Quantum-noise quenching in atomic tweezers

The efficiency of extracting single atoms or molecules from an ultracold bosonic reservoir is theoretically investigated for a protocol based on lasers, coupling the hyperfine state in which the atoms form a condensate to another stable state, in which the atom experiences a tight potential in the regime of collisional blockade, the quantum tweezers. The transfer efficiency into the single-atom ground state of the tight trap is fundamentally limited by the collective modes of the condensate, which are thermally and dynamically excited. The noise due to these excitations can be quenched for sufficiently long laser pulses, thereby achieving high efficiencies. These results show that this protocol can be applied to initializing a quantum register based on tweezer traps for neutral atoms.

Figure 1

An atom is transferred from a Bose-Einstein condensate (prepared in the electronic state $|b\rangle$) to the ground state of a tweezer trap (realized when the atom is in state $|a\rangle$) by a Raman or microwave transition coherently coupling the two stable states. The protocol is based on spectrally resolving the one-atom ground state of the tweezer trap, which is in the collisional blockade regime [19]. The efficiency of the extraction protocol can be enhanced by quenching the quantum noise caused by the condensate excitations.

Figure 2

(a) Efficiency $P$ of preparing the tweezers in state $|1\rangle {}_a$ ($\theta =\pi /2$) as a function of ${\Omega }_{\mathrm{eff}}$ and at the corresponding time $\tau ={\tau }_0$, for $g_{\mathit{ab}}=g_b$. The arrows indicate the values of ${\Omega }_{\mathrm{eff}}$ used in (b) and (c). $P$ is displayed in (b) at ${\Omega }_{\mathrm{eff}}=2\pi \times 1.7$ kHz and in (c) at ${\Omega }_{\mathrm{eff}}=2\pi \times 17$ kHz as a function of the interparticle collision strength $g_{\mathit{ab}}$ (in units of $g_b$). (d) Same as (b) but for state $\theta =\pi /4$. The reservoir is here a condensate of ${}^{87}\mathrm{Rb}$ atoms in a spherical harmonic trap with ${\omega }_b=2\pi \times 200$ Hz and density at the trap center $n=2\times {10}^{21}\hspace{0.5em}{\mathrm{m}}^{-3}$ ($3\times {10}^6$ atoms). The tweezer trap frequency is ${\omega }_a=2\pi \times 1$ MHz, such that ${\omega }_{\mathrm{gap}}~2\pi \times 0.2$ MHz. The curves are evaluated at $T=0$ (solid line), $T=300$ nK (dash-dotted line) for the frequency of the Bogoliubov modes ${\omega }_{j,\ell }=\sqrt{2j^2+2j\ell +3j+\ell }$ [24, 25]: the gray (black) lines are a sum over $j\in [1,500]$ and $\ell =0$ ($\ell =0,2$). The dashed horizontal line marks the efficiency when $g_{\mathit{ab}}=0$ and $T=0$. The solid-thick-black line in (d) corresponds to the efficiency of preparing state $|1\rangle {}_a$ at $T=0$ [same as the solid-black line in (b)].

Figure 3

(a) Efficiency of preparing the tweezers in state $|1\rangle {}_a$ as a function of ${\omega }_b$ for a condensate of ${}^{87}\mathrm{Rb}$ atoms at $T=0$ and for $g_{\mathit{ab}}=4g_b$ (solid lines) and $g_{\mathit{ab}}=g_b$ (dashed lines). The curves are found summing up to 500 Bogoliubov modes, for either constant atomic number of atoms $3\times {10}^6$ (thick lines) or constant density $n=2\times {10}^{21}$ ${\mathrm{m}}^{-3}$ (thin lines). Plots (b) and (c) display the corresponding dependence of density and atom number on ${\omega }_b$. The other parameters are as in Fig. 2.