Abstract
Classical microwave circuit theory is incapable of representing some phenomena at the quantum level. To include quantum statistical effects, various theoretical treatments can be employed. Quantum input-output network (QION) theory is one such treatment. Another formalism, called SLH theory, incorporates scattering matrices ( S ), coupling vectors ( L ), and system Hamiltonians ( H ). These theoretical treatments require a reformulation of classical microwave theory. To make these topics comprehensible to an electrical engineer, we demonstrate some underpinnings of microwave quantum optics in terms of microwave engineering. For instance, we equate traveling-wave phasors in a transmission line ( $V_0^+$ ) directly to bosonic field operators. Furthermore, we extend QION to include a state-space representation and a transfer function for a single port quantum network. This serves as a case study to highlight how microwave methodologies can be applied in open quantum systems. Although the same conclusion could be found from a full SLH theory treatment, our method was derived directly from first principles of QION.
Highlights
INTRODUCTION classical circuit theory has been the forefront of microwave engineering for many decades, the theory is incapable of explaining quantum noise from single-photon detection, long distance communication, phase amplifiers, etc
A lumped LC circuit coupled to a transmission line can be modeled as an open quantum system, where the dynamical solutions can be turned into a state-space representation and a corresponding transfer function
We provided a formalism of quantum circuits in terms of microwave engineering, resulting in an easier understanding to solving microwave systems
Summary
Classical circuit theory has been the forefront of microwave engineering for many decades, the theory is incapable of explaining quantum noise from single-photon detection, long distance communication, phase amplifiers, etc. [1]. With growing interest to utilize microwave networks for quantum communication [1], quantum computing [2], quantum information [3], and quantum networking [4], a second quantization of circuit components has provided a successful transition from classical to quantum treatment for microwave networks Such models include QION theory [5]–[9] and SLH theory [10]–[12], which SLH has success in applying classical methodologies to quantum mechanics including a state-space representation. To illustrate the analogies between classical and quantum methodologies, this article focuses on a simple single-port lumped LC example This approach can be extended to a multiport system and/or more complicated systems
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