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In this chapter, we will discuss in detail the classical, semi-classical, and quantum representations of the effective Hamiltonian of the squeeze-driven Kerr oscillator (SKO), obtained by rapidly driving the SNAIL transmon superconducting circuit (see detailed modeling in Chap. 2 ). As we will see, different representations are convenient to understand different properties. There are two properties we will investigate as a function of the drive frequency and the drive amplitude: spectral degeneracies, and the inter-well tunneling amplitude. As we uncover the SKO’s tunneling properties, we will also contrast them with the tunneling properties of an ordinary double-well potential. Relevant literature is surveyed along the way.

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Representations and Properties of the SKO

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  • 发表日期：

    2025年

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  • Jayameenakshi Venkatraman

摘要

In this chapter, we will discuss in detail the classical, semi-classical, and quantum representations of the effective Hamiltonian of the squeeze-driven Kerr oscillator (SKO), obtained by rapidly driving the SNAIL transmon superconducting circuit (see detailed modeling in Chap. 2 ). As we will see, different representations are convenient to understand different properties. There are two properties we will investigate as a function of the drive frequency and the drive amplitude: spectral degeneracies, and the inter-well tunneling amplitude. As we uncover the SKO’s tunneling properties, we will also contrast them with the tunneling properties of an ordinary double-well potential. Relevant literature is surveyed along the way.