We present the experimental observation of self-organised criticality in the dynamics of a driven-dissipative gas of ultracold atoms and a first characterisation of its universal properties. Self organisation provides an elegant explanation for how complex structures emerge and persist throughout nature and society. Surprisingly often, these self-organised structures are found to exhibit remarkably similar fractal-like or scale-invariant properties. While this is sometimes captured by simple models featuring a critical point as an attractor for the dynamics, the connection to real-world complex systems is exceptionally hard to test quantitatively. We show that the competition between facilitated excitation and population decay gives rise to complex nonlinear dynamics that drives the system to a stationary state that is largely independent of the initial conditions and exhibits scale invariance as well as a strong response to perturbations. This establishes a well-controlled platform for investigating self-organisation phenomena and non-equilibrium universality with unprecedented experimental access to the underlying microscopic details of the system. S. Helmrich et al., Nature 577, 481 – 486 (2020)

# Category: Publications

For a full list of publications by the Exotic Quantum Matter group, please see Google scholar citations

## Diffusive to non-ergodic dipolar transport in a dissipative atomic medium in Phys. Rev. Lett.

We highlight a well controlled experimental system for studying transport phenomena consisting of strongly interacting impurities in a Rydberg-dressed ultracold gas, which due to its long-range 1/R^3 hopping and controllable dissipation, sits at the frontiers of current theoretical understanding. The question of how an excitation propagates through an underlying medium is central to numerous domains of physics, ranging from condensed matter physics, to optical physics, quantum information, and biophysics. Often, one would like to know how this behavior is linked to the microscopic physics - such as the nature of disorder, the interactions between the particles and coupling to environmental degrees of freedom leading to decoherence - a task that is exceedingly hard to achieve in conventional materials. We show in this system that the laser fields used to observe the transport dynamics also directly controls the rate of diffusive transport. In the case where these fields are switched off completely we observe a transition to a regime in which transport effectively stops altogether which can be attributed to the system entering a highly sought after non-ergodic extended phase. Together this establishes a much needed platform for studying transport and localization phenomena spanning classical and quantum coherent limits and where all relevant degrees of freedom can be manipulated at will. Phys. Rev. Lett. 123, 213606 (2019) https://arxiv.org/abs/1809.07532

## Rydberg-Dressed Ramsey Interferometer and Electrometer in Phys. Rev. Lett.

We present the experimental realization and characterization of a Ramsey interferometer and electrometer based on optically trapped ultracold potassium atoms, where one state is continuously coupled by an off-resonant laser field to a highly-excited Rydberg state. Atomic clocks based on trapped ensembles of neutral atoms or single ions have enabled the most precise measurements ever made. Besides their importance for defining future time and frequency standards, they also hold great promise for searches for physics beyond the standard model, exploring the physics of complex quantum systems, and for realizing sensors capable of operating at the fundamental quantum limit. By design however, atomic clocks typically involve the coherent evolution of atoms that interact very weakly, either with one another or with external fields, seemingly precluding many possible applications. Here we demonstrate an alkali atomic clock involving two magnetically insensitive hyperfine ground states, where one state is continuously coupled to a Rydberg state by an off-resonant laser field. This Rydberg-dressing approach provides the means to combine the outstanding coherence properties of atomic clocks with greatly enhanced sensitivity to external fields or controllable interparticle interactions mediated by the Rydberg state admixture. As a proof-of-principle, we use the Rydberg-enhanced interferometer to demonstrate an application for measuring small, static electric fields with high sensitivity. The basic essence of our scheme can be applied to atomic and molecular systems in metrological applications and studies of new phases of matter. Phys. Rev. Lett. 122, 053601 (2019) https://arxiv.org/abs/1810.04151

