Abstract
Interference of two independently prepared ideal Bose gases is discussed, on the basis of the idea of measurement-induced interference. It is known that, even if the number of atoms in each gas is individually fixed finite and the symmetry of the system is not broken, an interference pattern is observed on each single snapshot. The key role is played by the Hanbury Brown and Twiss effect, which leads to an oscillating pattern of the cloud of identical atoms. Then, how essential is the Bose-Einstein condensation to the interference? In this work, we describe two ideal Bose gases trapped in two separate three-dimensional harmonic traps at a finite temperature T, using the canonical ensembles (with fixed numbers of atoms). We compute the full statistics of the snapshot profiles of the expanding and overlapping gases released from the traps. We obtain a simple formula valid for finite T, which shows that the average fringe spectrum (average fringe contrast) is given by the purity of each gas. The purity is known to be a good measure of condensation, and the formula clarifies the relevance of the condensation to the interference. The results for T=0, previously known in the literature, can be recovered from our analysis. The fluctuation of the interference spectrum is also studied, and it is shown that the fluctuation is vanishingly small only below the critical temperature Tc, meaning that interference pattern is certainly observed on every snapshot below Tc. The fact that the number of atoms is fixed in the canonical ensemble is crucial to this vanishing fluctuation.
| Original language | English |
|---|---|
| Article number | 033611 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 83 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2011 Mar 14 |
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ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
Cite this
Relevance of Bose-Einstein condensation to the interference of two independent Bose gases. / Iazzi, Mauro; Yuasa, Kazuya.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 83, No. 3, 033611, 14.03.2011.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Relevance of Bose-Einstein condensation to the interference of two independent Bose gases
AU - Iazzi, Mauro
AU - Yuasa, Kazuya
PY - 2011/3/14
Y1 - 2011/3/14
N2 - Interference of two independently prepared ideal Bose gases is discussed, on the basis of the idea of measurement-induced interference. It is known that, even if the number of atoms in each gas is individually fixed finite and the symmetry of the system is not broken, an interference pattern is observed on each single snapshot. The key role is played by the Hanbury Brown and Twiss effect, which leads to an oscillating pattern of the cloud of identical atoms. Then, how essential is the Bose-Einstein condensation to the interference? In this work, we describe two ideal Bose gases trapped in two separate three-dimensional harmonic traps at a finite temperature T, using the canonical ensembles (with fixed numbers of atoms). We compute the full statistics of the snapshot profiles of the expanding and overlapping gases released from the traps. We obtain a simple formula valid for finite T, which shows that the average fringe spectrum (average fringe contrast) is given by the purity of each gas. The purity is known to be a good measure of condensation, and the formula clarifies the relevance of the condensation to the interference. The results for T=0, previously known in the literature, can be recovered from our analysis. The fluctuation of the interference spectrum is also studied, and it is shown that the fluctuation is vanishingly small only below the critical temperature Tc, meaning that interference pattern is certainly observed on every snapshot below Tc. The fact that the number of atoms is fixed in the canonical ensemble is crucial to this vanishing fluctuation.
AB - Interference of two independently prepared ideal Bose gases is discussed, on the basis of the idea of measurement-induced interference. It is known that, even if the number of atoms in each gas is individually fixed finite and the symmetry of the system is not broken, an interference pattern is observed on each single snapshot. The key role is played by the Hanbury Brown and Twiss effect, which leads to an oscillating pattern of the cloud of identical atoms. Then, how essential is the Bose-Einstein condensation to the interference? In this work, we describe two ideal Bose gases trapped in two separate three-dimensional harmonic traps at a finite temperature T, using the canonical ensembles (with fixed numbers of atoms). We compute the full statistics of the snapshot profiles of the expanding and overlapping gases released from the traps. We obtain a simple formula valid for finite T, which shows that the average fringe spectrum (average fringe contrast) is given by the purity of each gas. The purity is known to be a good measure of condensation, and the formula clarifies the relevance of the condensation to the interference. The results for T=0, previously known in the literature, can be recovered from our analysis. The fluctuation of the interference spectrum is also studied, and it is shown that the fluctuation is vanishingly small only below the critical temperature Tc, meaning that interference pattern is certainly observed on every snapshot below Tc. The fact that the number of atoms is fixed in the canonical ensemble is crucial to this vanishing fluctuation.
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UR - http://www.scopus.com/inward/citedby.url?scp=79952673686&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.83.033611
DO - 10.1103/PhysRevA.83.033611
M3 - Article
AN - SCOPUS:79952673686
VL - 83
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 3
M1 - 033611
ER -