Techniques to measure quantum criticality in cold atoms

Abstract

Attempts to understand zero temperature phase transitions have forced physicists to consider a regime where the standard paradigms of condensed matter physics break down [1-4]. These quantum critical systems lack a simple description in terms of weakly interacting quasiparticles, but over the past 20 years physicists have gained deep insights into their properties. Most dramatically, theory predicts that universal scaling relationships describe their finite temperature thermodynamics up to remarkably high temperatures. Unfortunately, these universal functions are hard to calculate: for example there are no reliable general techniques [4,5] to calculate the scaling functions for dynamics. Viewing a cold atom experiment as a quantum simulator [6], we show how to extract universal scaling functions from (non-universal) atomic density profiles or spectroscopic measurements. Such experiments can resolve important open questions about the Mott-Metal crossover [7,8] and the dynamics of the finite density O(2) rotor model [1,9], with direct impact on theories of, for example, high temperature superconducting cuprates [10,11], heavy fermion materials [12], and graphene [13].Comment: 12 double spaced pages (main text), 12 double spaced pages (supplementary information), 4 figures (10 panels

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

“…(15) is not a function of µ−µc T alone. If one uses the Hazzard-Mueller [30] prescription, the entirety of Eq. (19) has to be treated as n reg (µ, T ), whence the LHS of Eq.…”

“…The scaled density n(µ, T )t/T (where temperature T is expressed in energy units so that β ≡ 1/T ) near the Mottsuperfluid transition is expected to show universal scaling that is characteristic of the quantum critical point at low enough temperatures [19,30]. The scaling theory requires the scaled density to be a universal scaling function of the form…”

“…A key issue in this context is the choice of n reg . In the prescription by Hazzard and Muller [30], n reg is the t = 0 density, and in the prescription of Zhou and Ho [19], n reg = 0 for the vacuum to superfluid transition.…”

Quantitative studies of the critical regime near the superfluid-to-Mott-insulator transition

“…Besides of quantum phase diagrams and transition boundaries, more and more attention are drawn to investigate the critical properties near the phase transition points [8][9][10][11][12][13][14][15][16][17][18][19], because finite temperature and finite size effects are very important and unavoidable in a cold atom experiment. From theoretical points of view, critical regime is mainly controlled and determined by the effective theory near the transition point, while the validity of the effective theory has to be determined only by higher order effects or full numerical simulations.…”

Quantum fluctuation-driven first-order phase transitions in optical lattices

“…Several schemes have been proposed to determine the critical properties by extracting the universal scaling functions from the atomic density profiles [1][2][3] . The experimental observations of quantum critical behaviors of ultracold atoms have also been reported 4,5 .…”