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:0901.4385 · Physical Review A

Metastable quantum phase transitions in a periodic one-dimensional Bose gas: Mean-field and Bogoliubov analyses

Rina Kanamoto, Lincoln D. Carr, Masahito Ueda

Published Jun 10, 2009• 62 citations
arXivHTMLPDF

Abstract

We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for metastable states in finite-size systems. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear perturbation or Bogoliubov--de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist two topologically distinct quantum phases. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is where one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity. The phase of the condensate can therefore be continuously wound and unwound.

DOI
10.1103/physreva.79.063616

Related papers

Metastable Quantum Phase Transitions in a One-Dimensional Bose Gas

Lincoln D. Carr, Rina Kanamoto, Masahito Ueda

This is a chapter for a book. The first paragraph of this chapter is as follows: "Ultracold quantum gases offer a wonderful playground for quantum many body physics, as experimental systems are widely controllable, both statically and dynamically. One such system is the one-dimensional (1D) Bose gas on a ring. In this system binary contact interactions between the constituent bosonic atoms, usually alkali metals, can be controlled in both sign and magnitude; a recent experiment has tuned interactions over seven orders of magnitude, using an atom-molecule resonance called a Feshbach resonance. Thus one can directly realize the Lieb-Liniger Hamiltonian, from the weakly- to the strongly-interacting regime. At the same time there are a number of experiments utilizing ring traps. The ring geometry affords us the opportunity to study topological properties of this system as well; one of the main properties of a superfluid is the quantized circulation in which the average angular momentum per particle, L/N, is quantized under rotation. Thus we focus on a tunable 1D Bose system for which the main control parameters are interaction and rotation. We will show that there is a critical boundary in the interaction-rotation control-parameter plane over which the topological properties of the system change. This is the basis of our concept of \textit{metastable quantum phase transitions} (QPTs). Moreover, we will show that the finite domain of the ring is necessary for the QPT to occur at all because the zero-point kinetic pressure can induce QPTs, i.e., the system must be finite; we thus seek to generalize the concept of QPTs to inherently finite, mesoscopic or nanoscopic systems."

arXiv:1005.0656•May 5, 2010•2 citations

Metastable Quantum Phase Transitions in a One-Dimensional

Bose Gas Lincoln D. Carr, Rina Kanamoto, and Masahito Ueda

Department of Physics, Colorado School of Mines, Golden, CO 80401, U.S.A. Rina Kanamoto Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610 Japan Masahito Ueda Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 Japan Ultracold quantum gases offer a wonderful playground for quantum manybody physics [1], as experimental systems are widely controllable, both statically and dynamically. One such system is the one-dimensional (1D) Bose gas on a ring. In this system binary contact interactions between the constituent bosonic atoms, usually alkali metals, can be controlled in both sign and magnitude; a recent experiment has tuned interactions over seven orders of magnitude [2], using an atom-molecule resonance called a Feshbach resonance. Thus one can directly realize the Lieb-Liniger Hamiltonian (LLH) [3,4], from the weakly-to the strongly-interacting regime. At the same time there are a number of experiments utilizing ring traps [5]. The ring geometry affords us the opportunity to study topological properties of this system as well; one of the main properties of a superfluid is the quantized circulation in which the average angular momentum per particle, L/N , is quantized under rotation [6]. Thus we focus on a tunable 1D Bose system for which the main control parameters are interaction and rotation. We will show that there is a critical boundary in the interaction-rotation control-parameter plane over which the topological properties of the system change. This is the basis of our concept of metastable quantum phase transitions (QPTs). Moreover, we will show that the finite domain of the ring is necessary for the QPT to occur at all because the zero-point kinetic pressure can induce QPTs, i.e., the system must be finite; we thus seek to generalize the concept of QPTs to inherently finite, mesoscopic or nanoscopic systems.1

CRC Press eBooks•Nov 2, 2010•0 citations

Metastable quantum phase transitions in a periodic one-dimensional Bose gas. II. Many-body theory

