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Updated: Jul 16, 2026

Spatial Separation of Molecular Conformers and Clusters
Published on: January 9, 2014
Observing the formation of long-range order during Bose-Einstein condensation
Stephan Ritter1, Anton Ottl, Tobias Donner
1Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland.
Researchers experimentally observed the real-time formation of long-range order in ultracold atoms as they crossed the Bose-Einstein condensation phase transition from a nonequilibrium state. This study tracks the growth of phase coherence and its relation to atomic density and momentum distribution.
Area of Science:
- Atomic Physics
- Quantum Gases
- Condensed Matter Physics
Background:
- Bose-Einstein condensation (BEC) is a state of matter formed by cooling atoms to near absolute zero.
- Understanding the dynamics of phase transitions, especially from nonequilibrium states, is crucial for quantum gas research.
- Off-diagonal long-range order signifies the development of quantum coherence in a many-body system.
Purpose of the Study:
- To experimentally investigate the real-time formation of off-diagonal long-range order in ultracold atomic gases.
- To analyze the thermalization process and phase transition dynamics in a highly nonequilibrium atomic cloud.
- To correlate the growth of spatial coherence with atomic density and momentum distribution evolution.
Main Methods:
- Utilized magnetic trapping to prepare a gas of ultracold atoms in a nonequilibrium state.
- Monitored the evolution of phase coherence by measuring the spatial first-order correlation function.
- Observed the real-time dynamics of atomic density and momentum distribution during condensation.
Main Results:
- Observed the spontaneous emergence and growth of spatial coherence, indicating the formation of long-range order.
- Demonstrated that the atomic cloud thermalizes and crosses the Bose-Einstein condensation phase transition.
- Provided real-time data correlating coherence growth with atomic density increase and changes in momentum distribution.
Conclusions:
- The study successfully captured the dynamic formation of Bose-Einstein condensation and long-range order from a nonequilibrium state.
- Real-time measurements offer new insights into the kinetics of quantum phase transitions in ultracold atomic systems.
- The findings contribute to a deeper understanding of coherence development in quantum gases.
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