析揭示了基波和二次谐波之间独特的纠缠结构。我们的方法也很容易与量子轨道理论兼容，允许完全量子处理的传播损耗和退相干。我们希望这项工作能够建立MPS技术，作为宽带量子光子学新兴领域统一工程框架的一部分。
Ultra-short pulses propagating in nonlinear nanophotonic waveguides can simultaneously leverage both temporal and spatial field confinement, promising a route towards single-photon nonlinearities in an all-photonic platform. In this multimode quantum regime, however, faithful numerical simulations of pulse dynamics na\"ively require a representation of the state in an exponentially large Hilbert space. Here, we employ a time-domain, matrix product state (MPS) representation to enable efficient simulations by exploiting the entanglement structure of the system. In order to extract physical insight from these simulations, we develop an algorithm to unravel the MPS quantum state into constituent temporal supermodes, enabling, e.g., access to the phase-space portraits of arbitrary pulse waveforms. As a demonstration, we perform exact numerical simulations of a Kerr soliton in the quantum regime. We observe the development of non-classical Wigner-function negativity in the solitonic mode as well as quantum corrections to the semiclassical dynamics of the pulse. A similar analysis of $\chi^{(2)}$ simultons reveals a unique entanglement structure between the fundamental and second harmonic. Our approach is also readily compatible with quantum trajectory theory, allowing full quantum treatment of propagation loss and decoherence. We expect this work to establish the MPS technique as part of a unified engineering framework for the emerging field of broadband quantum photonics.