Coherence-Mediated Quantum Thermometry in a Hybrid Circuit-QED Architecture

Abstract

Quantum thermometry plays a critical role in the development of low-temperature sensors and quantum information platforms. In this work, we propose and theoretically analyze a hybrid circuit quantum electrodynamics architecture in which a superconducting qubit is dispersively coupled to two distinct bosonic modes: one initialized in a weak coherent state and the other coupled to a thermal environment. We show that the qubit serves as a sensitive readout of the probe mode, mapping the interference between thermal and coherent photon-number fluctuations onto measurable dephasing. This mechanism enables enhanced sensitivity to sub-millikelvin thermal energy fluctuations through Ramsey interferometry. We derive analytic expressions for the qubit coherence envelope, compute the quantum Fisher information for temperature estimation, and demonstrate numerically that the presence of a coherent reference amplifies the qubit's sensitivity to small changes in thermal photon occupancy. Our results establish a new paradigm for quantum-enhanced thermometry and provide a scalable platform for future calorimetric sensing in high-energy physics and quantum metrology.

Figures (8)

• Figure 1: Schematic of the proposed thermometry architecture. A low-$Q$ thermal resonator $\hat{a}$ is thermalized by a bath at temperature $T$. Through an engineered cross-Kerr interaction $\lambda$, realized with two fixed-frequency transmons ($Q_1$, $Q_2$), fluctuations of $\hat{a}$ are mapped onto a high-$Q$ 3D cavity probe mode $\hat{b}$. A sensing transmon couples strongly to the probe with dispersive strength $\chi_b$ for readout, while any residual coupling $\chi_a$ to the thermal mode acts as a parasitic dephasing channel. Temperature information encoded in the probe can be extracted either via qubit Ramsey (coherence-mediated) or direct heterodyne detection (phase-shift).
• Figure 2: Simulated coherence-based QFI $\mathcal{F}_C$ and corresponding temperature sensitivity $\delta T$, with thermal frequency $\omega_a /2\pi = 1~\mathrm{GHz}$, coherent amplitude $\alpha = 2.0$, and cross-Kerr coupling $\lambda / 2\pi = 50~\mathrm{kHz}$. (a) Heatmap of $\mathcal{F}_C$ as a function of thermal bath temperature $T$ and interaction time $\tau$. The red dashed line indicates the optimal $\tau(T)$ that maximizes $\mathcal{F}_C$ for each temperature. (b) Minimum detectable temperature change $\delta T_{\mathrm{min}} = 1 / \sqrt{\nu \mathcal{F}_C}$ (blue solid line) as a function of temperature, computed at the optimal $\tau$ (green dashed line). A sensitivity of approximately $60~\mu\mathrm{K}$ is achieved near $T \sim 10~\mathrm{mK}$ with $\tau = 10~\mu\mathrm{s}$. In this simulation, we set the number of measurement repetitions to $\nu = 10^4$.
• Figure 3: Quantum Fisher information and sensitivity of the phase-shift thermometry scheme. (a) Quantum Fisher information $\mathcal{F}_\Phi(T)$ quantifies the temperature information encoded in the probe phase $\phi_b(T)=\lambda\tau\bar{n}_a(T)$, shown for interaction times $\tau=10,\,100,$ and $1000~\mu$s. At low temperatures ($k_BT\!\ll\!\hbar\omega_a$), $\mathcal{F}_\Phi$ is exponentially suppressed, while at high $T$ it saturates to a constant. Across curves, $\mathcal{F}_\Phi$ scales as $\propto\tau^2$. (b) Corresponding temperature resolution $\delta T(T)=1/\sqrt{\nu\,\mathcal{F}_\Phi(T)}$ for $\nu=10^4$ repetitions. Sensitivity improves as $1/\tau$ and flattens in the high-temperature limit.
• Figure 4: Heatmap of the two--qubit–mediated cross–Kerr rate $\lambda/2\pi$ (kHz) versus the dispersive pulls $\chi_{a1}/2\pi$ and $\chi_{b2}/2\pi$ (MHz). Values are computed from $\lambda = 8\,\chi_{a1}\chi_{b2}J_{XY}^2/\Delta_{12}^3$ with $J_{XY}$ and $\Delta_{12}$ held fixed (here $J_{XY}/2\pi=30~\mathrm{MHz}$ and $\Delta_{12}/2\pi=180~\mathrm{MHz}$, so $J_{XY}/\Delta_{12}=0.17$). White dashed contours denote $\lambda/2\pi=\{10,20,30,40,50\}\,\mathrm{kHz}$. The map highlights that the target $10$–$50~\mathrm{kHz}$ range is readily reached with modest probe pull $\chi_{b2}$ by increasing the thermal--side pull $\chi_{a1}$.
• Figure 5: Qubit Ramsey visibility as a function of dispersive coupling strengths during the Ramsey window $\tau_R$. (a) Dependence on $\chi_b/2\pi$ for $10,\,20,\,50$ kHz. (b) Dependence on $\chi_a/2\pi$ for $1,\,5,\,10$ kHz. The y-axis shows the normalized Ramsey visibility (qubit contrast) versus the Ramsey integration time $\tau_R$. Larger dispersive couplings increase dephasing during readout, shortening the usable $\tau_R$ window.