Continuous-variable versus electromagnetically-induced-transparency-based quantum memories

We discuss a general model of a quantum memory for a single light mode in a collective mode of atomic oscillators. The model includes interaction Hamiltonians that are of second order in the canonical position and momentum operators of the light and atomic oscillator modes. We also consider the possibility of measurement and feedback. We identify an interaction Hamiltonian that leads to an ideal mapping by pure unitary evolution and compare several schemes which realize this mapping using a common continuous-variable description. In particular, we discuss schemes based on the off-resonant Faraday effect supplemented by measurement and feedback and proper preparation of the atoms in a squeezed state and schemes based on off-resonant Raman coupling as well as electromagnetically induced transparency.

Figure 1

(Color online) Fidelity of storing the odd Schrödinger cat states $\mid \alpha ,-⟩\propto \mid \alpha ⟩-\mid -\alpha ⟩$ (with real $\alpha$) in the one-pass scheme of [12]. The atomic ensemble is initially prepared in a spin squeezed state: the smaller the position variance ${\sigma }_{X,A}$, the higher the squeezing. The thick line corresponds to the coherent spin state with no squeezing and it reaches the classical limit of fidelity 0.5 (thick dashed contour line) at about ${\mid \alpha \mid }^2\approx 2.0$. Since the measurement alters the input state, the scheme cannot efficiently store superpositions of states with very different momenta.

Figure 2

(Color online) Quantum memory scheme based on Faraday rotation. The atoms with doubly degenerate ground states are polarized in the polarization direction of the strong classical light field. The inset shows a simplified atomic level structure when the quantization axis is the direction of light propagation. The atoms are in an equal-weighted coherent superposition of the ground levels. The presence of a weak $y$-polarized light field results in an imbalance of the dynamic Stark shifts for the two levels, developing a relative phase in the superposition. The atomic spins are, thus, coherently rotated in the $xy$ plane as a back action of light on atoms.

Figure 3

(Color online) Quantum memory scheme based on off-resonant Raman scattering. The inset shows the $\Lambda$-type atomic configuration. The degenerate ground states ∣1⟩ and ∣2⟩ are off-resonantly coupled to the intermediate levels ∣3⟩ and ∣4⟩ via right and left circularly polarized monochromatic light beams. Light shifts of the lower levels are canceled by tuning the laser fields right between the two upper levels. The classical control field is the right polarized one. Only level ∣2⟩ is macroscopically populated, which corresponds to a quasispin polarization in the direction of light propagation. Absorption of a signal photon results in a collective atomic excitation in level ∣1⟩.

Figure 4

(Color online) $\Lambda$-type atomic configuration in the EIT scheme. Levels ∣1⟩ and ∣3⟩ are coupled by the classical field of Rabi frequency $\Omega \left(t\right)$ which is controlled externally. Levels ∣2⟩ and ∣3⟩ are coupled by the weak signal field. Initially, only level ∣2⟩ is populated.