Spinor Bose–Einstein condensates

Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here, we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement, which we confirm by Bayesian phase estimation with sub–shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.

Fisher information and entanglement of non-Gaussian spin states

A new technique uses up to 30 Bose-Einstein condensates simultaneously to make ultraprecise measurements.

Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

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Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics.

Although SU(1,1) interferometry achieves Heisenberg-limited sensitivities, it suffers from one major drawback: Only those particles outcoupled from the pump mode contribute to the phase measurement. Since the number of particles outcoupled to these "side modes" is typically small, this limits the interferometer's absolute sensitivity. We propose an alternative "pumped-up" approach where all the input particles participate in the phase measurement and show how this can be implemented in spinor Bose-Einstein condensates and hybrid atom-light systems-both of which have experimentally realized SU(1,1) interferometry. We demonstrate that pumped-up schemes are capable of surpassing the shot-noise limit with respect to the total number of input particles and are never worse than conventional SU(1,1) interferometry. Finally, we show that pumped-up schemes continue to excel-both absolutely and in comparison to conventional SU(1,1) interferometry-in the presence of particle losses, poor particle-resolution detection, and noise on the relative phase difference between the two side modes. Pumped-up SU(1,1) interferometry therefore pushes the advantages of conventional SU(1,1) interferometry into the regime of high absolute sensitivity, which is a necessary condition for useful quantum-enhanced devices.

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Pumped-Up SU(1,1) Interferometry

We investigate controlled phase separation of a binary Bose-Einstein condensate in the proximity of a mixed-spin-channel Feshbach resonance in the $|F=1,{m}_{F}=+1\ensuremath{\rangle}$ and $|F=2,{m}_{F}=\ensuremath{-}1\ensuremath{\rangle}$ states of $^{87}\mathrm{Rb}$ at a magnetic field of 9.10 G. Phase separation occurs on the lower-magnetic-field side of the Feshbach resonance while the two components overlap on the higher-magnetic-field side. The Feshbach resonance curve of the scattering length is obtained from the shape of the atomic cloud by comparison with the numerical analysis of coupled Gross-Pitaevskii equations.

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Controlling phase separation of binary Bose-Einstein condensates via mixed-spin-channel Feshbach resonance

We studied spin-dependent two-body inelastic collisions in $F=2$ $^{87}\text{R}\text{b}$ Bose-Einstein condensates both experimentally and theoretically. The $^{87}\text{R}\text{b}$ condensates were confined in an optical trap and selectively prepared in various spin states in the $F=2$ manifold at a magnetic field of 3.0 G. The measured atom loss rates depend on the spin states of colliding atoms. We measured two fundamental loss coefficients for two-body inelastic collisions with total spins of 0 and 2. The loss coefficients determine the loss rates of all the spin pairs. The experimental results for mixtures of all spin combinations are in good agreement with numerical solutions of the Gross-Pitaevskii equations that include the effect of a magnetic field gradient.

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Taro Hayashi

Papers

Controlling phase separation of binary Bose-Einstein condensates via mixed-spin-channel Feshbach resonance

Spin-dependent inelastic collisions in spin-2 Bose-Einstein condensates