Observation of Quantum Spin Noise in a 1D Light-Atoms Quantum Interface

We observe collective quantum spin states of an ensemble of atoms in a one-dimensional light-atom interface. Strings of hundreds of cesium atoms trapped in the evanescent field of a tapered nanofiber are prepared in a coherent spin state, a superposition of the two clock states. A weak quantum nondemolition measurement of one projection of the collective spin is performed using a detuned probe dispersively coupled to the collective atomic observable, followed by a strong destructive measurement of the same spin projection. For the coherent spin state we achieve the value of the quantum projection noise 40 dB above the detection noise without atoms, well above the 3 dB required for reconstruction of the negative Wigner function of nonclassical states. We analyze the effects of strong spatial inhomogeneity inherent to atoms trapped and probed by the evanescent waves. We furthermore study temporal dynamics of quantum fluctuations relevant for measurement-induced spin squeezing and assess the impact of thermal atomic motion. This work paves the road towards observation of spin-squeezed and entangled states and many-body interactions in 1D spin ensembles.

Popular Summary

Interactions between light and atoms offer an efficient means for studying quantum superpositions, exotic “squeezed” states of light and matter, and multiparticle entanglement—all central ingredients for quantum information science. Optical nanofibers are a recent and promising platform for studying these interactions. If an optical fiber is thinned to below a micrometer in diameter, propagating light is concentrated and travels along its surface where cold atoms can be trapped. We optically trap about 1000 laser-cooled atoms in this light field and measure their electronic quantum state with light propagating through such a fiber.

We trap rows of ultracold cesium atoms in the tapered waist of an hourglass-shaped nanowire. The tight confinement of light and atoms allows us to detect quantum fluctuations of the collective atomic state for the first time and with unprecedented resolution in such a system. Additionally, we find that thermal motion of the atoms within the localized light field strongly affects our ability to prepare the atomic quantum state by such measurements, showing that cooling is an essential prerequisite for further advancement.

Our results pave the way for fiber-coupled ensembles of atoms in entangled quantum states, which are an attractive building block for future quantum communication networks.

Figure 1

(a) Sketch of nanofiber trap setup with light fields for trapping and probing and microwave source for coherent transfer between clock levels (MW: Microwave; PD: Photo detector). (b) Relevant atomic energy levels for cesium. (c) Transverse section of nanofiber with atomic trap sites, local probe light polarization, and magnetic bias field direction indicated. (d) Dispersive detection of the clock state populations for an increasing number (bottom to top) of atoms prepared in the superposition state $|\mathrm{\Psi }⟩$. Solid lines are averages over typically 300 realizations. Dashed lines are fits to the model presented in Eq. (2). See main text for state preparation and measurement procedure; shaded areas indicate interruption of the probing.

Figure 2

Noise scaling of the atomic population estimators. Green and blue symbols are variances of ${\phi }_4$ and ${\phi }_3$, red filled circles show the variance of ${\phi }_{\mathrm{\Delta }}$, rose circles show variance of ${\phi }_4$ scaled by a factor of 4. Error bars are statistical, dashed lines are linear fits to the data of same color. The top $x$ axis shows the inferred effective atom number $N_{\mathrm{eff}}$. Data were taken under similar conditions as in Fig. 1.

Figure 3

(a) Constant part ${\mathit{C}}_{\mathbf{0}}$ (lower left-hand triangle: shot noise) and linear part ${\phi }_N{\mathit{C}}_{\mathbf{1}}$ (upper right-hand triangle: atomic correlations) of the symmetric covariance matrix $\mathit{C}={\mathit{C}}_{\mathbf{0}}+{\phi }_N{\mathit{C}}_{\mathbf{1}}$ for ${\phi }_N=0.16(1)\mathrm{rad}$ (see text); red (blue) denotes positive (negative) correlations. Shaded areas indicate interruption of the probing. Side panels: Correlation coefficient obtained by averaging over the minor diagonals of the corresponding matrix of correlation coefficients. (b) Upper panel: QND pulse sequence; temporal dependence of the main diagonal entries of ${\mathit{C}}_{\mathbf{0}}$ (constant part, red dots) and of ${\phi }_N{\mathit{C}}_{\mathbf{1}}$ (atom number dependent part, blue dots). Solid blue line, $({\phi }_N\overrightarrow{m}(t)/2{)}^2/N_{\mathrm{eff}}$; solid red line, phase shot noise $\delta {{\phi }_{\mathrm{sn}}}^2$. Lower panel: Ramsey-type pulse sequence and temporal evolution of the Ramsey fringe contrast in the absence (solid purple) or presence (solid green) of an $8\mu \mathrm{s}$ probe pulse. Dotted traces denote the corresponding optimal detection mode function.