Experimental realization of para-particle oscillators

TL;DR

This work addresses the experimental realization of para-particles, generalizing bosons and fermions, by mapping para-particle oscillators of even order onto a two-mode trapped-ion system. It implements parity-deformed oscillator dynamics in a single ion with two orthogonal motional modes and a spin-1/2 qubit, realizing para-fermion and para-boson statistics through effective spin-motion couplings. The authors demonstrate para-Fermi dynamics for orders p=2 and p=10 and para-Bose dynamics for order p=2, measuring spin and motional populations and observing phenomena such as inter-mode energy exchange, damping, and revivals, in good agreement with theory and Lindblad-inclusive simulations. The results constitute the first experimental analogue of para-particle dynamics and establish a route to exploring para-particle statistics and potential topological phases in engineered quantum systems.

Abstract

Para-particles are fascinating because they are neither bosons nor fermions. While unlikely to be found in nature, they might represent accurate descriptions of physical phenomena like topological phases of matter. We report the quantum simulation of para-particle oscillators by tailoring the native couplings of two orthogonal motional modes of a trapped ion. Our system reproduces the dynamics of para-bosons and para-fermions of even order very accurately. These results represent the first experimental analogy of para-particle dynamics in any physical system and demonstrate full control of para-particle oscillators.

Figures (7)

• Figure 1: Ladder of para-particle states. The states in the ion frame (red and blue shadows), $\vert \psi, n_{x}, n_{y} \rangle$, correspond to a ladder of a para-particle states (green and orange spheres), $\vert p; k\rangle$, are shown here for order $p=2$. The action of the para-particle raising and lowering operators, $\hat{A}^{\dagger}_{\vartheta}$ and $\hat{A}_{\vartheta}$, are also indicated (arrows) with $\vartheta=pF$ for para-fermions and $\vartheta=pB$ for para-bosons.
• Figure 2: Experimental scheme. (a) The system consist of a single $^{171}$Yb$^{+}$ ion confined in a linear Paul trap, addressed by a pair of counter-propagating Raman beams. (b) Applying a drive near the red (blue) sideband of the $x$ mode produces a para-Fermi (para-Bose) interaction in combination with a simultaneous red sideband on the $y$ mode. (c) Experimental sequence consisting of state preparation by sideband cooling and Fock state initialization pulses, para-particle evolution and spin or motional read out.
• Figure 3: Para-Fermi dynamics. Experimental realization of a para-Fermi oscillator of order 2 (upper row) and 10 (lower row) starting from the vacuum state. (a) and (d) show the spin evolution, $P_{\uparrow}$, (b) and (e) the evolution of the average phonon number, $\langle \hat{n}_{x(y)} \rangle$, in the $x~(y)$ mode, blue (yellow) line, (c) and (f) the corresponding evolution of the para-Fermi number operator, $\langle \hat{\mathcal{N}}_{pF} \rangle$. Continuous lines are simulations of the dynamics based on our experimental settings with no free parameters, dashed lines include effects of motional heating.
• Figure 4: Para-Bose dynamics. Experimental realization of a para-Bose oscillator of order 2 starting from the vacuum state. (a) shows the spin evolution, $P_{\uparrow}$, (b) the evolution of the average phonon number, $\langle \hat{n}_{x(y)} \rangle$, in the $x~(y)$ mode, blue (yellow) line, (c) the corresponding evolution of the para-Bose number operator, $\langle \hat{\mathcal{N}}_{pB} \rangle$. Shaded lines are simulations of the dynamics based on our experimental settings with no free parameters, dashed lines include effects of motional heating.
• Figure 5: Fock State Preparation (a) Sequence of red sideband, blue sideband and carrier pulses to prepare $\vert \downarrow, n=3 \rangle$. (b) the measured relative Rabi frequencies $\Omega_{n,n+1} /\Omega_{0,1}$. The solid line corresponds $\Omega_{n,n+1} /\Omega_{0,1}=\sqrt{n+1}$, which holds in the Lamb-Dicke regime.