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Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms

Abstract

For a system at a temperature of absolute zero, all thermal fluctuations are frozen out, while quantum fluctuations prevail. These microscopic quantum fluctuations can induce a macroscopic phase transition in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value. Here we observe such a quantum phase transition in a Bose–Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. As the potential depth of the lattice is increased, a transition is observed from a superfluid to a Mott insulator phase. In the superfluid phase, each atom is spread out over the entire lattice, with long-range phase coherence. But in the insulating phase, exact numbers of atoms are localized at individual lattice sites, with no phase coherence across the lattice; this phase is characterized by a gap in the excitation spectrum. We can induce reversible changes between the two ground states of the system.

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Figure 1: Schematic three-dimensional interference pattern with measured absorption images taken along two orthogonal directions.
Figure 2: Absorption images of multiple matter wave interference patterns.
Figure 3: Restoring coherence.
Figure 4: Excitation gap in the Mott insulator phase with exactly n = 1 atom per lattice site.
Figure 5: Probing the excitation probability versus an applied vertical potential gradient.
Figure 6: Energy difference between neighbouring lattice sites ΔE for which the Mott insulator phase can be resonantly perturbed versus the lattice potential depth Vmax.

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Acknowledgements

We thank W. Zwerger, H. Monien, I. Cirac, K. Burnett and Yu. Kagan for discussions. This work was supported by the DFG, and by the EU under the QUEST programme.

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Correspondence to Immanuel Bloch.

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Greiner, M., Mandel, O., Esslinger, T. et al. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002). https://doi.org/10.1038/415039a

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