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:2205.11007 · Communications in Theoretical Physics

Hierarchical dimensional crossover of an optically-trapped quantum gas with disorder

Kangkang Li, Zhaoxin Liang

Published Sep 4, 2022• 3 citations
arXivHTMLPDF

Abstract

Abstract Dimensionality serves as an indispensable ingredient in any attempt to formulate low-dimensional physics, and studying the dimensional crossover at a fundamental level is challenging. The purpose of this work is to study the hierarchical dimensional crossovers, namely the crossover from three dimensions (3D) to quasi-2D and then to 1D. Our system consists of a 3D Bose–Einstein condensate trapped in an anisotropic 2D optical lattice characterized by the lattice depths V 1 along the x direction and V 2 along the y direction, respectively, where the hierarchical dimensional crossover is controlled via V 1 and V 2. We analytically derive the ground-state energy, quantum depletion and the superfluid density of the system. Our results demonstrate the 3D-quasi-2D-1D dimensional crossovers in the behavior of quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.

DOI
10.1088/1572-9494/ac8f2f

Related papers

Optically trapped quasi-two-dimensional Bose gases in a random environment: Quantum fluctuations and superfluid density

Kezhao Zhou, Ying Hu, Zhaoxin Liang +1 more

We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground-state energy, quantum depletion, and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-two-dimensional (2D) regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground-state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density ${n}_{n}$ and quantum depletion ${n}_{d}$ both exhibit a characteristic $1/\mathrm{ln}(1/{n}_{2\mathrm{D}}{a}_{2\mathrm{D}}^{2})$ dependence. Their ratio ${n}_{n}/{n}_{d}$ increases to $2$ compared to the familiar $4/3$ in lattice-free three-dimensional (3D) geometry, signifying a more pronounced contrast between superfluidity and Bose-Einstein condensation in low dimensions. The conditions for possible experimental realization of our scenario are also proposed.

arXiv:1008.4273•Physical Review A•Oct 15, 2010•6 citations

Dimensional crossover of a Rabi-coupled two-component Bose–Einstein condensate in an optical lattice

Kangkang Li, Zhaoxin Liang

Abstract Dimensionality is a central concept in developing the theory of low-dimensional physics. However, previous research on dimensional crossover in the context of a Bose–Einstein condensate (BEC) has focused on the single-component BEC. To our best knowledge, further consideration of the two-component internal degrees of freedom on the effects of dimensional crossover is still lacking. In this work, we are motivated to investigate the dimensional crossover in a three-dimensional (3D) Rabi-coupled two-component BEC. The spin degrees of freedom consist of the Rabi-like and inter- and intra- interaction coupling constants. The dimensional crossovers from 3D to 2D or 1D are controlled by the continuous increase of 1D or 2D lattice depth respectively. Then we analyze how the dimensionality of the model system combined with spin degrees of freedom can affect quantum fluctuations. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the dimensional crossover induces a characteristic 3D to quasi-2D or 1D crossover in the behavior of quantum fluctuations, with an emphasis on the separated effects of Rabi-like and inter- and intra- interaction coupling constants on the quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.

Communications in Theoretical Physics•Nov 4, 2022•2 citations

Interaction-induced dimensional crossover from fully three-dimensional to one-dimensional spaces

Tao Yu, Xiaoran Ye, Zhaoxin Liang

The exploration of dimensional crossover carries profound fundamental significance, serving as a crucial bridge in comprehending the remarkable disparities observed in transitional phenomena across the two distinct dimensions of a physical system. The prevalent strategy for manipulating the dimensionality involves meticulously controlling the external trapping geometry, thereby restricting the degrees of freedom of the kinetic energy from three-dimensional (3D) to lower-dimensional spaces, while maintaining the 3D nature of the interaction energy degrees of freedom. The aim of this work is to introduce an innovative scenario to achieve dimensional crossover, characterized by lower-dimensional nature of both the kinetic and the interaction energy degrees of freedom. To accomplish this objective, we delve deeply into the realm of a two-dimensional optically trapped Bose gas, focusing specifically on its finite-range interaction. Our emphasis lies in exploring the lattice-induced dimensional crossover from full 3D to one-dimensional (1D) in both kinetic and interaction terms. Utilizing the functional path integral method, we derive the equation of states of the model system, encompassing crucial quantities, such as the ground-state energy and quantum depletion. These equations enable us to analyze the combined effects of finite-range interaction and an optical lattice on quantum fluctuations of the BEC system. Notably, our analytical findings reconcile the Lee-Huang-Yang (LHY) correction to the ground-state energy in the 3D and Lieb-Liniger (LL) ones in the 1D limit, thereby providing fresh insights into the intriguing disparities between LHY and LL corrections.

