Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.15630 · Physical review. B./Physical review. B

Controlling correlations of a polaritonic Luttinger liquid by engineered cross-Kerr nonlinearity

Nabaneet Sharma, Anushree Dey, Bimalendu Deb

quant-phSubmitted Feb 17, 2026• Announced Feb 18, 2026• 0 citations
arXivHTMLPDF

Abstract

We study correlation properties of polaritons at zero temperature in a multiconnected Jaynes--Cummings (MCJC) lattice on a superconducting circuit quantum electrodynamics platform with engineered cross-Kerr nonlinearity that mimics attractive nearest-neighbour interaction. A multi-connected Jaynes--Cummings lattice is a one-dimensional lattice constructed from alternating qubits and resonators with different left and right couplings. The nearest-neighbour interaction or cross-Kerr coupling is implemented dispersively through ladder-type qutrits between each nearest neighboring pair of resonator modes. Projecting onto the lower-polaritonic manifold, we derive an extended two-mode (bipartite) Bose--Hubbard-like model featuring on-site and attractive nearest-neighbor interactions. Employing a continuum bosonization approach, we express the Hamiltonian in terms of symmetric ($+$) and antisymmetric ($-$) collective modes. In the regime where the ($-$) sector acquires a finite gap, one can reduce the system to an effective single-component Luttinger liquid model for the $+$ sector. The cross-Kerr term reduces the compressibility of the ($+$) mode, thereby enhancing the corresponding Luttinger parameter $K_{+}$, resulting in the slower algebraic decay of single-particle correlations, $G(x)\propto|x|^{-1/(4K_{+})}$.

Journal reference
Phys. Rev. B 113, 174520 (2026)
DOI
10.1103/yjtj-c22v

Related papers

Quantum phase transition in a multiconnected Jaynes-Cummings lattice

Jian Yang Xue, Kangjun Seo, Lin Tian +1 more

The rapid progress in quantum technology enables the implementation of artificial many-body systems with correlated photons and polaritons. A multiconnected Jaynes-Cummings (MCJC) lattice can be constructed by connecting qubits and cavities alternately. Such models can be realized with superconducting qubits coupled to superconducting microwave resonators or with quantum dots coupled to optical nanocavities. We study the physical properties of a one-dimensional MCJC lattice using the density-matrix renormalization-group method. This model has an intrinsic symmetry between the left and right qubit-cavity couplings. The competition between these couplings may drive the ground state either to a Mott-insulating phase or to a superfluid phase at integer fillings. We calculate the single-particle and density-density correlation functions, the correlation lengths in the Mott-insulating phase, and the Luttinger parameters in the superfluid phase and determine accurately the critical points that separate these two phases.

arXiv:1702.01922•Physical review. B./Physical review. B•Nov 7, 2017•11 citations

Bose–Hubbard models with photon pairing in circuit-QED

Benjamin Villalonga, Andreas Kurcz, Juan José García‐Ripoll

In this work, we study a family of bosonic lattice models that combine an on-site repulsion term with a nearest-neighbour pairing term, Like the original Bose–Hubbard model, the nearest-neighbour term is responsible for the mobility of bosons and it competes with the local interaction, inducing two-mode squeezing. However, unlike a trivial hopping, the counter-rotating terms form a pairing that cannot be studied with a simple mean-field theory and does not present a quantum phase transition in phase space. Instead, we show that there is a cross-over from a pure insulator to long-range correlations that start up as soon as the two-mode squeezing is switched on. We also show how this model can be naturally implemented using coupled microwave resonators and superconducting qubits.

arXiv:1304.7196•Journal of Physics B Atomic Molecular and Optical Physics•Nov 7, 2013•6 citations

Attractively bound pairs of atoms in the Bose-Hubbard model and antiferromagnetism

Bernd G Schmidt, Michael Bortz, Sebastian Eggert +2 more

We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the intersite tunneling rate. An ensemble of such lattice dimers is accurately described by an effective Hamiltonian of hard-core bosons with strong nearest-neighbor repulsion, which is equivalent to the $XXZ$ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system, which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that provides simple quantitative explanation of these features. To describe the long-range correlations of the system, we employ the Luttinger-liquid theory with the relevant Luttinger parameter $K$ obtained exactly using the Bethe-ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density-matrix renormalization-group methods.

arXiv:0902.4442•Physical Review A•Jun 30, 2009•22 citations

Circuit QED lattices: Towards quantum simulation with superconducting circuits

Sebastian Schmidt, Jens Koch

Abstract The Jaynes‐Cummings model describes the coupling between photons and a single two‐level atom in a simplified representation of light‐matter interactions. In circuit QED, this model is implemented by combining microwave resonators and superconducting qubits on a microchip with unprecedented experimental control. Arranging qubits and resonators in the form of a lattice realizes a new kind of Hubbard model, the Jaynes‐Cummings‐Hubbard model, in which the elementary excitations are polariton quasi‐particles. Due to the genuine openness of photonic systems, circuit QED lattices offer the possibility to study the intricate interplay of collective behavior, strong correlations and non‐equilibrium physics. Thus, turning circuit QED into an architecture for quantum simulation, i.e., using a well‐controlled system to mimic the intricate quantum behavior of another system too daunting for a theorist to tackle head‐on, is an exciting idea which has served as theorists’ playground for a while and is now also starting to catch on in experiments. This review gives a summary of the most recent theoretical proposals and experimental efforts.

arXiv:1212.2070•Annalen der Physik•Apr 26, 2013•312 citations

Phase diagram of the one-dimensional extended attractive Hubbard model for large nearest-neighbor repulsion

