Noise- and disorder-resilient optical lattices

We show how a dressed lattice scheme can provide control over certain types of noise for atomic quantum gases in the lowest band of an optical lattice, removing the effects of global lattice amplitude noise to first order for particular choices of the dressing field parameters. We investigate the nonequilibrium many-body dynamics of bosons and fermions induced by noise away from this parameter regime, and show how the same technique can reduce spatial disorder in projected lattice potentials.

Figure 1

(a) Laser intensity fluctuations give rise to amplitude noise on an optical lattice potential which can produce different heating processes depending on the intensity noise spectrum $S_I\left(\omega \right)$. (b) Noise with frequencies of the order of Bloch band separations can give rise to interband transitions (red/gray arrow), while processes with frequencies of the order of $J$ and $U$ will give rise to intraband heating (blue/dark gray arrows).

Figure 2

(a) Schematic plot showing coupled internal states used to create dressed lattices for noise or disorder suppression. Two long-lived states $|g\rangle$ and $|h\rangle$ have far-detuned optical lattices created from the same laser (i.e., with identical intensity fluctuations). (b) These internal states are coupled to give rise to a dressed lattice. If the lattice for $|g\rangle$ is blue detuned, and the lattice for $|h\rangle$ red detuned (as indicated by the dashed lines, showing the energy at zero ac-Stark shift), then when the lattice depth increases, the effective detuning decreases, allowing for a larger admixture of $|h\rangle$, and hence an increase in the effective tunneling rate of the dressed atoms. (c) Correlation parameter $\xi$ for different detunings and couplings in an isotropic three-dimensional (3D) lattice of depth $V=7E_R$ along each dimension. (d) Reduction of disorder, shown as the absolute value of the multiplication factor $\left|f\right(p,q\left)\right|$ from Eq. (5) for a 3D lattice with $V=7E_R$, plotted along the lines of symmetry of the first Brillouin zone, i.e., connecting the points $\Gamma =(0,0,0),X=(\pi /a,0,0),R=(\pi /a,\pi /a,\pi /a)$, and $M=(0,\pi /a,\pi /a)$, computed from coupling the lowest Bloch bands.

Figure 3

(a) Short-time ($tJ\le 2$) heating rates of superfluid ($U=2J$) and Mott insulator states ($U=6J$) in 1D as a function of the relative magnitude of noise on $J$ and $U$, $\theta$. Results are from linear regression over 500 t-DMRG trajectories in a system with $M=30$ sites and $N=30$ particles with open boundary conditions. In both cases heating is strongly suppressed in the vicinity of the sweet spot at $\theta \sim 0.25\pi$ (expanded in the inset). Dashed lines show results in the presence of a harmonic trap with ${\varepsilon }_i/J=0.0356i^2$, $\sqrt{S}(d{\varepsilon }_i/dV)/{\varepsilon }_i=5\times {10}^{-3}{J}^{-1/2}$, and $N=30$ (t-DMRG bond dimension $D=100$). (b), (c) The effect of amplitude noise on parity-parity correlations on an initial Mott insulator state ($U=6J$), with anticorrelated noise $\theta =0.75\pi$. (b) Short-time evolution for a single noise trajectory with $M=30$ (t-DMRG bond dimension $D=200$). (c) Long-time evolution of these correlations calculated for $M=10$ sites averaged over 1000 noise trajectories. (For all parts, $\lambda =0.02J^{-1/2}$, time step $\Delta t={10}^{-2}/J$.)

Figure 4

Heating rates around the sweet spot for a two-species Fermi-Hubbard model in 1D, with an initial antiferromagnetic ground state with interspecies interaction $U=10J$. The noise is parametrized as in Fig. 3. The solid lines show a system with $M=30$, and 15 particles of each species, the dashed lines a trapped case with ${\varepsilon }_i/J=0.015i^2$, and 20 particles of each species.