Orthogonalization speed-up from quantum coherence after a sudden quench

TL;DR

The paper investigates how quantum coherence in the initial state affects non-equilibrium dynamics after a sudden quench with a localized defect, revealing a coherence-driven orthogonalization that mirrors Anderson's orthogonality catastrophe in the transient regime. By analyzing a particle in a harmonic trap subjected to a delta-function perturbation, it shows the Loschmidt echo decays as $|\nu(t)| \approx 1 - \beta(t) N^{\gamma(t)}$, with $\gamma(t)>0$ for coherent states and $\gamma(t)<0$ for incoherent states, and connects this to a discrete spectral-function discontinuity and to the Kirkwood-Dirac quasiprobability distribution of work. The study extends to two-fermion systems, finds analogous scaling and amplified non-classical KDQ features, and demonstrates that coherence increases the average work and speeds up orthogonalization via the quantum speed limit $\tau_{\rm QSL}$. An experimental path using Ramsey interferometry with ultracold atoms is proposed to test coherence-enhanced OC dynamics. These results highlight a fundamental role for initial coherence in driving speed-ups in non-equilibrium quantum perturbations and open routes to coherence-assisted quantum sensing and control.

Abstract

We introduce a nonequilibrium phenomenon, reminiscent of Anderson's orthogonality catastrophe (OC), that arises in the transient dynamics following an interaction quench between a quantum system and a localized defect. Even if the system comprises only a single particle, the overlap between the asymptotic and initial superposition states vanishes according to a power-law scaling with the number of energy eigenstates entering the initial state and an exponent that depends on the interaction strength. The presence of quantum coherence in the initial state is reflected onto the discrete counterpart of an infinite discontinuity in the system spectral function, a hallmark of Anderson's OC, as well as in the quasiprobability distribution of work due to the quench transformation. The positivity loss of the work distribution is directly linked with a reduction of the minimal time imposed by quantum mechanics for the state to orthogonalize. We propose an experimental test of coherence-enhanced orthogonalization dynamics based on Ramsey interferometry of a trapped cold-atom system.

Figures (7)

• Figure 1: Decay of the LE for a single particle initialized in the state of Eq. \ref{['eq:EqualSupState']}, after the interaction with a delta perturbation of strength $k$ is switched on. Panels (a)-(b): Time-behaviour of $\abs{\nu(t)}$ taking the superposition state of Eq. \ref{['eq:EqualSupState']} [panel (a)] or the corresponding diagonal state of Eq. \ref{['eq:diag_state']} [panel (b)] as initial states, for $k=100$ and $N \in \{2,5,8,11,14,17,20\}$. The solid lines represent the values of $\abs{\nu(t)}$ obtained numerically, while the dashed lines are the fitted curves following the scaling law of Eq. \ref{['eq:LE_fit_formula_Intro']}. Panels (c)-(d): Time dependence of $\beta(t),\gamma(t)$ for $k=1,10,100$; here solid lines refer to taking $\ket{\psi(0)}$ equal to the superposition state, while the dashed lines are associated to the corresponding diagonal state.
• Figure 2: Squared modulus of LE as a function of time, initializing the system in the superposition state of Eq. \ref{['eq:EqualSupState']} [panel (a)] and in the corresponding diagonal state of Eq. \ref{['eq:diag_state']} [panel (b)], with $k=1000$ for $N=1,2,4,10,100$. All the lines are solid, except for the dashed one that represents the reference case $N=1$ where the initial state is the ground state.
• Figure 3: Time evolution the LE modulus for two fermions subjected to a delta perturbation. (a)-(b) $|\nu(t)|$ as a function of time, for two fermions initialized in the coherent anti-symmetrized superposition of energy eigenstates (\ref{['eq:anti-symmetric_state']}) [panel (a)] and in the corresponding incoherent diagonal state [panel (b)], respectively. Here, the fermions are perturbed by a delta-function potential of strength $k=100$. Solid lines represent the numerical results, while dashed lines refer to the fitted curves according to the scaling law of Eq. \ref{['eq:LE_fit_formula_Intro']}. Panels (c)-(d): time-dependence of $\beta(t)$ and $\gamma(t)$ for different perturbation strengths $k$, both in the coherent (solid lines) and incoherent case (dashed lines).
• Figure 4: Time-behaviour of $\abs{\nu(t)}^2$ for two fermions initialized in the anti-symmetric state of Eq. \ref{['eq:anti-symmetric_state']} [panel (a)] and in the corresponding diagonal state [panel (b)], with $N \in \{2,5,10,49\}$.
• Figure 5: Distribution of the work done by the delta perturbation on the quantum system. Panel (a): Work MHQ distributions from initializing the system in the superposition state (\ref{['eq:EqualSupState']}) (light blue) and in the corresponding diagonal state (pink), with $N=50$. The inset shows the growth of the non-positivity functional $\mathcal{N}_{\rm Re}$ with $N$; the fit of the curve gives us $\mathcal{N}_{\rm Re} \approx 1.08 (N^{0.17} - 1)$ (dashed line). Panels (b)-(c): Average work done by the perturbation and quantum speed limit $\tau_{\rm QSL}$, respectively, as a function of $N$, assuming the state of Eq. \ref{['eq:EqualSupState']} (solid line) and the corresponding diagonal state (dashed lines) as initial states, for $k=1,2,5,10$.