Engineering Topological Many-Body Materials in Microwave Cavity Arrays

Anderson, Brandon; Ma, Ruichao; Owens, Clai; Schuster, David I.; Simon, Jonathan

doi:10.1103/physrevx.6.041043

Cited by 104 publications

(104 citation statements)

References 58 publications

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“…(29). A numerical study of these correlation functions shows manifest power law decays, which indicates that the correlation length ξ is very large, or equivalently that the gap is small.…”

Section: Correlation Functionsmentioning

confidence: 93%

“…Originally discovered in two-dimensional electron gases [14], the fractional quantum Hall effect has eluded implementation in quantum simulators, despite multiple theoretical proposals suitable for ultracold atoms [15][16][17][18][19][20][21], photonic systems [22,23], Jaynes-Cummings-Hubbard in coupled cavity arrays [24][25][26], circuit quantum electrodynamics [27,28], or circuit QED arrays of microwave cavities [29]. Recent proposals have been put forth for cylindrical geometries [30,31].…”

Section: Introductionmentioning

confidence: 99%

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Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

et al. 2017

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We study hard core bosons on a two-leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength of the flux. When the density is commensurate with the flux, analytical arguments predict the possibility to stabilize a ground state of central charge c = 1, which is a precursor of the two-dimensional Laughlin state at ν = 1/2. This differs from the coupled wire construction of the Laughlin state in that there exists a nonzero backscattering term in the edge Hamiltonian. By using a combination of bosonization and density matrix renormalization group (DMRG) calculations, we construct a phase diagram versus density and flux from local observables and central charge. We delimit the region where the finite-size ground state displays signatures compatible with this precursor to the Laughlin state. We show how bipartite charge fluctuations allow access to the Luttinger parameter for the edge Luttinger liquid corresponding to the precursor Laughlin state. The properties studied with local observables are confirmed by the long distance behavior of correlation functions. Our findings are consistent with an exact-diagonalization calculation of the many body ground state transverse conductivity in a thin torus geometry for parameters corresponding to the precursor Laughlin state. The model considered is simple enough such that the precursor to the Laughlin state could be realized in current ultracold atom, Josephson junction array, and quantum circuit experiments.

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Section: Correlation Functionsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

et al. 2017

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“…For instance, ferrite circulators cannot be integrated with superconducting qubits and circuits, and Faraday isolators cannot be miniaturized for integration with onchip photonics. A broad experimental effort has therefore emerged to develop alternative non-reciprocal devices, including approaches based on: nonlinear materials [4,5], quantum Hall physics [6][7][8][9], and active modulation [10][11][12][13][14][15][16][17][18][19][20][21][22].Many active circuits realize non-reciprocity with parametric coupling between resonant modes [21,[23][24][25][26][27][28][29][30]. The parametric interaction creates a frequency conversion process, illustrated in Fig.…”

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confidence: 99%

Breaking Lorentz Reciprocity with Frequency Conversion and Delay

et al. 2017

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We introduce a method for breaking Lorentz reciprocity based upon the non-commutation of frequency conversion and delay. The method requires no magnetic materials or resonant physics, allowing for the design of scalable and broadband non-reciprocal circuits. With this approach, two types of gyrators -universal building blocks for linear, non-reciprocal circuits -are constructed. Using one of these gyrators, we create a circulator with > 15 dB of isolation across the 5 − 9 GHz band. Our designs may be readily extended to any platform with suitable frequency conversion elements, including semiconducting devices for telecommunication or an on-chip superconducting implementation for quantum information processing.Lorentz reciprocity follows from Maxwell's equations, and places strong physical constraints on the operation of electromagnetic devices and networks [1]. In the case where propagating fields, entering through ports as guided modes, are scattered by a closed network, Lorentz reciprocity implies that the scattering between a pair of ports is invariant upon exchange of the source and detector [2,3]. In other words, fields flow backward through the network as easily as they flow forward. When directional scattering is required, such as the ubiquitous case of unidirectional information flow in a communication network, the reciprocity theorem must be broken by violating one of its assumptions.Typical non-reciprocal elements such as microwave circulators and optical isolators rely on ferromagnetic effects, which are odd under time-reversal, to break Lorentz reciprocity. This approach, however, is incompatible with some desirable chip-based technologies. For instance, ferrite circulators cannot be integrated with superconducting qubits and circuits, and Faraday isolators cannot be miniaturized for integration with onchip photonics. A broad experimental effort has therefore emerged to develop alternative non-reciprocal devices, including approaches based on: nonlinear materials [4,5], quantum Hall physics [6][7][8][9], and active modulation [10][11][12][13][14][15][16][17][18][19][20][21][22].Many active circuits realize non-reciprocity with parametric coupling between resonant modes [21,[23][24][25][26][27][28][29][30]. The parametric interaction creates a frequency conversion process, illustrated in Fig. 1a. Time-dependence of a system parameter is the fundamental source of the nonreciprocity: the phase of parametric modulation provides a gauge freedom [31][32][33] and imprints a non-reciprocal phase shift on the frequency-converted signals. However, such approaches have been limited in bandwidth to a small fraction of the operating frequency, constrained by the linewidths of the coupled resonant modes.In this Letter, we propose and demonstrate an alternative method for breaking reciprocity, based upon the noncommutation of frequency conversion and delay. This approach requires no resonant physics, and allows for the design of broadband circuits, in which the bandwidth is comparable to the operating frequency. We...

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“…These resonators arrays have now been demonstrated in the strongly interacting [40] and ultra-low disorder [10] regimes, though not yet both simultaneously; furthermore, there are proposals [41] and recently, demonstrations [42] of tight-binding microwave Chern insulators in resonator arrays.…”

Section: Appendix D: Potential Experimental Applicationsmentioning

confidence: 99%

Hamiltonian tomography of photonic lattices

Owens

LaChapelle

et al. 2017

Phys. Rev. A

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In this letter we introduce a novel approach to Hamiltonian tomography of non-interacting tightbinding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from S αβ (ω), the (suitably normalized) two-port measurement between sites α and β at frequency ω. This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band-projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in-between.

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Engineering Topological Many-Body Materials in Microwave Cavity Arrays

Cited by 104 publications

References 58 publications

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

Breaking Lorentz Reciprocity with Frequency Conversion and Delay

Hamiltonian tomography of photonic lattices

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