Quantum simulation of driven para-Bose oscillators

Quantum mechanics allows paraparticles with mixed Bose-Fermi statistics that have not been experimentally confirmed. We propose a trapped-ion scheme whose effective dynamics are equivalent to a driven para-Bose oscillator of even order. Our mapping suggest highly entangled vibrational and internal ion states as the laboratory equivalent of quantum simulated parabosons. Furthermore, we show the generation and reconstruction of coherent oscillations and para-Bose analogs of Gilmore-Perelomov coherent states from population inversion measurements in the laboratory frame. Our proposal, apart from demonstrating an analog quantum simulator of para-Bose oscillators, provides a quantum state engineering tool that foreshadows the potential use of paraparticle dynamics in the design of quantum information systems.

Figure 1

Time evolution of the mean para-Bose number operator in the quantum simulation frame, ${\langle {\widehat{n}}_N\rangle }_{\mathrm{Osc}}$, and corresponding population inversion in the laboratory frame, ${\langle {\widehat{\sigma }}_z\rangle }_{\mathrm{Lab}}$, for a starting $p=2(N+1)=2$ para-Bose vacuum state under weak coupling, (a),(b) $g=0.1\omega$, and pure pumping, (c),(d) $\omega =0$, dynamics.

Figure 2

Husimi $Q$ function in the laboratory frame for the reduced density matrix of the first vibrational mode of the para-Bose analog of a Gilmore-Perelomov coherent state of order $p=2$ and coherent parameter $\beta =igt,|+,0;\beta \rangle$, obtained via evolution of the para-Bose vacuum state of order $p=2$ under purely pumped dynamics, $\omega =0$, at the scaled time $gt=1$.