Figure 1

Experimental scheme. (a) State-selective Kapitza–Dirac diffraction of a two-component Bose–Einstein condensate. (b) Four-wave mixing (solid arrows) with pump modes $|b,0⟩$, $|a,2⟩$ and seed mode $|a,0⟩$ transfers $|b⟩$ atoms to the output mode $|b,2⟩$. Because of the symmetry of the problem, the process also occurs for the modes $|a,-2⟩$ and $|b,-2⟩$ (dashed arrows).Reuse & Permissions

Figure 2

Typical absorption images taken after application of the state-selective Kapitza–Dirac pulse (${\tau }_{\mathrm{KD}}=25\mu \mathrm{s}$, $V_a=6E_R$), 15 ms time of flight and Stern–Gerlach separation along $x$, for the case of (a) only $|a⟩$ atoms present ($f_a=1$), (b) only $|b⟩$ atoms ($f_a=0$), and (c) equal populations of both components ($f_a=0.5$).Reuse & Permissions

Figure 3

Mode populations after four-wave mixing. (a) Fraction of atoms with momenta $\pm 2\hslash k_L$ in state $|a⟩$ (green circles) and $|b⟩$ (orange squares). (b) Populations $|c_{n\alpha }{|}^2=N_{n\alpha }/N$ of the modes $|\alpha ,n⟩$, as indicated in the plaquette. The dashed lines (1), (2), and (3) indicate the initial conditions before FWM, $|b_0(0){|}^2$, $|a_0(0){|}^2=|a_{\pm 2}(0){|}^2$, and $|b_{\pm 2}(0){|}^2$ (where $\pm 2$ indicates the combined populations). The arrows indicate the temporal evolution of the populations. The solid lines represent the predictions of the model ($V_a=5.6E_R$, ${\tau }_{\mathrm{KD}}=25\mu \mathrm{s}$, ${\omega }_z=2\pi \times 51\mathrm{Hz}$, $N=1.4\times {10}^5$). The inset shows the transferred $|b⟩$ population vs the transferred $|a⟩$ population, where the dashed line represents a slope of unity. (c) Growth of the population in $|b,\pm 2⟩$ following the Kapitza–Dirac pulse for $V_b=0$ (orange squares) and for $V_b=V_a$ (blue triangles, $\times 1/2$). The FWM was interrupted after a variable time $\tau$ by blasting away the $|a⟩$ atoms. Each data point is averaged over 2–6 runs (here, ${\omega }_z=2\pi \times 41\mathrm{Hz}$, $f_a=0.5$). The dashed lines are the predictions of the uncorrected model (including higher order FWM terms), whereas the solid lines take into account the loss of atoms during the blasting process (see text). The blast-loss model was calibrated by fitting to the $V_b=V_a$ data.Reuse & Permissions

Figure 4

Four-wave mixing effects for an adiabatically ramped-up optical lattice. (a) An $|a⟩$-selective lattice is ramped up to a depth of $6.0E_R$ within 100 ms onto an equal mixture ($f_a=0.5$). After release and 17 ms time of flight, $|b⟩$ atoms appear in $|\pm 2⟩$. (b) Growth of population in $|b,\pm 2⟩$ as determined by blasting away the $|a⟩$ atoms after an evolution time $\tau$. Each data point is averaged over 6 runs.Reuse & Permissions