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arXiv:2210.14681

Theory of strong down-conversion in multi-mode cavity and circuit QED

Mehta, Nitish, Cristiano Ciuti, Roman Kuzmin, Vladimir Manucharyan

Published Oct 26, 2022• 1 citation
arXivHTMLPDF

Abstract

We revisit the superstrong coupling regime of multi-mode cavity quantum electrodynamics (QED), defined to occur when the frequency of vacuum Rabi oscillations between the qubit and the nearest cavity mode exceeds the cavity's free spectral range. A novel prediction is made that the cavity's linear spectrum, measured in the vanishing power limit, can acquire an intricate fine structure associated with the qubit-induced cascades of coherent single-photon down-conversion processes. This many-body effect is hard to capture by a brute-force numerics and it is sensitive to the light-matter coupling parameters both in the infra-red and the ultra-violet limits. We focused at the example case of a superconducting fluxonium qubit coupled to a long transmission line section. The conversion rate in such a circuit QED setup can readily exceed a few MHz, which is plenty to overcome the usual decoherence processes. Analytical calculations were made possible by an unconventional gauge choice, in which the qubit circuit interacts with radiation via the flux/charge variable in the low-/high-frequency limits, respectively. Our prediction of the fine spectral structure lays the foundation for the "strong down-conversion" regime in quantum optics, in which a single photon excited in a non-linear medium spontaneously down-converts faster than it is absorbed.

