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AIP conference proceedings

Entanglement and Squeezing in Solid State Circuits

Wen Yi Huo, Gui Lu Long, Hsi‐Sheng Goan, Yueh-Nan Chen

Published Jan 1, 2008• 2 citations
Publisher

Abstract

We investigate the dynamics of a system consisting of a Cooper‐pair box and two superconducting transmission line resonators. There exist both linear and nonlinear interactions in such a system. We show that single‐photon entanglement state can be generated in a simple way in the linear interaction regime. In nonlinear interaction regime, we derive the Hamiltonian of degenerate three‐wave mixing and propose a scheme for generating squeezed state of microwave using the three‐wave mixing in solid state circuits. In the following, we design a system for generating squeezed states of nanamechanical resonator.

DOI
10.1063/1.3037131

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We investigate the dynamics of a system consisting of a Cooper‐pair box and two superconducting transmission line resonators. There exist both linear and nonlinear interactions in such a system. We show that single‐photon entanglement state can be generated in a simple way in the linear interaction regime. In nonlinear interaction regime, we derive the Hamiltonian of degenerate three‐wave mixing and propose a scheme for generating squeezed state of microwave using the three‐wave mixing in solid state circuits. In the following, we design a system for generating squeezed states of nanamechanical resonator.
We propose a scheme for generating squeezed states of nanomechanical resonator in a solid state circuit system which consists of a nanomechanical resonator, a superconducting Cooper-pair box, and a superconducting transmission line resonator. The nonlinear interaction between the nanomechanical resonator and superconducting transmission line resonator can be implemented by setting the external biased flux of the Cooper-pair box at some special values. The squeezed states of the nanomechanical resonator can be generated by degenerate three-wave mixing and the Cooper-pair box plays the role of “nonlinear medium” in the squeezing process.
We propose a scheme for generating squeezed states in solid state circuits consisting of a nanomechanical resonator (NMR), a superconducting Cooper-pair box (CPB) and a superconducting transmission line resonator (STLR). The nonlinear interaction between the NMR and the STLR can be implemented by setting the external biased flux of the CPB at certain values. The interaction Hamiltonian between the NMR and the STLR is derived by performing Fro¨\rm\ddot oo¨hlich transformation on the total Hamiltonian of the combined system. Just by adiabatically keeping the CPB at the ground state, we get the standard parametric down-conversion Hamiltonian. The CPB plays the role of ``nonlinear media", and the squeezed states of the NMR can be easily generated in a manner similar to the three-wave mixing in quantum optics. This is the three-wave mixing in a solid-state circuit.
We propose a scheme for generating squeezed states in solid state circuits which consist a superconducting transmission line resonator (STLR), a superconducting Cooper-pair box (CPB) and a nanoelectromechanical resonator (NMR). The nonlinear interaction between the STLR and the CPB can be implemented by setting the external biased flux of the CPB at some certain points. The interaction Hamiltonian between the STLR and the NMR is derived by performing Frohlich transformation on the total Hamiltonian of the combined system. Just by adiabatically keeping the CPB at the ground state, we get the standard parametric down-conversion Hamiltonian, and the squeezed states of the STLR can be easily generated, which is similar to the three-wave mixing in quantum optics.
We study the theory of degenerate three-wave mixing and the generation of squeezed microwaves using circuit quantum electrodynamics in solid state circuits. The Hamiltonian for degenerate three-wave mixing, which seemed to be given phenomenologically in quantum optics, is derived by quantum mechanical calculations. The nonlinear medium needed in three-wave mixing is composed of a series of superconducting charge qubits which are located inside two superconducting transmission-line resonators. Here, the multiqubit ensemble is present to enhance the effective coupling constant between the two modes in the transmission-line resonators. In the squeezing process, the qubits are kept in their ground states so that their decoherence does not corrupt the squeezing. The main obstacle preventing a large squeezing efficiency is the decay rate of the transmission-line resonator.
We study theoretically the parametric down-conversion and squeezing of microwaves using cavity quantum electrodynamics of a superconducting Cooper-pair box (CPB) qubit located inside a transmission line resonator. The nonlinear susceptibility chi2 describing three-wave mixing can be tuned by dc gate voltage applied to the CPB and vanishes by symmetry at the charge degeneracy point. We show that the coherent coupling of different cavity modes through the qubit can generate a squeezed state. Based on parameters realized in recent successful circuit QED experiments, squeezing of 95% approximately 13 dB below the vacuum noise level should be readily achievable.