Spin-Nematic Squeezed Vacuum in a Quantum Gas

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. Squeezed states were first demonstrated in optical fields and later with ensembles of pseudo spin-1/2 atoms using non-linear atom-light interactions. Recently, collisional interactions in ultracold atomic gases have been used to generate a large degree of quadrature spin squeezing in two-component Bose condensates. For pseudo spin-1/2 systems, the complementary properties are the different components of the total spin vector , 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 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(-0.7 +0.6) dB (-10.3(-0.9 +0.7) 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

Non-equilibrium dynamics of an unstable quantum pendulum

A pendulum prepared perfectly inverted and motionless is a prototype of unstable equilibria and corresponds to an unstable hyperbolic fixed point in the dynamical phase space. Unstable fixed points are central to understanding Hamiltonian chaos in classical systems. In many-body quantum systems, mean-field approximations fail in the vicinity of unstable fixed points and lead to dynamics driven by quantum fluctuations. Here, we measure the non-equilibrium dynamics of a many-body quantum pendulum initialized to a hyperbolic fixed point of the phase space. The experiment uses a spin-1 Bose condensate, which exhibits Josephson dynamics in the spin populations that correspond in the mean-field limit to motion of a non-rigid mechanical pendulum. The condensate is initialized to a minimum uncertainty spin state, and 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 compared to no loss case as orbits depart from the separatrix. This demonstrates how decoherence of a many-body system can result in more 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.Comment: Main text 6 pages, 5 figures; Supplement 4 pages, 1 figur