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Register a new userObservation of scale invariance and universality in two-dimensional Bose gases
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The collective behavior of a many-body system near a continuous phase transition is insensitive to the details of its microscopic physics[1]. Characteristic features near the phase transition are that the thermodynamic observables follow generalized scaling laws[1]. The Berezinskii-Kosterlitz-Thouless (BKT) phase transition[2,3] in two-dimensional (2D) Bose gases presents a particularly interesting case because the marginal dimensionality and intrinsic scaling symmetry[4] result in a broad fluctuation regime which manifests itself in an extended range of universal scaling behavior. Studies on BKT transition in cold atoms have stimulated great interest in recent years[5-10], clear demonstration of a critical behavior near the phase transition, however, has remained an elusive goal. Here we report the observation of a scale-invariant, universal behavior of 2D gases through in-situ density and density fluctuation measurements at different temperatures and interaction strengths. The extracted thermodynamic functions confirm a wide universal region near the BKT phase transition, provide a sensitive test to the universality prediction by classical-field theory[11,12] and quantum Monte Carlo (MC) calculations[13], and point toward growing density-density correlations in the fluctuation region. Our assay raises new perspectives to explore further universal phenomena in the realm of classical and quantum critical physics.
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We prepare and study strongly interacting two-dimensional Bose gases in the superfluid, the classical Berezinskii-Kosterlitz-Thouless (BKT) transition, and the vacuum-to-superfluid quantum critical regimes. A wide range of the two-body interaction strength 0.05 < g < 3 is covered by tuning the scattering length and by loading the sample into an optical lattice. Based on the equations of state measurements, we extract the coupling constants as well as critical thermodynamic quantities in different regimes. In the superfluid and the BKT transition regimes, the extracted coupling constants show significant down-shifts from the mean-field and perturbation calculations when g approaches or exceeds one. In the BKT and the quantum critical regimes, all measured thermodynamic quantities show logarithmic dependence on the interaction strength, a tendency confirmed by the extended classical-field and renormalization calculations.
We experimentally investigate the quantum criticality and Tomonaga-Luttinger liquid (TLL) behavior within one-dimensional (1D) ultracold atomic gases. Based on the measured density profiles at different temperatures, the universal scaling laws of thermodynamic quantities are observed. The quantum critical regime and the relevant crossover temperatures are determined through the double-peak structure of the specific heat. In the TLL regime, we obtain the Luttinger parameter by probing sound propagation. Furthermore, a characteristic power-law behavior emerges in the measured momentum distributions of the 1D ultracold gas, confirming the existence of the TLL.
We measure collective excitations of a harmonically trapped two-dimensional (2D) SU($N$) Fermi gas of $^{173}$Yb confined to a stack of layers formed by a one-dimensional optical lattice. Quadrupole and breathing modes are excited and monitored in the collisionless regime $lvertln(k_F a_{2D})rvertgg 1$ with tunable spin. We observe that the quadrupole mode frequency decreases with increasing number of spin components due to the amplification of the interaction effect by $N$ in agreement with a theoretical prediction based on 2D kinetic equations. The breathing mode frequency, however, is measured to be twice the dipole oscillation frequency regardless of $N$. We also follow the evolution of collective excitations in the dimensional crossover from two to three dimensions and characterize the damping rate of quadrupole and breathing modes for tunable SU($N$) fermions, both of which reveal the enhanced inter-particle collisions for larger spin. Our result paves the way to investigate the collective property of 2D SU($N$) Fermi liquid with enlarged spin.
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.
Due to the vast growth of the many-body level density with excitation energy, its smoothed form is of central relevance for spectral and thermodynamic properties of interacting quantum systems. We compute the cumulative of this level density for confined one-dimensional continuous systems with repulsive short-range interactions. We show that the crossover from an ideal Bose gas to the strongly correlated, fermionized gas, i.e., partial fermionization, exhibits universal behavior: Systems with very few up to many particles share the same underlying spectral features. In our derivation we supplement quantum cluster expansions with short-time dynamical information. Our nonperturbative analytical results are in excellent agreement with numerics for systems of experimental relevance in cold atom physics, such as interacting bosons on a ring (Lieb-Liniger model) or subject to harmonic confinement. Our method provides predictions for excitation spectra that enable access to finite-temperature thermodynamics in large parameter ranges.
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