Using squeezed states it is possible to surpass the standard quantum limit of measurement uncertainty by reducing the measurement uncertainty of one property at the expense of another complementary property [1]. Squeezed states were first demonstrated in optical fields [2] and later with ensembles of pseudo spin-1/2 atoms using non-linear atom-light interactions [3]. Recently, collisional interactions in ultracold atomic gases have been used to generate a large degree of quadrature spin squeezing in two-component Bose condensates [4,5]. For pseudo spin-1/2 systems, the complementary properties are the different components of the total spin vector S , which fully characterize the state on an SU(2) Bloch sphere. Here, we measure squeezing in a spin-1 Bose condensate, an SU(3) system, which requires measurement of the rank-2 nematic or quadrupole tensor Q ij as well to fully characterize the state. Following a quench through a nematic to ferromagnetic quantum phase transition, squeezing is observed in the variance of the quadratures up to −8.3 +0.6 −0.7 dB (−10.3 +0.7 −0.9 dB corrected for detection noise) below the standard quantum limit. This spin-nematic squeezing is observed for negligible occupation of the squeezed modes and is analogous to optical two-mode vacuum squeezing. This work has potential applications to continuous variable quantum information and quantum-enhanced magnetometry.The study of many-body quantum entangled states including atomic spin squeezed states is an active research frontier. In addition to being intrinsically fascinating, such states have applications in precision measurements [6], quantum information and fundamental tests of quantum mechanics [7]. Atomic squeezed states were first considered for ensembles of two-level (pseudo spin-1/2) atoms. For spin-1/2 particles, coherent states of the system are uniquely specified by the components of the total spin vector S , typically illustrated on a SU(2) Bloch sphere. For particles with higher spin, additional degrees of freedom beyond the spin vector are required to fully specify the state. For spin-1 particles, a natural basis to describe the wavefunction is the SU(3) Cartesian dipole-quadrupole basis, consisting of the three components of the spin vector,Ŝ i , and the moments of the rank-2 quadrupole or nematic tensor,Q ij ({i, j} ∈ {x, y, z}). In matrix form, the nematic moments can be written. Spin-1 atomic Bose-Einstein condensates [9-13] provide an exceptionally clean experimental platform to investigate the quantum dynamics of many-body spin sys-tems. They feature controllable quantum phase transitions, well-understood underlying microscopic models, and flexible defect-free geometries. Importantly, it is possible to initialize non-equilibrium or excited states of the system and to directly measure both the spin vector and the nematic tensor using standard atomic state manipulation tools. Law, et al., demonstrated that the spinor interaction can be written as total spin angular momentum, λŜ 2 whereŜ 2 =Ŝ 2x +Ŝ 2 y +Ŝ 2 z [14]. It is ...

A pendulum prepared perfectly inverted and motionless is a prototype of unstable equilibrium and corresponds to an unstable hyperbolic fixed point in the dynamical phase space. Here, we measure the non-equilibrium dynamics of a spin-1 Bose-Einstein condensate initialized as a minimum uncertainty spin-nematic state to a hyperbolic fixed point of the phase space. Quantum fluctuations lead to non-linear spin evolution along a separatrix and non-Gaussian probability distributions that are measured to be in good agreement with exact quantum calculations up to 0.25 s. At longer times, atomic loss due to the finite lifetime of the condensate leads to larger spin oscillation amplitudes, as orbits depart from the separatrix. This demonstrates how decoherence of a many-body system can result in apparent coherent behaviour. This experiment provides new avenues for studying macroscopic spin systems in the quantum limit and for investigations of important topics in non-equilibrium quantum dynamics.

We demonstrate dynamic stabilization of a strongly interacting quantum spin system realized in a spin-1 atomic Bose-Einstein condensate. The spinor Bose-Einstein condensate is initialized to an unstable fixed point of the spin-nematic phase space, where subsequent free evolution gives rise to squeezing and quantum spin mixing. To stabilize the system, periodic microwave pulses are applied that rotate the spin-nematic many-body fluctuations and limit their growth. The stability diagram for the range of pulse periods and phase shifts that stabilize the dynamics is measured and compares well with a stability analysis.

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