Observation of Quantum Criticality with Ultracold Atoms in Optical Lattices

Zhang, Xibo; Hung, Chen-Lung; Tung, Shih-Kuang; Chin, Cheng

doi:10.1126/science.1217990

Cited by 133 publications

(187 citation statements)

References 33 publications

(49 reference statements)

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“…Fig. 6 shows the comparison between our results and the experimentally measured scaled density [20] at different temperatures. Our calculations with second-order corrections included (red dots) match well with the experimental data (solid black lines) for temperatures 5.8 nK and 6.7 nK as shown in Fig.…”

Section: Scaling Analysis For the Vacuum To Superfluid Transitionmentioning

confidence: 85%

“…7, panel (a). This would indeed seem to be a verification of universal quantum critical scaling, as suggested in the experimental analysis [20,21].…”

Section: B Scaling Properties Of the Theoretical Resultsmentioning

confidence: 99%

“…Our calculations are done for a 2D square lattice with an overall harmonic trap. The parameters are chosen to be the same as in the experiments [20] and are listed in the panels of the figures. Fig.…”

Section: Scaling Analysis For the Vacuum To Superfluid Transitionmentioning

confidence: 99%

“…6 the "11 nK" data match much better with theoretical calculations carried out at 8.2 nK, "13 nK" data match with calculations at 9.4 nK and "15 nK" match with calculations at 10 nK (solid red lines). The parameters used in the experiment are t=2.7 nK and U =15 nK, the total number of atoms are typically in the range of 4000 to 20000 and the plots are an average of different sets of data [20]. In the perturbative calculations, we have kept the chemical potential at the central site fixed.…”

Section: Scaling Analysis For the Vacuum To Superfluid Transitionmentioning

confidence: 99%

“…It has been suggested both theoretically [19] and experimentally [20][21][22] that the scaling properties can be verified by using real space density profiles at different temperatures. We have analyzed the scaling properties of our calculations in detail and find that they do not quite give universal scaling behavior for the vacuum to superfluid transition in the regimes that have been studied experimentally, in that the non-scaling corrections are substantial, and the exactly scaling part is trivial.…”

Section: Introductionmentioning

confidence: 99%

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Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

2013

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We develop a strong-coupling (t ≪ U ) expansion technique for calculating the density profile for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperature and finite on site interaction in the presence of superfluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We also show that the superfluid order parameter never vanishes in the trap due to proximity effect. Our calculations for the scaled density in the vacuum to superfluid transition agree well with the experimental data for appropriate temperatures. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments.

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Section: Scaling Analysis For the Vacuum To Superfluid Transitionmentioning

confidence: 85%

“…7, panel (a). This would indeed seem to be a verification of universal quantum critical scaling, as suggested in the experimental analysis [20,21].…”

Section: B Scaling Properties Of the Theoretical Resultsmentioning

confidence: 99%

Section: Scaling Analysis For the Vacuum To Superfluid Transitionmentioning

confidence: 99%

Section: Scaling Analysis For the Vacuum To Superfluid Transitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

2013

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Fluctuations and quantum criticality in the two‐dimensional Bose Hubbard model

Duchon

Trivedi

2013

Annalen der Physik

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At a quantum phase transition, one ground state evolves into a different one by passing through a quantum critical region with enhanced spatial and temporal fluctuations. A method to map the quantum critical region using the single, local quantity R, the ratio of compressibility to local number fluctuations is proposed. R can be calculated from in situ experiments and also enables thermometry and phase diagnosis (for example whether superfluid or Mott insulating). The definition of R can be generalized to inhomogeneous systems and provides a powerful tool for experimentally mapping the finite temperature phase diagram demonstrated here for the two-dimensional Bose Hubbard model.

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Nonlocal Correlation and Entanglement of Ultracold Bosons in the 2D Bose–Hubbard Lattice at Finite Temperature

2022

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The temperature‐dependent behavior emerging in the vicinity of the superfluid (SF) to Mott‐insulator (MI) transition of interacting bosons in a 2D optical lattice, described by the Bose–Hubbard model is investigated. The equilibrium phase diagram at finite‐temperature is computed using the cluster mean‐field (CMF) theory including a finite‐cluster‐size‐scaling. The SF, MI, and normal fluid (NF) phases are characterized as well as the transition or crossover temperatures between them are estimated by computing physical quantities such as the superfluid fraction, compressibility and sound velocity using the CMF method. It is found that the nonlocal correlations included in a finite cluster, when extrapolated to infinite size, leads to quantitative agreement of the phase boundaries with quantum Monte Carlo (QMC) results as well as with experiments. Moreover, it is shown that the von Neumann entanglement entropy within a cluster corresponds to the system's entropy density and that it is enhanced near the SF–MI quantum critical point (QCP) and at the SF–NF boundary. The behavior of the transition lines near this QCP, at and away from the particle‐hole (p–h) symmetric point located at the Mott‐tip, is also discussed. The results obtained by using the CMF theory can be tested experimentally using the quantum gas microscopy method.

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Observation of Quantum Criticality with Ultracold Atoms in Optical Lattices

Cited by 133 publications

References 33 publications

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

Fluctuations and quantum criticality in the two‐dimensional Bose Hubbard model

Nonlocal Correlation and Entanglement of Ultracold Bosons in the 2D Bose–Hubbard Lattice at Finite Temperature

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