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:1305.1423

Observation of the universal jump across the Berezinskii-Kosterlitz-Thouless transition in two-dimensional Bose gases

Jiho Noh, Jeongwon Lee, Jongchul Mun

Published May 7, 2013• 0 citations
arXivHTMLPDF

Abstract

The physics in two-dimensional (2D) systems is very different from what we observe in three-dimensional (3D) systems. Thermal fluctuations in 2D systems are enhanced, and they prevent the conventional Bose-Einstein condensation (BEC) at non-zero temperatures by destroying the long-range order. However, a phase transition to a superfluid phase is still expected to occur in a 2D system along with an emergence of a quasi-long-range order, explained by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. Within the BKT mechanism, a universal jump of the superfluid density in a 2D Bosonic system was theoretically predicted by Nelson and Kosterlitz, and was first observed in 2D \textsuperscript{4}He films by Bishop and Reppy. Recent experiments in trapped ultracold 2D Bose gas systems have shown signatures of the BKT transition, and its superfluidity. However, the universal jump in the superfluid density was not observed in these systems. Here we report the first observation of the universal jump in the superfluid density using an optically trapped ultracold 2D Bose gas. The measured superfluid phase space density at the BKT transition agrees well with the predicted value within our measurement uncertainty. Additionally, we measure the phase fluctuations in our density profiles to show that the BKT transition occurs first, followed by the BEC transition.

DOI
10.48550/arxiv.1305.1423

Related papers

Exploring the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional dipolar bose gas

Yifei He, Ziting Chen, Haoting Zhen +3 more

Long-range and anisotropic dipolar interactions induce complex order in quantum systems, particularly interesting in 2D where superfluidity emerges via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. We observe a superfluid phase with algebraically decaying correlation in a quasi-2D dipolar Bose gas of erbium atoms and further identify the superfluid phase transition by monitoring extended coherence. We also measure equations of state with tunable dipolar interactions. Our findings show a transition point shift due to dipole orientation, aligning with BKT transition with effective short-range interaction. However, we observe that in-plane tilted dipoles show nonlocal effects in the superfluid regime, preventing the effective short-range interaction from revealing universal behavior near the BKT critical point. We also measure anisotropic atom number fluctuations in the superfluid regime, highlighting its dipolar nature. Our results provide a foundation for understanding dipolar bosons in 2D and pave the way for investigating complex orders in dipolar superfluids.

arXiv:2403.18683•Science Advances•Apr 9, 2025•11 citations

Signatures of a universal jump in the superfluid density of a two-dimensional Bose gas with a finite number of particles

Krzysztof Gawryluk, Mirosław Brewczyk

We study, within the classical fields approximation, a two-dimensional weakly interacting uniform Bose gas of a finite number of atoms. By using a grand canonical ensemble formalism we show that such systems exhibit, in addition to the Berezinskii-Kosterlitz-Thouless (BKT) and thermal phases, an intermediate region. This intermediate region is characterized by a decay of current-current correlations at low momenta and by an algebraic decay of the first-order correlations with an exponent being larger than the critical value predicted by the BKT theory. The density of the superfluid fraction at the temperature which separates the BKT phase from the intermediate region approaches the one found by Nelson and Kosterlitz for two-dimensional superfluids while the number of atoms is increased.

