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


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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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).

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