Synthetic fractional flux quanta in a ring of superconducting qubits

TL;DR

The work demonstrates that a ring of capacitively coupled transmons, driven by Leviton Lorentzian pulses, can realize an effective attractive Bose-Hubbard system with a synthetic gauge field and exhibit fractional flux quanta via soliton-like many-body bands. The synthetic flux is encoded in a Floquet-engineered Peierls phase, while readout is achieved through a microwave-scattering absorption spectrum that reveals the band structure for different bound-state numbers $N_p$. The authors provide both perturbative large-$U$ analytics and numerically exact driven-dissipative simulations to support the observation of reduced periodicities $2\pi/N_s$ scaled by $N_p$, and discuss experimental feasibility including decoherence limits. Overall, the approach expands the toolbox for superconducting circuit quantum simulators, enabling exploration of soliton physics, synthetic gauge fields, and potential metrological applications in a controllable, tunable platform.

Abstract

A ring of capacitively coupled transmons threaded by a synthetic magnetic field is studied as a realization of a strongly interacting bosonic system. The synthetic flux is imparted through a specific Floquet modulation scheme based on a suitable periodic sequence of Lorentzian pulses that are known as 'Levitons'. Such scheme has the advantage to preserve the translation invariance of the system and to work at the qubit sweet spots. We employ this system to demonstrate the concept of fractional values of flux quanta. Although such fractionalization phenomenon was originally predicted for bright solitons in cold atoms, it may be in fact challenging to access with that platform. Here, we show how fractional flux quanta can be read out in the absorption spectrum of a suitable 'scattering experiment' in which the qubit ring is driven by microwaves.

Figures (10)

• Figure 1: (a) Schematics of a circuit constituted by a chain of transmons, which realizes an attractive Bose-Hubbard model. (b) Floquet modulation protocol, consisting in local transmon frequency modulation.
• Figure 2: (a) Phase and (b) modulus of the complex hopping between two transmons modulated through Levitons, as a function of the time delay $\delta t/T$ for four different values of the Lorentzian width $\tau/T$ [in (a), only the curve for the smallest width can be distinguished from the other three curves].
• Figure 3: (a) Modulus of the wave reflected off the driven system as a function of the synthetic flux $\Phi$, detuning $\omega_d-\omega$ (in GHz), and driving amplitude $\Omega = 0.01$ GHz, for a chain of $N_s=4$ transmons. A clear single-particle spectrum ($N_p=1$) appears as a broad bright signal around zero detuning and shows the expected $2\pi$ periodicity as a function of the synthetic flux. At negative detuning, a band made of two-particle bound states characterizing bright solitons appears with the predicted periodicity halved to $\pi$ (lower part of the spectra). (b) For further increasing the external drive $\Omega = 0.04$ GHz three-particle bound states emerge with one third periodicity. (c) Superimposed spectra of the $N_p=1,2,3$ sectors, showing the correspondence with the output signal. (d) Zoom of the $N_p=3$ sector. The rest of the system parameters are given in the main text. The color bar in a) is made non-linear by setting $z(x,y)^{2/5}$.
• Figure S1: Evolution in time of the real part of the wave function components, ${\rm Re}~\psi_j(t)$ with $j=1,\ldots,N_s$, for a $N_s=4$ transmons chain in the $N_p=1$ particle sector for three different conditions: (top panels) the Hamiltonian is the target one Eq. \ref{['Eq:Htarget']} and the time-evolution is for different values of the phase $\phi/2\pi=\delta t/T$, (middle panels) the Hamiltonian is the effective one in the fundamental Floquet band, and (bottom panels) the Hamiltonian is the exact one Eq. \ref{['Eq:Hmodulated']}, all shown as a function of the time-shift $\delta t/T$. The parameters are $J_0=0.041~{\rm GHz}$, $T=0.5~{\rm ns}$, $\tau/T=0.3$, and $J_0'=J_0 e^{2\pi\tau/T}$.
• Figure S2: Infidelity of the time-dependent exact evolution in the $N_p=1$ sector of the Floquet modulated Hamiltonian with respect to the target evolution. Parameters are $J_0=0.041~{\rm GHz}$, $\tau/T=0.3$, and we vary $T$.