Spin Squeezing of Atomic Ensembles via Nuclear-Electronic Spin Entanglement

We demonstrate spin squeezing in a room temperature ensemble of $\approx {10}^{12}$ cesium atoms using their internal structure, where the necessary entanglement is created between nuclear and electronic spins of each individual atom. This state provides improvement in measurement sensitivity beyond the standard quantum limit for quantum memory experiments and applications in quantum metrology and is thus a complementary alternative to spin squeezing obtained via interatom entanglement. Squeezing of the collective spin is verified by quantum state tomography.

Figure 1

Pulse sequence and level scheme for atomic state preparation and quantum state reconstruction. (a) Optical pumping creates a macroscopic spin $\overrightarrow{J}$ in a CSS, aligned with the magnetic field $\overrightarrow{B}$ in the $x$ direction. (b) A Raman transition creates a coherent superposition of even magnetic sublevels, which shears the QPD in the rotating frame and decreases the mean spin. (c) The spin state of the ensemble is characterized via off-resonant Faraday interaction with a linearly polarized probe beam, propagating in the $z$ direction. Quantum noise limited polarization measurements in a 45° basis reveal the statistics of the atomic angular momentum projections ${\widehat{J}}_{y^{\prime }}$ and ${\widehat{J}}_{z^{\prime }}$, which are precessing about the $x$ axis. Simultaneously, a weak measurement along the $x$ axis determines the magnitude of the mean atomic spin $⟨{\widehat{J}}_x⟩$.

Figure 2

Exemplified quantum state reconstruction (at $\approx 3\mathrm{dB}$ squeezing) with ${\kappa }^2\approx 0.8$. (a) Scatter plot of ${10}^4$ realizations. The atomic covariance (inner ellipse with $\sqrt{2}\sigma$ radii) is determined by correcting the total covariance (outer ellipse) for light and back-action noise (circle). (b) Maximum likelihood estimation of the density matrix $\widehat{\rho }$ for the collective spin state, showing alternating excitation numbers $m$, $n$ in the harmonic oscillator approximation.

Figure 3

(a) Results of the quantum state reconstruction for varied pulse length. Shown are atomic squeezed ($\equiv {\chi }^2/2$) and antisqueezed variances (diamonds). For useful squeezing, they have to be compared to the variance of a CSS with the same mean spin (squares). (b) Resulting squeezing parameters ${\zeta }^2$ (diamonds) and ${\xi }^2$ (crosses) in decibels, representing renormalized data from the indicated region in (a). Theoretical predictions are shown as solid and dashed lines.