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arXiv:1408.6696 · Physical Review A

Microwave degenerate parametric down-conversion with a single cyclic three-level system in a circuit-QED setup

Zhihai Wang, C. P. Sun, Yong Li

Published Apr 2, 2015• 30 citations
arXivHTMLPDF

Abstract

With the assistance of a cyclic three-level artificial atom of a superconducting flux quantum circuit interacting with a two-mode superconducting transmission-line resonator, we study theoretically the degenerate microwave parametric down-conversion (PDC) in a circuit-QED system. By adiabatically eliminating the excited states of the three-level artificial atom, we obtain an effective microwave PDC Hamiltonian for the two resonator modes (i.e., the fundamental and second-harmonic modes). The corresponding PDC efficiency in our model can be much larger than that in the similar circuit-QED system based on a single two-level superconducting qubit [K. Moon and S. M. Girvin, Phys. Rev. Lett. 95, 140504 (2005)]. Furthermore, we investigate the squeezing and bunching behavior of the fundamental resonator mode resulting from the coherent driving to the second-harmonic one.

DOI
10.1103/physreva.91.043801

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With the assistance of a cyclic three-level artificial atom of a superconducting flux quantum circuit interacting with a two-mode superconducting transmission-line resonator, we study theoretically the degenerate microwave parametric down-conversion (PDC) in a circuit-QED system. By adiabatically eliminating the excited states of the three-level artificial atom, we obtain an effective microwave PDC Hamiltonian for the two resonator modes (i.e., the fundamental and second-harmonic modes). The corresponding PDC efficiency in our model can be much larger than that in the similar circuit-QED system based on a single two-level superconducting qubit [K. Moon and S. M. Girvin, Phys. Rev. Lett. 95, 140504 (2005)]. Furthermore, we investigate the squeezing and bunching behavior of the fundamental resonator mode resulting from the coherent driving to the second-harmonic one.
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.
We describe a scheme for the efficient generation of microwave photon pairs by parametric down-conversion in a superconducting transmission line resonator coupled to a Cooper-pair box serving as an artificial atom. By properly tuning the first three levels with respect to the cavity modes, the down-conversion probability may reach the percentage level at good fidelity. We show this by numerically simulating the dissipative quantum dynamics of the coupled cavity-box system and discussing the effects of dephasing and relaxation in the solid state environment. The setup analyzed here might form the basis for a future on-chip source of entangled microwave photons, e.g., using Franson's idea of energy-time entanglement.
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 present an alternative scheme for generating the asymmetric steering of microwave photons via using a superconducting circuit system, where a single Δ -type three-level fluxoninum qubit interacts dispersively with three superconducting resonators. The nondegenerate parametric down-conversion occurs among three microwave modes by adiabatically eliminating the atomic variables of the artificial atom, which is responsible for the existence of quantum correlation. Furthermore, the asymmetric steering is easily established with the help of coherent driving of the resonators, and its directionality can be controlled by adjusting the driving strengths to two modes among three modes without additional noise. The scheme we present is based on general quantum operations under conditions of decoherence and nonideal coupling efficiency, and the asymmetric steering of microwave photons is a useful resource for the construction of long-distance quantum communication networks in solid-state systems.
We propose an experimentally accessible superconducting quantum circuit, consisting of two coplanar waveguide resonators (CWRs), to enhance the microwave squeezing via parametric down-conversion (PDC). In our scheme, the two CWRs are nonlinearly coupled through a superconducting quantum interference device embedded in one of the CWRs. This is equivalent to replacing the transmission line in a flux-driven Josephson parametric amplifier (JPA) by a CWR, which makes it possible to drive the JPA by a quantized microwave field. Owing to this design, the PDC coefficient can be considerably increased to be about tens of megahertz, satisfying the strong-coupling condition. Using the Heisenberg-Langevin approach, we numerically show the enhancement of the microwave squeezing in our scheme. In contrast to the JPA, our proposed system becomes stable around the critical point and can generate stronger transient squeezing. In addition, the strong-coupling PDC can be used to engineer the photon blockade.
By strongly driving a cyclic-transition three-level artificial atom, demonstrated by such as a flux-based superconducting circuit, we show that coherent microwave signals can be excited along a coupled one-dimensional transmission line. Typically, the intensity of the generated microwave is tunable via properly adjusting the Rabi frequencies of the applied strong-driving fields or introducing a probe field with the same frequency. In practice, the system proposed here could work as an on-chip quantum device with controllable atom-photon interaction to implement a total-reflecting mirror or switch for the propagating probe field.