DOI
10.48550/arxiv.2210.14681

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We revisit the superstrong coupling regime of multi-mode cavity quantum electrodynamics (QED), defined to occur when the frequency of vacuum Rabi oscillations between the qubit and the nearest cavity mode exceeds the cavity's free spectral range. A novel prediction is made that the cavity's linear spectrum, measured in the vanishing power limit, can acquire an intricate fine structure associated with the qubit-induced cascades of coherent single-photon down-conversion processes. This many-body effect is hard to capture by a brute-force numerics and it is sensitive to the light-matter coupling parameters both in the infra-red and the ultra-violet limits. We focused at the example case of a superconducting fluxonium qubit coupled to a long transmission line section. The conversion rate in such a circuit QED setup can readily exceed a few MHz, which is plenty to overcome the usual decoherence processes. Analytical calculations were made possible by an unconventional gauge choice, in which the qubit circuit interacts with radiation via the flux/charge variable in the low-/high-frequency limits, respectively. Our prediction of the fine spectral structure lays the foundation for the "strong down-conversion" regime in quantum optics, in which a single photon excited in a non-linear medium spontaneously down-converts faster than it is absorbed.
Cavity quantum electrodynamics (QED) investigates the interaction between resonator-confined radiation and natural atoms. Similar phenomena can be explored using superconducting artificial atoms coupled to microwave resonators. Here, we examine incoherent and coherent spectra in a circuit QED system consisting of a flux qubit coupled to an LC resonator, considering different coupling configurations to the output transmission line. Although such systems can be effectively described by the quantum Rabi model, we demonstrate that the choice of the coupling between the resonator and the input-output channel can significantly affect the emission properties, particularly in the ultrastrong coupling regime. Specifically, we show that when the resonator is capacitively coupled with the input-output transmission line, the spectral features at zero flux offset can be mapped onto those of the cavity QED model. However, this correspondence breaks down for the mutual inductive coupling case. Extending our analysis to the parity-symmetry broken regime of the flux qubit, we further highlight how capacitive and inductive coupling mechanisms lead to distinct spectral features, emphasizing the necessity of a careful input-output treatment for an accurate description of the emission processes.
The field of cavity quantum electrodynamics (cavity QED) studies the interaction between light and matter on a fundamental level: a single atom interacts with a single photon. If the atom-photon coupling is larger than any dissipative effects, the system enters the strong-coupling limit. A peculiarity of this regime is the possibility to form coherent superpositions of light and matter excitations - a kind of 'molecule' consisting of an atomic and a photonic contribution. The novel research field of circuit QED extends cavity QED concepts to solid-state based system. Here, a superconducting quantum bit is coupled to an on-chip superconducting one-dimensional waveguide resonator. Owing to the small mode-volume of the resonant cavity, the large dipole moment of the 'artificial atom' and the enormous engineering potential inherent to superconducting quantum circuits, remarkable atom-photon coupling strengths can be realized. This thesis describes the theoretical framework, the development of fabrication techniques and the implementation of experimental characterization techniques for superconducting quantum circuits for circuit QED applications. In particular, we study the interaction between superconducting flux quantum bits and high-quality coplanar waveguide resonators in the strong-coupling limit. Furthermore, we report on the first experimental realization of a circuit QED system operating in the ultrastrong-coupling regime, where the atom-photon coupling rate reaches a considerable fraction of the relevant system frequencies. In these experiments we could observe phenomena that can not be explained within the renowned Jaynes-Cummings model.
The quantum Rabi model (QRM) is a cornerstone in the study of light-matter interactions within cavity and circuit quantum electrodynamics (QED). It effectively captures the dynamics of a two-level system coupled to a single-mode resonator, serving as a foundation for understanding quantum optical phenomena in a great variety of systems. However, this model may produce inaccurate results for large coupling strengths, even in systems with high anharmonicity. Moreover, issues of gauge invariance further undermine its reliability. In this work, we introduce a renormalized QRM that incorporates the effective influence of higher atomic energy levels, providing a significantly more accurate representation of the system while still maintaining a two-level description. To demonstrate the versatility of this approach, we present two different examples: an atom in a double-well potential and a superconducting artificial atom (fluxonium qubit). This procedure opens new possibilities for precisely engineering and understanding cavity and circuit QED systems, which are highly sought-after, especially for quantum information processing.
Abstract Vacuum fluctuations fundamentally affect an atom by inducing a finite excited state lifetime along with a Lamb shift of its transition frequency. Here we report the reverse effect: modification of vacuum modes by a single atom in circuit quantum electrodynamics. Our one-dimensional vacuum is a long section of a high wave impedance (comparable to resistance quantum) superconducting transmission line. It is directly wired to a transmon qubit circuit. Owing to the combination of high impedance and galvanic connection, the transmon’s spontaneous emission linewidth can greatly exceed the discrete transmission line modes spacing. This condition defines a previously unexplored superstrong coupling regime of quantum electrodynamics where many frequency-resolved vacuum modes hybridize with a single atom. We establish this regime by observing the spontaneous emission line of the transmon, revealed through the mode-by-mode measurement of the vacuum’s density of states. The linewidth as well as the atom-induced dispersive photon−photon interaction are accurately described by a physically transparent Caldeira−Leggett model, with the transmon’s quartic nonlinearity treated as a perturbation. Nonperturbative modification of vacuum, including inelastic scattering of single photons, can be enabled by the superstrong coupling regime upon replacing the transmon by more anharmonic qubits, with broad implications for simulating quantum impurity models of many-body physics.
We study a circuit QED setup where multiple superconducting qubits are ultrastrongly coupled to a single radio-frequency resonator. In this extreme parameter regime of cavity QED the dynamics of the electromagnetic mode is very slow compared to all other relevant timescales and can be described as an effective particle moving in an adiabatic energy landscape defined by the qubits. The focus of this paper is placed on settings with two or multiple qubits, where different types of symmetry-breaking transitions in the ground- and excited-state potentials can occur. Specifically, we show how the change in the level structure and the wave-packet dynamics associated with these transition points can be probed via conventional excitation spectra and Ramsey measurements performed at GHz frequencies. More generally, this analysis demonstrates that state-of-the-art circuit QED systems can be used to access a whole range of particlelike quantum-mechanical phenomena beyond the usual paradigm of coupled qubits and oscillators.
Interaction of the vacuum field of an optical mode with an electronic two-level system can drive non-perturbative light-matter dynamics, resulting in an exotic quantum ground state containing a sizeable population of virtual excitations. In the deep-strong coupling (DSC) regime, where the Rabi frequency,ΩR\Omega_{\mathrm{R}}ΩR​, exceeds the eigen-frequencies of the coupled systems, this extreme ground state can result in spectacular effects of cavity-QED, such as the expected release of the virtual photon ground state population as vacuum radiation by non-adiabatic modulation of the coupling mechanism [1], [2]. However, for resonant coupling of two single modes [3], the finite oscillator strength of resonant electronic excitation sets a natural limit to the achievable coupling strength, hindering further exploration of this exciting field.