arXiv:1809.10967•Physical Review A•Mar 20, 2019•13 citations

Thermal Phase Fluctuations in a Quasi-2D Bose-Einstein Condensate

최재윤

Quantum gases are well isolated, highly controllable, and defect-free systems which can simulate many body quantum phenomena that have been studied in condensed matter systems.To study two-dimensional superfluid, we have developed an experimental apparatus that can produce Bose-Einstein condensates (BEC) of 23 Na atoms.The apparatus can generate a pure condensate of 10 7 atoms in an optically plugged magnetic quadrupole trap within 17 s.The Berezinskii-Kosterlitz-Thouless (BKT) theory provides a general framework of the superfluid phase transition in two dimension, which does not involve spontaneous symmetry breaking and emergence of an order parameter below a critical temperature.Instead, it is the formation of vortex pairs with opposite circulations below the critical temperature that mediates the superfluid phase transition.Recently, it has been demonstrated that degenerate Bose gases confined in highly oblate harmonic potentials undergo the BKT phase transition.This thesis focuses on our experimental research on thermal phase fluctuations (i.e., long-wavelength phonons and vortex pairs) in the superfluid i phase of trapped quasi-2D BECs.We have developed a quantitative probe to measure phase fluctuations in the 2D superfluid by free expansion, where the phase fluctuations in the sample were revealed as density modulations in the course of expansion.The power spectrum of the density fluctuations showed an oscillatory shape and the scaling behavior of the peak positions could be understood as a Talbot effect in matter waves.Employing this method, we demonstrated the thermal origin of phase fluctuations.We also investigated relaxation dynamics of nonequilibrium states of the quasi-2D system using the power spectrum.Thermally excited vortex pairs are the characteristic feature of the 2D superfluid.The quantized vortices are conventionally observed by a densitydepleted core after expanding a trapped sample.The method, however, cannot be applied to the 2D sample because the density modulations after free expansion lower the vortex core visibility.We enhanced the core visibility by radial compression of the sample before the expansion so the phonon modes in the 2D sample were relaxed in a 3D environment.Measuring vortex distributions, we revealed the pairing feature by spatial correlations of the vortex positions.We also studied BKT-BEC crossover phenomena in a finite-size sample trapped in a quasi-2D harmonic potential by investigating the vortex profiles at various temperatures.Condensates of atoms have an internal spin structure so they can host various kinds of topological excitations.The two-dimensional Skyrmion is one of the topological spin textures in the anti-ferromagnetic spinor condensate and ii we imprinted the structure using the magnetic field sweep technique.The 2D Skyrmion spin texture has a finite Berry curvature because of the non-coplanar spin configuration.We studied a geometric Hall effect, with condensates trapped in a harmonic potential with the Skyrmion spin texture.Under a linear driving of the spin texture, we observed a condensate dipole motion resonantly developed into a circular motion, which demonstrates the existence of an effective Lorentz force.

•Jan 1, 2014•0 citations

The Berezinskii–Kosterlitz–Thouless transition in imbalanced 2D Fermi gases: The role of fluctuations

Jacques Tempere, Serghei N. Klimin, J. T. Devreese

Abstract The physics of two-dimensional (2D) quantum gases can be revealed in strongly confining optical lattices. Upon cooling, 2D bosonic quantum gases as well as Fermi gases where pairing is present, become superfluid. The superfluid-to-normal transition is no longer governed by the presence or absence of a condensate, but by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism: above a critical temperature, vortices and antivortices proliferate and destroy phase coherence. We investigate the BKT transition for superfluid 2D Fermi gases in the whole range of the BCS–BEC crossover, from weakly bound Cooper pairing (the BCS state), up to strongly bound molecules (the BEC state). Using a path-integral description, we then focus on the case of imbalanced gases: when the number of ‘spin-up’ and ‘spin-down’ fermions that form the pair is no longer equal. When an excess of one spin species exists, pairing is frustrated and the vortex energetics is strongly affected, influencing the KT mechanism. In the present work we are concentrated on the effect of both phase and amplitude fluctuations on phase diagrams of the fermion system. The amplitude fluctuations only slightly influence the BKT phase transition temperature. However, they lead to a substantial modification of the complete phase diagram for the Fermi gas in 2D with respect to that obtained taking into account only phase fluctuations.

Physica C Superconductivity•Feb 24, 2010•3 citations

Observation of a 2D Bose Gas: From Thermal to Quasicondensate to Superfluid

Pierre Cladé, Changhyun Ryu, Anand K. Ramanathan +2 more

We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz, and Thouless (BKT) transition temperature. By measuring the density profile after time of flight and the coherence length, we identify different states of the gas. We observe that the gas develops a bimodal distribution without long range order. In this regime, the gas presents a longer coherence length than the thermal cloud; it is quasicondensed but is not superfluid. Experimental evidence indicates that we also observe the superfluid transition (BKT transition). For a sufficiently long time of flight, we observe a trimodal distribution when the gas has developed a superfluid component.