Rina Kanamoto, Lincoln D. Carr, Masahito Ueda

We show that quantum solitons in the Lieb-Liniger Hamiltonian are precisely the yrast states. We identify such solutions with Lieb's type II excitations from weak to strong interactions, clarifying a long-standing question of the physical meaning of this excitation branch. We demonstrate that the metastable quantum phase transition previously found in mean-field analysis of the weakly interacting Lieb-Liniger Hamiltonian [Phys. Rev. A 79, 063616 (2009)] extends into the medium- to strongly interacting regime of a periodic one-dimensional Bose gas. Our methods are exact diagonalization, finite-size Bethe ansatz, and the boson-fermion mapping in the Tonks-Girardeau limit.

arXiv:0910.2805•Physical Review A•Feb 24, 2010•60 citations

Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions

Rina Kanamoto, Hiroki Saito, Masahito Ueda

Motivated by the recent development of the Feshbach technique, we studied the ground and low-lying excited states of attractive Bose-Einstein condensates on a one-dimensional ring as a function of the strength of interactions. The Gross-Pitaevskii mean-field theory predicts a quantum phase transition between a uniform condensate and a bright soliton, and a gapless singular cusp in the Bogoliubov excitation spectrum at the critical point. However, the exact diagonalization reveals the presence of an energy gap at the critical point, where the singularity is smeared by quantum fluctuations.

arXiv:cond-mat/0210229•Physical Review A•Jan 23, 2003•148 citations

Quantum phase transition of Bose-Einstein condensates on a nonlinear ring lattice

Zheng-Wei Zhou, Shaoliang Zhang, Xiang-Fa Zhou +3 more

We study the phase transitions in a one-dimensional Bose-Einstein condensate on a ring whose atomic scattering length is modulated periodically along the ring. By using a modified Bogoliubov method to treat such a nonlinear lattice in the mean-field approximation, we find that the phase transitions are of different orders when the modulation period is 2 and greater than 2. We further perform a full quantum mechanical treatment based on the time-evolving block decimation algorithm which confirms the mean-field results and reveals interesting quantum behavior of the system. Our studies yield important knowledge of competing mechanisms behind the phase transitions and the quantum nature of this system.

arXiv:1205.1094•Physical Review A•Apr 29, 2011•15 citations

Bose-Einstein condensates on a ring with periodic scattering length: Spontaneous symmetry breaking and entanglement

Lisa Qian, Michael L. Wall, Shaoliang Zhang +2 more

We study the properties of Bose-Einstein condensates in a one-dimensional ring with periodically modulated interaction strength. We demonstrate that within the semiclassical mean-field theory, a condensate can undergo a quantum phase transition between a solitonlike state and a spatially periodic condensate that matches the scattering length modulation. However, we show via exact diagonalization of the full many-body Hamiltonian that the solitonic ground states do not exist in the true quantum treatment. Instead, the system is driven into an entangled macroscopic-quantum-superposition-like state and the semiclassical soliton state may be regarded as a decohered macroscopic quantum superposition state. We investigate how the properties of the quantum ground state scales with the total number of atoms. Our work elucidates how semiclassical properties emerge from quantum behavior.

