Quantum interference of a single spin excitation with a macroscopic atomic ensemble

We report on the observation of quantum interference of a collective single spin excitation with a spin ensemble of $N_{\mathrm{a}}\approx {10}^5$ atoms. Detection of a single photon scattered from the atoms creates the single spin excitation, a Fock state embedded in the collective spin of the ensemble. The state of the atomic ensemble is then detected by a quantum nondemolition measurement of the collective spin. A macroscopic difference of the order of ${\sqrt{N}}_{\mathrm{a}}$ in the marginal distribution of the collective spin state arises from the interference between the single excited spin and $N_{\mathrm{a}}$ atoms. These hybrid discrete-continuous manipulation and measurement procedures of collective spin states in an atomic ensemble pave the road towards generation of even more exotic ensemble states for quantum information processing, precision measurements, and communication.

Figure 1

The simplified atomic level structure and the collective Bloch sphere at different stages of the experiment. (a) All atoms are prepared in the $|\uparrow \rangle$ state via optical pumping. (b) Detection of a scattered anti-Stokes photon following a weak excitation of the ensemble signals that a single atom has been transferred to the $|\downarrow \rangle$ state. (c) A microwave $\pi /2$ pulse causes the single excited atom in $|\downarrow \rangle$ to interfere with the remaining atoms in $|\uparrow \rangle$ by rotating all spins into the equatorial plane. This creates the collective state $|{\Psi }_1^{\prime }\rangle$, which is characterized by a continuous-variable measurement. The inset shows the probability density of ${\widehat{J}}_z$ for $|{\Psi }_0^{\prime }\rangle$ [solid orange] and $|{\Psi }_1^{\prime }\rangle$ [dashed blue].

Figure 2

(a) Experimental setup. The dipole-trapped atomic ensemble is overlapped with one arm of a MZI, using dichroic (DC) mirrors. The input mode of the MZI is used for the weak Raman excitation and for the dual-color QND measurement of atoms. A single-photon counter module (SPCM) detects the heralding photon. To select a photon in the desired decay channel, polarization (via PBS) and frequency (via Fabry-Pérot cavities) filters are implemented. The atomic state is characterized by a dispersive QND measurement using balanced homodyne detection. A beam splitter (BS) is used to calibrate the probe power. (b) Pulse sequence.

Figure 3

Variance of the measured optical phase shift $\varphi$ as a function of the atom number. Different noise contributions are distinguished by a scaling analysis. The dominating linear part (dashed line) corresponds to atomic quantum projection noise; the quadratic and constant contributions (A) originate from technical fluctuations and light shot noise. Nine percent of the projection noise originates from noise-canceling reference measurements; the remaining fraction (B) constitutes ${\eta }_{\mathrm{noise}}=50\%$ of the total noise.

Figure 4

Cumulative statistics for the variance of the measurement outcomes of $\Delta N$ for the two created states, showing an increased variance for heralding events. The sample variance is plotted against the number of observations with a heralding photon (no heralding photon) as depicted on the top (bottom) axis.

Figure 5

Experimental sequence in order to estimate ${\eta }_{\text{scatter}}$.