Frozonium: Freezing Anharmonicity in Floquet Superconducting Circuits

Floquet engineering is a powerful method that can be used to modify the properties of interacting many-body Hamiltonians via the application of periodic time-dependent drives. Here we consider the physics of an inductively shunted superconducting Josephson junction in the presence of Floquet drives in the fluxonium regime and beyond, which we dub the frozonium artificial atom. We find that in the vicinity of special ratios of the drive amplitude and frequency, the many-body dynamics can be tuned to that of an effectively linear bosonic oscillator, with additional nonlinear corrections that are suppressed in higher powers of the drive frequency. By analyzing the inverse participation ratios between the time-evolved frozonium wavefunctions and the eigenbasis of a linear oscillator, we demonstrate the ability to achieve a novel dynamical control using a combination of numerical exact diagonalization and Floquet-Magnus expansion. We discuss the physics of resonances between quasi-energy states induced by the drive, and ways to mitigate their effects. We also highlight the enhanced protection of frozonium against external sources of noise present in experimental setups. This work lays the foundation for future applications in quantum memory and bosonic quantum control using superconducting circuits.

💡 Research Summary

The authors investigate a superconducting artificial atom formed by an inductively shunted Josephson junction (a fluxonium‑type circuit) subjected to periodic Floquet drives. By adding an inductive shunt they eliminate the offset‑charge degree of freedom and replace it with a flux loop whose noise is slower than the system’s intrinsic frequencies. Two drive functions, f(t) (coupling to the charge operator) and g(t) (coupling to the phase operator), are introduced. Choosing g(t)=−E_L Θ(t) with Θ(t)=∫₀^t f(t′)dt′ cancels mixed terms after a time‑dependent unitary transformation, leaving a moving‑frame Hamiltonian that contains only the original transmon part with a shifted phase and a quadratic inductive term E_L φ².

A Floquet‑Magnus expansion of this Hamiltonian shows that the leading (zero‑order) effective Hamiltonian is a simple harmonic oscillator H_quad=4E_C n²+E_L φ², while all nonlinear cosine contributions are suppressed by powers of 1/ω. The suppression is exact at special drive amplitude‑to‑frequency ratios α=A/ω. For a triangle‑wave drive, the freezing points occur at α≈2n (n∈ℤ); for a sine‑wave drive they correspond to the zeros of the Bessel function J₀(α). At these points the system’s dynamics become effectively linear, yet quantum‑mechanical, unlike previous “dynamical freezing” schemes where the infinite‑frequency limit yields a purely classical Hamiltonian.

Numerical exact diagonalization combined with time‑evolution over 10 000 Floquet periods is used to compute the inverse participation ratio (IPR) of the evolved state in the basis of H_quad. An IPR close to one indicates that the state remains in a single harmonic‑oscillator eigenstate, confirming the freezing. The authors find broad horizontal bands of high IPR centered at α=2, 4,… and a clear dependence on the drive frequency ω: above a threshold set by the oscillator frequency ν≈√(8E_C E_L) the IPR stays near unity, while at lower ω vertical streaks of low IPR appear, signalling resonances between quasi‑energy levels that re‑introduce anharmonicity. Increasing ω suppresses these resonances, restoring the frozen behavior.

The paper also addresses decoherence. Because the inductive shunt removes the offset charge, the dominant noise source becomes flux noise in the loop. At the freezing points the effective Hamiltonian’s dependence on the external flux is strongly reduced (the cosine term is suppressed), making the energy splitting |ε₁−ε₀| insensitive to slow flux fluctuations. Consequently, both relaxation (T₁) and dephasing (T₂) times are expected to improve relative to conventional fluxonium or transmon devices.

In summary, the work introduces “frozonium,” a Floquet‑engineered fluxonium circuit that (i) dynamically freezes its anharmonicity, yielding an effectively linear bosonic mode; (ii) retains full quantum dynamics even in the high‑frequency limit; (iii) eliminates charge‑noise sensitivity via the inductive shunt; and (iv) exhibits enhanced robustness against flux noise. These properties make frozonium a promising platform for quantum memory, bosonic quantum control, and scalable superconducting architectures where chaos and decoherence must be mitigated. Future directions include extending the scheme to multi‑mode arrays and exploring its utility for protected qubits and error‑corrected bosonic codes.