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A two-particle, four-mode atom interferometer (Orale)

Christoph Ira Westbrook

Published Jun 3, 2017• 0 citations
OpenAlex

Abstract

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).

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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 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.
The celebrated Hong - Ou - Mandel effect is one of the simplest illustrations of two-particle interference, and is unique to the quantum realm. In the original experiment, two photons arriving simultaneously in the input channels of a beam-splitter were observed to always emerge together in one of the output channels. I will discuss the realisation of a closely analogous experiment with atoms instead of photons. This opens the prospect of setting up experiments to violate Bell's inequalities involving mechanical observables of massive particles, such as momentum, using methods inspired by quantum optics. Our work also demonstrates a new way to produce and benchmark twin-atom pairs that are of interest for quantum information processing and quantum simulation.
The quantum theory has introduced physicists to two major counter-intuitive concepts. On the one hand, there is wave-particle duality, expressing the idea that objects normally described as particles can also behave as waves, while entities primarily described as waves, such as light, can behave as particles. This revolutionary idea nev- ertheless relies on concepts borrowed from classical physics, either waves or particles evolving in an ordinary space-time. On the other hand, entanglement can lead to interferences between the amplitudes of multi-particle states, which are described via Hilbert space and have no classical counter-part.This fundamental feature has of course been strikingly demonstrated by the violation of Bell’s inequalities. There is however, a conceptually simpler situation in which the interference between two-particle amplitudes entails a behavior impossible to describe by any classical model. This is the celebrated Hong Ou and Mandel experiment, in which two photons arriving simultaneously in the input channels of a beam-splitter always emerge together in one of the output channels. This effect has been extensively used to characterize the quality of non- classical light sources.Our group in Palaiseau has recently realized a Hong-Ou-Mandel experiment using metastable helium atoms [1]. A schematic diagram of the apparatus is shown in Fig. 1. We monitor the cross correlation signal between the two output ports ⟨nˆcnˆd⟩ as a function of the time t3 of application of the beam splitter. At this time we observe a 65% reduction in the cross correlation. This degree of supression cannot be explained by either a wavelike or particlelike description of the atoms.
Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.
• 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 show that multimode entanglement of electrons in a mesoscopic conductor can be detected by a measurement of the zero-frequency current correlations in an electronic Hong-Ou-Mandel interferometer. By this means, one can further establish a lower bound to the entanglement of formation of two-electron input states. Our results extend the work of Burkard and Loss [Phys. Rev. Lett. 91, 087903 (2003)] to many channels and provide a way to test the existence of entangled states involving both orbital and spin degrees of freedom.