Phases of the disordered Bose-Hubbard model with attractive interactions

Mansikkamäki, Olli; Laine, Sami; Silveri, Matti

doi:10.1103/physrevb.103.l220202

Cited by 16 publications

(16 citation statements)

References 50 publications

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“…An array of superconducting transmon devices [Fig. 1(c)] can be described using the disordered Bose-Hubbard model with attractive interactions [3,[29][30][31][32], defined by the Hamiltonian Ĥ = ĤJ + ĤU + Ĥω…”

Section: Transmon Arrays and The Attractive Bose-hubbard Modelmentioning

confidence: 99%

“…, L. Note that the dimensionality of A is independent of N and grows linearly in L, as opposed to the exponential growth of the full Hilbert space. The analysis here is closely related to the calculation of the ground state of the model within the W phase [31].…”

Section: Collective Motion Of a Boson Stackmentioning

confidence: 99%

“…Initially, the quasiparticle is delocalized and symmetric in the reciprocal space [31], meaning that it essentially has zero momentum. In order for the momentum to be conserved, the quasiparticle needs to be able to move in both directions simultaneously.…”

Section: Interplay Between a Boson Stack And A Single Bosonmentioning

confidence: 99%

“…It has been experimentally demonstrated that the higher excited states of a transmon are almost as well controllable and measurable as the ones in the qubit subspace [23][24][25][26][27][28]. With the higher levels included, coupled transmons naturally realize the attractive Bose-Hubbard model [3,[29][30][31]. As coupled anharmonic oscillators, sets of transmons obey bosonic many-body statistics, yielding vastly larger Hilbert spaces compared to those of the qubit arrays.…”

Section: Introductionmentioning

confidence: 99%

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Beyond hard-core bosons in transmon arrays

Mansikkamäki¹,

Laine²,

Atte³

et al. 2022

Preprint

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Arrays of transmons have proven to be a viable medium for quantum information science and quantum simulations. Despite their widespread popularity as qubit arrays, there remains yet untapped potential beyond the two-level approximation or, equivalently, the hard-core boson model. With the higher excited levels included, coupled transmons naturally realize the attractive Bose-Hubbard model. The dynamics of the model has been difficult to study due to unfavorable scaling of the dimensionality of the Hilbert space with the system size. In this work, we present a framework for describing the effective unitary dynamics of highly-excited states of coupled transmons based on high-order degenerate perturbation theory. This allows us to describe various collective phenomenasuch as bosons stacked onto a single site behaving as a single particle, edge-localization, and effective longer-range interactions -in a unified, compact and accurate manner. While our examples deal with one-dimensional chains of transmons for the sake of clarity, the theory can be readily applied to more general geometries.

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Section: Transmon Arrays and The Attractive Bose-hubbard Modelmentioning

confidence: 99%

Section: Collective Motion Of a Boson Stackmentioning

confidence: 99%

Section: Interplay Between a Boson Stack And A Single Bosonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Beyond hard-core bosons in transmon arrays

Mansikkamäki¹,

Laine²,

Atte³

et al. 2022

Preprint

Self Cite

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show abstract

“…Thus, a transmon can be seen as an intermediate between a qubit, which it resembles for large anharmonicity, and a harmonic oscillator in the opposite limit. The excitations in a transmon can be interpreted as bosons, and an array of transmons can be described accurately with the Bose-Hubbard model with attractive interactions [16,[28][29][30][31]. Bosonic statistics has a large impact on the collective decay of the system, and the difference becomes visible already with two sites one wavelength apart from each other, as depicted in Fig.…”

Section: Introductionmentioning

confidence: 99%

Collective bosonic effects in an array of transmon devices

Orell,

Zanner,

Juan

et al. 2021

Preprint

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Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in M. Zanner et al., arXiv.2106.05623 (2021, and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.

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Magnetic supersolid phases of two-dimensional extended Bose–Hubbard model with spin–orbit coupling

Pu,

Wang,

Song

et al. 2024

New J. Phys.

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We investigate the quantum phases and phase transitions forspin-orbit coupled two-species bosons with nearest-neighbor (NN)interaction in a two-dimensional square lattice usinginhomogeneous dynamical Guztwiller mean-field (IDGMF) method.Under the effect of spin-orbit coupling (SOC) and NN interaction,we uncover a rich variety of different magnetic supersolid (SS)phases. In the presence of intraspecies NN interaction, the phasediagram exhibits the phase-twisted double-checkerboard SS(PT-DCSS) and phase-striped double-checkerboard SS (PS-DCSS)phases. For both intra- and interspecies NN interactions, apartfrom the phase-twisted lattice SS (PT-LSS) and phase-stripedlattice SS (PS-LSS) phases, some nontrivial SS phases withinteresting properties occur. More importantly, we find that theemergences of these nontrivial SS phases are dependent of theinterspecies on-site interaction. To further characterize the SSphases, we also discuss the spin-dependent momentum distributionsand magnetic textures. The magnetic textures, such asantiferromagnetic, spiral and stripe orders are shown. Finally, wegive the fully analytical insights into the numerical results.

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Phases of the disordered Bose-Hubbard model with attractive interactions

Cited by 16 publications

References 50 publications

Beyond hard-core bosons in transmon arrays

Beyond hard-core bosons in transmon arrays

Collective bosonic effects in an array of transmon devices

Magnetic supersolid phases of two-dimensional extended Bose–Hubbard model with spin–orbit coupling

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