arXiv:0805.3519•Physical Review Letters•Apr 27, 2009•233 citations

Observation of the Berezinskii-Kosterlitz-Thouless Transition in a Two-Dimensional Bose Gas via Matter-Wave Interferometry

Shinichi Sunami, Vijay Pal Singh, D. Garrick +6 more

We probe local phase fluctuations of trapped two-dimensional Bose gases using matter-wave interferometry. This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. We determine the temperature dependence of the BKT exponent η and find the critical value η_{c}=0.17(3) for our trapped system. Furthermore, we measure the local vortex density as a function of the local phase-space density, which shows a scale-invariant behavior across the transition. Our experimental investigation is supported by Monte Carlo simulations and provides a comprehensive understanding of the BKT transition in a trapped system.

arXiv:2108.08840•Physical Review Letters•Jun 22, 2022•34 citations
The physics in two-dimensional (2D) systems is very different from what we observe in three-dimensional (3D) systems. Thermal fluctuations in 2D systems are enhanced, and they prevent the conventional Bose-Einstein condensation (BEC) at non-zero temperatures by destroying the long-range order. However, a phase transition to a superfluid phase is still expected to occur in a 2D system along with an emergence of a quasi-long-range order, explained by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. Within the BKT mechanism, a universal jump of the superfluid density in a 2D Bosonic system was theoretically predicted by Nelson and Kosterlitz, and was first observed in 2D \textsuperscript{4}He films by Bishop and Reppy. Recent experiments in trapped ultracold 2D Bose gas systems have shown signatures of the BKT transition, and its superfluidity. However, the universal jump in the superfluid density was not observed in these systems. Here we report the first observation of the universal jump in the superfluid density using an optically trapped ultracold 2D Bose gas. The measured superfluid phase space density at the BKT transition agrees well with the predicted value within our measurement uncertainty. Additionally, we measure the phase fluctuations in our density profiles to show that the BKT transition occurs first, followed by the BEC transition.
Long-range and anisotropic dipolar interactions induce complex order in quantum systems, particularly interesting in 2D where superfluidity emerges via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. We observe a superfluid phase with algebraically decaying correlation in a quasi-2D dipolar Bose gas of erbium atoms and further identify the superfluid phase transition by monitoring extended coherence. We also measure equations of state with tunable dipolar interactions. Our findings show a transition point shift due to dipole orientation, aligning with BKT transition with effective short-range interaction. However, we observe that in-plane tilted dipoles show nonlocal effects in the superfluid regime, preventing the effective short-range interaction from revealing universal behavior near the BKT critical point. We also measure anisotropic atom number fluctuations in the superfluid regime, highlighting its dipolar nature. Our results provide a foundation for understanding dipolar bosons in 2D and pave the way for investigating complex orders in dipolar superfluids.
We study, within the classical fields approximation, a two-dimensional weakly interacting uniform Bose gas of a finite number of atoms. By using a grand canonical ensemble formalism we show that such systems exhibit, in addition to the Berezinskii-Kosterlitz-Thouless (BKT) and thermal phases, an intermediate region. This intermediate region is characterized by a decay of current-current correlations at low momenta and by an algebraic decay of the first-order correlations with an exponent being larger than the critical value predicted by the BKT theory. The density of the superfluid fraction at the temperature which separates the BKT phase from the intermediate region approaches the one found by Nelson and Kosterlitz for two-dimensional superfluids while the number of atoms is increased.
Quantum gases are well isolated, highly controllable, and defect-free systems which can simulate many body quantum phenomena that have been studied in condensed matter systems.To study two-dimensional superfluid, we have developed an experimental apparatus that can produce Bose-Einstein condensates (BEC) of 23 Na atoms.The apparatus can generate a pure condensate of 10 7 atoms in an optically plugged magnetic quadrupole trap within 17 s.The Berezinskii-Kosterlitz-Thouless (BKT) theory provides a general framework of the superfluid phase transition in two dimension, which does not involve spontaneous symmetry breaking and emergence of an order parameter below a critical temperature.Instead, it is the formation of vortex pairs with opposite circulations below the critical temperature that mediates the superfluid phase transition.Recently, it has been