## Uncovering the nonequilibrium phase structure of an open quantum spin system, in Phys. Rev. A

We experimentally and theoretically investigate the nonequilibrium phase structure of a well-controlled driven-dissipative quantum spin system governed by the interplay of coherent driving, spontaneous decay, and long-range spin-spin interactions. Statistical mechanics provides a powerful framework for understanding and classifying states of matter close to thermal equilibrium - a seminal example being the transition between paramagnetic and ferromagnetic phases of Ising magnets and the liquid-gas transition in fluids. However, most systems found in nature are not in thermodynamic equilibrium, as for instance, their inevitable coupling to the environment leads to a continuous exchange of energy or information that can give rise to fundamentally new physics. For understanding quantum many-body systems, this poses a significant challenge, since theoretical methods capable of dealing with open many-body systems are less developed and it is experimentally difficult to devise observables capable of distinguishing their vastly different types of behavior. This is especially relevant now, due to the emergence of a new generation of experiments that that are genuinely non-equilibrium in nature, such as crystals of laser cooled ions, semiconductor exciton-polariton condensates, ensembles of nitrogen-vacancy centers in diamond, superconducting circuits, ultracold atomic gases in optical cavities and laser driven ensembles of Rydberg atoms. We addressed this challenge by probing a prototypical driven-dissipative quantum system consisting of an ultracold atomic gas driven far from equilibrium by a laser field, thus creating a small number of (Rydberg) excitations. These excitations are short-lived, but exhibit strong and long-range interactions such that a single excitation strongly influences many nearby atoms resulting in complex non-equilibrium many-body dynamics. As a function of the driving strength and detuning from atomic resonance we discover that the rate of population loss obeys remarkably simple scaling laws over several orders of magnitude (in analogy with the scaling of thermodynamic properties often encountered in the vicinity of equilibrium phase transitions). The measured scaling exponents reflect the underlying non-equilibrium phase structure of the many-body system, which we use to distinguish the different regimes, including dissipation-dominated, paramagnetic and critical regimes as well as an instability which drives the system towards states with high excitation density. While some features of the system can be linked to corresponding equilibrium models, we also find genuinely non-equilibrium features such as the crossover from the dissipation-dominated regime to a critical regime governed by collectively enhanced atom-light interactions. These results show that scaling laws can provide a much needed tool for identifying universal and non-universal aspects of non-equilibrium quantum many-body systems and as a benchmark for state-of-the-art many-body theory. This opens up a new means to study and classify quantum systems out of equilibrium and extends the domain where scale-invariant behavior may be found in nature. S. Helmrich, A. Arias, and S. Whitlock, Phys. Rev. A 98, 022109 (2018)

## Relaxation of an isolated dipolar-interacting Rydberg quantum spin system, in Phys. Rev. Lett.

How do isolated quantum systems approach an equilibrium state? In collaboration with Prof. Matthias Weidemüller (Physics Institute, University of Heidelberg) and Prof. Jürgen Berges (Institute for theoretical physics, University of Heidelberg) we experimentally and theoretically addressed this question for a prototypical spin system formed by ultracold atoms prepared in two Rydberg states with different orbital angular momenta. By coupling these states with a resonant microwave driving, we realize a dipolar XY spin-1/2 model in an external field. Compared to laser-dressed Rydberg gases, this system allows for highly coherent dynamics over timescales much larger than the typical decoherence time. Starting from a spin-polarized state, we suddenly switch on the external field and monitor the subsequent many-body dynamics. Our key observation was density dependent relaxation of the total magnetization much faster than typical decoherence rates. To determine the processes governing this relaxation, we employed different theoretical approaches that treat quantum effects on initial conditions and dynamical laws separately. This allowed us to identify an intrinsically quantum component to the relaxation attributed to primordial quantum fluctuations. Our findings identify a fundamental component governing the relaxation of isolated many-body quantum systems and will motivate more efficient theoretical approaches for addressing non-equilibrium problems. Phys. Rev. Lett. 120 063601 (2018)

## A versatile, high-power 460nm laser system for Rydberg excitation of ultracold potassium, in Opt. Express

We present a versatile laser system which provides more than 1.5W of narrowband light, tunable in the range from 455-463 nm. It consists of a commercial Titanium-Sapphire laser which is frequency doubled using resonant cavity second harmonic generation and stabilized to an external reference cavity. We demonstrate a wide wavelength tuning range combined with a narrow linewidth and low intensity noise. This laser system is ideally suited for atomic physics experiments such as two-photon excitation of Rydberg states of potassium atoms with principal quantum numbers n > 18. To demonstrate this we perform two-photon spectroscopy on ultracold potassium gases in which we observe an electromagnetically induced transparency resonance corresponding to the 35s1/2 state and verify the long-term stability of the laser system. Additionally, by performing spectroscopy in a magneto-optical trap we observe strong loss features corresponding to the excitation of s, p, d and higher-l states accessible due to a small electric Field. Opt. Express 25, 14829-14839 (2017)

