Classical Bifurcation and Entanglement Generation in an Internal Bosonic Josephson Junction

In this work the dynamical behavior of an internal bosonic Josephson junction is investigated. The junction is realized using two Zeeman sub states of the ground state hyperfine manifold in a Bose-Einstein condensate of 87 Rb . With several hundreds of atoms, the size of the system is at the crossover where its classical description breaks down and quantum mechanical effects become important. The system allows for a high level of control in terms of state preparation, readout and its important parameters. Thus its classical dynamics, which show a striking bifurcating behavior, can be studied by mapping out the full phase space and revealing its topological change. Furthermore the dynamics at the unstable classical fixed point arising in the course of the bifurcation are investigated. The dynamics at this point clearly show the breakdown of the classical description. The dynamical evolution leads to spin squeezing and entanglement and subsequently to macroscopic superposition states. The generation of squeezing is quantitatively analyzed and the generated states are reconstructed in terms of their Wigner functions by tomography. This work is an important step for the understanding of highly entangled macroscopic quantum states

Spin nematic order in antiferromagnetic spinor condensates

Large spin systems can exhibit unconventional types of magnetic ordering different from the ferromagnetic or N\'eel-like antiferromagnetic order commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not break time-reversal invariance and their magnetic order parameter is characterized by a second rank tensor with the symmetry of an ellipsoid. Here we show direct experimental evidence for spin-nematic ordering in a spin-1 Bose-Einstein condensate of sodium atoms with antiferromagnetic interactions. In a mean field description this order is enforced by locking the relative phase between spin components. We reveal this mechanism by studying the spin noise after a spin rotation, which is shown to contain information hidden when looking only at averages. The method should be applicable to high spin systems in order to reveal complex magnetic phases.Comment: published versio

Classical bifurcation at the transition from Rabi to Josephson dynamics

We report on the experimental realization of an internal bosonic Josephson junction in a Rubidium spinor Bose-Einstein condensate. The measurement of the full time dynamics in phase space allows the characterization of the theoretically predicted $\pi$-phase modes and quantitatively confirms analytical predictions, revealing a classical bifurcation. Our results suggest that this system is a model system which can be tuned from classical to the quantum regime and thus is an important step towards the experimental investigation of entanglement generation close to critical points

Einstein-Podolsky-Rosen experiment with two Bose-Einstein condensates

In 1935, Einstein, Podolsky and Rosen (EPR) conceived a Gedankenexperiment which became a cornerstone of quantum technology and still challenges our understanding of reality and locality today. While the experiment has been realized with small quantum systems, a demonstration of the EPR paradox with spatially separated, massive many-particle systems has so far remained elusive. We observe the EPR paradox in an experiment with two spatially separated Bose-Einstein condensates containing about 700 Rubidium atoms each. EPR entanglement in conjunction with individual manipulation of the two condensates on the quantum level, as demonstrated here, constitutes an important resource for quantum metrology and information processing with many-particle systems. Our results show that the conflict between quantum mechanics and local realism does not disappear as the system size is increased to over a thousand massive particles.Comment: 9 pages, 5 figure

Spin fragmentation of Bose-Einstein condensates with antiferromagnetic interactions

We study spin fragmentation of an antiferromagnetic spin 1 condensate in the presence of a quadratic Zeeman (QZ) effect breaking spin rotational symmetry. We describe how the QZ effect turns a fragmented spin state, with large fluctuations of the Zeemans populations, into a regular polar condensate, where atoms all condense in the $m=0$ state along the field direction. We calculate the average value and variance of the Zeeman state $m=0$ to illustrate clearly the crossover from a fragmented to an unfragmented state. The typical width of this crossover is $q \sim k_B T/N$, where $q$ is the QZ energy, $T$ the spin temperature and $N$ the atom number. This shows that spin fluctuations are a mesoscopic effect that will not survive in the thermodynamic limit $N\rightarrow \infty$, but are observable for sufficiently small atom number.Comment: submitted to NJ

Entanglement between Identical Particles Is a Useful and Consistent Resource

The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics. Due to their exchange symmetry, identical particles can appear to be entangled - another uniquely quantum phenomenon with far-reaching practical implications. However, a long-standing debate has questioned whether identical particle entanglement is physical or merely a mathematical artefact. In this work, we provide such particle entanglement with a consistent theoretical description as a quantum resource in processes frequently encountered in optical and cold atomic systems. This leads to a plethora of applications of immediate practical impact. On one hand, we show that the metrological advantage for estimating phase shifts in systems of identical bosons amounts to a measure of their particle entanglement, with a clearcut operational meaning. On the other hand, we demonstrate in general terms that particle entanglement is the property resulting in directly usable mode entanglement when distributed to separated parties, with particle conservation laws in play. Application of our tools to an experimental implementation with Bose-Einstein condensates leads to the first quantitative estimation of identical particle entanglement. Further connections are revealed between particle entanglement and other resources such as optical nonclassicality and quantum coherence. Overall, this work marks a resolutive step in the ongoing debate by delivering a unifying conceptual and practical understanding of entanglement between identical particles

Shortcut to adiabaticity in spinor condensates

We devise a method to shortcut the adiabatic evolution of a spin-1 Bose gas with an external magnetic field as the control parameter. An initial many-body state with almost all bosons populating the Zeeman sublevel $m=0$, is evolved to a final state very close to a macroscopic spin-singlet condensate, a fragmented state with three macroscopically occupied Zeeman states. The shortcut protocol, obtained by an approximate mapping to a harmonic oscillator Hamiltonian, is compared to linear and exponential variations of the control parameter. We find a dramatic speedup of the dynamics when using the shortcut protocol.Comment: 10 pages, 7 figure

Fundamental limit of phase coherence in two-component Bose-Einstein condensates

We experimentally and theoretically study phase coherence in two-component Bose-Einstein condensates of $^{87}{\rm Rb}$ atoms on an atom chip. Using Ramsey interferometry we measure the temporal decay of coherence between the $|F=1,m_{F}=-1\rangle$ and $|F=2,m_{F}=+1\rangle$ hyperfine ground states. We observe that the coherence is limited by random collisional phase shifts due to the stochastic nature of atom loss. The mechanism is confirmed quantitatively by a quantum trajectory method based on a master equation which takes into account collisional interactions, atom number fluctuations, and losses in the system. This decoherence process can be slowed down by reducing the density of the condensate. Our findings are relevant for experiments on quantum metrology and many-particle entanglement with Bose-Einstein condensates and the development of chip-based atomic clocks