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:1911.12347 · Science

Geometric squeezing into the lowest Landau level

Richard J. Fletcher, Airlia Shaffer, Cedric Wilson, Parth Patel, Zhenjie Yan, Valentin Crépel, Biswaroop Mukherjee, Martin W. Zwierlein

Published Jun 17, 2021• 72 citations
arXivHTMLPDF

Abstract

The equivalence between particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. For such systems, quantum mechanics dictates that translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. We implement squeezing of this geometric quantum uncertainty, resulting in a rotating Bose-Einstein condensate occupying a single Landau gauge wave function. We resolve the extent of zero-point cyclotron orbits and demonstrate geometric squeezing of the orbits' centers 7 decibels below the standard quantum limit. The condensate attains an angular momentum exceeding 1000 quanta per particle and an interatomic distance comparable to the cyclotron orbit. This offers an alternative route toward strongly correlated bosonic fluids.

DOI
10.1126/science.aba7202

Related papers

Rotating Bose gas dynamically entering the lowest Landau level

Vaibhav Sharma, Erich J. Mueller

Motivated by recent experiments, we model the dynamics of a condensed Bose gas in a rotating anisotropic trap, where the equations of motion are analogous to those of charged particles in a magnetic field. As the rotation rate is ramped from zero to the trapping frequency, the condensate stretches along one direction and is squeezed along another, becoming long and thin. When the trap anisotropy is slowly switched off on a particular timescale, the condensate is left in the lowest Landau level. We use a time-dependent variational approach to quantify these dynamics and give intuitive arguments about the structure of the condensate wave function. This preparation of a lowest Landau level condensate can be an important first step in realizing bosonic analogs of quantum Hall states.

arXiv:2111.10415•Physical Review A•Feb 7, 2022•7 citations

Spin-orbit coupling induced geometric squeezing in rotating Bose-Einstein condensates

Fei Zhu, Chunxia Guo, Rui Zhang +3 more

Squeezed states play a key role in diverse frontiers of quantum physics. Geometrically squeezed states, a squeezed state in the orbital phase space of rotating Bose-Einstein condensates (BEC), have been conventionally generated by anisotropic trapping potentials. In this work, we propose a different route to generate geometric squeezing via spin-orbit coupling (SOC) in a pseudospin-1/2 BEC. We show that the SOC enables effective two-phonon transitions within the lowest Landau level via virtual spin-flip processes, leading to exponential squeezing dynamics in both spin components. Furthermore, by applying a $π/2$ spin rotation, the two spin channels can be coherently coupled to produce two-mode geometric squeezing. We also investigate the influence of interatomic interactions on squeezing performance and identify parameters where robust squeezing can be achieved. Our work provides a viable pathway to realize and manipulate geometric squeezing in spinor quantum gases.

arXiv:2606.30187•Jun 29, 2026•0 citations

Floquet geometric squeezing in fast-rotating condensates

Li Chen, Fei Zhu, Yunbo Zhang +1 more

Constructing and manipulating quantum states in fast-rotating Bose-Einstein condensates (BEC) has long stood as a significant challenge as the rotating speed approaching the critical velocity. Although the recent experiment [Science, 372, 1318 (2021)] has realized the geometrically squeezed state of the guiding-center mode, the remaining degree of freedom, the cyclotron mode, remains unsqueezed due to the large energy gap of Landau levels. To overcome this limitation, in this paper, we propose a Floquet-based state-preparation protocol by periodically driving an anisotropic potential. This protocol not only facilitates the single cyclotron-mode squeezing, but also enables a two-mode squeezing. Such two-mode squeezing offers a richer set of dynamics compared to single-mode squeezing and can achieve wavepacket width well below the lowest Landau level limit. Our work provides a highly controllable knob for realizing diverse geometrically squeezed states in ultracold quantum gases within the quantum Hall regime.

arXiv:2501.02764•Physical Review A•Jan 14, 2025•3 citations

Geometric squeezing of rotating quantum gases into the lowest Landau level

Valentin Crépel, Ruixiao Yao, Biswaroop Mukherjee +2 more

The simulation of quantum Hall physics with rotating quantum gases is witnessing a revival due to recent experimental advances that enabled the observation of a Bose–Einstein condensate entirely contained in its lowest kinetic energy state, i.e. the lowest Landau level. We theoretically describe this experimental result, and show that it can be interpreted as a squeezing of the geometric degree of freedom of the problem, the guiding center metric. This “geometric squeezing” offers an unprecedented experimental control over the quantum geometry in Landau-level analogues, and at the same time opens a realistic path towards achieving correlated quantum phases akin to quantum Hall states with neutral atoms.

