Multiple beam splitter for single photons

We propose a method using “light storage” and fractional stimulated Raman adiabatic passage (F-STIRAP) to get entangled multiple Fock states from a single photon. A light storage technique is used to store the quantum information of a single-photon pulse in atoms. F-STIRAP pulses then split the stored coherence, such that reading pulses retrieve the quantum information from this new coherence. Since each reading pulse only retrieves part of the total coherence, we can obtain entangled multiple Fock states with arbitrary relative amplitude. This method to create entanglement is versatile for obtaining frequency, time, and∕or spatial entanglement. Indeed, we obtain a multiple beam splitter with easily adjustable parameters.

Figure 1

Four-level atomic system coupled with a probe field ${\widehat{\mathcal{E}}}_{12}$ and two strong classical fields: pump ${\Omega }_{13}$ and Stokes ${\Omega }_{14}$.

Figure 2

Split population and Raman coherence for a single atom using fractional STIRAP. (a) Rabi frequencies for F-STIRAP pump ${\Omega }_{13}$ and Stokes ${\Omega }_{14}$ pulses [Eq. (2) with $\tan \alpha =1∕\sqrt{2}$, ${\Omega }_0=\gamma$, and $\tau =10{\gamma }^{-1}$] as a function of time; time is given in terms of the inverse of decay rate $\gamma$ out of ∣1⟩ into each ∣2⟩, ∣3⟩, and ∣4⟩; Rabi frequencies are given in units of $\gamma$. (b) Population evolution as a result of the pulses in (a). (c) Evolution of coherences as a result of the pulses in (a).

Figure 3

F-STIRAP pulses split the Raman coherence of atoms in which a single photon has been stored. Pulses used are shown in Fig. 2a and the initial Raman coherence ${\rho }_{32}$ is caused by storage input photon ${\widehat{\mathcal{E}}}_{12}$. $\eta =3{\lambda }^{2}N\gamma ∕8\pi$. (a) Initial coherence ${\rho }_{23}$; final coherence ${\rho }_{23}^1$, $-{\rho }_{24}^1$, and ${\rho }_{34}^1$ in the medium. (b) Output wave packet from first reading pulse ${\Omega }_{14}$ on coherence ${\rho }_{24}^1$ as a function of time. (c) Overall F-STIRAP pulses and first reading pulse as a function of time. The shaded area covers the F-STIRAP pulse. Units as in Fig. 2.

Figure 4

Illustration of the output of a three-pulse Fock state with equal amplitudes. The initial Raman coherence is caused by storage input photon ${\widehat{\mathcal{E}}}_{12}$ as in Fig. 3. (a) F-STIRAP (shaded parts) and reading pulses ${\Omega }_{13}$ (solid line) and ${\Omega }_{14}$ (dash-dot line) applied to the medium. The equal amplitudes are determined by setting $\tan {\alpha }_1=\sqrt{2}$ and $\tan {\alpha }_2=1$. (b) Output wave packets as a result of (a) applied on the initial coherence. Units as in Fig. 2.

Figure 5

The same as in Fig. 4, except for output with amplitude ratio $\sqrt{3}:\sqrt{2}:2$. This is caused by setting $\tan {\alpha }_1=\tan {\alpha }_2=1∕\sqrt{2}$.