Exploiting the coupling between a Rydberg atom and a surface phonon polariton for single-photon subtraction

We investigate a hybrid quantum system that consists of a superatom coupled to a surface phonon-polariton. We apply this hybrid quantum system to subtract individual photons from a beam of light. A Rydberg atom blockade is used to attain absorption of a single photon by an atomic microtrap. Surface phonon-polariton coupling to the superatom then triggers the transfer of the excitation to a storage state, a single Rydberg atom. The approach utilizes the interaction between a superatom and a Markovian bath that acts as a controlled decoherence mechanism to irreversibly project the superatom state into a single Rydberg atom state that can be read out.

Figure 1

(a) Schematic view of the photon subtraction and counting concept. Atoms are trapped above an atom chip. On top of the chip is a dielectric substrate. Laser beams parallel to the chip surface excite atoms into a superatom state. The decay of the superatom is resonantly enhanced by coupling to a SPP, shown in the foreground. (b) Level scheme for single-photon absorption. A two-photon excitation, with coupling constants ${\Omega }_{\mathrm{sm}}$ and ${\Omega }_{\mathrm{ex}}$, produces a single excitation in a Rydberg state $|a\rangle$ shared by the trapped atoms. From there it decays with an enhanced rate ${\Gamma }_{\mathrm{sf}}$ due to the SPP coupling to $|s\rangle$. $|b\rangle$ represents all outcomes where information is lost via decay of the Rydberg atoms at rate ${\Gamma }_{\mathrm{r}}$.

Figure 2

(a) Rydberg pair interaction and blockade radius for the asymptotic states $\left(\right|a\rangle ,|a\rangle )=\left(\right|37S_{1/2}\rangle ,|37S_{1/2}\rangle )$ (lines above dashed line) and $\left(\right|a\rangle ,|s\rangle )=\left(\right|37S_{1/2}\rangle ,|31P_{3/2}\rangle )$ (lines below dashed line). For this combination of states the $C_6$ coefficients are similar. The excitation linewidth (dashed lines) for the case of strong ${\Omega }_{\mathrm{eff}}$ and critical damping is indicated, which defines blockade radii $r_{\mathrm{b}}$. ${\Omega }_{\mathrm{eff}}=2\pi \times 1\mathrm{MHz}$. (b) ${\mathrm{LaF}}_3$-induced decay rate for state $|a\rangle$ [blue (dark gray), top] in resonance and [red (medium gray), bottom] detuned by 3 cm${}^{-1}$ from a polariton resonance at 40.8 cm${}^{-1}$ with a width of 0.2 cm${}^{-1}$ in a 1 $\mu$m diameter trap. The dashed lines mark the spread due to the finite size of the trap. The proposed trapping distance of 3.8 $\mu$m is shown, and the green (light gray) lines indicate the decay rates ${\Gamma }_{\mathrm{r}}=6$ and 30 kHz used for simulations; see main text. As can be seen, the superatom is weakly coupled to the surface if transitions are detuned by $>$3 cm${}^{-1}$. These transition rates decrease if the change in $n$ is increased, as the transition dipole is much reduced. Transitions to lower Rydberg states via other ${\mathrm{LaF}}_3$ SPP modes are not resonant, making them negligible.

Figure 3

Probability of finding the system in $|s\rangle$ for different Rydberg atom decay rates ${\Gamma }_{\mathrm{r}}$ and effective Rabi frequencies ${\Omega }_{\mathrm{eff}}$. Normal case [blue (dark gray)]: ${\Gamma }_{\mathrm{r}}=2\pi \times 6\mathrm{kHz}$, ${\Omega }_{\mathrm{eff}}=2\pi \times 1\mathrm{MHz}$; fast decaying case [orange (light gray)]: ${\Gamma }_{\mathrm{r}}=2\pi \times 30\mathrm{kHz}$, ${\Omega }_{\mathrm{eff}}=2\pi \times 1\mathrm{MHz}$; fast excitation case [red (medium gray)]: ${\Gamma }_{\mathrm{r}}=2\pi \times 6\mathrm{kHz}$, ${\Omega }_{\mathrm{eff}}=2\pi \times 3\mathrm{MHz}$. The dashed line represents the underdamped case, ${\Gamma }_{\mathrm{sf}}={\Omega }_{\mathrm{eff}}/2$, and the dot-dashed line shows the overdamped regime, ${\Gamma }_{\mathrm{sf}}=4{\Omega }_{\mathrm{eff}}$. The solid line represents critical damping, ${\Gamma }_{\mathrm{sf}}=2{\Omega }_{\mathrm{eff}}$. The dotted black lines indicate the Rydberg decay ${\Gamma }_{\mathrm{r}}$. The inset shows the probability vs time of finding the system in $|g\rangle$ [orange (light gray)], $|a\rangle$ [green (very light gray)], $|s\rangle$ [blue (dark gray)], and $|b\rangle$ [red (light gray] for ${\Omega }_{\mathrm{eff}}=2\pi \times 1\mathrm{MHz},$ ${\Gamma }_{\mathrm{sf}}=2\Omega ,$ ${\Gamma }_{\mathrm{r}}=2\pi \times 6\mathrm{kHz}$.