Spin squeezing of 1011 atoms by prediction and retrodiction measurements.

The measurement sensitivity of quantum probes using N uncorrelated particles is restricted by the standard quantum limit1, which is proportional to [Formula: see text]. This limit, however, can be overcome by exploiting quantum entangled states, such as spin-squeezed states2. Here we report the measurement-based generation of a quantum state that exceeds the standard quantum limit for probing the collective spin of 1011 rubidium atoms contained in a macroscopic vapour cell. The state is prepared and verified by sequences of stroboscopic quantum non-demolition (QND) measurements. We then apply the theory of past quantum states3,4 to obtain spin state information from the outcomes of both earlier and later QND measurements. Rather than establishing a physically squeezed state in the laboratory, the past quantum state represents the combined system information from these prediction and retrodiction measurements. This information is equivalent to a noise reduction of 5.6 decibels and a metrologically relevant squeezing of 4.5 decibels relative to the coherent spin state. The past quantum state yields tighter constraints on the spin component than those obtained by conventional QND measurements. Our measurement uses 1,000 times more atoms than previous squeezing experiments5-10, with a corresponding angular variance of the squeezed collective spin of 4.6 × 10-13 radians squared. Although this work is rooted in the foundational theory of quantum measurements, it may find practical use in quantum metrology and quantum parameter estimation, as we demonstrate by applying our protocol to quantum enhanced atomic magnetometry.

Sub-Hertz resonance by weak measurement.

Weak measurement (WM) with state pre- and post-selection can amplify otherwise undetectable small signals and thus has potential in precision measurement applications. Although frequency measurements offer the hitherto highest precision due to the stable narrow atomic transitions, it remains a long-standing interest to develop new schemes to further escalate their performance. Here, we demonstrate a WM-enhanced correlation spectroscopy technique capable of narrowing the resonance linewidth down to 0.1 Hz in a room-temperature atomic vapour cell. The potential of this technique for precision measurement is demonstrated through weak magnetic-field sensing. By judiciously pre- and post-selecting frequency-modulated input and output optical states in a nearly orthogonal manner, a sensitivity of 7 fT Hz-1/2 at a low frequency near DC is achieved using only one laser beam with 15 µW of power. Additionally, our results extend the WM framework to a non-Hermitian Hamiltonian and shed new light on metrology and bio-magnetic field sensing.

Spatial Multiplexing of Squeezed Light by Coherence Diffusion.

Spatially splitting nonclassical light beams is in principle prohibited due to noise contamination during beam splitting. We propose a platform based on thermal motion of atoms to realize spatial multiplexing of squeezed light. Light channels of separate spatial modes in an antirelaxation coated vapor cell share the same long-lived atomic coherence jointly created by all channels through the coherent diffusion of atoms, which in turn enhances the individual channel's nonlinear process responsible for light squeezing. Consequently, it behaves as squeezed light in one optical channel transferring to other distant channels even with laser powers below the threshold for squeezed light generation. An array of squeezed light beams is created with low laser power ∼ milliwatt. This approach holds great promise for applications in a multinode quantum network and quantum enhanced technologies such as quantum imaging and sensing.