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:1304.7196 · Journal of Physics B Atomic Molecular and Optical Physics

Bose–Hubbard models with photon pairing in circuit-QED

Benjamin Villalonga, Andreas Kurcz, Juan José García‐Ripoll

Published Nov 7, 2013• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/0953-4075/46/22/224024

Related papers

Sitewise manipulations and Mott insulator-superfluid transition of interacting photons using superconducting circuit simulators

Xiu–Hao Deng, Chunjing Jia, Chih-Chun Chien

The Bose-Hubbard model (BHM) of interacting bosons in a lattice has been a paradigm in many-body physics, and it exhibits a Mott insulator-superfluid (MI-SF) transition at integer filling. Here a quantum simulator of the BHM using a superconducting circuit is proposed. Specifically, a superconducting transmission line resonator supporting microwave photons is coupled to a charge qubit to form one site of the BHM, and adjacent sites are connected by a tunable coupler. To obtain a mapping from the superconducting circuit to the BHM, we focus on the dispersive regime where the excitations remain photonlike. Standard perturbation theory is implemented to locate the parameter range where the MI-SF transition may be simulated. This simulator allows single-site manipulations, and we illustrate this feature by considering two scenarios where a single-site manipulation can drive a MI-SF transition. The transition can be analyzed by mean-field analyses, and the exact diagonalization was implemented to provide accurate results. The variance of the photon density and the fidelity metric clearly show signatures of the transition. Experimental realizations and other possible applications of this simulator are also discussed.

arXiv:1410.8458•Physical Review B•Feb 23, 2015•12 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

Ubiquitous light real-space pairing from long-range hopping and interactions

Ganiyu D. Adebanjo, J. P. Hague, P. E. Kornilovitch

We systematically examine how long-range hopping and its synergy with extended interactions leads to light bound pairs. Pair properties are determined for a dilute extended Hubbard model with large on-site repulsion (U) and both near- and next-nearest neighbour hopping (t and t′) and attraction (V and V′), for cubic and tetragonal lattices. The presence of t′ and V′ promotes light pairs. For tetragonal lattices, t′<0 pairs can be lighter than non-interacting particles, and d-symmetric pairs form. Close packing transition temperatures, T⁎ are estimated for the Bose-Einstein condensation (BEC) of pairs to be kBT⁎∼t‾0.1, where t‾ is the geometric mean of the hoppings on the Cartesian axes. When pairs have d-symmetry, the condensate has d-wave character. Thus, the presence of both t′ and V′ leads ubiquitously to small strongly bound pairs with an inverse mass that is linear in hopping, which could lead to high temperature BECs.

arXiv:2211.06498•Physics Letters A•Apr 5, 2024•11 citations

Creating lattice gauge potentials in circuit QED: The bosonic Creutz ladder

Hadiseh Alaeian, C. W. Sandbo Chang, Mehran Vahdani Moghaddam +3 more

In this work we propose two protocols to make an effective gauge potential for microwave photons in circuit QED. The first scheme is based on coupled transmons whose on-site energies are harmonically modulated in time. We investigate the effect of various types of capacitive and inductive couplings, and the role of the phase difference between adjacent sites on creating a complex hopping rate between coupled qubits. The second method relies on the parametrically coupling the modes of a SQUID in a resonator and controlling the hopping phase via a coherent pump. Both proposals can be readily realized in a superconducting circuit with the existing technology and are suitable for scalable lattices. As an example benefiting from these complex-valued hopping terms, we simulated the behavior of a plaquette of bosonic Creutz ladder as one of the important models with interdisciplinary interest in various branches of physics. Our results clearly show the emergence of chiral edge modes and directional transport between lattice sites. Combined with intrinsic nonlinearity of the transmon qubits such lattices would be an ideal platform for simulating many different Hamiltonians such as the Bose--Hubbard model with nontrivial gauge fields. Important direct applications of the presented results span a broad range from signal processing in nonreciprocal transport to quantum simulation of gauge-invariant models in fundamental physics.

arXiv:1805.12410•Physical Review A•May 22, 2019•44 citations

Anomalous pairing of bosons: Effect of multibody interactions in an optical lattice

Manpreet Singh, Sebastian Greschner, Tapan Mishra

A first-order type phase transition between Mott lobes has been reported in Phys. Rev. Lett. 109, 135302 (2012) for a two-dimensional Bose-Hubbard model in the presence of an attractive three-body interaction. We revisit the scenario in systems of ultracold bosons both in one- and two-dimensional lattices using the density matrix renormalization group method and the self-consistent cluster mean-field theory approach, respectively. We show that an unconventional pairing of particles occurs due to the competing repulsive two-body and attractive three-body interactions. This leads to a pair superfluid phase sandwiched between the Mott insulator lobes corresponding to densities density one and three in the strongly interacting regime. This is in contrast to the direct first-order jump as predicted before. Interestingly, the Mott to pair superfluid phase transitions are found to be continuous in nature. We also show that the pair superfluid phase is robust with respect to the ratio between the two- and three-body interaction strengths. In the end, we establish a connection between the Bose-Hubbard model presented in Phys. Rev. Lett. 109, 135302 (2012) with a more general Bose-Hubbard model and analyze the fate of the pair superfluid phase in the presence of an external trapping potential.

