Relativistic Measurement Backaction in the Quantum Dirac Oscillator

An elegant method to circumvent quantum measurement backaction is the use of quantum mechanics free subsystems (QMFS), with one approach involving the use of two oscillators with effective masses of opposite signs. Since negative energies, and hence masses, are a characteristic of relativistic systems a natural question is to what extent QMFS can be realized in this context. Using the example of a one-dimensional Dirac oscillator we investigate conditions under which this can be achieved, and identify Zitterbewegung or virtual pair creation as the physical mechanism that fundamentally limits the feasibility of the scheme. We propose a tabletop implementation of a Dirac oscillator system based on a spin-orbit coupled ultracold atomic sample that allows for a direct observation of the corresponding analog of virtual pair creation on quantum measurement backaction.

Figure 1

(a) Eigenenergies $E_n^{\pm }$, $n=0,\dots ,4$, in units of $m{c}^2$ as a function of the ratio $ϵ=\hslash \omega /m{c}^2$. (b) Probabilities $|A_n{|}^2$ and $|B_n{|}^2$, $n=0,\dots ,3$, of the two components of the eigenstates.

Figure 2

Time evolution of the dimensionless position $⟨\widehat{X}(t)⟩/\sqrt{2}{x}_{\text{zpt}}$ for a perturbation amplitude $f=0.1$, in units of $\hslash \omega /\sqrt{2}{x}_{\text{zpt}}$, and for increasing relativistic parameters $ϵ={10}^{-4}$ (red), ${10}^{-2}$ (blue), and ${10}^{-1}$ (purple), under the dimensionless measurement strengths $G=\sqrt{2}g⟨{\widehat{b}}^{†}\widehat{b}⟩x_{\text{zpt}}/\hslash \omega =0.05$ (left) and 0.25 (right). The lower plots show its detailed evolution near the time $\omega t=\pi$.