Spatial Pair Correlations of Atoms in Molecular Dissociation

Abstract

We perform first-principles quantum simulations of dissociation of trapped, spatially inhomogeneous Bose-Einstein condensates of molecular dimers. Specifically, we study spatial pair correlations of atoms produced in dissociation after time of flight. We find that the observable correlations may significantly degrade in systems with spatial inhomogeneity compared to the predictions of idealized uniform models. We show how binning of the signal can enhance the detectable correlations and lead to the violation of the classical Cauchy-Schwartz inequality and relative number squeezing. DOI: 10.1103/PhysRevLett.99.220404 PACS numbers: 03.75.Nt, 03.65.Ud, 03.75.Gg Producing and utilizing quantum mechanical correlations between entangled particle pairs are major themes in quantum mechanics research. In this Letter we investigate correlations of the kind used by Einstein, Podolsky, and Rosen (EPR) to argue that local realism is inconsistent with quantum mechanics being a complete theory of nature [1]. EPR type nonlocal correlations were first produced experimentally in the form of photon pairs from nondegenerate parametric down-conversion [2]. Here, the correlations are observed between the optical quadrature amplitudes of spatially separated signal and idler beams, which are analogous to canonical position and momentum variables originally discussed by EPR.It should be possible to extend this type of experiment to ultracold atoms, which would allow the investigation of EPR correlations for particles with nonzero rest mass. These might be produced by the transfer of correlations from photons to atoms [3], or else by nonlinear matterwave interactions. The latter include atomic four-wave mixing via Bose-Einstein condensate (BEC) collisions [4,5] and matter-wave down-conversion via dissociation of a molecular BEC [6 -9]. Although the direct measurement of matter-wave quadrature correlations of this type is a challenging task [9], a simpler measurement of densitydensity correlations -as a prerequisite for the EPR quadrature correlations -can be performed with current experimental techniques.In this Letter we perform first-principles quantum simulations of dissociation of a BEC of molecular dimers into pair-correlated bosonic atoms. This has been demonstrated experimentally using ultracold (but not Bose condensed) 87 Rb 2 dimers [10], although the atom correlations have not yet been measured. In the case of fermionic atoms [11,12], such as in dissociation of 40 K 2 dimers [13], the densitydensity correlations between the atoms in two different spin states have been measured; this case, however, currently resists first-principles quantum simulations. Nevertheless, many insights from the present bosonic case also apply to the fermionic case, and to correlations produced via BEC four-wave mixing [14]. For example, the importance of operationally well defined measures of correlations, the role of spatial inhomogeneity, and the trade-off between image resolution and binning to enhance correlation detection.Measurements now ch...

Role of spatial inhomogeneity in dissociation of trapped molecular condensates

“…The strong departure in the actual degree of squeezing from the prediction of the idealized uniform model is perhaps the strongest manifestation of the role of mode-mixing in realistic inhomogeneous systems. As shown previously [40,49], squeezing can be enhanced by binning the atomic signal into bins of larger size, in which case Eq. (24) is no longer applicable.…”

“…We treat these effects explicitly using two alternative phase-space representation techniques: first-principles simulations using the positive-P method [74] and a truncated Wigner approximation [75,76]. Owing to the fact that these phase-space methods are currently well established for bosonic fields (see, e.g., [39,40,42,46,47,77,78]), we restrict our study only to dissociation into bosonic atoms. Development of similar techniques for fermions is under way [41,43], but they are so far limited to treating homogeneous systems and therefore are not adopted yet to the present problem of dissociation of spatially inhomogeneous molecular condensates.…”

“…In the short-time limit, the converted fraction of molecules into constituent atoms is small and one can employ the undepleted molecular-field approximation, which was successfully used in theoretical descriptions of parametric down-conversion in quantum optics [38]. Even though a less restrictive description of dissociation dynamics can be accomplished via state-of-the-art numerical techniques, such as the first-principles simulations using the positive-P and Gaussian representations [39][40][41][42][43], the truncated Wigner function approach [42], the Hartree-FockBogoliubov method [37,42,44], and a generalized GrossPitaevskii (GP) equation [45], the main motivation of the present work is to obtain approximate analytic results which are less computationally expensive and have the intrinsic appeal of analytic simplicity. By comparing these results with the numerical ones, one can verify their accuracy and the range of validity in different parameter regimes.…”

Anisotropy ins-wave Bose-Einstein condensate collisions and its relationship to superradiance

“…Finally, in a broader context, one expects other situations that generate a scattered atom halo, such as molecular dissociation in a condensate [36,37,[42][43][44][45][46][47][48], atomic parametric down-conversion [4,[49][50][51][52][53], or the interaction of a condensate with barriers and obstacles [54][55][56][57][58], to also be susceptible to the same anisotropy-producing processes. …”

Enhanced association and dissociation of heteronuclear Feshbach molecules in a microgravity environment

“…Their heteronuclear counterparts are an important ingredient for the creation of ultracold polar molecules [13][14][15][16][17][18][19][20][21][22][23] and can be used to study universal few-body phenomena [24][25][26][27][28][29][30]. Additionally, Feshbach molecules can be used as a source of entangled states [31][32][33][34][35][36][37][38][39][40][41], or test the variation of fundamental constants with unprecedented sensitivity [42][43][44][45].…”