Disentanglement by deranking and by suppression of correlation

TL;DR

This work investigates spontaneous disentanglement as a nonlinear extension to quantum dynamics to address measurement and multistability. It introduces two nonlinear disentanglement operators—matrix deranking and correlation suppression—and applies them to a finite, two-spin system near Hartmann–Hahn resonance, using both density-matrix and state-vector formalisms. The study reveals that nonlinear disentanglement can generate limit-cycle steady states and affect red- vs blue-detuned driving responses, with clear distinctions between deranking and correlation-suppression implementations. The results offer experimentally testable predictions and argue that spontaneous disentanglement could diminish the necessity of the collapse postulate, while remaining falsifiable and applicable to multipartite systems.

Abstract

The spontaneous disentanglement hypothesis is motivated by some outstanding issues in standard quantum mechanics, including the problem of quantum measurement. The current study compares between some possible methods that can be used to implement the hypothesis. Disentanglement is formulated using a nonlinear operator, which can be used to modify both the Schrödinger equation for the quantum state vector, and the master equation for the density operator. Two types of nonlinear disentanglement operators are explored. The first one gives rise to matrix deranking, and the second one to correlation suppression. Both types are demonstrated using a two spin system that is driven close to the Hartmann--Hahn double resonance. It is shown that limit cycle steady state solutions, which are excluded by standard quantum mechanics, become possible in the presence of disentanglement.

Figures (3)

• Figure 1: Driving parameters. (a) A sketch of the two spin system. Steady state value of $\tau_{\mathrm{ab}}$ is shown in (b), whereas the other color coded plots display the steady state value of 15 Bloch matrix $B$ elements ($B_{1,1}$, which is a constant by definition, is not shown). Assumed parameters' values are $\gamma_{\mathrm{D}}=0$ (i.e. no disentanglement), $g/\omega_{\mathrm{a}}=10^{-3}$, $\Gamma_{1}^{\left( \mathrm{a}\right) }/g=10$, $\Gamma_{\varphi}^{\left( \mathrm{a}\right) }/\Gamma_{1}^{\left( \mathrm{a}\right) }=10^{-4}$, $\Gamma_{1}^{\left( \mathrm{b}\right) }/\Gamma_{1}^{\left( \mathrm{a}\right) }=10$, $\Gamma_{\varphi}^{\left( \mathrm{b}\right) }/\Gamma_{\varphi}^{\left( \mathrm{a}\right) }=10$, $\hat{n}_{0}^{\left( \mathrm{a}\right) }=10$ and $\hat{n}_{0}^{\left( \mathrm{b}\right) }=10^{-4}$. The overlaid white $\times$ symbols in (b) represent the assumed driving parameters (detuning $\Delta$ and amplitude $\omega_{1}$) for the plots shown in Fig. \ref{['FigMME']}.
• Figure 2: Density matrix disentanglement. The capital letters (A and B) in the subplots' labeling indicate the method to construct the operator $\Theta$ (A for the case $\Theta=\gamma_{\mathrm{D}}\mathcal{Q}_{\mathrm{ab}}^{\left( \mathrm{D}\right) }$, and B for the case $\Theta=\gamma _{\mathrm{D}}Q_{\mathrm{a}}$), the numbers (1, 2 and 3) indicate the driving parameters [see Fig. \ref{['FigDP']}(b)], and the lower-case letters (a and b) indicate the spin label. Time evolution of the single spin Bloch vectors $\mathbf{k}_{\mathrm{a}}$ and $\mathbf{k}_{\mathrm{b}}$ is evaluated by numerically integrating the modified master equation (\ref{['MME Theta']}). The blue $\times$ symbol represents initial state, which is determined from the steady state solution of the modified master equation (\ref{['MME Theta']}) for the case $\Theta=0$. Assumed parameters' values are $g/\omega_{\mathrm{a}}=1$, $\Gamma_{1}^{\left( \mathrm{a}\right) }/\omega_{\mathrm{a}}=0.1$, $\Gamma_{\varphi}^{\left( \mathrm{a}\right) }/\Gamma_{1}^{\left( \mathrm{a}\right) }=10^{-1}$, $\Gamma_{1}^{\left( \mathrm{b}\right) }/\Gamma_{1}^{\left( \mathrm{a}\right) }=10$, $\Gamma_{\varphi}^{\left( \mathrm{b}\right) }/\Gamma_{\varphi}^{\left( \mathrm{a}\right) }=10$, $\hat{n}_{0}^{\left( \mathrm{a}\right) }=5\times10^{-4}$, $\hat{n}_{0}^{\left( \mathrm{b}\right) }=1\times10^{-5}$ and $\gamma_{\mathrm{D}}/\omega_{\mathrm{a}}=0.5$.
• Figure 3: State vector disentanglement. Time evolution of the single spin Bloch vectors $\mathbf{k}_{\mathrm{a}}$ and $\mathbf{k}_{\mathrm{b}}$ is evaluated by numerically integrating the modified Schrödinger--Langevin equation [see Eqs. (\ref{['MSE Theta']}) and (\ref{['SLE']})]. Assumed parameters' values are $\Delta/\omega_{\mathrm{a}}=\omega_{1}/\omega_{\mathrm{a}}=1/\sqrt{2}$ [these driving parameters correspond to the point labeled by the number 2 in Fig. \ref{['FigDP']}(b)], $g/\omega_{\mathrm{a}}=100$, $\Gamma _{1}^{\left( \mathrm{a}\right) }/\omega_{\mathrm{a}}=10^{-3}$, $\Gamma_{\varphi}^{\left( \mathrm{a}\right) }/\Gamma_{1}^{\left( \mathrm{a}\right) }=0.1$, $\Gamma_{1}^{\left( \mathrm{b}\right) }/\Gamma_{1}^{\left( \mathrm{a}\right) }=10$, $\Gamma_{\varphi}^{\left( \mathrm{b}\right) }/\Gamma_{\varphi}^{\left( \mathrm{a}\right) }=10$, $\hat{n}_{0}^{\left( \mathrm{a}\right) }=5\times10^{-4}$ and $\hat{n}_{0}^{\left( \mathrm{b}\right) }=1\times10^{-5}$. For plots labeled by upper-case letters A and B, $\gamma_{\mathrm{D}}/\omega_{\mathrm{a}}=0.1$ and $\gamma_{\mathrm{D}}/\omega_{\mathrm{a}}=0.5$ , respectively.