Fig. 3: Temperature-independent relative error bound with dynamical control.
From: Enhanced precision bound of low-temperature quantum thermometry via dynamical control
Relative error bound \(\xi\) for the estimation of bath temperature at \(T={T}_{-1}=({\omega }_{0}-\Delta )/4\), by a harmonic-oscillator dynamically controlled quantum thermometer under sinusoidal modulation (cf. Eq. (6)), for the following bath spectra: nearly flat bath spectrum (magenta solid curve), sub-Ohmic bath spectrum with \(s=0.1,{\omega }_{c}=100\) (black dashed curve) and the same spectra in the absence of control (turquoise dotted curve). Dynamical control reduces the relative error bound significantly, with \(\xi\) remaining constant over a broad range of low temperatures \(T\ll {\omega }_{0}\). The sidebands \(m=0,\pm 1,\pm 2,\pm 3\) are included in the calculation. Here, the modulation amplitude \(\mu =0.2\), and \({\omega }_{0}=1\). Inset: Corresponding spectral-response functions scaled by \(\gamma\).
