Passive detection of Schwinger boson dynamics via a qubit

TL;DR

The paper introduces a transmon–photonic cross-resonator device to passively detect time-reversal symmetry breaking in quantum materials by encoding dielectric and Hall responses into the resonator dynamics. By aligning the transmon–resonator coupling with the cross-resonator rotation vector, the system accesses a bright state and tunable hybridization, allowing readout through the transmon's excited-state population and its Fourier spectrum. The analysis leverages a quantum metric Q, with Q = sum over i>j of (Δλ_ij)^2 |c_i|^2 |c_j|^2, to quantify state sensitivity and identify optimal operation near resonance ρ ≈ |R|. This approach yields a compact, noninvasive spectroscopy method for probing time-reversal breaking in correlated materials and suggests avenues for optimization and nonequilibrium studies.

Abstract

The quantum sensing landscape has been revolutionized by advanced technologies like superconducting circuits and qubit-based systems which have furthered the ability to probe and understand fundamental properties of quantum matter. Here, we propose an integrated photonic device where a transmon qubit capacitively couples to a microwave cross-resonator, and the setup is employed for sensing of time reversal broken order in materials. In this sensing scheme, the transmon qubit plays a dual role as both a control element and a passive detector, while the photonic cross-resonator serves as the host for the sample, enabling a contact-free spectroscopic method suitable for studying materials where reliable electrical contacts are challenging to obtain, e.g., in van der Waal 2D heterostructures. We show that by tuning the coupling strength and phase between the transmon and the cross-resonator, the system allows selective control over the interaction dynamics and leads to a highly sensitive detection method that can be compactly understood in terms of evolution of excited state population and quantum metric of the resonator-transmon hybrid state. This architecture has the potential to host a wide range of quantum phenomena that can be precisely encoded in the dynamics of the transmon qubit and, in this way, potentially allows access to elusive aspects of correlated materials.

Figures (4)

• Figure 1: Proposed cross resonator-transmon device: (a) A transmon qubit (blue accents) capacitively coupled to a cross-resonator device (red accents), where Rx and Ry denote the two resonators. The transmon's energy splitting can be controlled via a magnetic flux threading. The device is externally driven and measured via capacitive coupling to transmission lines (gray). (b) The evolution of the transmon's (cross-resonator's) state vector $\langle\hat{\bm \sigma}\rangle$ ($\langle\hat{\bm S}\rangle$) is equivalent to the precession around the rotation vector $\bm B$ ($\bm R$).
• Figure 2: (a) The coupling between the transmon and cross-resonator is compactly represented by a vector in a three-dimensional sphere with radius $g=\sqrt(g_a^2 + g_b ^2)/2$ given by the root mean squared interaction strength, polar angle $\theta = \arctan\frac{|g_b|}{|g_a|}$ and azimuthial angle $\phi = \frac{1}{2}\arg (g_a g^*_b)$. (b) Partially diagonalizing the coupling Hamiltonian $\hat{H}_{coupling}$ results in the rotation of the cross-resonator's rotation vector $\bm R$ according to the coupling strengths $g_a$ and $g_b$, and the relative phase difference $\phi$.
• Figure 3: (a) The spectrum of the three-dimensional subspace spanned by initially exciting the transmon, and where the coupling vector is fixed to $\phi-\phi_0$. (b) Similarly, the spectrum of the three-dimensional subspace for $\theta=\theta_0$ for two differnet values of $\phi=\phi_0$ or $\phi_0+\pi/5$. (c) Density plot of the energy difference between the eigenenergies shows a degeneracy when the coupling vector has the same coordinates as the cross-resonator's rotational vector.
• Figure 4: (a) The Fourier transform of the transmon's dynamics. Depending on the coupling vector, the transmon coupled to the photonic modes and its population oscillates with a maximum of three different frequencies. The amplitude of the oscillation associated to each frequency depends on the overlap of the initial state with the systems hybrid modes. (b) The quantum metric extracted from the frequency and amplitude of oscillations. For each pair of eigenmodes, the quantum metric is maximized depending on the direction and magnitude of the cross-resonator's rotation vector.