## Simulating quantum spin models using Rydberg-excited atomic ensembles in magnetic microtrap arrays

In collaboration with Prof. Peter Hannaford (Swinburne, Australia) and Dr. Alexander Glaetzle (IQOQI, Innsbruck, Austria, and Oxford, UK), we proposed a scheme to simulate lattice spin models based on strong, long-range interacting Rydberg atoms stored in a large-spacing array of magnetic microtraps. Periodic arrays of quantum spins coupled through magnetic interactions represent an archetypal model system in quantum many-body physics, non-equilibrium physics, statistical physics and condensed matter physics, with potential implications ranging from quantum magnetism to quantum information science, spintronics and high-temperature superconductivity. Apart from a few special cases, such models are generally computationally intractable due to extreme complexity arising from quantum entanglement between the spins. Furthermore, experimental studies on solid-state spin systems are often restricted by uncontrolled disorder and random couplings to the environment as well as limited control over system parameters. In our proposal, each spin is encoded in a collective spin state involving a single nS or (n+1)S Rydberg atom excited from an ensemble of ground-state alkali atoms prepared via Rydberg blockade. After the excitation laser is switched off, the Rydberg spin states on neighbouring lattice sites interact via general XXZ spin–spin interactions. To read out the collective spin states we propose a single Rydberg atom triggered avalanche scheme in which the presence of a single Rydberg atom conditionally transfers a large number of ground-state atoms in the trap to an untrapped state which can be readily detected by site-resolved absorption imaging. Such a quantum simulator should allow the study of quantum spin systems in almost arbitrary one-dimensional and two-dimensional configurations. This paves the way towards engineering exotic spin models, such as spin models based on triangular-symmetry lattices which can give rise to frustrated-spin magnetism. Journal of Physics B: Atomic, Molecular and Optical Physics 50, 074001 #s3gt_translate_tooltip_mini { display: none !important; }

## Two-body interactions and decay of three-level Rydberg-dressed atoms in J. Phys. B

We theoretically analyzed the two-body interactions and decay rates for atoms dressed by multiple laser fields to strongly interacting Rydberg states using a quantum master equation approach. Particular attention was paid to the relative merits of the three-level dressing scheme (e.g., using 767 nm and 457 nm light) compared to the two-level dressing scheme (e.g. using a 288 nm UV laser). While two-level dressing eliminates loss due to the decay of short-lived intermediate states. We also found conditions for three-level dressing which benefit from electromagnetically-induced transparency (EIT) on the two-photon resonance and a cooperative multiphoton resonance which could significantly enhance the dressed state potentials while providing remarkably long coherence times. As a consequence, near-resonant Rydberg dressing in three-level atomic systems may enable the realization of laser driven quantum fluids with long-range and anisotropic interactions and with controllable dissipation. S. Helmrich, A. Arias, N. Pehoviak, S. Whitlock, Journal of Physics B: Atomic, Molecular and Optical Physics 49, 03LT02 (2016)

## Correlated Exciton Transport in Rydberg-Dressed-Atom Spin Chains, in Phys. Rev. Lett.

Transport is an archetypical example of complex non-equilibrium phenomena impacting essentially all areas of physics. This theoretical work was motivated by the lack of a good theoretical description of our recent experiments on dipolar energy transport in a gas of atoms optically-coupled to short-lived states acting as a reservoir [related experiments: Günter et al, Science 2013]. We investigated the transport of excitations through a chain of atoms with nonlocal dissipation introduced through coupling to additional short-lived states. We found the system can be described by an effective spin-1/2 model where the ratio of the exchange interaction strength to the reservoir coupling strength determines the type of transport, including coherent exciton motion, incoherent hopping, and a regime in which an emergent length scale leads to a preferred hopping distance far beyond nearest neighbors. For multiple impurities, in addition to the immediate applications for introducing and controlling new types of transport, we discover this system may also serve as a concrete realisation of recent proposals for entanglement creation through dissipative coupling to engineered reservoirs. H. Schempp, G. Günter, S. Wüster, M. Weidemüller, S. Whitlock, Phys. Rev. Lett. 115, 093002 (2015)

## Quantum Simulation of Energy Transport with Embedded Rydberg Aggregates, in Phys. Rev. Lett.

In a collaboration with Sebastian Wüster and Alexander Eisfeld (MPIPKS Dresden) we showed that impurities embedded in a Rydberg dressed gas could be used as a quantum simulator for energy transport. Energetic disorder and decoherence introduced by the interaction with the background gas atoms can be controlled by the laser parameters. This allows for an almost ideal realization of a Haken-Reineker-Strobl-type model for energy transport. The transport can be monitored using the same mechanism that provides control over the environment. The degree of decoherence is traced back to information gained on the excitation location through the monitoring, turning the setup into an experimentally accessible model system for studying the effects of quantum measurements on the dynamics of a many-body quantum system. D. W. Schönleber, A. Eisfeld, M. Genkin, S. Whitlock, S .Wüster, Phys. Rev. Lett. 114, 123005 (2015)