Many-body entanglement is often created through system evolution, aided by non-linear interactions between the constituting particles. The very dynamics, however, can also lead to fluctuations and degradation of the entanglement if the interactions cannot be controlled. Here, we demonstrate neardeterministic generation of an entangled twin-Fock condensate of ∼ 11000 atoms by driving a 87 Rb Bose-Einstein condensate undergoing spin mixing through two consecutive quantum phase transitions (QPTs). We directly observe number squeezing of 10.7 ± 0.6 dB and normalized collective spin length of 0.99 ± 0.01. Together, these observations allow us to infer an entanglementenhanced phase sensitivity of ∼ 6 dB beyond the standard quantum limit and an entanglement breadth of ∼ 910 atoms. Our work highlights the power of generating large-scale useful entanglement by taking advantage of the differ-1

Interferometry is a paradigm for most precision measurements. Using N uncorrelated particles, the achievable precision for a two-mode (two-path) interferometer is bounded by the standard quantum limit (SQL), [Formula: see text], due to the discrete (quanta) nature of individual measurements. Despite being a challenging benchmark, the two-mode SQL has been approached in a number of systems, including the Laser Interferometer Gravitational-Wave Observatory and today's best atomic clocks. For multimode interferometry, the SQL becomes [Formula: see text] using modes. Higher precision can also be achieved using entangled particles such that quantum noises from individual particles cancel out. In this work, we demonstrate an interferometric precision of [Formula: see text] dB beyond the three-mode SQL, using balanced spin-1 (three-mode) Dicke states containing thousands of entangled atoms. The input quantum states are deterministically generated by controlled quantum phase transition and exhibit close to ideal quality. Our work shines light on the pursuit of quantum metrology beyond SQL.

We report the observation of synthesized spin-orbit coupling (SOC) for ultracold spin-1 87Rb atoms. Different from earlier experiments where a one dimensional (1D) atomic SOC of pseudo-spin-1/2 is synthesized with Raman laser fields, the scheme we demonstrate employs a gradient magnetic field (GMF) and ground-state atoms, thus is immune to atomic spontaneous emission. The strength of SOC we realize can be tuned by changing the modulation amplitude of the GMF, and the effect of the SOC is confirmed through the studies of: 1) the collective dipole oscillation of an atomic condensate in a harmonic trap after the synthesized SOC is abruptly turned on; and 2) the minimum energy state at a finite adiabatically adjusted momentum when SOC strength is slowly ramped up. The condensate coherence is found to remain very good after driven by modulating GMFs. Our scheme presents an alternative means for studying interacting many-body systems with synthesized SOC.

The single-mode Dicke model is well known to undergo a quantum phase transition from the so-called normal phase to the superradiant phase (hereinafter called the 'superradiant quantum phase transition'). Normally, quantum phase transitions can be identified by the critical behavior of quantities such as entanglement, quantum fluctuations, and fidelity. In this paper, we study the role of the quantum Fisher information (QFI) of both the field mode and the atoms in the ground state of the Dicke Hamiltonian. For a finite but large number of atoms, our numerical results show that near the critical atom-field coupling, the QFI of the atomic and the field subsystems can surpass their classical limits, due to the appearance of nonclassical quadrature squeezing. As the coupling increases far beyond the critical point, each subsystem becomes a highly mixed state, which degrades the QFI and hence the ultimate phase sensitivity. In the thermodynamic limit, we present the analytical results of the QFI and their relationship with the reduced variances of the field mode and the atoms. For each subsystem, we find that there is a singularity in the derivative of the QFI at the critical point, a clear signature of the quantum criticality in the Dicke model.Quantum phase transitions in many-body systems are of fundamental interest [1] and have potential applications in quantum information [2][3][4][5][6][7] and quantum metrology [8][9][10][11][12][13][14][15]. Consider, for instance, a collection of N two-level atoms interacting with a single-mode bosonic field, described by the Dicke model (with =  1) [16]:z 0 whereb andˆ † b are annihilation and creation operators of the bosonic field with oscillation frequency ω, which is nearly resonant with the atomic energy splitting ω 0 . The collective spin operators σ ≡ˆ±ˆ= ∑± ± J J iJ x y k k and σ = ∑Ĵ 2 z k k z obey the SU(2) Lie algebra, where σ ± k and σ k z are Pauli operators of the kth atom. The atom-field coupling strength λ ∝ N V depends on the atomic density N V . For a finite number of atoms N (= j 2 ), the Hamiltonian (1) commutes with the parity, where Tr A (Tr B ) is the partial trace of the ground state |g over the atomic (bosonic field) degrees of freedom. The QFI is one of the central quantities used to qualify the utility of an input state [35,36], especially in Mach-Zehnder (or, equivalently, Ramsey) interferometer-based phase or parameter estimation. The achievable phase sensitivity is well known to be limited by the quantum Cramér-Rao bound δφ ρ ∝ˆF G 1 ( , ) min in , where the QFI ρF G ( , ) in depends on the input state ρ in and the New J. Phys. 16 (2014) 063039 T-L Wang et al B 2 . Therefore, the ultimate sensitivity is limited by δφ =n 1/(2 ) min cl , known as New J. Phys. 16 (2014) 063039 T-L Wang et al

We investigate the relaxation dynamics of an interacting Stark-localized system coupled to a dephasing bath, and compare its behavior to the conventional disorder-induced many body localized system. Specifically, we study the dynamics of population imbalance between even and odd sites, and the growth of the von Neumann entropy. For a large potential gradient, the imbalance is found to decay on a time scale τ that grows quadratically with the Wannier-Stark tilt. For the non-interacting system, it shows an exponential decay, which becomes a stretched exponential decay in the presence of finite interactions. This is different from a system with disorder-induced localization, where the imbalance exhibits a stretched exponential decay also for vanishing interactions. As another clear qualitative difference, we do not find a logarithmically slow growth of the von-Neumann entropy as it is found for the disordered system. Our findings can immediately be tested experimentally with ultracold atoms in optical lattices.