arXiv:2403.13295•Physical Review A•Jul 9, 2024•3 citations

Nonuniversal equation of state of a quasi-two-dimensional Bose gas in dimensional crossover

Xiaoran Ye, Tao Yu, Zhaoxin Liang

The equation of state (EOS) for a pure two-dimensional (2D) Bose gas exhibits a logarithmic dependence on the $s$-wave scattering length [L. Salasnich, Phys. Rev. Lett. 118, 130402 (2017)]. The pronounced disparity between the EOS of a 2D Bose gas and its three-dimensional (3D) counterpart underscores the significance of exploring the dimensional crossover between these two distinct dimensions. In this paper, we are motivated to deduce nonuniversal corrections to the EOS for an optically trapped Bose gas along the dimensional crossover from 3D to 2D, incorporating the finite-range effects of the interatomic potential. Employing the framework of effective field theory, we derive the analytical expressions for both the ground-state energy and quantum depletion. The introduction of the lattice induces a transition from a 3D to a quasi-2D regime. In particular, we systematically analyze the asymptotic behaviors of both the 2D and 3D aspects of the model system, with a specific focus on the nonuniversal effects on the EOS arising from finite-range interactions. The nonuniversal effects proposed in this paper along the dimensional crossover represent a significant stride toward unraveling the intricate interplay between dimensionality and quantum fluctuations.

arXiv:2402.04703•Physical Review A•Jun 3, 2024•4 citations

Dimensional Crossover in the Bose–Einstein Condensation Confined to Anisotropic Three-Dimensional Lattices

Kornel Witkowski, T. K. Kopeć

Abstract The Bose–Einstein condensation (BEC) in three-dimensional (3D) anisotropic lattices is studied. We present theoretical results for the critical temperature for BEC, chemical potential, condensate fraction and relevant thermodynamic quantities like: internal energy, entropy, specific heat and compressibility as a function of anisotropy parameter being the ratio of the nearest-neighbor in-plane ( $$t_\parallel$$ t ‖ ) and out-of-plane ( $$t_\perp$$ t ⊥ ) hopping amplitudes. In particular, considered scenarios include weakly coupled two-dimensional (2D) planes ( $$t_\perp /t_\parallel \ll 1$$ t ⊥ / t ‖ ≪ 1 , relevant for layered structures) as well as a rod-like geometry of interacting one-dimensional (1D) chains ( $$t_\parallel /t_\perp \ll 1$$ t ‖ / t ⊥ ≪ 1 ). The impact of the dimensional crossover as the system is tuned away from a set of disconnected 2D layers, or traverses from a set of separate 1D chains to a regime where a fully isotropic 3D structure emerges is elucidated. Both numerical and analytic approaches are employed, (the latter in a form of series expansions involving $$t_\parallel ,t_\perp$$ t ‖ , t ⊥ amplitudes) for internal energy, entropy, specific heat and isothermal compressibility. The theoretical outcome of the present study may be of interest to a number of scenarios in solid-state physics, where the relevant quasi-particles are bosonic-like, as well as might be applicable to the physics of cold bosons loaded in artificially engineered 3D optical lattices.

