Cavity quantum electrodynamics of strongly correlated electron systems: A no-go theorem for photon condensation

Andolina, Gian Marcello; Pellegrino, Francesco; Giovannetti, Vittorio; MacDonald, Allan H.; Polini, Marco

doi:10.1103/physrevb.100.121109

Cited by 112 publications

(138 citation statements)

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“…A central topic of interest in the field of USC cavity QED is the so-called superradiant phase transition, which is predicted for the ground and thermal equilibrium states of the standard Dicke model [45,46,47]. While in more accurate models for light-matter interactions this transition does not occur for noninteracting dipoles [28,29,30,31,32,33,34,35], the system can still undergo a regular ferroelectric phase transition in the case of attractive electrostatic interactions, J ij < 0. Within the framework of the LMG model, such a transition is well-described by a mean-field decoupling of the collective interaction term, S 2…”

Section: Usc Modifications Of the Ferroelectric Phase Transitionmentioning

confidence: 99%

“…Since an exact theoretical treatment of light-matter systems in the USC regime is in general not possible, one usually resorts to simplified descriptions, for example, based on the Dicke [25,26] or the Hopfield [27] model. However, such reduced models often do not represent the complete energy of the system [28,29,30,31,32,33,34,35] or contain gauge artefacts [33,36,37,38,39] that prevent their applicability in the USC regime. More generally, while in weakly coupled cavity QED systems the role of static dipole-dipole interactions can often be neglected or modelled independently of the dynamical EM mode, this is no longer the case in the USC regime [33,40,41,42,43,44].…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamics of ultrastrongly coupled light-matter systems

Pilar

Bernardis

Rabl

2020

Quantum

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We study the thermodynamic properties of a system of two-level dipoles that are coupled ultrastrongly to a single cavity mode. By using exact numerical and approximate analytical methods, we evaluate the free energy of this system at arbitrary interaction strengths and discuss strong-coupling modifications of derivative quantities such as the specific heat or the electric susceptibility. From this analysis we identify the lowest-order cavity-induced corrections to those quantities in the collective ultrastrong coupling regime and show that for even stronger interactions the presence of a single cavity mode can strongly modify extensive thermodynamic quantities of a large ensemble of dipoles. In this non-perturbative coupling regime we also observe a significant shift of the ferroelectric phase transition temperature and a characteristic broadening and collapse of the black-body spectrum of the cavity mode. Apart from a purely fundamental interest, these general insights will be important for identifying potential applications of ultrastrong-coupling effects, for example, in the field of quantum chemistry or for realizing quantum thermal machines.

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Section: Usc Modifications Of the Ferroelectric Phase Transitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermodynamics of ultrastrongly coupled light-matter systems

Pilar

Bernardis

Rabl

2020

Quantum

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“…[30,31]). Full gauge invariance requires consistency of the band and matter-light coupling Hamiltonians [33] and is crucial to recover the no-go theorems precluding ground state superradiance [33,34].…”

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confidence: 99%

Crescent States in Charge-Imbalanced Polariton Condensates

et al. 2020

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We study two-dimensional charge-imbalanced electron-hole systems embedded in an optical microcavity. We find that strong coupling to photons favors states with pairing at zero or small center-of-mass momentum, leading to a condensed state with spontaneously broken time-reversal and rotational symmetry and unpaired carriers that occupy an anisotropic crescent-shaped sliver of momentum space. The crescent state is favored at moderate charge imbalance, while a Fulde-Ferrel-Larkin-Ovchinnikov-like state-with pairing at large center-of-mass momentum-occurs instead at strong imbalance. The crescent state stability results from long-range Coulomb interactions in combination with extremely long-range photon-mediated interactions.

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“…2, we represent the two terms contributing to the Fock self-energy in Eq. (87). We want to stress the representation of the U [6] term as a hexagon with three oriented sides and three distinct fermionic frequencies.…”

Section: Second-order Termmentioning

confidence: 99%

“…In fact, the physical self-energy depends on the physical GF, which should be inserted in the place of the independent variable G into Eqs. (80), (87), and (89). As the physical GF depends on the EPI matrix elements up to all orders, so does the physical self-energy.…”

Section: Second-order Termmentioning

confidence: 99%

Phonon-mediated superconductivity in strongly correlated electron systems: A Luttinger–Ward functional approach

Secchi

Polini

Katsnelson³

2020

Annals of Physics

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We use a Luttinger-Ward functional approach to study the problem of phononmediated superconductivity in electron systems with strong electron-electron interactions (EEIs). Our derivation does not rely on an expansion in skeleton diagrams for the EEI and the resulting theory is therefore nonperturbative in the strength of the latter. We show that one of the building blocks of the theory is the irreducible six-leg vertex related to EEIs. Diagrammatically, this implies five contributions (one of the Fock and four of the Hartree type) to the electronic self-energy, which, to the best of our knowledge, have never been discussed in the literature. Our approach is applicable to (and in fact designed to tackle superconductivity in) strongly correlated electron systems described by generic lattice models, as long as the glue for electron pairing is provided by phonons. solid-state system. No approximations are made, except for the truncation of the LWF (such a truncation is necessary to develop any practical theory). Our main general results can be found in Eqs. (87)-(89), (92), and (93).Sect. 8 is specific to the problem of phonon-mediated superconductivity. Here, we apply the previously developed general formalism to derive a set of extended Eliashberg equations. Our aim is to provide a way to compute the anomalous components of the electronic self-energy, accounting as much as possible for the EEI effects derived in Sections 3-6. This task requires some approximations. Most importantly, we need to adopt a tractable, explicit expression for the electronic self-energy functional; this cannot be done exactly, because the functional corresponding to the EEI self-energy is not known analytically (and even if it was, it would be overwhelmingly complicated). In Sect. 8 we therefore: 1) neglect the EEI vertices appearing in the EPI self-energy functionals and 2) confine ourselves to the regime of temperatures close to the critical temperature, where the expressions can be linearized in the anomalous self-energy. We then assume that the EEI self-energy functional in the normal state can be obtained via other theoretical/computational means [71][72][73], and plugged into the resulting extended Eliashberg equations, (135)-(140). These equations include the vertex corrections arising from the EEI self-energy functional, which are not captured by the Tolmachev-Morel-Anderson pseudopotential method [74,75] and the McMillan formula [76].A brief set of conclusions and future perspectives are reported in Sect. 9. Numerous technical details are reported in Appendix A-Appendix G. Model HamiltonianWe consider a system of electrons and phonons, in the presence of EEIs and EPIs. The Hamiltonian has the following general formwhere the independent-electron (IE) term iŝthe electron-electron interaction (EEI) iŝthe independent-phonon (IP) term iŝ

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Cavity quantum electrodynamics of strongly correlated electron systems: A no-go theorem for photon condensation

Cited by 112 publications

References 70 publications

Thermodynamics of ultrastrongly coupled light-matter systems

Thermodynamics of ultrastrongly coupled light-matter systems

Crescent States in Charge-Imbalanced Polariton Condensates

Phonon-mediated superconductivity in strongly correlated electron systems: A Luttinger–Ward functional approach

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