Fermionic Collective Excitations in a Lattice Gas of Rydberg Atoms

We investigate the many-body quantum states of a laser-driven gas of Rydberg atoms confined to a large spacing ring lattice. If the laser driving is much stronger than the van der Waals interaction among the Rydberg atoms, these many-body states are collective fermionic excitations. The first excited state is a spin wave that extends over the entire lattice. We demonstrate that our system permits us to study fermions in the presence of disorder although no external atomic motion takes place. We analyze how this disorder influences the excitation properties of the fermionic states. Our work shows a route towards the creation of complex many-particle states with atoms in lattices.

Figure 1

(a) Ring lattice with spacing $a$ being much larger than the extension $\sigma$ of the Wannier functions (deep lattice). The internal atomic degrees of freedom at each site are described by the (collective) states $|P{⟩}_k$ and $|R{⟩}_k$. (b) Level structure in the regime in which ${\Omega }_k=\Omega \gg \beta$ and $|\Delta |\ll \Omega$. The spectrum splits into manifolds which can be labeled by the quantum number $m$ of the operator $\sum _k{\sigma }_z^{(k)}$. For sufficiently large $\Omega$, the coupling between manifolds established by $H_1$ and $H_2$ can be neglected. The (constrained) dynamics inside the $m$ subspaces is then determined by $H_{xy}$.

Figure 2

Energy spectrum (fully symmetric states) of Hamiltonian (1) for a lattice with 10 sites in units of $\beta$. Many-particle states can be accessed from the state $|0⟩$ by a temporal variation of the laser parameters. If ${\Delta }_0>0$ (background figure and right inset [magnified view]) the state $|0⟩$ is adiabatically connected to the ground state $|G⟩$ of $H_{xy}$ (thick orange line). See text for further explanation. If ${\Delta }_0<0$ (left inset) the state $|0⟩$ cuts through a number of avoided crossings as $\Omega$ is increased. The dashed line shows a passage to the state $|5_{23456}⟩$.

Figure 3

Absorption profile (excitation probability of a single fermion state) for the $|G⟩\to |1⟩$ transition for two strengths of disorder, $\Omega /\beta =10$ and $L=50$. The disorder strength is controlled by the mean number of atoms $N_0$ per site. The results are averages over 1000 realizations.