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 Poincar{\'e} 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.

}, doi = {10.1103/PhysRevLett.128.013601}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.128.013601}, author = {Bienias, Przemyslaw and Boettcher, Igor and Belyansky, Ron and Kollar, Alicia J. and Gorshkov, Alexey V.} } @article {curtis_critical_2021, title = {Critical theory for the breakdown of photon blockade}, journal = {Phys. Rev. Res.}, volume = {3}, number = {2}, year = {2021}, note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article}, abstract = {Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons. We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes-Cummings model, in which case the photon blockade breaks down in a second-order phase transition at a critical drive strength. We show that this transition is associated to the spontaneous breaking of an antiunitary PT symmetry. Within a semiclassical approximation, we calculate the expectation values of observables in the steady state. We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve. The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power law, allowing us to calculate the critical scaling of steady-state observables without invoking mean-field theory. We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state. We list several experimental platforms where this phenomenon may be observed.}, doi = {10.1103/PhysRevResearch.3.023062}, author = {Curtis, Jonathan B. and Boettcher, Igor and Young, Jeremy T. and Maghrebi, Mohammad F. and Carmichael, Howard and Gorshkov, V, Alexey and Foss-Feig, Michael} } @article { WOS:000646067200012, title = {Optimal measurement of field properties with quantum sensor networks}, journal = {Phys. Rev. A}, volume = {103}, number = {3}, year = {2021}, month = {MAR 29}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We consider a quantum sensor network of qubit sensors coupled to a field f (x; theta) analytically parameterized by the vector of parameters theta. The qubit sensors are fixed at positions x(1), ..., x(d). While the functional form of f (x; theta) is known, the parameters theta are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function q(theta) 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.}, issn = {2469-9926}, doi = {10.1103/PhysRevA.103.L030601}, author = {Qian, Timothy and Bringewatt, Jacob and Boettcher, Igor and Bienias, Przemyslaw and Gorshkov, V, Alexey} } @article { WOS:000669569500009, title = {Protocols for estimating multiple functions with quantum sensor networks: Geometry and performance}, journal = {Phys. Rev. Res.}, volume = {3}, number = {3}, year = {2021}, month = {JUL 2}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We consider the problem of estimating multiple analytic functions of a set of local parameters via qubit sensors in a quantum sensor network. To address this problem, we highlight a generalization of the sensor symmetric performance bounds of Rubio et al., {[}J. Phys. A 53, 344001 (2020)] and develop an optimized sequential protocol for measuring such functions. We compare the performance of both approaches to one another and to local protocols that do not utilize quantum entanglement, emphasizing the geometric significance of the coefficient vectors of the measured functions in determining the best choice of measurement protocol. We show that, in many cases, especially for a large number of sensors, the optimized sequential protocol results in more accurate measurements than the other strategies. In addition, in contrast to the sensor symmetric approach, the sequential protocol is known to always be explicitly implementable. The sequential protocol is very general and has a wide range of metrological applications.}, doi = {10.1103/PhysRevResearch.3.033011}, author = {Bringewatt, Jacob and Boettcher, Igor and Niroula, Pradeep and Bienias, Przemyslaw and Gorshkov, V, Alexey} } @article { WOS:000655930100005, title = {Topological Defect Engineering and PT Symmetry in Non-Hermitian Electrical Circuits}, journal = {Phys. Rev. Lett.}, volume = {126}, number = {21}, year = {2021}, month = {MAY 28}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry PT and chiral symmetry anti-PT (APT). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of PT-symmetric gain and loss on localized edge and defect states in a non-Hermitian Su-Schrieffer-Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the APT-symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel PT-symmetric Z(2) invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not PT symmetric, the topological defect state disappears and only reemerges when APT symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.126.215302}, author = {Stegmaier, Alexander and Imhof, Stefan and Helbig, Tobias and Hoefmann, Tobias and Lee, Ching Hua and Kremer, Mark and Fritzsche, Alexander and Feichtner, Thorsten and Klembt, Sebastian and Hofling, Sven and Boettcher, Igor and Fulga, Ion Cosma and Ma, Libo and Schmidt, Oliver G. and Greiter, Martin and Kiessling, Tobias and Szameit, Alexander and Thomale, Ronny} } @article { ISI:000530023600007, title = {d-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals}, journal = {Phys. Rev. B}, volume = {101}, number = {18}, year = {2020}, month = {MAY 4}, pages = {184503}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We uncover the properties of complex tensor (d-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-3/2 fermions at a fourfold linear band-crossing point. Although the general theory of d-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-3/2 nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is toward the {\textquoteleft}{\textquoteleft}cyclic state,{{\textquoteright}{\textquoteright}} well known from the studies of multicomponent Bose-Einstein condensates, which breaks time-reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov-Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic d-wave superconductors where the d-wave superconducting phase is uniquely selected by the quartic expansion of the mean-field free energy, and is not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.101.184503}, author = {Link, Julia M. and Boettcher, Igor and Herbut, Igor F.} } @article { ISI:000575024200001, title = {Infrared fixed points of higher-spin fermions in topological semimetals}, journal = {Phys. Rev. B}, volume = {102}, number = {15}, year = {2020}, month = {OCT 5}, pages = {155104}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We determine the fate of interacting fermions described by the Hamiltonian H = p . J in three-dimensional topological semimetals with linear band crossing, where p is momentum and J are the spin- j matrices for half-integer pseudospin j >= 3/2. While weak short-range interactions are irrelevant at the crossing point due to the vanishing density of states, weak long-range Coulomb interactions lead to a renormalization of the band structure. Using a self-consistent perturbative renormalization group approach, we show that band crossings of the type p . J are unstable for j >= 7/2. Instead, through an intriguing interplay between cubic crystal symmetry, band topology, and interaction effects, the system is attracted to a variety of infrared fixed points. We also unravel several other properties of higher-spin fermions for general j, such as the relation between fermion self-energy and free energy, or the vanishing of the renormalized charge. An O(3) symmetric fixed point composed of equal chirality Weyl fermions is stable for j <= 7/2 and very likely so for all j. We then explore the rich fixed point structure for j = 5/2 in detail. We find additional attractive fixed points with enhanced 0(3) symmetry that host both emergent Weyl or massless Dirac fermions, and identify a puzzling, infrared stable, anisotropic fixed point without enhanced symmetry in close analogy to the known case of j = 3/2.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.102.155104}, author = {Boettcher, Igor} } @article {16681, title = {Interplay of Topology and Electron-Electron Interactions in Rarita-Schwinger-Weyl semimetals}, journal = {Phys. Rev. Lett.}, volume = {124}, year = {2020}, month = {Mar}, pages = {127602}, abstract = {We study, for the first time, the effects of strong short-range electron-electron interactions in generic Rarita-Schwinger-Weyl semimetals hosting spin-3/2\ electrons with linear dispersion at a fourfold band crossing point. The emergence of this novel quasiparticle, which is absent in high-energy physics, has recently been confirmed experimentally in the solid state. We combine symmetry considerations and a perturbative renormalization group analysis to discern three interacting phases that are prone to emerge in the strongly correlated regime: The chiral topological semimetal breaks a\ Z2\ symmetry and features four Weyl nodes of monopole charge\ +1\ located at vertices of a tetrahedron in momentum space. The\ s-wave superconducting state opens a Majorana mass gap for the fermions and is the leading superconducting instability. The Weyl semimetal phase removes the fourfold degeneracy and creates two Weyl nodes with either equal or opposite chirality depending on the anisotropy of the band structure. We find that symmetry breaking occurs at weaker coupling if the total monopole charge remains constant across the transition.

