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arXiv:cond-mat/0509302

Parametric Amplification of Atoms

Gretchen K. Campbell, Jongchul Mun, Micah Boyd, Erik W. Streed, Wolfgang Ketterle, David E. Pritchard

Published Sep 12, 2005• 2 citations
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Abstract

We have observed parametric generation and amplification of ultracold atom pairs. A 87Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k0 and spontaneously scattered into two final states with quasimomenta k1 and k2 . Furthermore, when a seed of atoms was first created with quasimomentum k1 we observed parametric amplification of scattered atoms pairs in states k1 and k2 when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation (OPG) and amplification (OPA) of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.

DOI
10.48550/arxiv.cond-mat/0509302

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We have observed parametric generation and amplification of ultracold atom pairs. A 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum k0{k}_{0}k0​ and spontaneously scattered into two final states with quasimomenta k1{k}_{1}k1​ and k2{k}_{2}k2​. Furthermore, when a seed of atoms was first created with quasimomentum k1{k}_{1}k1​ we observed parametric amplification of scattered atoms pairs in states k1{k}_{1}k1​ and k2{k}_{2}k2​ when the phase-matching condition was fulfilled. This process is analogous to optical parametric generation and amplification of photons and could be used to efficiently create entangled pairs of atoms. Furthermore, these results explain the dynamic instability of condensates in moving lattices observed in recent experiments.
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We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the quasimomentum state. This is unambiguously attributed to the onset of dynamical instability, after a comparison with the predictions of the Gross-Pitaevskii theory. Deeply in the unstable region we observe the rapid appearance of complex structures in the atomic density profile, as a consequence of the condensate phase uniformity breakdown.
A Bose-Einstein condensate in an optical lattice exhibits parametric resonances when the intensity of the lattice is periodically modulated in time. These resonances correspond to an exponential growth of the population of counter-propagating Bogoliubov excitations. A suitable linearization of the Gross-Pitaevskii (GP) equation is used to calculate the stability diagram and the growth rates of the unstable modes. The results agree with the ones extracted from time-dependent GP simulations, supporting our previous claim [M. Kr\"amer et al., Phys. Rev. A 71, 061602(R) (2005)] concerning the key role of parametric resonances in the response observed by St\"oferle et al. [Phys. Rev. Lett. 92, 130403 (2004)] in the superfluid regime. The role of the seed excitations required to trigger the parametric amplification is discussed. The possible amplification of the quantum fluctuations present in the quasiparticle vacuum, beyond GP theory, is also addressed, finding interesting analogies with similar processes in nonlinear quantum optics and with the dynamic Casimir effect. Our results can be used in exploiting parametric instabilities for the purpose of spectroscopy, selective amplification of a particular excitation mode and for establishing a new type of thermometry.