demonstrated that degenerate Bose gases confined in highly oblate harmonic potentials undergo the BKT phase transition.This thesis focuses on our experimental research on thermal phase fluctuations (i.e., long-wavelength phonons and vortex pairs) in the superfluid i phase of trapped quasi-2D BECs.We have developed a quantitative probe to measure phase fluctuations in the 2D superfluid by free expansion, where the phase fluctuations in the sample were revealed as density modulations in the course of expansion.The power spectrum of the density fluctuations showed an oscillatory shape and the scaling behavior of the peak positions could be understood as a Talbot effect in matter waves.Employing this method, we demonstrated the thermal origin of phase fluctuations.We also investigated relaxation dynamics of nonequilibrium states of the quasi-2D system using the power spectrum.Thermally excited vortex pairs are the characteristic feature of the 2D superfluid.The quantized vortices are conventionally observed by a densitydepleted core after expanding a trapped sample.The method, however, cannot be applied to the 2D sample because the density modulations after free expansion lower the vortex core visibility.We enhanced the core visibility by radial compression of the sample before the expansion so the phonon modes in the 2D sample were relaxed in a 3D environment.Measuring vortex distributions, we revealed the pairing feature by spatial correlations of the vortex positions.We also studied BKT-BEC crossover phenomena in a finite-size sample trapped in a quasi-2D harmonic potential by investigating the vortex profiles at various temperatures.Condensates of atoms have an internal spin structure so they can host various kinds of topological excitations.The two-dimensional Skyrmion is one of the topological spin textures in the anti-ferromagnetic spinor condensate and ii we imprinted the structure using the magnetic field sweep technique.The 2D Skyrmion spin texture has a finite Berry curvature because of the non-coplanar spin configuration.We studied a geometric Hall effect, with condensates trapped in a harmonic potential with the Skyrmion spin texture.Under a linear driving of the spin texture, we observed a condensate dipole motion resonantly developed into a circular motion, which demonstrates the existence of an effective Lorentz force.
Abstract The physics of two-dimensional (2D) quantum gases can be revealed in strongly confining optical lattices. Upon cooling, 2D bosonic quantum gases as well as Fermi gases where pairing is present, become superfluid. The superfluid-to-normal transition is no longer governed by the presence or absence of a condensate, but by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism: above a critical temperature, vortices and antivortices proliferate and destroy phase coherence. We investigate the BKT transition for superfluid 2D Fermi gases in the whole range of the BCS–BEC crossover, from weakly bound Cooper pairing (the BCS state), up to strongly bound molecules (the BEC state). Using a path-integral description, we then focus on the case of imbalanced gases: when the number of ‘spin-up’ and ‘spin-down’ fermions that form the pair is no longer equal. When an excess of one spin species exists, pairing is frustrated and the vortex energetics is strongly affected, influencing the KT mechanism. In the present work we are concentrated on the effect of both phase and amplitude fluctuations on phase diagrams of the fermion system. The amplitude fluctuations only slightly influence the BKT phase transition temperature. However, they lead to a substantial modification of the complete phase diagram for the Fermi gas in 2D with respect to that obtained taking into account only phase fluctuations.
We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz, and Thouless (BKT) transition temperature. By measuring the density profile after time of flight and the coherence length, we identify different states of the gas. We observe that the gas develops a bimodal distribution without long range order. In this regime, the gas presents a longer coherence length than the thermal cloud; it is quasicondensed but is not superfluid. Experimental evidence indicates that we also observe the superfluid transition (BKT transition). For a sufficiently long time of flight, we observe a trimodal distribution when the gas has developed a superfluid component.
We probe local phase fluctuations of trapped two-dimensional Bose gases using matter-wave interferometry. This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. We determine the temperature dependence of the BKT exponent η and find the critical value η_{c}=0.17(3) for our trapped system. Furthermore, we measure the local vortex density as a function of the local phase-space density, which shows a scale-invariant behavior across the transition. Our experimental investigation is supported by Monte Carlo simulations and provides a comprehensive understanding of the BKT transition in a trapped system.