Decoherence dynamics across sub-Planckian to arbitrary scales using kitten states

TL;DR

The paper investigates how environmental decoherence affects quantum phase-space features, focusing on sub-Planck structures in compass and kitten states.It uses a thermal reservoir model, Wigner-function evolution, optical tomograms, and entropy measures to map the state’s quantum-to-classical transition across phase-space scales.Key findings show that finer sub-Planck features are more fragile to decoherence, while photon subtraction can stabilize phase-space structures and isotropic sub-Planck patterns can emerge.The authors propose a general phase-space–guided framework that relates decoherence rates to the size of phase-space features, with implications for quantum sensing and metrology using extreme phase-space features.

Abstract

Environmental decoherence occurs when a quantum system interacts with its surroundings, progressively reducing quantum interference and coherence, complicating the preservation of critical quantum properties over time, especially during experimental implementation. The effect of decoherence varies depending on the phase-space features of quantum states, which are theoretically characterized by the Wigner phase space and appear at different scales. We explore the compass state and its photon-added and photon-subtracted variants, each of which exhibits phase-space features with dimensions beyond the Planck scale, making them suitable for quantum sensing applications. We investigate the interaction of these states with a heat reservoir by employing a range of well-established theoretical techniques, revealing a clear tradeoff between the degree of fineness in the smallest features, such as the sub-Planck structure, and the extent of decoherence. Specifically, increasing the parameters enhances sub-Planck precision in phase space, concomitantly amplifying the fragility of these compass states to undesired decoherence. Our general illustration, validated through these compass states, also applies to any pure quantum state interacting with the considered heat reservoir, exhibiting enhanced sustainability of features at larger phase-space extensions.

Figures (8)

• Figure 1: The Wigner distributions $W_{\ket{\ltimes}}(\beta),$ with $\beta = \frac{(x+\text{i}y)}{\sqrt{2}}$: (a) $p = q = 0$ and $X_0 = 3$; (b) $p = q = 14$ and $X_0 = 1.5$; (c) $p=q=14$ and $X_0=0.5$. The black box in (a)–(c) marks the focused phase-space region, shown also across each main figure. The white contours represent regions where the Wigner distributions have virtually zero amplitudes near the origin. (d) The overlap $F = |\langle C | \ltimes \rangle|^2$ between the compass state $\ket{C}$ and its optimized version $\ket{\ltimes}$ in the case of $p = q = 14$.
• Figure 2: Variation of negativity in the Wigner function $W_{\ket{\ltimes}}(\beta)$: (a) $p=q=0$, (b) $q=14$, $X_0=1.5$, and (c) $p=14$, with $X_0=1.5$.
• Figure 3: The evolution over time of the Wigner functions corresponding to the compass states. The white contour highlights the regions of the Wigner distribution that have substantially decayed, ultimately evolving toward a Gaussian lobe over time. The left column represents the cases when $p = q = 0$, $X_0 = 3$, and the right column belongs to $p = q = 14$, $X_0 = 1.5$, each evaluated at multiple values of $\tau$. (a) $\tau = 0.06$, (b) $\tau = 0.12$, (c) $\tau = 10$, (d) $\tau = 0.06$, (e) $\tau = 0.12$, and (f) $\tau = 10$. In all cases, we set $\overline{n} = 0.5$.
• Figure 4: Tomogram function for the case when $p = q = 0$ and $X_0=3$, illustrating the compass state.
• Figure 5: Tomogram function for the case when $p = q = 14$ and $X_0=1.5$, illustrating the optimized compass state.