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Classical Bifurcation and Entanglement Generation in an Internal Bosonic Josephson Junction

Tilman Zibold

Published Jan 1, 2012• 4 citations
Publisher

Abstract

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.

DOI
10.11588/heidok.00013529

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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.
We report on the experimental demonstration of the internal bosonic Josephson effect in a rubidium spinor Bose-Einstein condensate. The measurement of the full time dynamics in phase space allows the characterization of the theoretically predicted π-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.
The twist-and-turn dynamics of spin squeezing results from the interplay of the one-axis-twisting (nonlinear in the collective-spin operators) and the transverse-field turning (linear) term in the underlying Lipkin-Meshkov-Glick-type Hamiltonian, both with constant (time-independent) prefactors. Using shortcuts to adiabaticity (STA) and the recently developed enhanced version thereof (eSTA), we demonstrate here that dynamics of this type can be utilized for a fast and robust preparation of spin-squeezed states in internal bosonic Josephson junctions, i.e., condensates of cold bosonic atoms in two different internal (hyperfine) states (single-boson modes) coupled through Rabi rotations. Assuming that the initial state of this system is its ground state for a given initial value of the (time-dependent) linear coupling strength and that the nonlinear coupling strength remains constant, we set out to determine the time dependence of the linear (Rabi) coupling strength that allows for the generation of spin-squeezed states using the STA- and eSTA-based approaches. We then characterize the modified twist-and-turn dynamics of this system by evaluating the coherent spin-squeezing and number-squeezing parameters, as well as the fidelity of the target spin-squeezed states. In this way, we show that the eSTA approach allows for a particularly robust realization of strongly spin-squeezed states in this system, consistently outperforming its adiabatic and STA-based counterparts, even for systems with several hundred particles. Our method could also be employed for the generation of metrologically-useful non-Gaussian states.
We analyze the formation of squeezed states in a condensate of ultracold bosonic atoms confined by a double-well potential. The emphasis is set on the dynamical formation of such states from initially coherent many-body quantum states. Two cases are described: the squeezing formation in the evolution of the system around the stable point, and in the short-time evolution in the vicinity of an unstable point. The latter is shown to produce highly squeezed states on very short times. On the basis of a semiclassical approximation to the Bose-Hubbard Hamiltonian, we are able to predict the amount of squeezing, its scaling with NNN, and the speed of coherent spin formation with simple analytical formulas which successfully describe the numerical Bose-Hubbard results. This method of producing highly squeezed spin states in systems of ultracold atoms is compared to other standard methods in the literature.
In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the discrete self-trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from quantum information theory, i.e., the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero-temperature case, but considers thermal effects as well.
Quantum simulators built from ultracold atoms promise to study quantum phenomena in interacting many-body systems. However, it remains a challenge to experimentally prepare strongly correlated continuous systems such that the properties are dominated by quantum fluctuations. Here, we show how to enhance the quantum correlations in a one-dimensional multimode bosonic Josephson junction, which is a quantum simulator of the sine-Gordon field theory. Our approach is based on the ability to track the nonequilibrium dynamics of quantum properties. After creating a bosonic Josephson junction at the stable fixed point of the classical phase space, we observe squeezing oscillations in the two conjugate variables. We show that the squeezing oscillation frequency can be tuned by more than one order of magnitude, and we are able to achieve a spin squeezing close to 10 dB by utilizing these oscillatory dynamics. The impact of improved spin squeezing is directly revealed by detecting enhanced spatial phase correlations between decoupled condensates. Our work provides new ways for engineering correlations and entanglement in the external degree of freedom of interacting many-body systems. Published by the American Physical Society 2024
We study the decay of phase coherence in an extended bosonic Josephson junction realized via two tunnel-coupled Bose-Einstein condensates. Specifically, we focus on the \pi π -trapped state of large population and phase imbalance, which, similar to the breakdown of macroscopic quantum self-trapping, becomes dynamically unstable due to the amplification of quantum fluctuations. We analytically identify early tachyonic and parametric instabilities connected to the excitation of atom pairs from the condensate to higher momentum modes along the extended direction. Furthermore, we perform Truncated Wigner numerical simulations to observe the build-up of non-linearities at later times and explore realistic experimental parameters.