Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models.

Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincaré disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example, by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically frustrated hyperbolic quantum spin models with finite-range or exponentially decaying interaction.

Localization and Criticality in Antiblockaded Two-Dimensional Rydberg Atom Arrays.

Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under antiblockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.

Asymmetric Blockade and Multiqubit Gates via Dipole-Dipole Interactions.

Because of their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multiqubit Rydberg-blockade gates that involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multiqubit gates can drastically simplify both quantum algorithms and state preparation. To illustrate this, we show that a 25-atom Greenberger-Horne-Zeilinger state can be created using only three gates with an error of 5.8%.

Tunable Three-Body Loss in a Nonlinear Rydberg Medium.

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential for generating novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wave function and analytical estimates based on Fermi's golden rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

Quench Dynamics of a Fermi Gas with Strong Nonlocal Interactions.

We induce strong nonlocal interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing. The system is approximately described by a t - V model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction. We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime. To probe the interplay of nonlocal interactions with tunneling, we investigate the short-time-relaxation dynamics of charge-density waves in the gas. We find that strong nearest-neighbor interactions slow down the relaxation. Our work opens the door for quantum simulations of systems with strong nonlocal interactions such as extended Fermi-Hubbard models.

Optimal measurement of field properties with quantum sensor networks.

We consider a quantum sensor network of qubit sensors coupled to a field f ( x ; θ ) analytically parameterized by the vector of parameters θ . The qubit sensors are fixed at positions x 1, …, x d . While the functional form of f ( x ; θ ) is known, the parameters θ are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function q( θ ) of these parameters and construct the optimal protocols that achieve these bounds. Our results are obtained from a combination of techniques from quantum information theory and duality theorems for linear programming. They can be applied to many problems, including optimal placement of quantum sensors, field interpolation, and the measurement of functionals of parametrized fields.

Photon propagation through dissipative Rydberg media at large input rates.

We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency. Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.

Minimal Model for Fast Scrambling.

We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled nonlinear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.

Exotic Photonic Molecules via Lennard-Jones-like Potentials.

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a Förster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters ("molecules") of photons. We demonstrate that for a few-body problem, the multibody interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in two dimensions preferentially arrange themselves in a line configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry.

We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

Nondestructive Cooling of an Atomic Quantum Register via State-Insensitive Rydberg Interactions.

We propose a protocol for sympathetically cooling neutral atoms without destroying the quantum information stored in their internal states. This is achieved by designing state-insensitive Rydberg interactions between the data-carrying atoms and cold auxiliary atoms. The resulting interactions give rise to an effective phonon coupling, which leads to the transfer of heat from the data atoms to the auxiliary atoms, where the latter can be cooled by conventional methods. This can be used to extend the lifetime of quantum storage based on neutral atoms and can have applications for long quantum computations. The protocol can also be modified to realize state-insensitive interactions between the data and the auxiliary atoms but tunable and nontrivial interactions among the data atoms, allowing one to simultaneously cool and simulate a quantum spin model.

Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator.

The multiscale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with a finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wave function with a nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.

Fractional Quantum Hall Phases of Bosons with Tunable Interactions: From the Laughlin Liquid to a Fractional Wigner Crystal.

Highly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

Three-Body Interaction of Rydberg Slow-Light Polaritons.

We study a system of three photons in an atomic medium coupled to Rydberg states near the conditions of electromagnetically induced transparency. Based on the analytical analysis of the microscopic set of equations in the far-detuned regime, the effective three-body interaction for these Rydberg polaritons is derived. For slow light polaritons, we find a strong three-body repulsion with the remarkable property that three polaritons can become essentially noninteracting at short distances. This analysis allows us to derive the influence of the three-body repulsion on bound states and correlation functions of photons propagating through a one-dimensional atomic cloud.

Spontaneous solitons in the thermal equilibrium of a quasi-1D Bose gas.

We show that solitons occur generically in the thermal equilibrium state of a weakly interacting elongated Bose gas, without the need for external forcing or perturbations. This reveals a major new quality to the experimentally widespread quasicondensate state, usually thought of as primarily phase-fluctuating. Thermal solitons are seen in uniform 1D, trapped 1D, and elongated 3D gases, appearing as shallow solitons at low quasicondensate temperatures, becoming widespread and deep as temperature rises. This behavior can be understood via thermal occupation of the type II excitations in the Lieb-Liniger model of a uniform 1D gas. Furthermore, we find that the quasicondensate phase includes very appreciable density fluctuations while leaving phase fluctuations largely unaltered from the standard picture derived from a density-fluctuation-free treatment.