arXiv:1710.07316•Physical Review A•Aug 14, 2018•12 citations

Strong-coupling expansion for the two-species Bose-Hubbard model

M. Iskin

To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into $d$-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e., Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two, and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.

arXiv:1001.0021•Physical Review A•Sep 30, 2010•30 citations
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.
The Bose-Hubbard model (BHM) of interacting bosons in a lattice has been a paradigm in many-body physics, and it exhibits a Mott insulator-superfluid (MI-SF) transition at integer filling. Here a quantum simulator of the BHM using a superconducting circuit is proposed. Specifically, a superconducting transmission line resonator supporting microwave photons is coupled to a charge qubit to form one site of the BHM, and adjacent sites are connected by a tunable coupler. To obtain a mapping from the superconducting circuit to the BHM, we focus on the dispersive regime where the excitations remain photonlike. Standard perturbation theory is implemented to locate the parameter range where the MI-SF transition may be simulated. This simulator allows single-site manipulations, and we illustrate this feature by considering two scenarios where a single-site manipulation can drive a MI-SF transition. The transition can be analyzed by mean-field analyses, and the exact diagonalization was implemented to provide accurate results. The variance of the photon density and the fidelity metric clearly show signatures of the transition. Experimental realizations and other possible applications of this simulator are also discussed.
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.
We systematically examine how long-range hopping and its synergy with extended interactions leads to light bound pairs. Pair properties are determined for a dilute extended Hubbard model with large on-site repulsion (U) and both near- and next-nearest neighbour hopping (t and t′) and attraction (V and V′), for cubic and tetragonal lattices. The presence of t′ and V′ promotes light pairs. For tetragonal lattices, t′<0 pairs can be lighter than non-interacting particles, and d-symmetric pairs form. Close packing transition temperatures, T⁎ are estimated for the Bose-Einstein condensation (BEC) of pairs to be kBT⁎∼t‾0.1, where t‾ is the geometric mean of the hoppings on the Cartesian axes. When pairs have d-symmetry, the condensate has d-wave character. Thus, the presence of both t′ and V′ leads ubiquitously to small strongly bound pairs with an inverse mass that is linear in hopping, which could lead to high temperature BECs.
In this work we propose two protocols to make an effective gauge potential for microwave photons in circuit QED. The first scheme is based on coupled transmons whose on-site energies are harmonically modulated in time. We investigate the effect of various types of capacitive and inductive couplings, and the role of the phase difference between adjacent sites on creating a complex hopping rate between coupled qubits. The second method relies on the parametrically coupling the modes of a SQUID in a resonator and controlling the hopping phase via a coherent pump. Both proposals can be readily realized in a superconducting circuit with the existing technology and are suitable for scalable lattices. As an example benefiting from these complex-valued hopping terms, we simulated the behavior of a plaquette of bosonic Creutz ladder as one of the important models with interdisciplinary interest in various branches of physics. Our results clearly show the emergence of chiral edge modes and directional transport between lattice sites. Combined with intrinsic nonlinearity of the transmon qubits such lattices would be an ideal platform for simulating many different Hamiltonians such as the Bose--Hubbard model with nontrivial gauge fields. Important direct applications of the presented results span a broad range from signal processing in nonreciprocal transport to quantum simulation of gauge-invariant models in fundamental physics.
A first-order type phase transition between Mott lobes has been reported in Phys. Rev. Lett. 109, 135302 (2012) for a two-dimensional Bose-Hubbard model in the presence of an attractive three-body interaction. We revisit the scenario in systems of ultracold bosons both in one- and two-dimensional lattices using the density matrix renormalization group method and the self-consistent cluster mean-field theory approach, respectively. We show that an unconventional pairing of particles occurs due to the competing repulsive two-body and attractive three-body interactions. This leads to a pair superfluid phase sandwiched between the Mott insulator lobes corresponding to densities density one and three in the strongly interacting regime. This is in contrast to the direct first-order jump as predicted before. Interestingly, the Mott to pair superfluid phase transitions are found to be continuous in nature. We also show that the pair superfluid phase is robust with respect to the ratio between the two- and three-body interaction strengths. In the end, we establish a connection between the Bose-Hubbard model presented in Phys. Rev. Lett. 109, 135302 (2012) with a more general Bose-Hubbard model and analyze the fate of the pair superfluid phase in the presence of an external trapping potential.
To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into ddd-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e., Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two, and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.