Atom-atom correlations in colliding Bose-Einstein condensates

Abstract

We analyze atom-atom correlations in the s-wave scattering halo of two colliding condensates. By developing a simple perturbative approach, we obtain explicit analytic results for the collinear ͑CL͒ and back-toback ͑BB͒ correlations corresponding to realistic density profiles of the colliding condensates with interactions. The results in the short-time limit are in agreement with the first-principles simulations using the positive-P representation and provide analytic insights into the experimental observations of Perrin et al. ͓Phys Experiments with colliding Bose-Einstein condensates ͑BECs͒ ͓1,2͔ are currently attracting considerable attention in the field of ultracold quantum gases ͓3-11͔. A recent breakthrough in this area is the direct detection ͓2͔ of atomatom pair correlations in the s-wave scattering halo formed in the collision of metastable helium ͑ 4 He * ͒ condensates. Experimental advances like this pose increasingly demanding challenges to theory due to the need to provide quantitatively accurate descriptions in realistic parameter regimes.Theoretical developments are taking place on two fronts, using ͑i͒ numerical techniques based on stochastic phasespace methods ͑such as the first-principles simulations in the positive-P representation ͓9,11͔ or approximate simulations based on the truncated Wigner-function expansion ͓8͔͒, and ͑ii͒ analytic methods such as the Bogoliubov theory ͓5-7͔, undepleted source approximation ͓4,11͔, and a simple Gaussian ansatz ͓10͔. ͑The analytic methods often represent extensions of quantum optics approaches describing closely related systems of parametric down-conversion and four-wave mixing ͓12͔.͒ Despite these developments, the existing numerical techniques still fall short of fully describing the experimental measurements of Ref. ͓2͔, whereas the approximations of the analytic methods are usually too severe to lead to full quantitative agreement with the experiments.In this Rapid Communication, we develop an alternative analytic scheme to obtain explicit results for atom-atom correlations in condensate collisions. The scheme is rather simple, yet it compares surprisingly well with the exact positive-P simulations in the short-time limit. The main advantages of the method are the analytic transparency and the fact that it can model realistic density profiles of the colliding condensates with interactions. This is important for addressing the role of mode mixing due to the inhomogeneity of trapped atomic clouds, which is the strongest effect that influences the strengths and the width of atom-atom correlations. Our results may also have implications for future experiments aimed at producing relative atom number squeezing ͓11,13-15͔ and Einstein-Podolsky-Rosen correlations ͓16,17͔.Additionally, we perform first-principles positive-P simulations of the collision dynamics and analyze the widths of the collinear ͑CL͒ and back-to-back ͑BB͒ correlations as per measurements of Ref. ͓2͔. These characterize, respectively, the pair correlations between the scattered atoms propa...

Role of spatial inhomogeneity in dissociation of trapped molecular condensates

“…A similar behavior is seen in the CL correlation width, except that it starts For longer durations of dissociation-while still within the range of validity of the undepleted molecular-field approximation-we see that the BB correlation width grows faster (for bosons) than the CL correlation width, indicating the possibility that it may eventually become broader than the CL width. A similar behavior has been recently found in first-principle simulations of a related system of atomic four-wave mixing via condensate collisions [46]. Moreover, it has been shown that in the long-time limit the BB correlation width indeed becomes broader than the CL correlation, in agreement with the experimental measurements of Ref.…”

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

“…This can, in principle, be achieved with, e.g., an ∼5 times larger value of the coupling G; however, for the same trap frequencies, such a large value of G would require an ∼5 times larger peak density ρ 0 (0) of the source condensate. The respective initial total atom number in this case would have to be N ∼ 5 × 10 6 [due to the Thomas-Fermi scaling of N ∝ ρ 0 (0) 5/2 ], which is about 50 times larger than in the experiment.…”

“…[3,6]. The undepleted pump refers to the source condensate, which will be assumed to stay constant in time.…”

“…In this model, the scattered atoms can be described by a small fluctuating component ( δ) of the field operator , which is decomposed as in the Bogoliubov approach [7], = 0 + δ, where 0 is the mean-field component. The corresponding Heisenberg equations for δ can be written down as [6] (2) where k 0 is the collision momentum of each condensate and G(x) = gρ 0 (x)/ is an effective parametric coupling spatially dependent on the initial condensate density…”

Surpassing the standard quantum limit in an atom interferometer with four-mode entanglement produced from four-wave mixing

“…Atomic four-wave mixing [15] has long been considered a possible method of creating entanglement between spatially separated atomic modes [16][17][18][19][20][21][22][23], and the generation and detection of quantum correlations using this process has recently been demonstrated [24,25]. Four-wave mixing has an advantage over one-axis-twisting schemes because the correlations produced by the interaction are number correlations and are not as sensitive to the total number of particles.…”