Generation of Macroscopic Pair-Correlated Atomic Beams by Four-Wave Mixing in Bose-Einstein Condensates

Vogels, J. M.; Xu, Kuan‐Man; Ketterle, Wolfgang

doi:10.1103/physrevlett.89.020401

Cited by 127 publications

(201 citation statements)

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“…We also note that a recent analysis [12] of the break-up of a bright matter wave soliton was analyzed in terms of dispersion and phase-matching. Phase-matched FWM has been realized in collisions of two condensates in two dimensions [13,14,15], but in the present paper we show that the process can take place with atomic motion along a single direction, for example inside an atomic waveguide.The basic idea of our proposal is illustrated in Fig. 1.…”

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confidence: 97%

Phase-matched four wave mixing and quantum beam splitting of matter waves in a periodic potential

Hilligsøe

Mølmer

2005

Phys. Rev. A

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We show that the dispersion properties imposed by an external periodic potential ensure both energy and quasi-momentum conservation such that correlated pairs of atoms can be generated by four wave mixing from a Bose-Einstein condensate moving in an optical lattice potential. In our numerical solution of the Gross-Pitaevskii equation, a condensate with initial quasi-momentum k0 is transferred almost completely ( > 95%) into a pair of correlated atomic components with quasimomenta k1 and k2, if the system is seeded with a smaller number of atoms with the appropriate quasi-momentum k1.PACS numbers: 03.75. Kk, 03.75.Lm, Bose-Einstein condensates in optical lattices provide flexible systems for studying the behavior of coherent matter in periodic potentials. Considerable attention is given to studies in regimes far from the region of validity of mean-field analysis and the Gross-Pitaevskii equation [1], but also the highly non-trivial mean-field dynamics has been and continues to be subject to theoretical and experimental investigations [2,3,4].The process we wish to consider is a four wave mixing (FWM) process, which transfers pairs of atoms coherently from an initial momentum state k 0 to new states with momenta k 1 and k 2 . We consider a Bose-Einstein condensate in a quasi-1D geometry and we will consider only the longitudinal dynamics of the condensate. This geometry is relevant, e.g., for atomic wave guides and atom interferometers based on atom chips [5].In Refs. [6,7], it was shown that nonlinear interaction originating from the s-wave scattering between atoms leads to depletion of the condensate and emission of pairs of atoms at other momenta when a continuous matter wave beam passes through a finite region with enhanced interactions. For a larger condensate, however, the process will not be effective unless it conserves both energy and momentum, i.e., the waves must be phase-matched over the extent of the sample. We shall show how the characteristic energy band structure in a one-dimensional optical lattice can be used to ensure both energy and quasi-momentum conservation, i.e., phase-matching of the FWM process.Our tailoring of the dispersion properties of matter waves by an external potential is inspired by approaches to non-linear optics, which employ various means to ensure phase-matching, e.g., of the FWM process [8,9,10]. A similar phase-matched FWM process has been used to explain giant amplification from semiconductor microcavities, where the polariton dispersion properties can be controlled by the strong photon-exciton coupling [11]. We also note that a recent analysis [12] of the break-up of a bright matter wave soliton was analyzed in terms of dispersion and phase-matching. Phase-matched FWM has been realized in collisions of two condensates in two dimensions [13,14,15], but in the present paper we show that the process can take place with atomic motion along a single direction, for example inside an atomic waveguide.The basic idea of our proposal is illustrated in Fig. 1. In a periodic potentia...

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confidence: 97%

Phase-matched four wave mixing and quantum beam splitting of matter waves in a periodic potential

Hilligsøe

Mølmer

2005

Phys. Rev. A

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“…The initial positions of the pairs are also generated randomly, weighted using a probability distribution that is proportional to ρ 0 (x) 2 , where ρ 0 (x) is the density profile of the initial t = 0 condensate. This takes into account the fact that the probability of scattering and hence the probability of pair creation are proportional to the product of the densities of the split condensates ρ 1 (x,t)ρ 2 (x,t), which at time t = 0 is proportional to ρ 0 (x) 2 /4.…”

Section: Appendix: a Classical Test-particle Treatmentmentioning

confidence: 99%

“…Of particular interest is the coherent amplification of matter waves [1][2][3][4] and the generation of paircorrelated atoms [5][6][7][8][9]. Atoms scattered during the collision appear in the form of a spherical shell (a "scattering halo"), with strong correlations in diametrically opposed regions.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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We report the experimental realization of a single-species atomic four-wave mixing process with BoseEinstein-condensate collisions for which the angular distribution of scattered atom pairs is not isotropic, despite the collisions being in the s-wave regime. Theoretical analysis indicates that this anomalous behavior can be explained by the anisotropic nature of the gain in the medium. There are two competing anisotropic processes: classical trajectory deflections due to the mean-field potential and Bose-enhanced scattering which bears similarity to superradiance. We analyze the relative importance of these processes in the dynamical buildup of the anisotropic density distribution of scattered atoms and compare the Bose enhancement effects to those in optically pumped superradiance.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Haine

Ferris

2011

Phys. Rev. A

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We theoretically investigate a scheme for atom interferometry that surpasses the standard quantum limit. A four-wave mixing scheme similar to the recent experiment performed by Pertot et al. [Phys. Rev. Lett. 104, 200402 (2010)] is used to generate subshotnoise correlations between two modes. These two modes are then interfered with the remaining two modes in such a way as to surpass the standard quantum limit, whilst utilizing all of the available atoms. Our scheme can be viewed as using two correlated interferometers. That is, the signal from each interferometer when looked at individually is classical, but there are correlations between the two interferometers that allow for the standard quantum limit to be surpassed.

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Generation of Macroscopic Pair-Correlated Atomic Beams by Four-Wave Mixing in Bose-Einstein Condensates

Cited by 127 publications

References 13 publications

Phase-matched four wave mixing and quantum beam splitting of matter waves in a periodic potential

Phase-matched four wave mixing and quantum beam splitting of matter waves in a periodic potential

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

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

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