Anthony Vogliano

Quantum simulation of open quantum systems offers a pathway towards better understanding various non-equilibrium physics that would otherwise be challenging to study. Most open quantum systems studied are modeled as obeying the Markov approximation, where the bath into which the system dissipates information is assumed to be unaffected by the system-bath interaction. However, real baths are in general influenced by this interaction to some degree, and some systems which exist in structured non-Markovian environments can display novel behavior as a result. Here we utilize a trapped ion quantum simulator to simulate a single spin-$1/2$ driven-dissipative system with a non-Markovian dissipation channel, and experimentally compare steady-states to those from an analogous Markovian bath. We observe that a non-Markovian dissipative channel can dramatically change the steady-state even for a single qubit, to a regime inaccessible for Markovian dissipation. This demonstrates the added richness available to quantum systems in structured environments. The techniques used here are compatible with many-body extensions of the model, which can not be simulated efficiently on a classical computer in general. Our work also opens up new possibilities in quantum reservoir engineering beyond the Markovian regime.

Optical systems capable of generating fields with sub-wavelength spatial features have become standard in science and engineering research and industry. Pertinent examples include atom- and ion-based quantum computers and optical lithography setups. So far, no tools exist to characterize such fields - both intensity and polarization - at sub-wavelength length scales. We use a single trapped atomic ion, confined to approximately 40 nm X 40 nm X 180 nm to sense a laser light field at a wavelength of 370 nm. With its spatial extent smaller than the absorption cross-section of a resonant detector, the ion-sensor operates at the fundamental limit of spatial resolution. Our technique relies on developing an analytical model of the ion-light interaction and using the model to extract the intensity and polarization. An important insight provided in this work is also that the inverse of this model can be learned, in a restricted sense, on a deep neural network, speeding up the intensity and polarization readout by five orders of magnitude. This speed-up makes the technique field-deployable to characterize optical instruments by probing light at the sub-wavelength scale.

We propose and experimentally demonstrate an analog scheme for generating XY-type ($J_{ij}^x σ_x^i σ_x^j \;$ + $J_{ij}^y σ_y^i σ_y^j \;$) Hamiltonians on trapped ion spins with independent control over the $J_{ij}^x$ and $J_{ij}^y$ terms. The Ising-type interactions $σ_x^i σ_x^j \;$ and $σ_y^i σ_y^j \;$ are simultaneously generated by employing two spin-dependent forces operating in parallel on the same set of normal modes. We analytically calculate the region of validity of this scheme, and provide numerical and experimental validation with $^{171}\rm{Yb}^+\;$ ions. This scheme inherits the programmability and scalability of the Ising-type interactions with trapped ions that have been explored in numerous quantum simulation experiments. Our approach extends the capabilities of existing trapped ion quantum simulators to access a large class of spin Hamiltonians relevant for exploring exotic quantum phases such as superfluidity and spin liquids.