Dissipative Spectroscopy

Abstract

We introduce dissipative spectroscopy as a framework for extracting spectral information from quantum systems via controlled dissipation. By establishing a general dissipative response theory applicable to both Markovian and non-Markovian environments, we develop a protocol to access the dissipative spectrum (DS) through driven oscillation-dissipation resonance. We show that the DS can identify two-particle soft modes near quantum critical points and, on the normal-phase side, predict the emergence of macroscopic order exhibiting power-law growth following a dissipation quench. These distinctive signatures appear in quasiparticle-dominant regimes, previously considered trivial. Furthermore, we introduce extended dissipative susceptibilities that capture leading memory effects and demonstrate their utility in a dissipative fermionic model. Our results indicate that the DS is readily accessible and offers a versatile tool for probing equilibrium properties as well as predicting nonequilibrium dissipative dynamics.

Figures (3)

• Figure 1: (a) Free-fermion chain locally coupled to a dissipative bath. (b) Dissipation dynamics of the even-odd particle imbalance $N_e - N_o$ for varying dissipation strengths $\gamma$. (c) Applying an extra oscillation in dissipation strength, a resonance behavior is found in the even-odd particle number deviation. (d) Dissipative spectroscopy extracted from the resonance signal in (c). Our protocol agrees well with theoretic result.
• Figure 2: (a) Dissipative spectrum $\chi^{\mathcal{D},[0]\Re}_{\hat{a},\hat{n}_{\rm ph}}(\omega)$ for $g/g_c=0.9998$ at different $N$. (b) Photon number dynamics under dissipation ($\kappa=0.05\omega_a$). For $N\!=\!1000$, early-time growth follows $t^3$. (c) Scaling of $(2\tilde{N}_{\rm s}\!-\! \tilde{N}_0)/\omega_{\rm s}$ with $N$ near criticality. This quantity is smaller than $N^{0.35}$ for large $N$. (d) $\tilde{N}_{\rm s} /\omega_{\rm s}$ as a function of $N$. Log-log plot reveals $\tilde{N}_{\rm s} /\omega_{\rm s} \propto N^{\eta}$ in the critical region, $\eta\approx0.95$ for $g=0.9998g_c$.
• Figure 3: (a) Feynman diagrams for fermions $c$ and $\psi$. Disorder average is indicated by dashed line; density-density interaction appears as vertex labeled by $V$. Two types of self-energies from system-bath coupling are shown. (b) Dissipation dynamics of the even-odd imbalance $N_e - N_o$: numerical result based on KBE (black solid), zeroth-order DRT (red dotted), and combined $0+1$-order response (blue dash-dotted). (c, d) Variance $\sigma(t)$ comparing full evolution to the leading-memory response theory. (c) Fixed $V=1$, varying memory time $\tau_{0} = 1/J$; (d) fixed $\tau_{0}=1/2$, varying dissipation time scale $t_d=J/V^2$. White lines mark empirical boundaries $\propto \tau_{0}$ and $t_d$, which the low variance confirms the validity of DRT.