ABSTRACT
The striking nonlinear effects exhibited by cavity QED systems make them a powerful tool in modern condensed matter and atomic physics. A recently discovered example is the quantized pumping of energy into a cavity by a strongly coupled, periodically driven spin. We uncover a remarkable feature of these energy pumps: they coherently translate, or boost, a quantum state of the cavity in the Fock basis. Current optical cavity and circuit QED experiments can realize the required Hamiltonian in a rotating frame. Boosting thus enables the preparation of highly excited nonclassical cavity states in near-term experiments.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
After two decades of development, cavity quantum electrodynamics with superconducting circuits has emerged as a rich platform for quantum computation and simulation. Lattices of coplanar waveguide resonators constitute artificial materials for microwave photons, in which interactions between photons can be incorporateded either through the use of nonlinear resonator materials or through coupling between qubits and resonators. Here we make use of the previously overlooked property that these lattice sites are deformable and permit tight-binding lattices that are unattainable even in solid-state systems. We show that networks of coplanar waveguide resonators can create a class of materials that constitute lattices in an effective hyperbolic space with constant negative curvature. We present numerical simulations of hyperbolic analogues of the kagome lattice that show unusual densities of states in which a macroscopic number of degenerate eigenstates comprise a spectrally isolated flat band. We present a proof-of-principle experimental realization of one such lattice. This paper represents a step towards on-chip quantum simulation of materials science and interacting particles in curved space.
ABSTRACT
Phase transitions, where observable properties of a many-body system change discontinuously, can occur in both open and closed systems. By placing cold atoms in optical cavities and inducing strong coupling between light and excitations of the atoms, one can experimentally study phase transitions of open quantum systems. Here we observe and study a non-equilibrium phase transition, the condensation of supermode-density-wave polaritons. These polaritons are formed from a superposition of cavity photon eigenmodes (a supermode), coupled to atomic density waves of a quantum gas. As the cavity supports multiple photon spatial modes and because the light-matter coupling can be comparable to the energy splitting of these modes, the composition of the supermode polariton is changed by the light-matter coupling on condensation. By demonstrating the ability to observe and understand density-wave-polariton condensation in the few-mode-degenerate cavity regime, our results show the potential to study similar questions in fully multimode cavities.
ABSTRACT
Digital micromirror devices (DMD) provide a robust platform with which to implement digital holography, in principle providing the means to rapidly generate propagating transverse electromagnetic fields with arbitrary mode profiles at visible and IR wavelengths. We use a DMD to probe a Fabry-Pérot cavity in single-mode and near-degenerate confocal configurations. Pumping arbitrary modes of the cavity is possible with excellent specificity by virtue of the spatial overlap between the incident light field and the cavity mode.
