Dynamics and decoherence of two cold bosons in a one-dimensional harmonic trap
- Instytut Fizyki PAN, Al. Lotnikow 32/46, PL-02-668 Warszawa (Poland)
- Wydzial Fizyki, Uniwersytet w Bialymstoku, ul. Lipowa 41, PL-15-424 Bialystok (Poland)
- Wydzial Matematyczno-Przyrodniczy SNS UKSW, Al. Lotnikow 32/46, PL-02-668 Warszawa (Poland)
We study dynamics of two interacting ultracold Bose atoms in a harmonic oscillator potential in one spatial dimension. Making use of the exact solution of the eigenvalue problem of a particle in the {delta}-like potential, we study the time evolution of an initially separable state of two particles. The corresponding time-dependent single-particle density matrix is obtained and diagonalized, and single-particle orbitals are found. This allows us to study decoherence as well as creation of entanglement during the dynamics. The evolution of the orbital corresponding to the largest eigenvalue is then compared to the evolution according to the Gross-Pitaevskii equation. We show that if initially the center of mass and relative degrees of freedom are entangled, then the Gross-Pitaevskii equation fails to reproduce the exact dynamics and entanglement is produced dynamically. We stress that predictions of our study can be verified experimentally in an optical lattice in the low-tunneling limit.
- OSTI ID:
- 21528711
- Journal Information:
- Physical Review. A, Vol. 82, Issue 5; Other Information: DOI: 10.1103/PhysRevA.82.053631; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ATOMS
BOSONS
CENTER-OF-MASS SYSTEM
DEGREES OF FREEDOM
DENSITY MATRIX
EIGENVALUES
EQUATIONS
EXACT SOLUTIONS
HARMONIC OSCILLATORS
MATHEMATICAL EVOLUTION
ONE-DIMENSIONAL CALCULATIONS
PARTICLES
POTENTIALS
QUANTUM ENTANGLEMENT
TIME DEPENDENCE
TUNNEL EFFECT
TWO-BODY PROBLEM
EVOLUTION
MANY-BODY PROBLEM
MATHEMATICAL SOLUTIONS
MATRICES