Dirac Equation in (
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)-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

Pedernales, J. S.; Beau, Mathieu; Pittman, S. M.; Egusquiza, I. L.; Lamata, Lucas; Solano, E.; Campo, Adolfo del

doi:10.1103/physrevlett.120.160403

Cited by 39 publications

(37 citation statements)

References 64 publications

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“…Analogs of event horizons and Hawking radiation [9] have been studied both exper-imentally and theoretically using acoustic waves [9,10], ultrashort optical pulses [11], Bose-Einstein condensates (BECs) [12,13], and exciton-polariton condensates [14]. Recently methods have also been proposed for realizing the Dirac equation in curved space times using ion traps [15,16], optical waveguides [17], and optical lattices with position-dependent hopping and non-Abelian artificial gauge fields [18].…”

Section: Introductionmentioning

confidence: 99%

Hyperbolic lattices in circuit quantum electrodynamics

Kollár

Fitzpatrick

Houck

2019

Nature

256

278

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After close to two decades of research and development, superconducting circuits have emerged as a rich platform for both quantum computation and quantum simulation. Lattices of superconducting coplanar waveguide (CPW) resonators have been shown to produce artificial materials for microwave photons, where weak interactions can be introduced either via non-linear resonator materials or strong interactions via qubit-resonator coupling. Here, we highlight the previouslyoverlooked property that these lattice sites are deformable and allow the realization of tight-binding lattices which are unattainable, even in conventional solid-state systems. In particular, we show that networks of CPW resonators can create a new class of materials which constitute regular lattices in an effective hyperbolic space with constant negative curvature. We present numerical simulations of a series of hyperbolic analogs of the kagome lattice which show unusual densities of states with a spectrally-isolated degenerate flat band. We also present a proof-of-principle experimental realization of one of these lattices. This paper represents the first step towards on-chip quantum simulation of materials science and interacting particles in curved space. arXiv:1802.09549v2 [quant-ph]

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Section: Introductionmentioning

confidence: 99%

Hyperbolic lattices in circuit quantum electrodynamics

Kollár

Fitzpatrick

Houck

2019

Nature

256

278

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“…[ 95,99 ] Other nonlinear process, such as quantum Rabi–Stark model, [ 64,100–103 ] can also cause spectrum collapse. [ 101,102 ] As extensions, bias two‐photon QRM [ 104 ] and multiphoton QRM [ 28,98,105,106 ] have also been explored.…”

Section: Quantum States In Polaron Picturementioning

confidence: 99%

“…[ 11,12 ] The case of

χ = 0

was also considered for integrability, [ 61,62 ] studied by mean‐field [ 60 ] and even used in mapping to the Dirac equations in (1+1)‐dimensional curved spacetime. [ 28 ]…”

Section: Quantum States In Polaron Picturementioning

confidence: 99%

“…Indeed, the intensive interdisciplinary dialogue triggered by Braak's work has lead to the finding of abundant physical phenomenology in the QRM‐related models, such as hidden symmetry, [ 8,9 ] spontaneous symmetry breaking, [ 10–13 ] few‐body quantum phase transitions, [ 10–17 ] universality classification, [ 13,15,17 ] spectral collapse, [ 18–24 ] photon blockade effect, [ 25,26 ] classical‐quantum correspondence, quantum metrology, [ 27 ] black hole physics, [ 28 ] multicriticalities, [ 12,13 ] spectral conical intersections, [ 29 ] topological phase transitions, [ 13 ] and so forth. Many of these phenomena are essentially related to the quantum phase transition (QPT).…”

Section: Introductionmentioning

confidence: 99%

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Fundamental Models in the Light–Matter Interaction: Quantum Phase Transitions and the Polaron Picture

Liu

Ying

et al. 2021

Adv Quantum Tech

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The light–matter interaction not only is ubiquitous in nature but also can be simulated in various artificial systems. Besides the tunability of artificial quantum systems, the experimental access to the ultra‐strong and even deep‐strong couplings has brought a regime with novel phenomenology. Theoretically the finding of the integrability for the quantum Rabi model (QRM) has attracted tremendous attention to the study of the QRM and its extensions which are fundamental models of the light–matter interaction. With the continuing enhancements of coupling strengths, a most fascinating phenomenon of these light–matter models is that they can exhibit few‐body quantum phase transitions (QPTs), while a full understanding of these QPTs is a challenge. The polaron picture is a method capable of analyzing these fundamental models in the entire coupling regime and extracting the essential physics behind the QPTs. A review of its extensive applications on the fundamental light–matter models is presented, with discussions on the phase diagrams and QPT‐related features. The universality of critical exponent of the anisotropic QRM as well as the possibility of QPTs in A2 terms are also addressed.

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“…More recently, Pedernales et al . proposed that a background of a (1 + 1)-dimensional black hole requires a QRM with both one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime 15 . So the QRM with both one- and two-photon couplings is not only a generic model in the circuit QED and trapped ions, but also has applications in other realm of physics.…”

Section: Introductionmentioning

confidence: 99%

The mixed quantum Rabi model

Duan¹,

Xie²,

Chen³

2019

Sci Rep

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The analytical exact solutions to the mixed quantum Rabi model (QRM) including both one- and two-photon terms are found by using Bogoliubov operators. Transcendental functions in terms of 4 × 4 determinants responsible for the exact solutions are derived. These so-called G-functions with pole structures can be reduced to the previous ones in the unmixed QRMs. The zeros of G-functions reproduce completely the regular spectra. The exceptional eigenvalues can also be obtained by another transcendental function. From the pole structure, we can derive two energy limits when the two-photon coupling strength tends to the collapse point. All energy levels only collapse to the lower one, which diverges negatively. The level crossings in the unmixed QRMs are relaxed to avoided crossings in the present mixed QRM due to absence of parity symmetry. In the weak two-photon coupling regime, the mixed QRM is equivalent to an one-photon QRM with an effective positive bias, suppressed photon frequency and enhanced one-photon coupling, which may pave a highly efficient and economic way to access the deep-strong one-photon coupling regime.

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Dirac Equation in ( 1+1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

Cited by 39 publications

References 64 publications

Hyperbolic lattices in circuit quantum electrodynamics

Hyperbolic lattices in circuit quantum electrodynamics

Fundamental Models in the Light–Matter Interaction: Quantum Phase Transitions and the Polaron Picture

The mixed quantum Rabi model

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