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arxiv: 1907.05030 · v1 · pith:DCJQGSXFnew · submitted 2019-07-11 · 🪐 quant-ph

Many-Body Physics and Quantum Simulations with Strongly Interacting Photons

Jirawat Tangpanitanon , Dimitris G. Angelakis This is my paper

Pith reviewed 2026-05-24 23:29 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum simulationinteracting photonssuperconducting circuitsmany-body physicsdriven-dissipative systemschiral edge statesMott transitionlocalization
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The pith

Interacting photons in superconducting circuits provide a controllable platform for simulating many-body quantum phenomena that classical computers cannot handle.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews how the exponential computational cost of simulating quantum many-body systems motivates quantum simulators as proposed by Feynman. It positions strongly interacting photons in superconducting circuits as a leading platform due to local controllability and long coherence times. Theoretical proposals cover phenomena such as Mott-superfluid transitions and fractional quantum Hall states of light. Experiments have realized interacting chiral edge states in small arrays and localization signatures in three- and nine-site circuits, with a 72-site circuit used to probe dissipative phase transitions. The work emphasizes that this platform also naturally supports driven-dissipative many-body physics.

Core claim

Coupled cavity arrays with interacting photons can realize quantum many-body effects of light, including Mott to superfluid transitions and fractional quantum Hall states, with superconducting circuits now demonstrating chiral edge states, photon localization, and dissipative phase transitions in circuits up to 72 sites.

What carries the argument

Coupled cavity arrays in superconducting circuits where photons interact strongly and can be locally controlled to emulate many-body Hamiltonians.

If this is right

  • Mott insulator to superfluid transitions become directly observable in photon systems.
  • Fractional quantum Hall states of light can be engineered and measured.
  • Driven-dissipative many-body phenomena can be studied in open quantum systems.
  • Larger circuits enable exploration of localization and edge-state physics beyond classical simulation reach.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The platform could be extended to hybrid systems by coupling photons to other degrees of freedom for broader condensed-matter simulations.
  • Scalability questions could be tested by comparing simulation accuracy against exact diagonalization in intermediate-size circuits.
  • Success here would motivate similar photon-based approaches in other circuit architectures or integrated photonic chips.

Load-bearing premise

Small-scale circuit demonstrations are representative of scalable progress toward accurate many-body simulations without dominant uncontrolled errors.

What would settle it

A larger circuit experiment in which decoherence or control inaccuracies prevent faithful reproduction of a known many-body signature such as a phase transition or edge-state transport.

Figures

Figures reproduced from arXiv: 1907.05030 by Dimitris G. Angelakis, Jirawat Tangpanitanon.

