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Bulletin of the American Physical Society

Parametric Amplification of Scattered Atom Pairs

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

Published May 17, 2006• 0 citations
OpenAlex

Abstract

We have observed parametric generation and amplification of ultracold atom pairs. A $^{87}\mathrm{Rb}$ Bose-Einstein condensate was loaded into a one-dimensional optical lattice with quasimomentum ${k}_{0}$ and spontaneously scattered into two final states with quasimomenta ${k}_{1}$ and ${k}_{2}$. Furthermore, when a seed of atoms was first created with quasimomentum ${k}_{1}$ we observed parametric amplification of scattered atoms pairs in states ${k}_{1}$ and ${k}_{2}$ 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 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.
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 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.
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.
Bose-Einstein condensates in optical lattices have proven to be a powerful tool for studying a wide variety of physics. In this thesis a series of experiments using optical lattices to manipulate 87Rb Bose-Einstein condensates are described. A systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms has been observed. The recoil frequency was measured interferometrically using a two-pulse Ramsey interferometer. The two pulses were created using a one dimensional optical lattice. By measuring the resulting frequency as a function of the lattice detuning from the atomic resonance, we found a distinctive dispersive shape for the recoil frequency that fit the recoil momentum as nr~k. A one-dimensional optical lattice was used to modify the dispersion relation of the condensate in order to demonstrate the matter-wave analogue of Optical Parametric Generation (OPG) and Amplification (OPA) of photons. A condensate was loaded into a moving optical lattice with adjustable quasimomentum k0. As the value for k0 was varied, we observed elastic scattering into two distinct final momentum states k1
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.
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.