arXiv subjects

Alan Kahan

Publications and source records attributed to Alan Kahan.

6 recordsLinked to original sources

arXiv2026

Entangling ions with engineered light gradients

Spectral crowding of collective motional modes limits the fidelity of entangling interactions in trapped-ion quantum processors by inducing off-resonant coupling to spectator modes. We introduce a geometric-phase entangling interaction driven by a transverse, time-dependent structured-light force. By applying the force in a plane orthogonal to the optical propagation direction, we reduce the effects of spectral crowding while preserving single-ion addressing. The scheme is compatible with arbitrary qubit encodings, provided that the qubit states experience a differential AC Stark shift. We experimentally realise high-fidelity two-qubit gates with error rates below $5\times10^{-3}$ in ion crystals containing up to 12 ions confined within a single potential well. These results establish gradient-field light-shift gates as a scalable approach to high-fidelity entangling generation in spectrally crowded trapped-ion systems.

quant-ph↗

arXiv2025

Real-time collisions of fractional charges in a trapped-ion Jackiw-Rebbi field theory

We propose and analyze a trapped-ion quantum simulator of the Jackiw-Rebbi model, a paradigmatic quantum field theory in (1+1) dimensions where solitonic excitations of a scalar field can bind fermionic zero modes leading to fractionally-charged excitations. In our approach, the scalar field is a coarse-grained description of the planar zigzag ion displacements in the vicinity of a structural phase transition. The internal electronic states of the ions encode spins with interactions mediated by the transverse phonons and in-plane spin-phonon couplings with a zigzag pattern, which together correspond to a Yukawa-coupled Dirac field. Instead of assuming a fixed soliton background, we study the effect of back-reaction and quantum fluctuations on the coupled dynamics of the full fermion-boson system. We start by applying a Born-Oppenheimer approximation to obtain an effective Peierls-Nabarro potential for the topological kink, unveiling how the fermionic back-reaction can lead to localization of the kink. Beyond this limit, a truncated Wigner approximation combined with fermionic Gaussian states captures the quantum spreading and localization of a kink and kink-antikink scattering. Our results reveal how back-reaction and quantum fluctuations modify the stability and real-time evolution of fractionalized fermions, predicting experimentally accessible signatures in current trapped-ion architectures.

quant-ph↗

arXiv2024

Entanglement across sliding-pinned transition of ion chains in optical cavities

Dissipative quantum systems can under appropriate conditions exhibit bi- or multi-partite entanglement at the steady state. The presence and properties of these quantum correlations depend on the relevant model parameters. Here, we characterize the steady-state entanglement in connection with the spatial structure of a small chain of three ions dispersively coupled with a pumped optical cavity. Within a semiclassical approximation, we describe the relation between entanglement, spatial organization, and vibrational modes of the ion chain. Upon increasing the pumping strength, our system undergoes a transition from a sliding to a pinned configuration, in which ions are expelled from the maxima of the optical potential. The features of the steady-state entanglement strongly depend on the kind of pinned configuration reached. We identify scenarios leading to entangled steady states, analyze the effect of defect formation upon entanglement between different system partitions, and observe the presence of multipartite quantum correlations.

quant-ph↗

arXiv2023

Fokker-Planck treatment of nonlinearities in the dispersive coupling of an ion and an optical cavity

We complement previous studies of an ion coupled with an optical cavity in the dispersive regime, for a model which exhibits bistability of different configurations in the semiclassical description. Our approach is based on a truncated evolution in phase space and is intended to explore an especially interesting parameter region where the fully quantum-mechanical solution becomes hard but the crudest semiclassical approach fails to capture essential phenomena. We compare the results of our techniques with the ones from numerical diagonalization of the quantum evolution and find that although the treatment leads to a smoothening and a slight shift of the transitions in the system, it still provides a clear improvement over localized semiclassical approximations.

quant-ph↗

arXiv2021

A trapped ion in an optical cavity: numerical study of an optomechanical transition in the few-photon regime

We consider an optomechanical system composed by a trapped ion dispersively coupled to a single mode of a pumped optical cavity. We focus in a parameter range for which the semiclassical description predicts two clearly distinct equilibrium configurations in the limits of small and large photon pumping, while a bistable regime is found for intermediate pumping. This semiclassical description, however, is not valid in close proximity of the system transitions or when the mean photon number is low. Here we provide a numerical analysis of the fully quantum state in the few-photon regime, exploring the features of the asymptotic state across the transition and analyzing possible markers of semiclassical bistability. We find an increase in the entropy of the system and of the entanglement in the transition region, but no clear signatures of metastability in the spectrum of the evolution.

quant-ph↗

arXiv2019

Driving interactions efficiently in a composite few-body system

We study how to efficiently control an interacting few-body system consisting of three harmonically trapped bosons. Specifically we investigate the process of modulating the interparticle interactions to drive an initially non-interacting state to a strongly interacting one, which is an eigenstate of a chosen Hamiltonian. We also show that for unbalanced subsystems, where one can individually control the different inter- and intra-species interactions, complex dynamics originates when the symmetry of the ground state is broken by phase separation. However, as driving the dynamics too quickly can result in unwanted excitations of the final state, we optimize the driven processes using shortcuts to adiabaticity, which are designed to reduce these excitations at the end of the interaction ramp ensuring that the target eigenstate is reached.

cond-mat.quant-gas↗