Single-Photon Interference due to Motion in an Atomic Collective Excitation

We experimentally demonstrate the heralded generation of bichromatic single photons from an atomic collective spin excitation (CSE). The photon arrival times display collective quantum beats, a novel interference effect resulting from the relative motion of atoms in the CSE. A combination of velocity-selective excitation with strong laser dressing and the addition of a magnetic field allows for exquisite control of this collective beat phenomenon. The present experiment uses a diamond scheme with near-IR photons that can be extended to include telecommunications wavelengths or modified to allow storage and retrieval in an inverted-$Y$ scheme.

Figure 1

Preparation of a single excitation as a collective superposition of two atomic velocity groups. (a) A thermal vapor of ${}^{87}\mathrm{Rb}$ is continuously driven by weak pump- and strong coupling-laser beams. A strong magnetic field of 0.6 T, applied with permanent magnets, simplifies the internal level structure by isolating only the four levels shown in the inset (in the semidressed picture). The coupling laser dresses the atoms, so that atoms with two different velocities (shown in red and blue in the inset) are preferentially excited. The detection of a “herald” photon heralds the preparation of a single excitation in level $|e⟩$ in the form of a spin wave. (b) The excitation is mostly split among two velocity classes, one stationary and one moving away from the signal detector in (c), with an initial phase difference of $\pi$. Because of the Doppler effect, light emitted from these two classes of atoms will be shifted in frequency, causing beats in the signal photon detection (d). The beats demonstrate that this setup forms an interferometer (e), where the detection of a herald photon coherently splits a single excitation and stores it in atoms moving at two different velocities, before recovering the excitation in a common signal channel.

Figure 2

Collective decay leading to beats. (a) Continuous driving prepares the system in a steady state, where atoms $i$ and $j$ (the sum over all possible $i$, $j$ is implied) are in a superposition of ground $|g⟩$ and bare $|b⟩$ states. Herald detection maps the steady-state amplitudes and phases (indicated by the size and color of the circles) into a superposition of excited states $|e⟩$. (b) Subsequently, the relative phase of the atoms evolves due to motion (see the insets for the spin-wave evolution in space with color coding of the relative phase; the $B$-field orientation is vertical). Since both atoms end up in the same ground state after emitting the signal photon, the emission amplitudes add coherently and a time-dependent factor appears in the collective signal [bottom of (a)]. (c) This interference leads to beats in the probability of directional signal photon emission over time, $\tau$.

Figure 3

The persistence of coherence between two collective excitation components. Experimental data (blue) showing interference resulting from the coherent splitting of a single excitation across two groups of atoms with relative motion. The Doppler shift leads to beats in the state readout with a frequency proportional to the relative velocity. The detuning of a strong dressing laser, ${\mathrm{\Delta }}_c$, sets the velocities of the excited atoms and thereby determines the beat frequency. A theoretical model (red curves) finds excellent agreement with the data across the entire range of detunings studied. The error bars on the experimental data are calculated assuming Poissonian noise on the individual histogram bins [38].