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arXiv:1707.01279 · Physical Review Letters

Two-Particle Four-Mode Interferometer for Atoms

Pierre Dussarrat, Maxime Perrier, Almazbek Imanaliev, Raphael Lopes, Alain Aspect, Marc Cheneau, Denis Boiron, Christoph Ira Westbrook

Published Oct 24, 2017• 25 citations
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Abstract

We present a free-space interferometer to observe two-particle interference of a pair of atoms with entangled momenta. The source of atom pairs is a Bose-Einstein condensate subject to a dynamical instability, and the interferometer is realized using Bragg diffraction on optical lattices, in the spirit of our recent Hong-Ou-Mandel experiment. We report on an observation ruling out the possibility of a purely mixed state at the input of the interferometer. We explain how our current setup can be extended to enable a test of a Bell inequality on momentum observables.

DOI
10.1103/physrevlett.119.173202

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We present a free-space interferometer to observe two-particle interference of a pair of atoms with entangled momenta. The source of atom pairs is a Bose-Einstein condensate subject to a dynamical instability, and the interferometer is realized using Bragg diffraction on optical lattices, in the spirit of our recent Hong-Ou-Mandel experiment. We report on an observation ruling out the possibility of a purely mixed state at the input of the interferometer. We explain how our current setup can be extended to enable a test of a Bell inequality on momentum observables.
• We present a free-space interferometer to observe two-particle interference of a pair of atoms with entangled momenta. • The source of atom pairs is a Bose-Einstein condensate subject to a dynamical instability, and the interferometer is realized using Bragg diiraction on optical lattices. • Our observations rule out the possibility of a purely mixed state at the input of the interferometer. • Our current setup can be extended to enable a test of a Bell inequality on momentum observables. Bragg mirror and splitters momentum energy excited state • Mirror: 100 µs pulse (π-pulse) • Splitter: 50 µs pulse (π/2-pulse) • The lasers imprint their phase on the atomic modes (φ A,B) • Spectral broadening induced by the short interaction time: → the same lattice addresses (p,-p') and (-p, p') → addition of a velocity-dependent phase away from the energy resonance • Correlation coefficient: E = V cos(φ A-φ B-2δτ) Interferometer diagram • Input state: • Joint detection probabilities: • Correlation coeecient: • Violation of a Bell inequality if V > 1/√2 Source of atom pairs quasimomentum in the lattice frame energy lowest Bloch band 1st BZ • Dynamical instability driven by moving optical lattice → emission of atom pairs with opposite momenta • Broad resonance → several pairs of modes are coherently populated • Filtering the data reduces the state to the desired form: center-of-mass frame • Analysis of 3 diierent sets of modes → access to 3 diierent phases (φ A-φ B-2δτ)
We have developed an atom interferometer to observe two-atom interference of a momentum entangled state. The setup is similar to one used recently in our laboratory to observe the Hong Ou Mandel (HOM) effect for atoms [1], but instead of using two input and two output modes on a beam splitter, we use four input and four output modes. A diagram is shown below. The configuration is essentially that proposed in Ref. [2]. We observe correlations consistent with the presence of an entangled state. An improved setup will allow a test Bell’s inequalities for mechanical degrees of freedom of massive particles.[1] R. Lopes, et al., Nature 520, 66 (2015).[2] M. Horne, A. Shimony, and A. Zeilinger, Phys. Rev. Lett. 62, 2495 (1989).
In this paper, we theoretically study the concept of the wave–particle duality of two entangled neutral Bragg diffracted atoms. This is an extension of a recent study where the same idea was proposed in the photonic setup [Man et al., Sci. Rep. 7, 42539 (2017)] using two independent Mach–Zehnder interferometers. Now, we propose a similar scheme using the cavity-QED based setup, which comprises two independent atomic de Broglie Mach–Zehnder–Bragg interferometers, a source cavity that generates two external momenta state entangled atoms. Once the atoms pass through the source cavity initially prepared in the superposition of zero and one photon, they emerge out of the cavity in entangled momenta state such that if one atom is transmitted to the upper interferometer, then the second atom must traverse the lower interferometer, and vice versa. The final atomic de Broglie beam splitter at the top interferometer is prepared in the superposition of zero and one photon and facilitates observing the wave or particle aspect in a single setting. This entire setup functions in off-resonant Bragg diffraction and the proposed schematics are shown to be experimentally feasible under contemporary research scenarios.
We propose and theoretically simulate an experiment for demonstrating a motional-state Bell inequality violation for pairs of momentum-entangled atoms produced in Bose-Einstein condensate collisions. The proposal is based on realizing an atom-optics analog of the Rarity-Tapster optical scheme: it uses laser-induced Bragg pulses to implement two-particle interferometry on the underlying Bell state for two pairs of atomic scattering modes with equal but opposite momenta. The collision dynamics and the sequence of Bragg pulses are simulated using the stochastic Bogoliubov approach in the positive-PPP representation. We predict values of the Clauser-Horne-Shimony-Holt (CHSH) parameter up to $S\ensuremath{\simeq}2.5$ for experimentally realistic parameter regimes, showing a strong violation of the CSHS-Bell inequality bounded classically by $S\ensuremath{\le}2$.
This manuscript describes quantum atom optics experiments using metastable helium atoms with a single-atom momentum resolved detector. In the first part of this manuscript, the second order correlation measurement of the superradiance from a metastable helium Bose-Einstein condensate is presented. The superradiance effect is the collective radiation of dense ensemble where a strong gain of the radiation is expected. We have shown the thermal like statistics of the emission even in the presence of the strong gain. The next part of the manuscript is devoted to the quantum nonlocality test using a pair of atoms entangled in momentum. The protocol we came up with is inspired from the one of Rarity and Tapster with pairs of photons entangled in momentum. The essential ingredients of this protocol are the atomic pair produced by dynamical instability of the Bose-Einstein condensate in a moving optical lattice, the coherent control of the atomic pair by Bragg diffraction and the correlation measurement of the atoms in different output modes of the interferometric protocol. The experimental characterization and preparation of coherent control by Bragg diffraction are presented showing the proof of principle of such a protocol. The last part of the manuscript discusses the realization of the atomic Hong-Ou-Mandel experiment using the same atomic pair with an atomic beamsplitter. The non-classical interference result of this experiment has opened an opportunity for us to realize Bell’s inequality test with massive particles correlated in external degrees of freedom.