Exploring light-induced phases of 2D materials in a modulated 1D quasicrystal

Abstract

Light-induced quantum phases offer the potential for simple and powerful tuning of material properties. For example, simply illuminating 2D materials in the integer quantum Hall regime with polarized light is predicted to drive quantum phase transitions. Such phenomena are largely beyond the current frontier of solid state experiments due to technical limitations on laser intensity and material purity. However, the Harper-Hofstadter mapping which relates a two-dimensional integer quantum Hall system to a 1D quasicrystal enables the same polarization-dependent light-induced phase transitions to be observed using a quantum gas in a driven quasiperiodic optical lattice. We report results of such an experiment. We observe an interlaced phase diagram of localization-delocalization phase transitions as a function of drive polarization and amplitude. Elliptically polarized driving can stabilize an extended critical phase featuring multifractal wavefunctions; we observe signatures of this phenomenon in anomalous polarization-dependent subdiffusive transport. In this regime, increasing the strength of the quasiperiodic potential can enhance rather than suppress transport. These experiments demonstrate a simple method for synthesizing exotic multifractal states and exploring light-induced quantum phases across different dimensionalities.

Figures (7)

• Figure 1: Correspondence between modulated 1D quasicrystal and optically-driven 2D crystal. a, The undriven 1D AAH system undergoes a localization phase transition as the quasiperiodic strength $\Delta$ increases, diagnosed by the inverse participation ratio (IPR) and the density profiles of a representative eigenstate. The localization phase transition in 1D is mapped to a 90${}^\circ$ rotation of directional localization in 2D, as shown by the calculated time-evolved 2D density profile. b, The 1D quasicrystal is subjected to both dipolar and phasonic modulation. In 2D, the quasiperiodic strength $\Delta$ becomes the tunneling along the additional dimension and thus controls the tunneling anisotropy see also Appendix \ref{['apd:HHmap']}). The dipolar and phasonic modulations map to orthogonal components of the vector potential of the irradiation in 2D.
• Figure 2: Interlaced localization-delocalization quantum phase transitions controlled by polarized driving. Figure shows theoretically predicted and experimentally measured phase diagrams at quasiperiodic strengths $\Delta/J \approx 1.2$, $2.5$ and $4.7$; below, near and above the critical strength without driving. Axes represent dipolar and phasonic components of the drive in 1D, corresponding to $x$ and $y$ components of the driving electric field in 2D. a-c Theoretically calculated inverse participation ratio (IPR) averaged over all Floquet eigenstates in the central Brillouin zone. System size is 200 lattice sites. d-f Measured effective fractional width $\sigma_\mathrm{eff}$ after $t_\mathrm{hold} = 1.25 \, \mathrm{s} \approx 400 \, T_J$. The patched data point in (d) is cut due to significant atom loss. All data, theoretical or experimental, are taken with $\vartheta=\pi/2$ (elliptical polarization).
• Figure 3: Elliptically polarized driving induces exotic transport. Phasonic driving modifies the dynamically localized state ($K_0\approx 2.405$) in a polarization-dependent way. a, Fractional expansion $\sigma$ as a function of phasonic modulation amplitude $\varphi_0$, for elliptical (circles) or linear (diamonds) polarization. For these data $t_\mathrm{hold} = 10 \, \mathrm{s}$ and $\hbar\omega = h\times 500\, \mathrm{Hz} \approx 9.8J$. Dashed lines and shaded areas represent the theoretically predicted phase transition into a multifractal phase $\vert\Delta_\mathrm{eff}\vert = 2\vert J_\mathrm{EP} \vert$ (see Eq.\ref{['eq:H1']} and Han_HarperNNN_PhysRevB.50.11365, and discussion in the text) for elliptically polarized driving. Error bars represent standard error of the mean (s.e.m.) of repeated measurements. b, Theoretically calculated fractal dimension $D_2$ of all eigenstates, zoomed in to the region $\varphi_0\in [1.8,3.2]$. c, Measured expansion exponents for elliptically and linearly polarized driving, using the same experimental parameters. Error bars represent 95% confidence interval of the fit. Inset is a visualization of the effective Hamiltonian under elliptical polarization in 2D, where red dashed arrows represent NNN hopping (Eq. \ref{['eq:H1']}).
• Figure 4: Anomalous expansion under elliptically polarized modulation is enhanced by the quasiperiodic strength. As the quasiperiodic strength $\Delta$ is increased, the expansion increases in the shaded region representing a multifractal phase, but remains localized otherwise. Here the condensate expands for $t_\mathrm{hold} = 10\, \mathrm{s}$ for all data sets. Error bars represent s.e.m. of repeated measurements.
• Figure 5: Unscaled fractional expansion $\sigma$ under dipolar and phasonic amplitudes. While the delocalized regions are still visible, their contrast is lower due to effectively reduced kinetic energy. Dashed white curves represent the theoretically predicted phase boundary.