Polarization entanglement and quantum beats of photon pairs from four-wave mixing in a cold⁸⁷Rb ensemble

Abstract

We characterize correlations in polarization and time of photon pairs generated from a cold cloud of 87 Rb atoms via a four-wave mixing process in a cascade level scheme. Quantum state tomography reveals entangled polarization states of high purity for each of the decay paths through two different intermediate hyperfine levels. When allowing both decay paths, we observe quantum beats in timeresolved correlation measurements.

Upper Bound on the Duration of Quantum Jumps

“…This indeterminacy causes that the atomic state conditioned to the detection of a signal photon is given by a superposition of the hyperfine states of level |1 , i.e., 5P 1/2 F = 1 and F = 2 states. This yields oscillations of ρ 33 (t 0 + ∆t) for ∆t > 0 with a frequency determined by the beating frequencies of these hyperfine levels [25]. These quantum beats can be well reproduced with our model by numerically solving the Bloch equations for a density matrix that involves all hyperfine sublevels of the |i , i=0,1,2,3 states.…”

“…The decay time constant is shorter than the natural decay time 1/γ 30 ≈ 27 ns and determined by the number of atoms involved and the detuning of the pump fields [26,27]. The oscillations on top of the exponential decay are due to quantum beats between the transition of interest and alternative decay paths involving nearby hyperfine levels [25]. The onset of the fluorescence in the idler mode, reflecting the quantum jump, shows a rise time much faster than the time scales of the transitions involved, commensurate with the time jitter of the avalanche photodetectors (see inset of Fig.…”

Cold atoms in micromachined waveguides: A new platform for atom-photon interactions

“…Demonstration of this technique within a more complex waveguide network, together with its use to produce coherent atom-optical effects such as electromagnetically induced transparency [39] and four-wave mixing [40][41][42], represents the next step towards a quantum information processing device based on this architecture.…”

Conversion of position correlation into polarization entanglement

“…The necessary and sufficient requirement for our method to generate polarization entanglement are photon-pairs with initial position correlation. This condition can be found in various processes, such as SPDC in bulk crystals or four-wave mixing in atomic vapours [24,25,30]. Applying this effect in atomic vapours could provide another route to observing polarization entangled photons with line-widths compatible with atomic systems.…”