We observe the coherence of an interacting two-component Bose-Einstein condensate (BEC) surviving for seconds in a trapped Ramsey interferometer. Mean-field driven collective oscillations of two components lead to periodic dephasing and rephasing of condensate wave functions with a slow decay of the interference fringe visibility. We apply spin echo synchronous with the self-rephasing of the condensate to reduce the influence of state-dependent atom losses, significantly enhancing the visibility up to 0.75 at the evolution time of 1.5 s. Mean-field theory consistently predicts higher visibility than experimentally observed values. We quantify the effects of classical and quantum noise and infer a coherence time of 2.8 s for a trapped condensate of 5.5 × 10 4 interacting atoms.

We investigate and model a method for producing entanglement between two spatially separated Bose-Einstein condensates (BECs). In our approach, a spin-polarized BEC is squeezed using a (S z ) 2 interaction, then are split into two separate clouds. After the split, we consider that the particle number in each cloud collapses to a fixed number. We show that this procedure is equivalent to applying an interaction corresponding to squeezing each cloud individually plus an entangling operation. We analyze the system's inter-well entanglement properties and show that it can be detected using correlation-based entanglement criteria. The nature of the states is illustrated by Wigner functions and have the form of a correlated squeezed state. The conditional Wigner function shows high degrees of non-classicality for dimensionless squeezing times beyond N 1 , where N is the number of particles per BEC.

We theoretically study a scheme for generating entanglement between two Bose–Einstein condensates (BECs). The scheme involves placing two BECs in the path of a Mach–Zehnder interferometer, where the coherent light interacts with the atoms due to a quantum nondemolition Hamiltonian. In contrast to standard approaches where a Holstein–Primakoff approximation is used, we use an exact wavefunction approach where the atoms can be initialized in an arbitrary state and the light–atom interaction times can be arbitrary. In the short time regime, it is possible to construct a very simple approximate theory for the overall effect of the scheme: amplitudes in the superposition between the two BECs with unequal spin eigenvalues are damped. We analyze the types of correlations, entanglement, Einstein–Podolsky–Rosen (EPR) steering, and Bell correlations that are produced and show that the state is similar to a spin-EPR state. Using a two-pulse sequence the correlations can be dramatically improved, where the state further approaches a spin-EPR state.

The states generated by the two-spin generalization of the two-axis countertwisting Hamiltonian are examined. We analyze the behavior at both short and long timescales, by calculating various quantities such as squeezing, spin expectation values, probability distributions, entanglement, Wigner functions, and Bell correlations. In the limit of large spin ensembles and short interaction times, the state can be described by a two-mode squeezed vacuum state; for qubits, Bell state entanglement is produced. We find that the Hamiltonian approximately produces two types of spin Einstein-Podolsky-Rosen (EPR) states, and the time evolution produces aperiodic oscillations between them. In a similar way to the basis invariance of Bell states and two-mode squeezed vacuum states, the Fock state correlations of spin EPR states are basis invariant. We find that it is possible to violate a Bell inequality with such states, although the violation diminishes with increasing ensemble size. Effective methods to detect entanglement are also proposed, and formulas for the optimal times to enhance various properties are calculated.

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We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. Using a Suzuki-Trotter decomposition, a sequence of measurements can produce the evolution approximating imaginary time evolution of an arbitrary Hamiltonian, up to a random sign coefficient. The randomness due to measurement is corrected using conditional unitary operations, making the evolution deterministic. The number of gates for a single iteration typically scales as a polynomial of the number of qubits in the system. We demonstrate the approach with several examples, including the transverse field Ising model and quantum search.

An ensemble density matrix model that includes one-and two-body losses is derived for a trapped-atom clock. A trapped-atom clock is mainly affected by one-and two-body losses, generally giving nonexponential decays of populations; nevertheless, three-body recombination is also quantitatively analyzed to demonstrate the boundaries of its practical relevance. The importance of one-body losses is highlighted without which population trapping behavior would be observed. The model is written with decay constants expressed through experimental parameters. It can complement, e.g., the ISRE (identical spin rotation effect) model to improve its predictions: ISRE dramatically increases the ensemble coherence time, hence it enables one to observe the influence of two-body losses on the interferometry contrast envelope. The presented model is useful for Ramsey interferometry and is ready for immediate experimental verification in existing systems.

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