Journal of Low Temperature Physics•Jul 25, 2020•4 citations

Effects of disorder on quantum fluctuations and superfluid density of a Bose-Einstein condensate in a two-dimensional optical lattice

Ying Hu, Zhaoxin Liang, Bambi Hu

We investigate a Bose-Einstein condensate (BEC) trapped in a two-dimensional optical lattice in the presence of weak disorder within the framework of the Bogoliubov theory. In particular, we analyze the combined effects of disorder and an optical lattice on quantum fluctuations and superfluid density of the BEC system. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the lattice still induces a characteristic three-dimensional (3D) to one-dimensional crossover in the behavior of quantum fluctuations, despite the presence of weak disorder. Furthermore, we use the linear response theory to calculate the normal fluid density of the condensate induced by disorder. Our results in the 3D regime show that the combined presence of disorder and lattice induce a normal fluid density that asymptotically approaches 4/3 of the corresponding condensate depletion. Conditions for possible experimental realization of our scenario are also proposed.

arXiv:0910.0419•Physical Review A•Oct 30, 2009•15 citations
Abstract Dimensionality serves as an indispensable ingredient in any attempt to formulate low-dimensional physics, and studying the dimensional crossover at a fundamental level is challenging. The purpose of this work is to study the hierarchical dimensional crossovers, namely the crossover from three dimensions (3D) to quasi-2D and then to 1D. Our system consists of a 3D Bose–Einstein condensate trapped in an anisotropic 2D optical lattice characterized by the lattice depths V 1 along the x direction and V 2 along the y direction, respectively, where the hierarchical dimensional crossover is controlled via V 1 and V 2. We analytically derive the ground-state energy, quantum depletion and the superfluid density of the system. Our results demonstrate the 3D-quasi-2D-1D dimensional crossovers in the behavior of quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.
We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground-state energy, quantum depletion, and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-two-dimensional (2D) regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground-state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density nn{n}_{n}nn​ and quantum depletion nd{n}_{d}nd​ both exhibit a characteristic 1/ln(1/n2Da2D2)1/\mathrm{ln}(1/{n}_{2\mathrm{D}}{a}_{2\mathrm{D}}^{2})1/ln(1/n2D​a2D2​) dependence. Their ratio nn/nd{n}_{n}/{n}_{d}nn​/nd​ increases to 222 compared to the familiar 4/34/34/3 in lattice-free three-dimensional (3D) geometry, signifying a more pronounced contrast between superfluidity and Bose-Einstein condensation in low dimensions. The conditions for possible experimental realization of our scenario are also proposed.
Abstract Dimensionality is a central concept in developing the theory of low-dimensional physics. However, previous research on dimensional crossover in the context of a Bose–Einstein condensate (BEC) has focused on the single-component BEC. To our best knowledge, further consideration of the two-component internal degrees of freedom on the effects of dimensional crossover is still lacking. In this work, we are motivated to investigate the dimensional crossover in a three-dimensional (3D) Rabi-coupled two-component BEC. The spin degrees of freedom consist of the Rabi-like and inter- and intra- interaction coupling constants. The dimensional crossovers from 3D to 2D or 1D are controlled by the continuous increase of 1D or 2D lattice depth respectively. Then we analyze how the dimensionality of the model system combined with spin degrees of freedom can affect quantum fluctuations. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the dimensional crossover induces a characteristic 3D to quasi-2D or 1D crossover in the behavior of quantum fluctuations, with an emphasis on the separated effects of Rabi-like and inter- and intra- interaction coupling constants on the quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.
