Abstract
To calculate static response properties of a many-body system, local density approximation (LDA) can be safely applied. But, to obtain dynamical response functions, the applicability of LDA is limited bacause dynamics of the system needs to be considered as well. To examine this in the context of cold atoms, we consider a system of non-interacting spin-\(\frac {1}{2}\) fermions confined by a harmonic trapping potential. We have calculated a very important response function, the spectral intensity distribution function (SIDF), both exactly and using LDA at zero temperature and compared with each other for different dimensions, trap frequencies and momenta. The behaviour of the SIDF at a particular momentum can be explained by noting the behaviour of the density of states (DoS) of the free system (without trap) in that particular dimension. The agreement between exact and LDA SIDFs becomes better with increase in dimensions and number of particles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E A Cornell and C E Wieman, Rev. Mod. Phys. 74, 875 (2002)
M Greiner, O Mandel, T Esslinger, T W Hansch and I Bloch, Nature 415, 39 (2002)
C A Regal and D S Jin, Adv. Atom. Mol. Opt. Phys. 54, 1 (2006)
Y-J Lin, R L Compton, K J Garcia, J V Porto and I B Spielman, Nature 462, 628 (2009)
Y-J Lin, R L Compton, A R Perry, W D Phillips, J V Porto and I B Spielman, Phys. Rev. Lett. 102, 130401 (2009)
J Dalibard, F Gerbier, G Juzeliünas and P Öhberg, Rev. Mod. Phys. 83, 1523 (2011)
S K Ghosh, J P Vyasanakere and V B Shenoy, Phys. Rev. A 84, 053629 (2011)
J P Vyasanakere and V B Shenoy, Phys. Rev. B 83, 094515 (2011)
H Hu, L Jiang, X-J Liu and H Pu, Phys. Rev. Lett. 107, 195304 (2011)
J P Vyasanakere, S Zhang and V B Shenoy, Phys. Rev. B 84, 014512 (2011)
P Wang, Z-Q Yu, Z Fu, J Miao, L Huang, S Chai, H Zhai and J Zhang, Phys. Rev. Lett. 109, 095301 (2012)
L W Cheuk, A T Sommer, Z Hadzibabic, T Yefsah,WS Bakr and MWZwierlein, Phys. Rev. Lett. 109, 095302 (2012)
R Comin and A Damascelli, arXiv preprint arXiv:1303.1438
A Damascelli, Z Hussain and Z-X Shen, Rev. Mod. Phys. 75, 473 (2003)
T L Dao, A Georges, J Dalibard, C Salomon and I Carusotto, Phys. Rev. Lett. 98, 240402 (2007)
J T Stewart, J P Gaebler and D S Jin, Nature 454, 744 (2008)
J P Gaebler, J T Stewart, T E Drake, D S Jin, A Perali, P Pieri and G C Strinati, Nature Phys. 6, 569 (2010)
B Fröhlich, M Feld, E Vogt, M Koschorreck, W Zwerger and M Köhl, Phys. Rev. Lett. 106, 105301 (2011)
V Pietilä, Phys. Rev. A 86, 023608 (2012)
E K U Gross and W Kohn, Phys. Rev. Lett. 55, 2850 (1985)
K Yabana and G F Bertsch, Int. J. Quant. Chem. 75, 55 (1999)
L Pezzè, L Pitaevskii, A Smerzi, S Stringari, G Modugno, E de Mirandes, F Ferlaino, H Ott, G Roati and M Inguscio, Phys. Rev. Lett. 93, 120401 (2004)
E J Mueller, Phys. Rev. Lett. 93, 190404 (2004)
F Gleisberg, W Wonneberger, U Schlöder and C Zimmermann, Phys. Rev. A 62, 063602 (2000)
P Vignolo, A Minguzzi and M P Tosi, Phys. Rev. Lett. 85, 2850 (2000)
D A Butts and D S Rokhsar, Phys. Rev. A 55, 4346 (1997)
D J Toms, Ann. Phys. 320, 487 (2005)
J Schneider and H Wallis, Phys. Rev. A 57, 1253 (1998)
T Loftus, C A Regal, C Ticknor, J L Bohn and D S Jin, Phys. Rev. Lett. 88, 173201 (2002)
Acknowledgements
The author acknowledges Vijay B Shenoy for extensive discussions. The financial support from CSIR, India through SRF grants is thankfully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
GHOSH, S.K. Spectral intensity distribution of trapped fermions. Pramana - J Phys 85, 605–616 (2015). https://doi.org/10.1007/s12043-014-0903-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-014-0903-6