Two-tooth bosonic quantum comb for temporal-correlation sensing

Abstract

We introduce a two-tooth bosonic quantum comb that captures the sequential interactions between a thermal absorber and a long-lived coherent probe. The comb provides a causal, multi-time description of coherence transport, tracking how the probe records both instantaneous fluctuations and their temporal correlations. Using a process-tensor formulation, we derive closed form expressions showing that interference between the two interaction windows generates a non-monotonic memory response that reflects a fundamental competition between the absorbers thermal population and its dynamical correlations. By sweeping the temporal separation between the interaction windows, the probe directly samples the absorbers population correlator, enabling bosonic noise spectroscopy that discriminates Markovian temperature noise from slow or spectrally structured fluctuations. The approach is readily compatible with circuit-QED platforms and offers a general method for probing fluctuating bosonic environments.

Figures (4)

• Figure 1: Schematic of two-tooth bosonic quantum comb for thermometry and noise discrimination. (a) A thermal absorber mode $a$, equilibrated with a local thermal bath, couples dispersively to a long-lived coherent probe mode $b$ via the cross-Kerr strength $\lambda$. Thermal fluctuations of $n_a$ induce both a deterministic phase shift and stochastic phase noise on the probe, encoding temperature information into the probe quadratures. A transmon is used to monitor the probe coherence via the dispersive pull $\chi$. (b) The sequence forms a two-tooth bosonic quantum comb: each tooth corresponds to an interaction map, while the probe's free evolution acts as a quantum memory channel linking them. The output probe state contains both (i) single-interaction phase diffusion $\lambda \tau_j \mathrm{Var}[n_a(t_j)]$ and (ii) mixed phase-phase terms proportional to the absorber’s autocorrelation $\langle\delta n_a(t_1)\delta n_a(t_2)\rangle_T$.
• Figure 2: Memory kernel and non-monotonic memory response of the two-tooth comb szhu_supplementary_information. (a) Lorentzian correlation kernel (Eq. \ref{['eq:Lor_K']}) showing the exponential correlation envelope and its temperature-dependent decay. The white dashed curve denotes $\tilde{\mathcal{K}}=e^{-1}$ (i.e., $\Delta=\tau_c(T)$). (b) Pure amplitude gain factor $1 + \partial_T \tilde{\mathcal{K}}$, which quantifies the correlation-induced boost to the probe's phase variance. (c) Relative responsivity $\partial_T \tilde{\mathcal{K}} / (1 + \tilde{\mathcal{K}})$, revealing the locus of minimum temperature sensitivity and a strong competition with the population responsivity (d) Two-tooth quantum Fisher information $\mathcal{F}_2$, inheriting the non-monotonic behavior of the kernel’s responsivity and correlation decay. (e) Corresponding memory advantage $\mathcal{A}=\mathcal{F}_2/[2\mathcal{F}_1]$, showing enhancement ($\mathcal{A}>1$) at short delays where correlations dominate and suppression ($\mathcal{A}<1$) where temperature responsivities compete. Black markers indicate the delay at which $\mathcal{A}$ reaches its minimum for selected temperatures. (f) Line cuts of $\mathcal{A}(\Delta)$ at three representative temperatures (15, 30, and 45 mK). At low temperature, the minimum of $\mathcal{A}$ is shifted away from the $1/e$ contour due to the weak temperature dependence of the correlation time, whereas at higher temperatures the minimum aligns with the correlation-time boundary.
• Figure 3: Delay-dependent visibility for different absorber noise spectra szhu_supplementary_information. (a) Normalized two-tooth coherence $\tilde{C}_2(\Delta)$ for white, Lorentzian, and $1/f$-like population noise, showing flat, sharp, and broad delay-dependent rolloffs, respectively. (b) Corresponding normalized spectra $\tilde{S}_{nn}(\omega)$ reconstructed from $\tilde{C}_2(\Delta)$, yielding flat, finite-bandwidth, and low-frequency–dominated line shapes.
• Figure 4: Competition between population and correlation responsivities in the two-tooth memory advantage. (a) Linecuts of the absorber population responsivity $S_{\bar{n}_a}$ (dashed) and the correlation responsivity $S_{\tilde{\mathcal{K}}}$ (solid) as a function of delay $\Delta$ for selected temperatures: 15 mK (Blue), 30 mK (yellow), and 45 mK (green). (b) Responsivity factor $(1+S_{\tilde{\mathcal{K}}}/S_{\bar{n}_a})^2$ entering the approximate expression for the memory efficiency. (c) Amplitude gain $1+\tilde{\mathcal{K}}$, illustrating the decay of temporal correlations with increasing delay. (d) Approximate memory advantage $\mathcal{A} \simeq (1+\tilde{\mathcal{K}})(1+S_{\tilde{\mathcal{K}}}/S_{\bar{n}_a})^2$ for the same temperatures, showing regions of enhancement ($\mathcal{A}>1$) and suppression ($\mathcal{A}<1$) arising from the competition between thermal population responsivity and kernel responsivity. Dashed-lines are reproduced from Fig. \ref{['fig:process_kernel']}(f).