• 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 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 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 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).
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-P 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 $S\ensuremath{\le}2$.
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 a scheme for trapped-atom interferometry using an interacting Bose-Einstein condensate. The condensate is controlled and spatially split into two confined external momentum modes through a series of Bragg pulses. The proposed scheme (i) allows the generation of large entanglement in a trapped-interferometer configuration via one-axis twisting dynamics induced by interatomic interaction and (ii) avoids the suppression of interactions during the interferometer sequence by a careful manipulation of the state before and after phase encoding. The interferometer can be used for the measurement of gravity with a sensitivity beyond the standard quantum limit.
This thesis contributes to the debate over the viability of using Bose-condensed sources to improve the sensitivity of atom interferometers. Specifically, we present theoretical investigations into (1) the effect of source momentum width on large momentum transfer (LMT) atom interferometry with Bragg pulses, and (2) the prospect of stabilising a high flux, narrow linewidth, continuously pumped atom laser via measurement-based feedback control of the BEC that forms the lasing mode of the atom laser. To begin, this thesis considers the effect of the atomic source's momentum width on the phase sensitivity of Bragg pulse atom interferometers in the Mach-Zehnder configuration. We show that an atomic cloud's momentum width places a fundamental upper bound on the maximum transfer efficiency of a Bragg mirror pulse, and furthermore limits the phase sensitivity of a Bragg pulse atom interferometer. We quantify these momentum width effects and precisely compute how mirror efficiencies and interferometer phase sensitivities vary as functions of Bragg order and source type. In particular, we show that narrow momentum width Bose-condensed sources give comparable sensitivities to broad momentum width thermal sources, even after incorporating the lower atom flux of Bose-condensed sources. Coupled with other favourable properties of Bose-condensed sources, such as their high tolerance to classical noise due to optical wavefront aberrations and the Coriolis effect, this suggests that LMT Bragg atom interferometry with Bose-condensed sources should yield improved sensitivities over current inertial sensors. Furthermore, our results and methodology allow for the efficient optimisation of Bragg pulses, which will help in the design of LMT Bragg mirrors and beamsplitters for atom-interferometer-based inertial sensors, irrespective of source type. In the second part of this thesis, we investigate the prospect of measurement-based feedback control of a BEC, with the aim of reducing density fluctuations by cooling the condensate to a stable spatial mode. Firstly, we consider the effects of experimental imperfections on the estimation-based feedback control of a weakly-interacting BEC undergoing continuous position measurement. These limitations violate the assumption that the estimator (i.e., filter) accurately models the underlying system, thus requiring a separate analysis of the system and filter dynamics. We show that the control scheme is robust to detector inefficiency, time delay, technical noise and miscalibrated parameters. These results imply that reasonable experimental imperfections do not limit the feasibility of cooling a BEC by continuous measurement and feedback. Secondly, we designed a feedback-control scheme for a trapped condensate, with interatomic interactions of any strength, based on a phase-contrast imaging setup. We derive the filtering equation for the system, and show that it gives a continuous measurement of the condensate's density. A semiclassical analysis of this control scheme shows that feedback-cooling of an interacting BEC is also possible, and that the interatomic interactions actually increase the effectiveness of the control. Therefore, measurement-based feedback control can stabilise the spatial mode of a BEC, which is a requirement for the high flux, narrow linewidth, continuously pumped atom laser sources that could potentially give inertial measurement sensitivities orders of magnitude beyond current state-of-the-art devices.