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:2206.09318

Quantum sensing of rotation velocity based on Bose-Hubbard model

Che Jiang, Yaojie Zeng, Qin, Qi, Zhirui Gong, Hong‐Chen Fu

Published Jun 19, 2022• 0 citations
arXivHTMLPDF

Abstract

This work theoretically study the Bose-Hubbard model in a ring geometry in a rotating frame. We obtain an effective Hamiltonian by using unitary transformation, where the effect of the rotating reference frame is introducing additional phases to the hopping constant. Within the mean-field theory, the phase transition edge of the Bose-Hubbard model not only depends on the particle numbers and the ring radius, but also depends on the rotation velocity. Therefore, we propose a sensing method of the rotation velocity using the phase transition edge of the Bose-Hubbard model. At the exact phase transition edge where this sensing method is most sensitive, the resolution depends on the rotation velocity, the particle numbers and the ring radius, while is independent of the parameters in the Bose-Hubbard model such as the hopping constant and the on-site interaction.

DOI
10.48550/arxiv.2206.09318

Related papers

Quantum sensing of rotation velocity based on Bose–Hubbard model

Wen Xu, Che Jiang, Yaojie Zeng +1 more

Abstract This work theoretically studies the Bose–Hubbard (BH) model in a ring geometry in a rotating frame. We obtain an effective Hamiltonian by using unitary transformation, where the effect of the rotating reference frame is introducing additional phases to the hopping constant. Within the mean-field theory, the phase transition edge depends not only on the particle number and ring radius, but also on rotation velocity. Therefore, we propose a sensing method of the rotation velocity using the phase transition edge of the Bose–Hubbard model. At the exact phase transition edge where this sensing method is most sensitive, the resolution depends on the rotation velocity, the particle number and the ring radius, while it is independent of the parameters in the Bose–Hubbard model such as the hopping constant and the on-site interaction.

Communications in Theoretical Physics•Apr 16, 2025•0 citations

Quantum rotation sensing with a four-site integrable model

Joel Bacellar Neves

In this work, we present a four-site integrable model that describes the interaction and tunneling of ultracold dipolar bosons trapped in a rotating, tetrahedral site arrangement. The model is derived from an extension of the Bose-Hubbard model in a rotating frame where the interaction and tunneling parameters have been appropriately selected to produce four independent and conserved quantities, establishing integrability. Two of these conserved quantities – related to the two nonzero circulation modes found in the system – are used to derive an effective Hamiltonian dynamically equivalent to the system for large interactions, allowing for the analytical prediction of its quantum dynamics. By analyzing the site population dynamics in this large interaction regime, we find that rotation induces population imbalance in a manner akin to the Sagnac effect. This is exploited to design a simple rotation sensing protocol capable of estimating reference frame rotation through population imbalance measurements. We calculate the sensitivity of the proposed protocol and demonstrate it has a scaling advantage due to a nontrivial manifestation of the system’s nonlinearity, enabled by integrability. The findings presented here open further investigations into the effects of rotation in multi-site integrable models, highlighting their great potential for modeling quantum devices and quantum sensors.

•Jan 1, 2026•0 citations

Bose-Hubbard Model in the Rotating Frame of Reference

T. P. Polak, T. K. Kopeć

Following a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz we discuss the ground state of the two-dimensional Bose-Hubbard Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing U(1) quantum rotor approach and the topologically constrained path integral.Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields.We derive an effective quantum action for the Bose-Hubbard model, which enables a non-perturbative treatment of the zero-temperature phase transition in the rotating frame.We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f = 0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice.Performed calculations revealed strong non-monotonical dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.

Acta Physica Polonica A•Aug 1, 2010•0 citations

Bose-Hubbard model in a ring-shaped optical lattice with high filling factors

Horacio M. Cataldo, Dora M. Jezek

The high-barrier quantum tunneling regime of a Bose-Einstein condensate confined in a ring-shaped optical lattice is investigated. By means of a change of basis transformation, connecting the set of ``vortex'' Bloch states and a Wannier-like set of localized wave functions, we derive a generalized Bose-Hubbard Hamiltonian. In addition to the usual hopping rate terms, such a Hamiltonian takes into account interaction-driven tunneling processes, which are shown to play a principal role at high filling factors, when the standard hopping rate parameter turns out to be negative. By calculating the energy and atomic current of a Bloch state, we show that such a hopping rate must be replaced by an effective hopping rate parameter containing the additional contribution an interaction-driven hopping rate. Such a contribution turns out to be crucial at high filling factors, since it preserves the positivity of the effective hopping rate parameter. Level crossings between the energies per particle of a Wannier-like state and the superfluid ground state are interpreted as a signature of the transition to configurations with macroscopically occupied states at each lattice site.

arXiv:1107.1188•Physical Review A•Jul 7, 2011•24 citations

Bose-Einstein condensates in rotating ring-shaped lattices: A multimode model

Nigro, Mauro, Capuzzi, Pablo, Jezek, Dora Marta

We develop a multimode model that describes the dynamics on a rotating Bose-Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross-Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross-Pitaevskii simulations finding a perfect agreement.

