Electro-optomechanical equivalent circuits for quantum transduction

Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals and has the potential of performing quantum state transfer between superconducting circuitry and a traveling optical signal. Such transducers are often operated in a linear regime, where the hybrid system can be described using linear response theory based on the Heisenberg-Langevin equations. While mathematically straightforward to solve, this approach yields little intuition about the dynamics of the hybrid system to aid the optimization of the transducer. As an analysis and design tool for such electro-optomechanical transducers, we introduce an equivalent circuit formalism, where the entire transducer is represented by an electrical circuit. Thereby we integrate the transduction functionality of optomechanical systems into the toolbox of electrical engineering allowing the use of its well-established design techniques. This unifying impedance description can be applied both for static (DC) and harmonically varying (AC) drive fields, accommodates arbitrary linear circuits, and is not restricted to the resolved-sideband regime. Furthermore, by establishing the quantized input-output formalism for the equivalent circuit, we obtain the scattering matrix for linear transducers using circuit analysis, and thereby have a complete quantum mechanical characterization of the transducer. Hence, this mapping of the entire transducer to the language of electrical engineering both sheds light on how the transducer performs and can at the same time be used to optimize its performance by aiding the design of a suitable electrical circuit.Comment: 30 pages, 9 figure

Finite element modeling of the neuron-electrode interface: stimulus transfer and geometry

The relation between stimulus transfer and the geometry of the neuron-electrode interface can not be determined properly using electrical equivalent circuits, since current that flows from the sealing gap through the neuronal membrane is difficult to model in these circuits. Therefore, finite element modeling is proposed as a tool for linking the electrical properties of the neuron-electrode interface to its geometr

Quantum Computation as Geometry

Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms, or to prove limitations on the power of quantum computers.Comment: 13 Pages, 1 Figur

Equivalent Circuit Modelling of Non-Symmetric Reciprocal Lossy Electromagnetic Structures

Lattice-network-based equivalent circuits of lossy symmetric reciprocal electromagnetic structures have shown superior performance when compared to other topologies like the T- or PI- networks. This is due to the realizability of their elements and the orthogonal-mode decomposition, which, in most cases, provides a deep physical insight into the behaviour of the modelled structure. The aim of this contribution is to provide a short description of these equivalent circuits and to compare their performances by modelling a misaligned complementary strip-slot element.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Marie Sklodowska-Curie grant agreement No 706334. Spanish Ministerio de Economía y Competitividad and the European Regional Development Funds under Grants TEC2016-76070-CR3-2-R and TEC2016-76070-CR3-3-R (ADDMATE)

Noiseless Quantum Circuits for the Peres Separability Criterion

In this Letter we give a method for constructing sets of simple circuits that can determine the spectrum of a partially transposed density matrix, without requiring either a tomographically complete POVM or the addition of noise to make the spectrum non-negative. These circuits depend only on the dimension of the Hilbert space and are otherwise independent of the state.Comment: 4 pages RevTeX, 7 figures encapsulated postscript. v5: title changed slightly, more-or-less equivalent to the published versio

Defining and Computing Equivalent Inductances of Gapped Iron Core Reactors

The paper revisits the fundamental definitions and explores computational alternatives of equivalent inductances of gapped iron core reactors. Unlike in a transformer, the physical meaning of component inductances of a reactor is subject to uncertainty and open to different interpretations, leading to various equivalent circuits. It is argued that a definition based on flux distribution may not be reliable and calculations based on energy or co-energy are thus preferable