Bogoliubov dynamics of condensate collisions using the positive-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:math>representation

Deuar, P.; Chwedeńczuk, Jan; Trippenbach, Marek; Ziń, P.

doi:10.1103/physreva.83.063625

Cited by 31 publications

(64 citation statements)

References 98 publications

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“…The figure also shows the results of a quantum-mechanical calculation of C using a stochastic Bogoliubov approach (green thick solid curve) [20,21,28]. The calculation is for the initial total number of atoms N ¼ 85 000 and is in good agreement with the observations.…”

Section: Prl 108 260401 (2012) P H Y S I C a L R E V I E W L E T T Esupporting

confidence: 68%

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Matter Waves and Quantum Correlations

Macovei¹

2012

Physics

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The Cauchy-Schwarz (CS) inequality-one of the most widely used and important inequalities in mathematics-can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities. Quantum-mechanical correlations can, however, exceed classical bounds. Here we realize four-wave mixing of atomic matter waves using colliding Bose-Einstein condensates, and demonstrate the violation of a multimode CS inequality for atom number correlations in opposite zones of the collision halo. The Cauchy-Schwarz (CS) inequality is ubiquitous in mathematics and physics [1]. Its utility ranges from proofs of basic theorems in linear algebra to the derivation of the Heisenberg uncertainty principle. In its basic form, the CS inequality simply states that the absolute value of the inner product of two vectors cannot be larger than the product of their lengths. In probability theory and classical physics, the CS inequality can be applied to fluctuating quantities and states that the expectation value of the cross correlation hI 1 I 2 i between two quantities I 1 and I 2 is bounded from above by the autocorrelations in each quantity,This inequality is satisfied, for example, by two classical currents emanating from a common source. In quantum mechanics, correlations can, however, be stronger than those allowed by the CS inequality [2][3][4]. Such correlations have been demonstrated in quantum optics using, for example, antibunched photons produced via spontaneous emission [5], or twin photon beams generated in a radiative cascade [6], parametric down conversion [7], and optical four-wave mixing [8]. Here the discrete nature of the light and the strong correlation (or anticorrelation in antibunching) between photons is responsible for the violation of the CS inequality. The violation has even been demonstrated for two light beams detected as continuous variables [8].In this work we demonstrate a violation of the CS inequality in matter-wave optics using pair-correlated atoms formed in a collision of two Bose-Einstein condensates (BECs) of metastable helium [9-12] (see Fig. 1). The CS inequality which we study is a multimode inequality, involving integrated atomic densities, and therefore is different from the typical two-mode situation studied in quantum optics. Our results demonstrate the potential of atom optics experiments to extend the fundamental tests of quantum mechanics to ensembles of massive particles. Indeed, violation of the CS inequality implies the possibility of (but is not equivalent to) formation of quantum states that exhibit the Einstein-Podolsky-Rosen (EPR) correlations or violate a Bell's inequality [3]. The EPR and Bell-state correlations are of course of wider significance FIG. 1 (color online). Diagram of the collision geometry. (a) Two cigar-shaped condensates moving in opposite directions along the axial direction z shortly after their creation by a Bragg laser pulse (the anisotropy and spatial separation are not to scale). (b) Spherical halo of scattered atoms produced by fou...

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Section: Prl 108 260401 (2012) P H Y S I C a L R E V I E W L E T T Esupporting

confidence: 68%

“…K. V. K. is supported by the ARC FT100100285 grant, P. D. [21] ) calculated using the experimental parameters and a stochastic Bogoliubov approach [20,28].…”

Section: Prl 108 260401 (2012) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Matter Waves and Quantum Correlations

Macovei¹

2012

Physics

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“…The differences have been analyzed, e.g., in Refs. [39,40]. The numerical lattice required to describe this model is too large for a direct solution of the Bogoliubov-de Gennes equations corresponding to (6) to be tractable, so in the stochastic Bogoliubov approach,δ is represented using the positive-P representation.…”

