Nondestructive interaction-free atom-photon controlled-NOT gate

We present a probabilistic (ideally 50%) nondestructive interaction-free atom-photon controlled-NOT gate, where nondestructive means that all four outgoing target photon modes of the gate are available and feed-forwardable. Individual atoms are controlled by a simulated Raman adiabatic passage transition and photons by a ring resonator with two outgoing ports. Realistic estimates we obtain for ions confined in a Paul trap around which the resonator is mounted show that a strong atom-photon coupling can be achieved. It is also shown how the resonator can be used for controlling superposition of atom states.

Figure 1

Schematic of an interaction-free device according to Ref. 20. A single photon enters the resonator. $M$’s are perfect mirrors (total-reflection Pellin-Broca prisms can be substituted for $M$’s for higher efficiency [20]). ABS’s are highly asymmetrical mirrors with $R=0,999$ or higher (with frustrated total reflection, i.e., optical tunneling [20]). (a) When there is no object in its path the photon exits into $D_t$ (with a realistic efficiency of over 98%). (b) When there is an object in its path, the photon is reflected into $D_r$.

Figure 2

$r$ as a function of $\mathcal{T}∕T$ for $\rho =0.99$ and $0.9⩽R⩽1$: $\mathcal{T}∕T=500$ (top), 150, 50, 20, and 10 (bottom). The differences in the shapes stem from the amount of losses.

Figure 3

(a) STIRAP $\mid g_1⟩\leftrightarrow \mid g_2⟩$ in which the population of $\mid e⟩$ is completely avoided is obtained by subsequent application of two laser beams of frequencies ${\omega }_2$ and ${\omega }_1$, detuned by amount $\Delta$. The ${\omega }_2$ one is called the “Stokes beam” and it corresponds to Rabi frequency ${\Omega }_2$. The ${\omega }_1$ one is called the “pump beam” (with Rabi frequency ${\Omega }_1$). (b) Two pump beams (${\Omega }_1$, ${\Omega }_2$) and a cavity with atom-cavity coupling $\left(G\right)$ instead of the Stokes laser beams produce superposition $\alpha \mid g_1⟩+\beta \mid g_2⟩$.

Figure 4

Interaction-free CNOT operation. (a) The atom is in state $\mid g_1⟩$ and can absorb a $-45°$ polarized photon. Therefore a photon in state ∣1⟩ cannot enter the cavity and thus $\mid 0⟩\to \mid 0⟩$ and $\mid 1⟩\to \mid 1⟩$. (b) The atom is in state $\mid g_2⟩$ and can absorb a $+45°$ polarized photon. Therefore photon ∣0⟩ cannot enter the cavity and thus $\mid 0⟩\to \mid 1⟩$ and $\mid 1⟩\to \mid 0⟩$. ABS are highly asymmetrical beam splitters with $R=0.999$; SBS is a symmetric 50:50 beam splitter; $M$ are perfect mirrors; PBS is a polarizing beam splitter which lets ∣0⟩ photons through and reflects ∣1⟩ photons; HWP and QWP are half- and quarter-wave plates, respectively—the plates in the resonator turn linear polarization into circular and back into linear and HWP after PBS turns ∣0⟩ (∣1⟩) photon into ∣1⟩ (∣0⟩) photon; $D$ is a detector—ideally, when it does not click, the target qubit exits at the other side of SMS.

Figure 5

Transitions which make an atom opaque for photons in the interaction-free resonators of Fig. 4. If an electron is in one of the $\mid g⟩$ states, then a photon will exit through one port of the gate, and if not, through the other.