•Dec 23, 2019•7 citations

Bose–Einstein condensates in rotating ring-shaped lattices: a multimode model

M Nigro, P. Capuzzi, D M Jezek

Abstract We develop a multimode model that describes the dynamics on a rotating Bose–Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross–Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross–Pitaevskii simulations finding a perfect agreement.

arXiv:2007.11096•Journal of Physics B Atomic Molecular and Optical Physics•Nov 12, 2019•9 citations
This work theoretically study the Bose-Hubbard model in a ring geometry in a rotating frame. We obtain an effective Hamiltonian by using unitary transformation, where the effect of the rotating reference frame is introducing additional phases to the hopping constant. Within the mean-field theory, the phase transition edge of the Bose-Hubbard model not only depends on the particle numbers and the ring radius, but also depends on the rotation velocity. Therefore, we propose a sensing method of the rotation velocity using the phase transition edge of the Bose-Hubbard model. At the exact phase transition edge where this sensing method is most sensitive, the resolution depends on the rotation velocity, the particle numbers and the ring radius, while is independent of the parameters in the Bose-Hubbard model such as the hopping constant and the on-site interaction.
Abstract This work theoretically studies the Bose–Hubbard (BH) model in a ring geometry in a rotating frame. We obtain an effective Hamiltonian by using unitary transformation, where the effect of the rotating reference frame is introducing additional phases to the hopping constant. Within the mean-field theory, the phase transition edge depends not only on the particle number and ring radius, but also on rotation velocity. Therefore, we propose a sensing method of the rotation velocity using the phase transition edge of the Bose–Hubbard model. At the exact phase transition edge where this sensing method is most sensitive, the resolution depends on the rotation velocity, the particle number and the ring radius, while it is independent of the parameters in the Bose–Hubbard model such as the hopping constant and the on-site interaction.
In this work, we present a four-site integrable model that describes the interaction and tunneling of ultracold dipolar bosons trapped in a rotating, tetrahedral site arrangement. The model is derived from an extension of the Bose-Hubbard model in a rotating frame where the interaction and tunneling parameters have been appropriately selected to produce four independent and conserved quantities, establishing integrability. Two of these conserved quantities – related to the two nonzero circulation modes found in the system – are used to derive an effective Hamiltonian dynamically equivalent to the system for large interactions, allowing for the analytical prediction of its quantum dynamics. By analyzing the site population dynamics in this large interaction regime, we find that rotation induces population imbalance in a manner akin to the Sagnac effect. This is exploited to design a simple rotation sensing protocol capable of estimating reference frame rotation through population imbalance measurements. We calculate the sensitivity of the proposed protocol and demonstrate it has a scaling advantage due to a nontrivial manifestation of the system’s nonlinearity, enabled by integrability. The findings presented here open further investigations into the effects of rotation in multi-site integrable models, highlighting their great potential for modeling quantum devices and quantum sensors.
Following a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz we discuss the ground state of the two-dimensional Bose-Hubbard Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing U(1) quantum rotor approach and the topologically constrained path integral.Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields.We derive an effective quantum action for the Bose-Hubbard model, which enables a non-perturbative treatment of the zero-temperature phase transition in the rotating frame.We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f = 0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice.Performed calculations revealed strong non-monotonical dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.
The high-barrier quantum tunneling regime of a Bose-Einstein condensate confined in a ring-shaped optical lattice is investigated. By means of a change of basis transformation, connecting the set of ``vortex'' Bloch states and a Wannier-like set of localized wave functions, we derive a generalized Bose-Hubbard Hamiltonian. In addition to the usual hopping rate terms, such a Hamiltonian takes into account interaction-driven tunneling processes, which are shown to play a principal role at high filling factors, when the standard hopping rate parameter turns out to be negative. By calculating the energy and atomic current of a Bloch state, we show that such a hopping rate must be replaced by an effective hopping rate parameter containing the additional contribution an interaction-driven hopping rate. Such a contribution turns out to be crucial at high filling factors, since it preserves the positivity of the effective hopping rate parameter. Level crossings between the energies per particle of a Wannier-like state and the superfluid ground state are interpreted as a signature of the transition to configurations with macroscopically occupied states at each lattice site.
We develop a multimode model that describes the dynamics on a rotating Bose-Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross-Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross-Pitaevskii simulations finding a perfect agreement.
Abstract We develop a multimode model that describes the dynamics on a rotating Bose–Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation frequency using full 3D Gross–Pitaevskii simulations. From such numerical calculations, we extract the velocity field induced at each site and analyze the relation and the differences between the phase of the hopping parameter of our model and the Peierls phase. To this end, a detailed discussion of such phases is presented in geometrical terms which takes into account the position of the junctions for different configurations. For circularly symmetric onsite densities a simple analytical relation between the hopping phase and the angular momentum is found for arbitrary number of sites. Finally, we confront the results of the rotating multimode model dynamics with Gross–Pitaevskii simulations finding a perfect agreement.