Figure 1
Figure 1. Figure 1: – Two types of non-analyticity at a quantum phase transition. Eigenenergies of Hˆ = Hˆ1 + gHˆ2 as a function of g in the case of (a) h Hˆ1, Hˆ2 i = 0 and (b) h Hˆ1, Hˆ2 i 6= 0. To concretize the above description of QPT, let us consider a Hamiltonian of the form Hˆ = Hˆ 1 + gHˆ 2, where g is a dimensionless parameter. The QTP concerns with non-analytic dependence of the ground-state energy E(g) = hG|Hˆ |Gi… view at source ↗
Figure 2
Figure 2. Figure 2: – The Bose-Hubbard model. (a) A sketch of cold atoms in optical lattices realizing the Bose-Hubbard model. b The mean-field energy as a function of µ/U for three different numbers of particles n = 1, 2, 3. The mean-field energy landscape in the Mott and the superfluid phase are shown in (b) and (c), respectively. strength between site i and j, µ is the chemical potential, and U is the on-site interaction. … view at source ↗
Figure 3
Figure 3. Figure 3: – Phase diagram of the Bose Hubbard model. The mean-field phase diagram showing the Mott and the superfluid phase is shown in (a). A more exact phase diagram calculated from DRMG for the one dimensional system is shown in (b). The result is reproduced from ref. [97] position space as in the Mott. This state is known as the superfluid state. 2 . 2. The mean-field phase diagram:. – Now let us consider an app… view at source ↗
Figure 4
Figure 4. Figure 4: – A sketch of a simplified optical cavity consisting of two plane mirrors at [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: – The Jaynes-Cummings model. (a) A sketch of an empty cavity with (b) its linear spectrum. When the modes of the cavity coupled to the two-level system, the total system is described by the Jaynes-Cummings model (c). (d) The resulting energy spectrum has non￾linear splitting proportional to g √ n. An external laser with frequency ωlaser = ωc − g will be resonant with the one-excitation state |1, −i but off… view at source ↗
Figure 6
Figure 6. Figure 6: – Quantum Rabi oscillation in a microwave cavity. (a) A simple diagram of the experiment. Rubidium atoms effuse from the oven O and circular Rydberg atoms are prepared in the box B. The atoms cross the cavity C made of two superconducting mirrors. (b) The observed Rabi oscillation according to the Hamiltonian in eq. (6). The result is reproduced from ref. [105]. In this limit, a single photon in the cavity… view at source ↗
Figure 7
Figure 7. Figure 7: – Experimental realization of photon blockade. (a) A simple diagram of the experiment. (b) The intensity correlation function g (2)(τ ) as a function of the time delay τ between two photons. g (2)(τ ) drops to near zero at τ = 0, indicating the probability of detecting two photons at the same time is strongly suppressed. The result is reproduced from ref. [113]. Hence the second photon is prevented from en… view at source ↗
Figure 8
Figure 8. Figure 8: – The Jaynes-Cummings-Hubbard model (a) A sketch of a coupled cavity array, implementing the Jaynes-Cummings-Hubbard model. (b) Energy spectrum of the JCH model. (c) The order parameter Var(Ni) of the lowest-energy state in the unit-filled manifold as a function of detuning (ωa − ωc)/g for 3-7 sites with and without decay. The order parameter exhibits a jump from zero to a finite value, corresponding to th… view at source ↗
Figure 9
Figure 9. Figure 9: – Phase diagram of the Jaynes-Cummings-Hubbard model. The mean-field phase diagrams with different detuning ∆ ≡ ωa − ωc = 0, −2J, 2J are shown in (a)-(c), respectively. The results are reproduced from ref. [61]. The DRMG phase diagram for the one-dimensional system with ∆ = 0 is shown in (d). The result is reproduced from ref. [117]. behavior of photonic excitations, one can adiabatically switch on either … view at source ↗
Figure 10
Figure 10. Figure 10: – Chiral edge states of interacting photons in superconducting circuits. (a) An optical image of the superconducting circuit made by standard nano-fabrication techniques. It can be described by the Bose-Hubbard Hamiltonian as shown in eq. (9). (b) Time evolution showing chiral current of two interacting photons. PQj is the probability of finding one photon at site j. Two photons are initialized at sites 1… view at source ↗
Figure 11
Figure 11. Figure 11: – The Hofstadter butterfly (a) The Fourier transform of χ (1)(t) is shown for 100 values of dimensionless magnetic field b ranging from 0 to 1. (b) For each b value, we identify 9 peaks and plot their location as a colored dot. The numerically computed eigenvalues of the Harper model are shown with gray lines. The color of each dot is the difference between the measured eigenvalue and the numerically comp… view at source ↗
Figure 12
Figure 12. Figure 12: – Driven-dissipative phases and dissipative phase transitions. (a) fermion￾ized photons at NESS. The plot shows total transmission spectra as a function of the detun￾ing for 5 cavities with J/γ = 20. Difference curves correspond to the pumping amplitude Ω/γ = 0.1, 0.3, 1, 2, 3. (b) Photon crystallization. The figure shows density correlations of the NESS for 16 cavities with ωp = ωc, U/γ = 10, Ω/γ = 2, an… view at source ↗
Figure 13
Figure 13. Figure 13: – Strong coupling of a single microwave photon to a superconducting qubit. (a) The superconducting chip including a coplanar transmission line that act as a cavity. (b) A capacitor to connect the transmission line to an input and output feed. (c) A superconduct￾ing qubit that acts as an artificial atom. (d) Vacuum Rabi mode splitting. The results are reproduced from ref. [83]. simulating the JCH model has… view at source ↗
Figure 14
Figure 14. Figure 14: – Basic elements in superconducting circuits. Because an LC circuit is a harmonic oscillator, it can be viewed as a linear cavity operating in the microwave regime or a mass attached to a spring. The circuit can be driven coherently by applying an external voltage in the same way that an external laser can drive a cavity. A capacitively-shunted Josephson junction (c) behaves like a χ (2) nonlinear cavity … view at source ↗
Figure 15
Figure 15. Figure 15: – Arrays of coupled transmon qubits fabricated by (a) Google with L = 9 [178, 70] , (b) IBM with L = 5 [85], (c) Regetti with L = 19 [86]. A 72-site superconducting chip implementing the JCH model to study dissipative phase transition [80] is shown in (d). where a, ˆ aˆ † [PITH_FULL_IMAGE:figures/full_fig_p031_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: – Circuit QED diagram showing an implementation of the Bose-Hubbard Hamiltonian. [PITH_FULL_IMAGE:figures/full_fig_p033_16.png] view at source ↗
read the original abstract