}, doi = {10.1103/PhysRevLett.124.127602}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.127602}, author = {Boettcher, Igor} } @article {17096, title = {Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry}, journal = {Phys. Rev. A}, volume = {102}, year = {2020}, month = {Sep}, pages = {032208}, 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 Poincar{\'e} 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.

}, keywords = {hyperbolic geometry, quantum simulation}, doi = {10.1103/PhysRevA.102.032208}, url = {https://link.aps.org/doi/10.1103/PhysRevA.102.032208}, author = {Boettcher, Igor and Bienias, Przemyslaw and Belyansky, Ron and Kollar, Alicia J. and Gorshkov, Alexey V.} } @article {ISI:000483803100006, title = {Ground state of the three-dimensional BCS d-wave superconductor}, journal = {Phys. Rev. B}, volume = {100}, number = {10}, year = {2019}, month = {SEP 4}, pages = {104503}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We determine the mean-field ground state of the three-dimensional rotationally symmetric d-wave (l = 2) superconductor at weak coupling. It is a noninert state, invariant under the symmetry C-2 only, which breaks time-reversal symmetry almost maximally, and features a high but again less-than-maximal average magnetization. The state obtained by minimization of the expanded sixth-order Ginzburg-Landau free energy is found to be an excellent approximation to the true ground state. The coupling to a parasitic s-wave component has only a minuscule quantitative and no qualitative effect on the ground state.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.100.104503}, author = {Herbut, Igor F. and Boettcher, Igor and Mandal, Subrata} } @article {ISI:000462898900011, title = {Optical response of Luttinger semimetals in the normal and superconducting states}, journal = {Phys. Rev. B}, volume = {99}, number = {12}, year = {2019}, month = {MAR 25}, pages = {125146}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We investigate the optical response properties of three-dimensional Luttinger semimetals with the Fermi energy close to a quadratic band touching point. In particular, in order to address recent experiments on the spectroscopy of pyrochlore iridates and half-Heusler superconductors, we derive expressions for the optical conductivity in both the normal and general superconducting states in the linear response regime within the random phase approximation. The response functions can be decomposed into contributions from intraband and interband transitions, the latter comprising a genuine signature of the quadratic band touching point. We demonstrate the importance of interband transitions in the optical response in the normal state both in the homogeneous and quasistatic limit. Our analysis reveals a factorization property of the homogeneous conductivity in the spatially anisotropic case and the divergence of the conductivity for strong spatial anisotropy. In the quasistatic limit, the response is dominated by interband transitions and significantly different from systems with a single parabolic band. As an applications of the formalism in the superconducting state we compute the optical conductivity and superfluid density for the s-wave singlet superconducting case for both finite and vanishing chemical potential.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.99.125146}, author = {Boettcher, Igor} }