Figure 1

(Color online) Schematic representations of (a) cyclic shifting, (b) mirror reflection, and (c) color-inversion symmetry for a 1D lattice with periodic boundary conditions. The colors represent atoms in two different hyperfine states $a$ and $b$.Reuse & Permissions

Figure 2

(Color online) Schematic energy-level structure for the two-component BHM with only one varying parameter $U/J$ and fixed $U/V$. The no-crossing rule assures that the system follows the instantaneous eigenstates and performs no level crossings if the states have all the same symmetry, there is only one varying parameter, and the evolution is performed sufficiently slowly.Reuse & Permissions

Figure 3

(Color online) (a) Spectrum of the two-component BHM $\widehat{H}$ for $M=6$ sites in the symmetric subspace ${\mathcal{S}}_6$, i.e., with $N_a=N_b=6$, as a function of $V/J$ with $U/V=0.1$ throughout. To the far left (not plotted) where $V/J⪢1$ the state $|{\Psi }_{ab}⟩$ is the nondegenerate ground state. To the right where $V/J=0$ the noninteracting SF state $|{\Psi }_{\text{sf}}^6⟩$ is the nondegenerate ground state. As expected, these two ground states are adiabatically connected (solid line). The first and second excited states (dotted and dashed lines, respectively) are also shown and become degenerate in the $V=0$ limit. (b) Overlap $\mathbf{\left|}⟨{\psi }_{\text{gs}}|{\Psi }_{\text{sf}}^{6,6}⟩\mathbf{\right|}$ between the instantaneous ground state $|{\psi }_{\text{gs}}⟩$ and the SF state $|{\Psi }_{\text{sf}}^{6,6}⟩$ as a function of $V/J$.Reuse & Permissions

Figure 4

(Color online) (a) Overlap of the initial ground state after evolution with the final ground state (twin Fock state) for different ramping times. We assume a linear ramp with $V_{\text{max}}/J=10$, $M=6$ sites, $N_a=N_b=6$, and $U/V=0.1$ throughout. (b) Maximum value during ramping of the ratio $\lambda$ in Eq. (7) as a function of the ramping time $t_r$.Reuse & Permissions

Figure 5

(Color online) (a) Melting of the product MI $|{\Psi }_{ab}⟩$ into the twin Fock SF state $|{\Psi }_{\text{tf}}⟩$. (b) Two internal states $a$ and $b$ represent the arms of an interferometer with the rotations R1, R2, and the phase shift $\varphi$ induced by appropriate laser pulses. Finally, a $\varphi$-dependent observable is measured at $\mathcal{M}$ from which $\varphi$ can be deduced.Reuse & Permissions

Figure 6

(Color online) (a) Low-energy spectrum of the two-component BHM $\widehat{H}$ for $M=6$ sites in the symmetric subspace ${\mathcal{S}}_4$ as a function of $U/J$ with $V/U=0.1$ throughout. The initial state $|{\Psi }_{aa+bb}⟩$ projected in this subspace is $|{\Psi }_{\text{ps}}^4⟩$. The adiabatic evolution of this state involves the ground state and the two lowest-lying excited states. In the SF limit with $U=0$ the first excited level is triply degenerate. Consistent with the no-crossing rule, we see that energy levels within ${\mathcal{S}}_4$ repel each other and only avoided crossings are seen. (b) Momentum distribution $⟨{\widehat{\mathtt{\text{n}}}}_k^a⟩$ for one component (it does not matter which, due to color symmetry) of the final adiabatically melted state $|{\Psi }_{\text{f}}⟩$ derived from $|{\Psi }_{aa+bb}⟩$ with $M=6$.Reuse & Permissions

Figure 7

(Color online) (a) Momentum-space particle number correlations $⟨{\widehat{\mathtt{\text{n}}}}_k^a{\widehat{\mathtt{\text{n}}}}_q^a⟩$ of the final melted state $|{\Psi }_{\text{f}}⟩$ for one component (it does not matter which due to color symmetry) for $M=6$. (b) Interspecies momentum-space particle number correlations $⟨{\widehat{\mathtt{n}}}_k^a{\widehat{\mathtt{n}}}_q^b⟩$ for $|{\Psi }_{\text{f}}⟩$.Reuse & Permissions

Figure 8

(Color online) (a) Number of MI ground states $\left(d_{\text{MI}}\right)$ that belong to each of the $g\left(9,18\right)=765$ independent states for finite $J$ for a lattice with $N/2=N_a=N_b=18$ and $U>V$. (b) Number of independent states with a given degeneracy $d_{\text{MI}}$. The total number of independent states is equal to $g\left(9,18\right)=765$. (c) First energy levels $(\ast )$ in the SF regime $\left(U=V=0\right)$ and their degeneracy $f$ (bar plot) for $M=18$. The points $(○)$ show the quadratic approximation to the dispersion relation. We plot only the first states such that ${\sum }_{l}f\left(l\right)=g$ for $g=765$.Reuse & Permissions

Figure 9

(Color online) (a) Momentum distribution of the final SF state $|{\Psi }_f⟩$ obtained via adiabatically melting the MI state $|{\Psi }_{aa+bb}⟩$ with $N_a=N_b=M=20=N/2$ and $U/V>1$. (b) Depletion $D=1-⟨{\widehat{\mathtt{n}}}_0^a⟩/N_a$ of the melted state $|{\Psi }_f^{N/2}⟩$ for $U/V>1$ as a function of the number of particles $N$. The solid line shows the best logarithmic fit $-0.0748{\left(\text{ln}N/2\right)}^2+0.8201\text{ln}N/2-1.3633$ to the calculated values (shown as $○$).Reuse & Permissions

Figure 10

(Color online) (a) Momentum correlations $⟨{\widehat{\mathtt{\text{n}}}}_k^a{\widehat{\mathtt{\text{n}}}}_q^a⟩$ for one mode for the state $|{\Psi }_f⟩$ obtained via the adiabatic melting of $|{\Psi }_{aa+bb}⟩$ with $N=40$ and $U/V>1$. (b) Interspecies momentum correlations $⟨{\widehat{\mathtt{n}}}_k^a{\widehat{\mathtt{n}}}_q^b⟩$ of $|{\Psi }_f⟩$ with $N=40$. Note that a twin Fock state (8) would show only a central peak in both distributions.Reuse & Permissions