TY - JOUR
T1 - Electrooptomechanical Equivalent Circuits for Quantum Transduction
AU - Zeuthen, Emil
AU - Schliesser, Albert
AU - Taylor, Jacob M.
AU - Sørensen, Anders Søndberg
PY - 2018/10/15
Y1 - 2018/10/15
N2 - With use of 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 with linear response theory based on the Heisenberg-Langevin equations. While these equations are 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 electrooptomechanical 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 for both static (dc) and harmonically varying (ac) bias 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.
AB - With use of 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 with linear response theory based on the Heisenberg-Langevin equations. While these equations are 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 electrooptomechanical 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 for both static (dc) and harmonically varying (ac) bias 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.
U2 - 10.1103/PhysRevApplied.10.044036
DO - 10.1103/PhysRevApplied.10.044036
M3 - Journal article
SN - 2331-7019
VL - 10
JO - Physical Review Applied
JF - Physical Review Applied
M1 - 044036
ER -