Ensemble propagators for quantum systems

Marco T. Manzoni, Darrick E. Chang, James S. Douglas

A powerful method to interface quantum light with matter is to propagate the light through an ensemble of atoms. Recently, a number of such interfaces have emerged, most prominently Rydberg ensembles, that enable strong nonlinear interactions between propagating photons. A largely open problem is whether these systems produce exotic many-body states of light and developing new tools to study propagation in the large photon number limit is highly desirable. Here we provide a method based on a "spin model" that maps quasi one-dimensional (1D) light propagation to the dynamics of an open 1D interacting spin system, where all photon correlations are obtained from those of the spins. The spin dynamics in turn are numerically solved using the toolbox of matrix product states. We apply this formalism to investigate vacuum induced transparency, wherein the different photon number components of a pulse propagate with number-dependent group velocity and separate at output.

L. E. Ballentine

D. I. Blokhint︠s︡ev

Vishesh Kaushik

We introduce the symmetric-folding principle, a geometric quantum-control framework that lifts quantum state steering to exact propagator synthesis. The required structure is a folding symmetry: a unitary transformation that reverses the drift Hamiltonian while preserving the admissible control space. The method recasts propagator synthesis on the unitary group as steering of a chosen quantum state variable between fibers of an equivariant quotient map, followed by a prescribed folded continuation of the controls. We prove that control inputs satisfying the resulting fiber-transfer condition, when extended by the prescribed folded continuation, generate the desired unitary propagator in the associated symmetry-selected target family. This gives two key structural advantages. The fiber-transfer condition constrains the midpoint propagator only to a coset of the folding symmetry's centralizer. The prescribed fold cancels this residual freedom exactly. Thus a full group-level endpoint constraint is replaced by a lower-codimension fiber/coset condition, giving additional freedom in control design. For quantum ensembles, different members may reach different midpoint propagators within the same coset, while the folded sequence still yields a common final propagator for all ensemble members. This parameter-dependent freedom can be especially significant for robust ensemble-propagator design. We demonstrate the construction on an SO(3) Bloch ensemble and an SU (4) scalar-coupled two-spin system.

Hallmann Óskar Gestsson, Charlie Nation, Alexandra Olaya-Castro

Abstract We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice, with interactions determined by the probability distribution of disorder realisations of the original heterogeneous quantum ensemble. This provides a geometric interpretation of the loss of coherence when averaging over the ensemble and allows computation of the observables of the ensemble in a single simulation. Conversely, the reverse map implies lattice particle dynamics to be equivalent to the dynamics of an ensemble of disordered quantum systems. The potential of the equivalence is demonstrated by computing the exact disorder-averaged density matrix dynamics for a qubit and a dimer ensemble, and interpreting dynamics of a tight-binding chain with constant and staggered hoppings in terms of an ensemble of disorder realisations.

V. Vimalan, Narayanan Chandrakumar