# Publications

## Efficient microwave-to-optical conversion using Rydberg atoms

PHYSICAL REVIEW A **99** (2019) ARTN 023832

## Mott polaritons in cavity-coupled quantum materials

New Journal of Physics IOP Publishing (2019)

## Heating-Induced Long-Range η Pairing in the Hubbard Model.

Physical review letters **123** (2019) 030603-

We show how, upon heating the spin degrees of freedom of the Hubbard model to infinite temperature, the symmetries of the system allow the creation of steady states with long-range correlations between η pairs. We induce this heating with either dissipation or periodic driving and evolve the system towards a nonequilibrium steady state, a process which melts all spin order in the system. The steady state is identical in both cases and displays distance-invariant off-diagonal η correlations. These correlations were first recognized in the superconducting eigenstates described in Yang's seminal Letter [Phys. Rev. Lett. 63, 2144 (1989)PRLTAO0031-900710.1103/PhysRevLett.63.2144], which are a subset of our steady states. We show that our results are a consequence of symmetry properties and entirely independent of the microscopic details of the model and the heating mechanism.

## Ultracold molecules for quantum simulation: rotational coherences in CaF and RbCs

QUANTUM SCIENCE AND TECHNOLOGY **4** (2019) ARTN 014010

## Bosonic fractional quantum Hall states on a finite cylinder

PHYSICAL REVIEW A **99** (2019) ARTN 033603

## Non-stationary coherent quantum many-body dynamics through dissipation.

Nature communications **10** (2019) 1730-

The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.

## Manipulating quantum materials with quantum light (vol 99, 085116, 2019)

PHYSICAL REVIEW B **99** (2019) ARTN 099907

## Diverging Exchange Force and Form of the Exact Density Matrix Functional.

Physical review letters **122** (2019) 013001-

For translationally invariant one-band lattice models, we exploit the ab initio knowledge of the natural orbitals to simplify reduced density matrix functional theory (RDMFT). Striking underlying features are discovered. First, within each symmetry sector, the interaction functional F depends only on the natural occupation numbers n. The respective sets P_{N}^{1} and E_{N}^{1} of pure and ensemble N-representable one-matrices coincide. Second, and most importantly, the exact functional is strongly shaped by the geometry of the polytope E_{N}^{1}≡P_{N}^{1}, described by linear constraints D^{(j)}(n)≥0. For smaller systems, it follows as F[n]=[under ∑]i,i^{'}V[over ¯]_{i,i^{'}}sqrt[D^{(i)}(n)D^{(i^{'})}(n)]. This generalizes to systems of arbitrary size by replacing each D^{(i)} by a linear combination of {D^{(j)}(n)} and adding a nonanalytical term involving the interaction V[over ^]. Third, the gradient dF/dn is shown to diverge on the boundary ∂E_{N}^{1}, suggesting that the fermionic exchange symmetry manifests itself within RDMFT in the form of an "exchange force." All findings hold for systems with a nonfixed particle number as well and V[over ^] can be any p-particle interaction. As an illustration, we derive the exact functional for the Hubbard square.

## Manipulating quantum materials with quantum light

PHYSICAL REVIEW B **99** (2019) ARTN 085116

## Collimated UV light generation by two-photon excitation to a Rydberg state in Rb vapor

OPTICS LETTERS **44** (2019) 2931-2934

## Quantum probe spectroscopy for cold atomic systems

NEW JOURNAL OF PHYSICS **20** (2018) ARTN 103006

## Generalized Pauli constraints in small atoms

PHYSICAL REVIEW A **97** (2018) ARTN 052503

## Role of the pair potential for the saturation of generalized Pauli constraints

PHYSICAL REVIEW A **97** (2018) ARTN 052105

## Tensor network states in time-bin quantum optics

PHYSICAL REVIEW A **97** (2018) ARTN 062304

## Multigrid renormalization

Journal of Computational Physics **372** (2018) 587-602

© 2018 Elsevier Inc. We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for solving partial differential equations. When the solution on a grid of N points is sought, our MGR method has a computational cost scaling as O(log(N)), as opposed to O(N) for the best standard MG method. Therefore MGR can exponentially speed up standard MG computations. To illustrate our method, we develop a novel algorithm for the ground state computation of the nonlinear Schrödinger equation. Our algorithm acts variationally on tensor products and updates the tensors one after another by solving a local nonlinear optimization problem. We compare several different methods for the nonlinear tensor update and find that the Newton method is the most efficient as well as precise. The combination of MGR with our nonlinear ground state algorithm produces accurate results for the nonlinear Schrödinger equation on N=1018grid points in three spatial dimensions.

## Communication: Relating the pure and ensemble density matrix functional.

The Journal of chemical physics **149** (2018) 231102-

A crucial theorem in Reduced Density Matrix Functional Theory (RDMFT) suggests that the universal pure and ensemble functionals coincide on their common domain of pure N-representable one-matrices. We refute this by a comprehensive analysis of the geometric picture underlying Levy's constrained search. Moreover, we then show that the ensemble functional follows instead as the lower convex envelop of the pure functional. It is particularly remarkable that the pure functional determines the ensemble functional even outside its own domain of pure N-representable one-matrices. From a general perspective, this demonstrates that relaxing pure RDMFT to ensemble RDMFT does not necessarily circumvent the complexity of the one-body pure N-representability conditions (generalized Pauli constraints). Instead, the complexity may simply be transferred from the underlying space of pure N-representable one-matrices to the structure of the universal one-matrix functional.

## Strongly correlated non-equilibrium steady states with currents - quantum and classical picture

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS **227** (2018) 421-444

## Coherent Microwave-to-Optical Conversion via Six-Wave Mixing in Rydberg Atoms.

Physical review letters **120** (2018) 093201-

We present an experimental demonstration of converting a microwave field to an optical field via frequency mixing in a cloud of cold ^{87}Rb atoms, where the microwave field strongly couples to an electric dipole transition between Rydberg states. We show that the conversion allows the phase information of the microwave field to be coherently transferred to the optical field. With the current energy level scheme and experimental geometry, we achieve a photon-conversion efficiency of ∼0.3% at low microwave intensities and a broad conversion bandwidth of more than 4 MHz. Theoretical simulations agree well with the experimental data, and they indicate that near-unit efficiency is possible in future experiments.

## Ground-state phase diagram of the one-dimensional t-J model with pair hopping terms

PHYSICAL REVIEW B **98** (2018) ARTN 035116

## Revealing missing charges with generalised quantum fluctuation relations.

Nature communications **9** (2018) 2006-

The non-equilibrium dynamics of quantum many-body systems is one of the most fascinating problems in physics. Open questions range from how they relax to equilibrium to how to extract useful work from them. A critical point lies in assessing whether a system has conserved quantities (or 'charges'), as these can drastically influence its dynamics. Here we propose a general protocol to reveal the existence of charges based on a set of exact relations between out-of-equilibrium fluctuations and equilibrium properties of a quantum system. We apply these generalised quantum fluctuation relations to a driven quantum simulator, demonstrating their relevance to obtain unbiased temperature estimates from non-equilibrium measurements. Our findings will help guide research on the interplay of quantum and thermal fluctuations in quantum simulation, in studying the transition from integrability to chaos and in the design of new quantum devices.