The exploration of dimensional crossover carries profound fundamental significance, serving as a crucial bridge in comprehending the remarkable disparities observed in transitional phenomena across the two distinct dimensions of a physical system. The prevalent strategy for manipulating the dimensionality involves meticulously controlling the external trapping geometry, thereby restricting the degrees of freedom of the kinetic energy from three-dimensional (3D) to lower-dimensional spaces, while maintaining the 3D nature of the interaction energy degrees of freedom. The aim of this work is to introduce an innovative scenario to achieve dimensional crossover, characterized by lower-dimensional nature of both the kinetic and the interaction energy degrees of freedom. To accomplish this objective, we delve deeply into the realm of a two-dimensional optically trapped Bose gas, focusing specifically on its finite-range interaction. Our emphasis lies in exploring the lattice-induced dimensional crossover from full 3D to one-dimensional (1D) in both kinetic and interaction terms. Utilizing the functional path integral method, we derive the equation of states of the model system, encompassing crucial quantities, such as the ground-state energy and quantum depletion. These equations enable us to analyze the combined effects of finite-range interaction and an optical lattice on quantum fluctuations of the BEC system. Notably, our analytical findings reconcile the Lee-Huang-Yang (LHY) correction to the ground-state energy in the 3D and Lieb-Liniger (LL) ones in the 1D limit, thereby providing fresh insights into the intriguing disparities between LHY and LL corrections.
The equation of state (EOS) for a pure two-dimensional (2D) Bose gas exhibits a logarithmic dependence on the sss-wave scattering length [L. Salasnich, Phys. Rev. Lett. 118, 130402 (2017)]. The pronounced disparity between the EOS of a 2D Bose gas and its three-dimensional (3D) counterpart underscores the significance of exploring the dimensional crossover between these two distinct dimensions. In this paper, we are motivated to deduce nonuniversal corrections to the EOS for an optically trapped Bose gas along the dimensional crossover from 3D to 2D, incorporating the finite-range effects of the interatomic potential. Employing the framework of effective field theory, we derive the analytical expressions for both the ground-state energy and quantum depletion. The introduction of the lattice induces a transition from a 3D to a quasi-2D regime. In particular, we systematically analyze the asymptotic behaviors of both the 2D and 3D aspects of the model system, with a specific focus on the nonuniversal effects on the EOS arising from finite-range interactions. The nonuniversal effects proposed in this paper along the dimensional crossover represent a significant stride toward unraveling the intricate interplay between dimensionality and quantum fluctuations.
Abstract The Bose–Einstein condensation (BEC) in three-dimensional (3D) anisotropic lattices is studied. We present theoretical results for the critical temperature for BEC, chemical potential, condensate fraction and relevant thermodynamic quantities like: internal energy, entropy, specific heat and compressibility as a function of anisotropy parameter being the ratio of the nearest-neighbor in-plane ( t∥t_\parallelt∥​ t ‖ ) and out-of-plane ( t⊥t_\perpt⊥​ t ⊥ ) hopping amplitudes. In particular, considered scenarios include weakly coupled two-dimensional (2D) planes ( t⊥/t∥≪1t_\perp /t_\parallel \ll 1t⊥​/t∥​≪1 t ⊥ / t ‖ ≪ 1 , relevant for layered structures) as well as a rod-like geometry of interacting one-dimensional (1D) chains ( t∥/t⊥≪1t_\parallel /t_\perp \ll 1t∥​/t⊥​≪1 t ‖ / t ⊥ ≪ 1 ). The impact of the dimensional crossover as the system is tuned away from a set of disconnected 2D layers, or traverses from a set of separate 1D chains to a regime where a fully isotropic 3D structure emerges is elucidated. Both numerical and analytic approaches are employed, (the latter in a form of series expansions involving t∥,t⊥t_\parallel ,t_\perpt∥​,t⊥​ t ‖ , t ⊥ amplitudes) for internal energy, entropy, specific heat and isothermal compressibility. The theoretical outcome of the present study may be of interest to a number of scenarios in solid-state physics, where the relevant quasi-particles are bosonic-like, as well as might be applicable to the physics of cold bosons loaded in artificially engineered 3D optical lattices.
We investigate a Bose-Einstein condensate (BEC) trapped in a two-dimensional optical lattice in the presence of weak disorder within the framework of the Bogoliubov theory. In particular, we analyze the combined effects of disorder and an optical lattice on quantum fluctuations and superfluid density of the BEC system. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the lattice still induces a characteristic three-dimensional (3D) to one-dimensional crossover in the behavior of quantum fluctuations, despite the presence of weak disorder. Furthermore, we use the linear response theory to calculate the normal fluid density of the condensate induced by disorder. Our results in the 3D regime show that the combined presence of disorder and lattice induce a normal fluid density that asymptotically approaches 4/3 of the corresponding condensate depletion. Conditions for possible experimental realization of our scenario are also proposed.