Each atom can be in three states, denoted as $\ket{0}$, $\ket{1}$ and $\ket{r}$. The states $\ket{0}$ and $\ket{1}$ are degenerate ground states and the state $\ket{r}$ is an excited state. Is this correct?

The time-independent part of the Hamiltonian includes the operators $\hat{n}_j$. Is this just the operator $\ket{r_j}\bra{r_j}$, which has eigenvalues $1$ or $0$ corresponding to whether the atom $j$ is in the Rydberg state?

Executing the program after In[6:], we get a plot of the Rydberg density on the 10 atom 1-dimensional crystal. Is this a plot of the expectation value of the operator $\ket{r_k}\bra{r_k}$ in the final state of the system, after applying the Hamiltonian?

My specific question is, what information is stored in the variable result, and how can I access it, besides using get_avg_density()? Is it possible to do other measurements, or some sort of tomography to find out what the full quantum state of the atoms is?

Each atom can be in three states, denoted as \ket{0}, \ket{1} and \ket{r}. The states \ket{0} and \ket{1} are degenerate ground states and the state \ket{r} is an excited state. Is this correct?

The \ket{0} and \ket{1} states are hyperfine split, but in Aquila indeed that split is not resolved. We only operate between a ground state \ket{g} which is a member of the hyperfine multiplet and the Rydberg \ket{r} state.

The time-independent part of the Hamiltonian includes the operators \hat{n}_j. Is this just the operator \ket{r_j}\bra{r_j}, which has eigenvalues 1 or 0 corresponding to whether the atom j is in the Rydberg state?

Yes!

Executing the program after In[6:], we get a plot of the Rydberg density on the 10 atom 1-dimensional crystal. Is this a plot of the expectation value of the operator \ket{r_k}\bra{r_k} in the final state of the system, after applying the Hamiltonian?

Also correct.

My specific question is, what information is stored in the variable result, and how can I access it, besides using get_avg_density()?

Metadata which includes your program itself along with the task ID, device ID, and the number of shots

The individual shot data which consists of:

The pre-shot sequence, indicating if the atoms are present or not at the specified locations before the program is executed (if a vacant site is specified, the pre-shot sequence will remain 0 for the site although it is possible for an atom to erroneously fill a vacant site)

The post-shot sequence, being the measurements after the program is executed

the status of the shot (did it succeed/fail/partially succeed)

Is it possible to do other measurements, or some sort of tomography to find out what the full quantum state of the atoms is?

It is not possible to do measurements beyond the Z basis as this is not natively supported on the hardware. However, I did consult with an expert at QuEra who pointed me to a resource for neutral atoms where it is possible to obtain information that would normally require full tomography without needing to do so (see here: Phys. Rev. Lett. 131, 110601 (2023) - Benchmarking Quantum Simulators Using Ergodic Quantum Dynamics)

Hope that answers your questions! Should you have any follow ups please feel free to continue this thread.