Simulating quantum many-body systems on a classical computer generally requires a computational cost that grows exponential with the number of particles. This computational complexity has been the main obstacle to understanding various fundamental emergent phenomena in condensed matters such as high-Tc superconductivity and the fractional quantum-Hall effect. The difficulty arises because even the simplest models that are proposed to capture those phenomena cannot be simulated on a classical computer. Recognizing this problem in 1981, Richard Feynman envisioned a quantum simulator, an entirely new type of machine that exploits quantum superposition and operates by individually manipulating its constituting quantum particles and their interactions. Recent advances in various experimental platforms from cold atoms in optical lattices, trapped ions, to solid-state systems have brought the idea of Feynman to the realm of reality. Among those, interacting photons in superconducting circuits has been one of the promising platforms thanks to their local controllability and long coherence times. Early theoretical proposals have shown possibilities to realize quantum many-body phenomena of light using coupled cavity arrays such as Mott to superfluid transitions and fractional quantum Hall states. Start-of-the-art experiments include realization of interacting chiral edge states and stroboscopic signatures of localization of interacting photons in a three-site and a nine-site superconducting circuit, respectively. Interacting photons also serve as a natural platform to simulate driven-dissipative quantum many-body phenomena. A 72-site superconducting circuit has also recently been fabricated to study a dissipative phase transition of light.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The manuscript is a review surveying the use of strongly interacting photons in superconducting circuits for quantum simulation of many-body phenomena. It describes the exponential cost of classical simulation, Feynman's quantum simulator concept, theoretical proposals for effects such as Mott-superfluid transitions and fractional quantum Hall states in coupled cavity arrays, and experimental milestones including interacting chiral edge states, stroboscopic localization signatures in three-site and nine-site circuits, and a dissipative phase transition studied in a 72-site circuit.

Significance. As a descriptive synthesis of an emerging platform with noted advantages in controllability and coherence, the review compiles key literature and could serve as a useful entry point for researchers. No new derivations, data, or falsifiable predictions are presented, so significance is limited to organization of existing work rather than advancing the central claims of the field.

minor comments (1)
  1. [Abstract] Abstract: 'Start-of-the-art' is a typographical error and should read 'State-of-the-art'.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive review of our manuscript and for recommending acceptance. The referee's summary accurately reflects the scope and content of the review, which compiles key theoretical proposals and experimental milestones in the field of strongly interacting photons in superconducting circuits.

Circularity Check

0 steps flagged

Review paper with no derivations or predictions; fully descriptive of external literature

full rationale

The manuscript is a review article that surveys existing experimental and theoretical work on interacting photons in superconducting circuits. It contains no original derivations, equations, predictions, or fitted parameters. All statements about phenomena (Mott transitions, chiral edge states, localization signatures, dissipative transitions) are explicitly attributed to prior literature via citations. No load-bearing steps exist that could reduce by construction to the paper's own inputs. The reader's assessment of score 0.0 is confirmed by direct inspection of the provided abstract and full-text description.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a review paper; no new free parameters, axioms, or invented entities are introduced by the authors.

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