Squeezing components in linear quantum feedback networks

Abstract

Phys. Rev. A 81, 023804 (2010) DOI: 10.1103/PhysRevA.81.023804 Sponsorship: EPSRCThe aim of this article is to extend linear quantum dynamical network theory to include static Bogoliubov components (such as squeezers). Within this integrated quantum network theory, we provide general methods for cascade or series connections, as well as feedback interconnections using linear fractional transformations. In addition, we define input-output maps and transfer functions for representing components and describing convergence. We also discuss the underlying group structure in this theory arising from series interconnection. Several examples illustrate the theory.preprintPeer reviewe

Non-Markovian quantum input-output networks

“…(12). Let t 1 → t, we can obtain the output equation (17). Furthermore, using the identities To derive the master equation (18), we first change into the interaction picture, in which the effective Hamiltonian H eff can be rewritten as…”

“…Under the Markovian assumption, the quantum input-output formalism [6] was extended to cascaded systems [7], and has been used to study quantum coherent feedforward and feedback networks [9][10][11][12][13][14]. Markovian quantum input-output networks can be described using two alternative formulations: the Hudson-Parthasarathy formalism in the Schrödinger picture [15]; and the quantum transfer function formalism in the Heisenberg picture [16,17]. The general algebraic structure of such systems has been well studied in the language of quantum Wiener and Poisson processes and quantum Ito rules [15].…”

Tunable Coupling to a Mechanical Oscillator Circuit Using a Coherent Feedback Network

“…We do not characterize performance in the quantum regime, but these devices feature regularly in such work and these capabilities are novel regardless. Moreover, because the network is linear and driven by Gaussian fields, the network characterization done in the classical regime should apply in the quantum one [1,[22][23][24][25][26][27]. Thus, we use the term ''coherent'' in the sense that an interferometer or resonator is coherent, which is the primary prerequisite for quantum dynamics.…”

“…(Rigorous derivations are well covered in the literature, e.g., Refs. [1,[22][23][24][25]30,31].) Also, because it employs theoretical approaches developed by an electrical engineering community, familiar concepts in electromechanics are described in more detail than usual.…”

“…Namely, while previous electromechanical systems make some compromise between better mechanical control and better mechanical measurement capabilities, we demonstrate that this network may be dynamically modulated between both extremes. While our network is too complex for traditional electromechanical models [4,20,21], it requires only three components, all of which are accessible to superconducting circuit labs (and feature regularly in our own work [6,10,13]), and is efficiently and intuitively modeled as a linear feedback system [1,2,22]. In other words, this network is easy to build (given familiar technologies, specifically, devices that are ''generic'' in our lab) and its mechanisms are easy to intuit.…”