A non-perturbative no-go theorem for photon condensation in approximate models

Andolina, Gian Marcello; Pellegrino, Francesco; Mercurio, Alberto; Stefano, Omar Di; Polini, Marco; Savasta, Salvatore

doi:10.1140/epjp/s13360-022-03571-0

Cited by 8 publications

(8 citation statements)

References 69 publications

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“…To the best of our knowledge, this phase transition has never been observed [12]. This is in agreement with a large body of "converging" literature [13][14][15][16][17][18][19][20][21][22][23][24][25][26] stating that photon condensation in light-matter interacting systems is forbidden by gauge invariance when the diamagnetic term, i.e. a term proportional to Â2 , is included into the theory.…”

supporting

confidence: 88%

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Photon condensation, Van Vleck paramagnetism, and chiral cavities

Mercurio¹,

Andolina²,

Pellegrino³

et al. 2023

Preprint

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We introduce a gauge-invariant model of planar, square molecules coupled to a quantized spatiallyvarying cavity electromagnetic vector potential Â(r). Specifically, we choose a temporally chiral cavity hosting a uniform magnetic field B, as this is the simplest instance in which a transverse spatially-varying Â(r) is at play. We show that when the molecules are in the Van Vleck paramagnetic regime, an equilibrium quantum phase transition to a photon condensate state occurs.

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supporting

confidence: 88%

“…The Peierls phase introduced in Eq. ( 4) is necessary to satisfy the gauge principle in the presence of magnetic fields and, more in general, in any theory beyond the dipole approximation [26,42,43].…”

mentioning

confidence: 99%

Photon condensation, Van Vleck paramagnetism, and chiral cavities

Mercurio¹,

Andolina²,

Pellegrino³

et al. 2023

Preprint

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“…Our result rules out phase transitions of any order in a single formulation and is valid at finite temperatures. This is a generalization of [28,49]. Then, we obtain critical conditions for photon condensation with spatially-varying electromagnetic fields, recovering [31].…”

Section: Minimal Couplingmentioning

confidence: 96%

“…If one adopts the correct gauge-invariant description of a single uniform cavity mode, the phase transition, defined as the appearance of a finite population of transverse photons, is forbidden. This has been proven true even without the dipole approximation [28,32,37,49]. This transition is often referred to as equilibrium superradiance or photon condensation, although some ambiguity still surrounds these terms [36].…”

Section: Equilibrium Superradiance (Photon Condensation) With Electri...mentioning

confidence: 99%

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Effective theory for matter in non-perturbative cavity QED

Román-Roche

Zueco

2022

SciPost Phys. Lect. Notes

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Starting from a general material system of NN particles coupled to a cavity, we use a coherent-state path integral formulation to produce a effective theory for the material degrees of freedom. We tackle the effects of image charges, the A^2A2 term and a multimode arbitrary-geometry cavity. The resulting (non-local) action has the photonic degrees of freedom replaced by an effective position-dependent interaction between the particles. In the large-NN limit, we discuss how the theory can be cast into an effective Hamiltonian where the cavity induced interactions are made explicit. The theory is applicable, beyond cavity QED, to any system where bulk material is linearly coupled to a diagonalizable bosonic bath. We highlight the differences of the theory with other well-known methods and numerically study its finite-size scaling on the Dicke model. Finally, we showcase its descriptive power with three examples: photon condensation, the 2D free electron gas in a cavity and the modification of magnetic interactions between molecular spins; recovering, condensing and extending some recent results in the literature.

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