arXiv:2309.02510•Comptes Rendus Physique•Mar 7, 2024•11 citations

Rapidly Rotating Bose-Einstein Condensates in and near the Lowest Landau Level

Volker Schweikhard, Ian R. Coddington, Peter Engels +2 more

We create rapidly rotating Bose-Einstein condensates in the lowest Landau level by spinning up the condensates to rotation rates Omega > 99% of the centrifugal limit for a harmonically trapped gas, while reducing the number of atoms. As a consequence, the chemical potential drops below the cyclotron energy 2 variant Planck's over 2pi Omega. While in this mean-field quantum-Hall regime we still observe an ordered vortex lattice, its elastic shear strength is strongly reduced, as evidenced by the observed very low frequency of Tkachenko modes. Furthermore, the gas approaches the quasi-two-dimensional limit. The associated crossover from interacting- to ideal-gas behavior along the rotation axis results in a shift of the axial breathing mode frequency.

arXiv:cond-mat/0308582•Physical Review Letters•Jan 29, 2004•436 citations

Crystallization of bosonic quantum Hall states in a rotating quantum gas

Biswaroop Mukherjee, Airlia Shaffer, Parth Patel +5 more

Abstract The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here, we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets, separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.

arXiv:2106.11300•Nature•Jan 5, 2022•76 citations
The equivalence between particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. For such systems, quantum mechanics dictates that translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. We implement squeezing of this geometric quantum uncertainty, resulting in a rotating Bose-Einstein condensate occupying a single Landau gauge wave function. We resolve the extent of zero-point cyclotron orbits and demonstrate geometric squeezing of the orbits' centers 7 decibels below the standard quantum limit. The condensate attains an angular momentum exceeding 1000 quanta per particle and an interatomic distance comparable to the cyclotron orbit. This offers an alternative route toward strongly correlated bosonic fluids.
Motivated by recent experiments, we model the dynamics of a condensed Bose gas in a rotating anisotropic trap, where the equations of motion are analogous to those of charged particles in a magnetic field. As the rotation rate is ramped from zero to the trapping frequency, the condensate stretches along one direction and is squeezed along another, becoming long and thin. When the trap anisotropy is slowly switched off on a particular timescale, the condensate is left in the lowest Landau level. We use a time-dependent variational approach to quantify these dynamics and give intuitive arguments about the structure of the condensate wave function. This preparation of a lowest Landau level condensate can be an important first step in realizing bosonic analogs of quantum Hall states.
Squeezed states play a key role in diverse frontiers of quantum physics. Geometrically squeezed states, a squeezed state in the orbital phase space of rotating Bose-Einstein condensates (BEC), have been conventionally generated by anisotropic trapping potentials. In this work, we propose a different route to generate geometric squeezing via spin-orbit coupling (SOC) in a pseudospin-1/2 BEC. We show that the SOC enables effective two-phonon transitions within the lowest Landau level via virtual spin-flip processes, leading to exponential squeezing dynamics in both spin components. Furthermore, by applying a π/2π/2π/2 spin rotation, the two spin channels can be coherently coupled to produce two-mode geometric squeezing. We also investigate the influence of interatomic interactions on squeezing performance and identify parameters where robust squeezing can be achieved. Our work provides a viable pathway to realize and manipulate geometric squeezing in spinor quantum gases.
Constructing and manipulating quantum states in fast-rotating Bose-Einstein condensates (BEC) has long stood as a significant challenge as the rotating speed approaching the critical velocity. Although the recent experiment [Science, 372, 1318 (2021)] has realized the geometrically squeezed state of the guiding-center mode, the remaining degree of freedom, the cyclotron mode, remains unsqueezed due to the large energy gap of Landau levels. To overcome this limitation, in this paper, we propose a Floquet-based state-preparation protocol by periodically driving an anisotropic potential. This protocol not only facilitates the single cyclotron-mode squeezing, but also enables a two-mode squeezing. Such two-mode squeezing offers a richer set of dynamics compared to single-mode squeezing and can achieve wavepacket width well below the lowest Landau level limit. Our work provides a highly controllable knob for realizing diverse geometrically squeezed states in ultracold quantum gases within the quantum Hall regime.
The simulation of quantum Hall physics with rotating quantum gases is witnessing a revival due to recent experimental advances that enabled the observation of a Bose–Einstein condensate entirely contained in its lowest kinetic energy state, i.e. the lowest Landau level. We theoretically describe this experimental result, and show that it can be interpreted as a squeezing of the geometric degree of freedom of the problem, the guiding center metric. This “geometric squeezing” offers an unprecedented experimental control over the quantum geometry in Landau-level analogues, and at the same time opens a realistic path towards achieving correlated quantum phases akin to quantum Hall states with neutral atoms.
We create rapidly rotating Bose-Einstein condensates in the lowest Landau level by spinning up the condensates to rotation rates Omega > 99% of the centrifugal limit for a harmonically trapped gas, while reducing the number of atoms. As a consequence, the chemical potential drops below the cyclotron energy 2 variant Planck's over 2pi Omega. While in this mean-field quantum-Hall regime we still observe an ordered vortex lattice, its elastic shear strength is strongly reduced, as evidenced by the observed very low frequency of Tkachenko modes. Furthermore, the gas approaches the quasi-two-dimensional limit. The associated crossover from interacting- to ideal-gas behavior along the rotation axis results in a shift of the axial breathing mode frequency.
Abstract The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here, we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets, separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.