Physical Review A•Jan 15, 2008•38 citations
We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for metastable states in finite-size systems. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schr"odinger equation, and linear perturbation or Bogoliubov--de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist two topologically distinct quantum phases. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is where one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity. The phase of the condensate can therefore be continuously wound and unwound.
This is a chapter for a book. The first paragraph of this chapter is as follows: "Ultracold quantum gases offer a wonderful playground for quantum many body physics, as experimental systems are widely controllable, both statically and dynamically. One such system is the one-dimensional (1D) Bose gas on a ring. In this system binary contact interactions between the constituent bosonic atoms, usually alkali metals, can be controlled in both sign and magnitude; a recent experiment has tuned interactions over seven orders of magnitude, using an atom-molecule resonance called a Feshbach resonance. Thus one can directly realize the Lieb-Liniger Hamiltonian, from the weakly- to the strongly-interacting regime. At the same time there are a number of experiments utilizing ring traps. The ring geometry affords us the opportunity to study topological properties of this system as well; one of the main properties of a superfluid is the quantized circulation in which the average angular momentum per particle, L/N, is quantized under rotation. Thus we focus on a tunable 1D Bose system for which the main control parameters are interaction and rotation. We will show that there is a critical boundary in the interaction-rotation control-parameter plane over which the topological properties of the system change. This is the basis of our concept of \textit{metastable quantum phase transitions} (QPTs). Moreover, we will show that the finite domain of the ring is necessary for the QPT to occur at all because the zero-point kinetic pressure can induce QPTs, i.e., the system must be finite; we thus seek to generalize the concept of QPTs to inherently finite, mesoscopic or nanoscopic systems."
Department of Physics, Colorado School of Mines, Golden, CO 80401, U.S.A. Rina Kanamoto Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610 Japan Masahito Ueda Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 Japan Ultracold quantum gases offer a wonderful playground for quantum manybody physics [1], as experimental systems are widely controllable, both statically and dynamically. One such system is the one-dimensional (1D) Bose gas on a ring. In this system binary contact interactions between the constituent bosonic atoms, usually alkali metals, can be controlled in both sign and magnitude; a recent experiment has tuned interactions over seven orders of magnitude [2], using an atom-molecule resonance called a Feshbach resonance. Thus one can directly realize the Lieb-Liniger Hamiltonian (LLH) [3,4], from the weakly-to the strongly-interacting regime. At the same time there are a number of experiments utilizing ring traps [5]. The ring geometry affords us the opportunity to study topological properties of this system as well; one of the main properties of a superfluid is the quantized circulation in which the average angular momentum per particle, L/N , is quantized under rotation [6]. Thus we focus on a tunable 1D Bose system for which the main control parameters are interaction and rotation. We will show that there is a critical boundary in the interaction-rotation control-parameter plane over which the topological properties of the system change. This is the basis of our concept of metastable quantum phase transitions (QPTs). Moreover, we will show that the finite domain of the ring is necessary for the QPT to occur at all because the zero-point kinetic pressure can induce QPTs, i.e., the system must be finite; we thus seek to generalize the concept of QPTs to inherently finite, mesoscopic or nanoscopic systems.1
We show that quantum solitons in the Lieb-Liniger Hamiltonian are precisely the yrast states. We identify such solutions with Lieb's type II excitations from weak to strong interactions, clarifying a long-standing question of the physical meaning of this excitation branch. We demonstrate that the metastable quantum phase transition previously found in mean-field analysis of the weakly interacting Lieb-Liniger Hamiltonian [Phys. Rev. A 79, 063616 (2009)] extends into the medium- to strongly interacting regime of a periodic one-dimensional Bose gas. Our methods are exact diagonalization, finite-size Bethe ansatz, and the boson-fermion mapping in the Tonks-Girardeau limit.
Motivated by the recent development of the Feshbach technique, we studied the ground and low-lying excited states of attractive Bose-Einstein condensates on a one-dimensional ring as a function of the strength of interactions. The Gross-Pitaevskii mean-field theory predicts a quantum phase transition between a uniform condensate and a bright soliton, and a gapless singular cusp in the Bogoliubov excitation spectrum at the critical point. However, the exact diagonalization reveals the presence of an energy gap at the critical point, where the singularity is smeared by quantum fluctuations.
We study the phase transitions in a one-dimensional Bose-Einstein condensate on a ring whose atomic scattering length is modulated periodically along the ring. By using a modified Bogoliubov method to treat such a nonlinear lattice in the mean-field approximation, we find that the phase transitions are of different orders when the modulation period is 2 and greater than 2. We further perform a full quantum mechanical treatment based on the time-evolving block decimation algorithm which confirms the mean-field results and reveals interesting quantum behavior of the system. Our studies yield important knowledge of competing mechanisms behind the phase transitions and the quantum nature of this system.
We study the properties of Bose-Einstein condensates in a one-dimensional ring with periodically modulated interaction strength. We demonstrate that within the semiclassical mean-field theory, a condensate can undergo a quantum phase transition between a solitonlike state and a spatially periodic condensate that matches the scattering length modulation. However, we show via exact diagonalization of the full many-body Hamiltonian that the solitonic ground states do not exist in the true quantum treatment. Instead, the system is driven into an entangled macroscopic-quantum-superposition-like state and the semiclassical soliton state may be regarded as a decohered macroscopic quantum superposition state. We investigate how the properties of the quantum ground state scales with the total number of atoms. Our work elucidates how semiclassical properties emerge from quantum behavior.