Section: Detailed Quantum Treatment: Stochastic Bogoliubovmentioning

confidence: 99%

“…[39] and was used previously to simulate our experiments and for other studies [7,8,12,22,40]. The approach boils down to evolving the system in a time-dependent Bogoliubov approximation, taking the condensate part 0 (x,t) at time t as the solution of the full Gross-Pitaevskii mean-field evolution equation for the colliding condensates:…”

Section: Detailed Quantum Treatment: Stochastic Bogoliubovmentioning

confidence: 99%

“…The numerical lattice required to describe this model is too large for a direct solution of the Bogoliubov-de Gennes equations corresponding to (6) to be tractable, so in the stochastic Bogoliubov approach,δ is represented using the positive-P representation. In this, we sample the distribution of two complex fields, δ(x,t) and δ(x,t), that representδ andδ † and obey the following linear Itō stochastic differential equations that can be numerically integrated [22,39]:…”

Section: Detailed Quantum Treatment: Stochastic Bogoliubovmentioning

confidence: 99%

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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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Ultracold Atoms for Foundational Tests of Quantum Mechanics

Lewis-Swan¹

2016

Springer Theses

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We investigate the generation, characterization and measurement of non-classical correlations and entanglement in ultracold atomic gases. Specifically, we propose new tests to demonstrate non-classical correlations, Einstein-Podolsky-Rosen (EPR) entanglement and Bell inequality violations, in systems involving dilute gas Bose-Einstein condensates (BECs). We focus on the challenges of generating and preserving these correlations in atom-optics schemes with massive particles and define appropriate operational measurements to demonstrate them experimentally. Further, we characterize how measures of EPR entanglement and violations of a Bell inequality evolve with time and scale with system size.To begin, we detail a theoretical proposal to demonstrate the well-known optical HongOu-Mandel (HOM) effect of destructive quantum interference with massive particles. Our proposed matter-wave experiment, realized recently in a related experimental setup [Lopes et. al., Nature 520, 66 (2015)], utilizes pair-correlated atoms produced via spontaneous fourwave mixing in colliding BECs. The atom pairs are then subjected to Bragg pulses -the atom-optics equivalent of optical mirrors and beam-splitters -to realize a HOM atom interferometer. By taking advantage of the multimode nature of the four-wave mixing process we formulate a measurement protocol which, unlike the optical case, does not require repeated measurements for different beam-splitter settings. We perform numerical simulations of a realistic experimental system and predict a HOM 'dip' visibility of ∼ 69%, indicating the correlations between atom pairs are stronger than classically allowed.In Chapter 5 we outline a theoretical proposal to demonstrate a violation of a motionalstate Bell inequality with massive particles. Identically to Chapter 4, the proposal uses pairs of momentum-entangled atoms produced via spontaneous four-wave mixing in colliding BECs. However, this scheme requires two pairs of atoms which are used as the input state of an atom-optics analog of the Rarity-Tapster interferometer, constructed via a sequence of Bragg pulses. We formulate a measurable form of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality taking into account experimental limitations, and perform numerical simulations of a realistic experimental system for a range of parameters. We predict values of the CHSH-Bell parameter up to S 2.5, demonstrating a violation of the CHSH-Bell inequality which is bounded by S ≤ 2 for local hidden-variable theories.In Chapter 6 we investigate the prospect of demonstrating EPR entanglement between massive particles via spin-changing collisions in a spinor BEC. This investigation is motivated by recent experimental work of Gross et al. [Nature 480, 219 (2011)] who reported inconclusive results in an attempt to measure EPR entanglement. In the experiment, spinchanging collisions between atoms in the (F, m F ) = (2, 0) state lead to pairs of strongly correlated atoms being created in opposing (F, m F ) = (2, ±1) states. For m F = ±1 states in...

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Bogoliubov dynamics of condensate collisions using the positive-Prepresentation

Cited by 31 publications

References 98 publications

Matter Waves and Quantum Correlations

Matter Waves and Quantum Correlations

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

Ultracold Atoms for Foundational Tests of Quantum Mechanics

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