Three-level atom optics via the tunneling interaction

Three-level atom optics is introduced as a simple, efficient, and robust method to coherently manipulate and transport neutral atoms. The tunneling interaction among three trapped states allows us to realize the spatial analog of the stimulated Raman adiabatic passage, coherent population trapping, and electromagnetically induced transparency techniques and offers a wide range of possible applications. We investigate an implementation in optical microtrap arrays and show that under realistic parameters the coherent manipulation and transfer of neutral atoms among dipole traps could be realized in the millisecond range.

Figure 1

Three-trap potential; $d^{LM}$ $\left(d^{MR}\right)$ is the separation between left and middle (middle and right) traps. In the limit of a large separation ${\mid n⟩}_L,{\mid n⟩}_M,{\mid n⟩}_R$ are the $n$th vibrational energy eigenstates of the corresponding single trap potentials.

Figure 2

(a) Approaching sequence for a STIRAP-like process, and (b) the corresponding ground-state populations; $d_{\max }^{LM}\alpha =d_{\max }^{MR}\alpha =9$, $d_{\min }^{LM}\alpha =d_{\min }^{MR}\alpha =1.5$, $t_r^{LM}{\omega }_x=t_r^{MR}{\omega }_x=300$, $t_i^{LM}{\omega }_x=t_i^{MR}{\omega }_x=0$, and $t_{\text{delay}}{\omega }_x=120$. (c) Transfer efficiency from ${\mid 0⟩}_L$ to ${\mid 0⟩}_R$ as a function of the time delay $t_{\text{delay}}$ between the two trap approaches (horizontal axis) and of the amplitude of a shaking in the positions of the outer traps (vertical axis) with ${\omega }_{\mathrm{shake}}={10}^{-2}{\omega }_x$; all other parameters as above. For $a_{\text{shake}}>0$, the shaking of the outer traps is in phase; for $a_{\text{shake}}<0$ it is out of phase by $\pi$. (d) Transfer efficiency for an additional tilted potential $V_{\mathrm{tilt}}\left(x\right)=\gamma \hslash {\omega }_x\alpha x$ parametrized by $\gamma$ as a function of the time $t_r$ needed to approach and separate the traps; all other parameters as in (b); $t_{\text{delay}}$ has been chosen as $t_{\text{delay}}=0.4t_r$.

Figure 3

(a) Approaching sequence for a CPT-like process; (b) ground state and dark state populations, $p_{\text{dark}}={\mathbf{\mid }⟨D(\Theta =\pi ∕2)\mathbf{\mid }\psi \left(t\right)⟩\mid }^2$; parameters as in Fig. 2 except for $t_i^{LM}{\omega }_x=0$, $t_i^{MR}{\omega }_x=t_{\text{delay}}{\omega }_x=180$ for $t{\omega }_x⩽780$ and $t_i^{MR}{\omega }_x=t_{\text{delay}}{\omega }_x=0$ for $t{\omega }_x>780$. (c) Dark state population $p_{\text{dark}}$ after the CPT process as a function of the time $t_r$ used to approach and separate the traps (horizontal axis) and of the amplitude $a_{\text{shake}}$ of a shaking in the trap positions (vertical axis). For $a_{\text{shake}}>0$, the shaking of the outer traps is in phase; for $a_{\text{shake}}<0$, it is out of phase by $\pi$; ${\omega }_{\text{shake}}={10}^{-2}{\omega }_x$ and all other parameters as above except for $t_{\text{delay}}=0.6t_r$. (d) $p_{\text{split}}$ [see Eq. (4)] for an additional tilted potential as in Fig. 2d parametrized by $\gamma$ as a function of the time $t_r$ needed to approach and separate the traps; parameters as in (c).

Figure 4

(a) Approaching sequence for an EIT-like process, and (b) corresponding ground-state populations; $d_{\max }^{LM}\alpha =d_{\max }^{MR}\alpha =9$, $d_{\min }^{LM}\alpha =d_{\min }^{MR}\alpha =1.5$, $t_r^{LM}{\omega }_x=t_r^{MR}{\omega }_x=300$, $t_i^{LM}{\omega }_x=50$, $t_i^{MR}{\omega }_x=200$, and $t_{\text{delay}}{\omega }_x=120$. (c) Ground-state populations as a function of the time delay.

Figure 5

Three-level atom optics for the first excited vibrational states: (a) transfer efficiency for STIRAP (dashed line: efficiency for the ground-state STIRAP for the same parameters); and (b) population for the coherent splitting between ${\mid 1⟩}_L$ and ${\mid 1⟩}_M$; the parameters are (a) $t_r^{LM}{\omega }_x=t_r^{MR}{\omega }_x=300$, $t_i^{LM}{\omega }_x=t_i^{MR}{\omega }_x=0$, (b) $t_r^{LM}{\omega }_x=550,t_r^{MR}{\omega }_x=400$, $t_i^{LM}{\omega }_x=75,t_i^{MR}{\omega }_x=400$. In both cases $d_{\max }^{LM}\alpha =d_{\max }^{MR}\alpha =9$ and $d_{\min }^{LM}\alpha =d_{\min }^{MR}\alpha =1.5$.