Photonic multiqubit states from a single atom

We propose a protocol for the creation of photonic Greenberger-Horne-Zeilinger and linear cluster states emitted from a single atom—or ion—coupled to an optical cavity field. The method is based on laser pulses with different polarizations and exploits the atomic transition amplitudes to state-selectively achieve the desired transitions. The scheme lies within reach of current technology.

Figure 1

Relevant fine level structure of ${}^{40}\mathrm{Ca}$. Only photons (red wavy lines) with ${\sigma }^{+}$ or ${\sigma }^{-}$ circular polarizations can decay into the cavity (resonant with $4S_{1/2}\leftrightarrow 4P_{1/2}$). (a) A $\pi$-polarized laser (blue lines) resonantly excites both ground-state sublevels $|4S_{1/2},m_J=\pm 1/2\rangle$ to the $4P_{1/2}$ manifold. The total effective process including spontaneous photon emission is represented by green dashed lines, and its successive repetition creates a GHZ state. (b) Same as (a) but with the laser possessing also a ${\sigma }^{+}/{\sigma }^{-}$-polarization component. Two effective processes are driven simultaneously by the same pulse, and its repetition generates a linear cluster state.

Figure 2

Relevant hyperfine level structure of ${}^{87}\mathrm{Rb}$. The cavity is resonant with the $1\leftrightarrow 2^{\text{'}}$ transition. (a) Two $\pi$-polarized lasers (blue lines), respectively, in resonance with $2\leftrightarrow 1^{\text{'}}$ and $1\leftrightarrow 1^{\text{'}}$, drive a STIRAP (green dashed lines) that partially transfers population from $|1,\pm 1\rangle$ to $|2,\pm 1\rangle$. (b) A bichromatic ${\sigma }^{+}/{\sigma }^{-}$-polarized laser, with color components, respectively, in resonance with $1\leftrightarrow 2^{\text{'}}$ and $2\leftrightarrow 2^{\text{'}}$, state selectively excites the atom to the $2^{\text{'}}$ manifold. State selection is achieved exploiting the dipole matrix elements, indicated in panel (c) in arbitrary units, and is such that excitations to the $|2,0\rangle$ state are blocked. Thus, photon emissions (red wavy lines) only from levels $|2^{\text{'}},\pm 2\rangle$ occur, giving rise to the effective process shown in green-dashed lines. The composed action of (a) and (b) implements transformation (1a). (d) If these processes are in turn preceded by a $\pi /2$ rotation between states $|1,\pm 1\rangle$, transformation (1b) is obtained. Such rotation is driven by a Raman transition induced by a ${\sigma }^{+}/{\sigma }^{-}$-polarized monochromatic laser $\Delta$-detuned from $1\leftrightarrow 1^{\text{'}}$. The optimal detuning is $\Delta ={\omega }_0^{\text{'}}/2$, with ${\omega }_0^{\text{'}}$ being the frequency difference between $1^{\text{'}}$ and $2^{\text{'}}$.