Armando A. Aligia

We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian ${H}_{\mathrm{eff}}$ for hopping $t\ensuremath{\ll}V$ and arbitrary $U<0.$ Retaining the most important terms, ${H}_{\mathrm{eff}}$ can be mapped onto two $\mathrm{XXZ}$ models, solved by the Bethe ansatz. The quantum phase diagram shows two Luttinger liquid phases and a region of phase separation between them. For density $n<0.422$ and $U<\ensuremath{-}4,$ singlet superconducting correlations dominate at large distances. For some parameters, the results are in qualitative agreement with experiments in ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{BiO}}_{3}.$

arXiv:cond-mat/9911385•Physical review. B, Condensed matter•Mar 1, 2000•4 citations

Extended Bose Hubbard model of interacting bosonic atoms in optical lattices: From superfluidity to density waves

G. Mazzarella, S. M. Giampaolo, Fabrizio Illuminati

For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.

arXiv:cond-mat/0509161•Physical Review A•Jan 26, 2006•76 citations
We study correlation properties of polaritons at zero temperature in a multiconnected Jaynes--Cummings (MCJC) lattice on a superconducting circuit quantum electrodynamics platform with engineered cross-Kerr nonlinearity that mimics attractive nearest-neighbour interaction. A multi-connected Jaynes--Cummings lattice is a one-dimensional lattice constructed from alternating qubits and resonators with different left and right couplings. The nearest-neighbour interaction or cross-Kerr coupling is implemented dispersively through ladder-type qutrits between each nearest neighboring pair of resonator modes. Projecting onto the lower-polaritonic manifold, we derive an extended two-mode (bipartite) Bose--Hubbard-like model featuring on-site and attractive nearest-neighbor interactions. Employing a continuum bosonization approach, we express the Hamiltonian in terms of symmetric (+++) and antisymmetric (−-−) collective modes. In the regime where the (−-−) sector acquires a finite gap, one can reduce the system to an effective single-component Luttinger liquid model for the +++ sector. The cross-Kerr term reduces the compressibility of the (+++) mode, thereby enhancing the corresponding Luttinger parameter K+K_{+}K+​, resulting in the slower algebraic decay of single-particle correlations, G(x)∝∣x∣−1/(4K+)G(x)\propto|x|^{-1/(4K_{+})}G(x)∝∣x∣−1/(4K+​).
The rapid progress in quantum technology enables the implementation of artificial many-body systems with correlated photons and polaritons. A multiconnected Jaynes-Cummings (MCJC) lattice can be constructed by connecting qubits and cavities alternately. Such models can be realized with superconducting qubits coupled to superconducting microwave resonators or with quantum dots coupled to optical nanocavities. We study the physical properties of a one-dimensional MCJC lattice using the density-matrix renormalization-group method. This model has an intrinsic symmetry between the left and right qubit-cavity couplings. The competition between these couplings may drive the ground state either to a Mott-insulating phase or to a superfluid phase at integer fillings. We calculate the single-particle and density-density correlation functions, the correlation lengths in the Mott-insulating phase, and the Luttinger parameters in the superfluid phase and determine accurately the critical points that separate these two phases.
In this work, we study a family of bosonic lattice models that combine an on-site repulsion term with a nearest-neighbour pairing term, Like the original Bose–Hubbard model, the nearest-neighbour term is responsible for the mobility of bosons and it competes with the local interaction, inducing two-mode squeezing. However, unlike a trivial hopping, the counter-rotating terms form a pairing that cannot be studied with a simple mean-field theory and does not present a quantum phase transition in phase space. Instead, we show that there is a cross-over from a pure insulator to long-range correlations that start up as soon as the two-mode squeezing is switched on. We also show how this model can be naturally implemented using coupled microwave resonators and superconducting qubits.
We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the intersite tunneling rate. An ensemble of such lattice dimers is accurately described by an effective Hamiltonian of hard-core bosons with strong nearest-neighbor repulsion, which is equivalent to the XXZXXZXXZ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system, which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that provides simple quantitative explanation of these features. To describe the long-range correlations of the system, we employ the Luttinger-liquid theory with the relevant Luttinger parameter KKK obtained exactly using the Bethe-ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density-matrix renormalization-group methods.
Abstract The Jaynes‐Cummings model describes the coupling between photons and a single two‐level atom in a simplified representation of light‐matter interactions. In circuit QED, this model is implemented by combining microwave resonators and superconducting qubits on a microchip with unprecedented experimental control. Arranging qubits and resonators in the form of a lattice realizes a new kind of Hubbard model, the Jaynes‐Cummings‐Hubbard model, in which the elementary excitations are polariton quasi‐particles. Due to the genuine openness of photonic systems, circuit QED lattices offer the possibility to study the intricate interplay of collective behavior, strong correlations and non‐equilibrium physics. Thus, turning circuit QED into an architecture for quantum simulation, i.e., using a well‐controlled system to mimic the intricate quantum behavior of another system too daunting for a theorist to tackle head‐on, is an exciting idea which has served as theorists’ playground for a while and is now also starting to catch on in experiments. This review gives a summary of the most recent theoretical proposals and experimental efforts.
We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian Heff{H}_{\mathrm{eff}}Heff​ for hopping $t\ensuremath{\ll}V$ and arbitrary U<0.U<0.U<0. Retaining the most important terms, Heff{H}_{\mathrm{eff}}Heff​ can be mapped onto two XXZ\mathrm{XXZ}XXZ models, solved by the Bethe ansatz. The quantum phase diagram shows two Luttinger liquid phases and a region of phase separation between them. For density n<0.422n<0.422n<0.422 and $U<\ensuremath{-}4,$ singlet superconducting correlations dominate at large distances. For some parameters, the results are in qualitative agreement with experiments in ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{BiO}}_{3}.$
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.