Enhancing molecular conversion efficiency by a magnetic field pulse sequence

We propose a strategy to enhance the atom-to-molecule conversion efficiency near a Feshbach resonance. Based on the mean-field approximation, we derive the fixed point solutions of the classical Hamiltonian. Rabi oscillation between the atomic and molecular states around fixed point solutions and its oscillation period are discussed. By designing a sequence of magnetic field pulses in analogy with Ramsey experiments, we show that a much higher atom-to-molecule conversion efficiency can be accessed by tuning the pulse durations appropriately.

Figure 1

Time dependence of Rabi oscillations for (a) ${ϵ}_{\text{m}}/g=-0.8$ and (b) ${ϵ}_{\text{m}}/g=0$. (c) The period of Rabi oscillation versus ${ϵ}_{\text{m}}/g$, where ${ϵ}_{\text{m}}\le 0$ is assumed. Note that all quantities have already been renormalized to be dimensionless.

Figure 2

(a) Time dependence of the atomic and molecular populations. (b) Schematic time dependence of ${ϵ}_{\text{m}}\left(t\right)$ under the sequence of magnetic field pulses. The horizontal line in (a) indicates the limit of the complete conversion of molecules, i.e., ${\rho }_{\text{m}}=1/2$. The two vertical lines separate the evolution process into three regions (I, II, and III) corresponding to the time-dependent magnetic field pulses. Durations of each region is denoted by $T_i$ ($i=1$, 2, and 3).

Figure 3

(Color online) Energy contour for (a) ${ϵ}_{\text{m}}/g=-0.8$ and (b) ${ϵ}_{\text{m}}/g=-50$ in the phase space of ${\rho }_{\text{m}}$ and $\theta$. The arrows show the evolution direction. The extreme points (marked by the plus sign) correspond to the fixed point solutions discussed in Sec. 3. ${\rho }_{\text{m}}=1/2$ is unmarked due to the not well defined $\theta$. Note that $\alpha$ $\left(\beta \right)$ and ${\alpha }^{\prime }$ $\left({\beta }^{\prime }\right)$ refer to the same point in the phase space.