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arXiv:1002.2516 · Physical Review A

Molecular Feshbach dissociation as a source for motionally entangled atoms

Clemens Gneiting, Klaus Hornberger

Published Jan 29, 2010• 13 citations
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Abstract

We describe the dissociation of a diatomic Feshbach molecule due to a time-varying external magnetic field in a realistic trap and guide setting. An analytic expression for the asymptotic state of the two ultracold atoms is derived, which can serve as a basis for the analysis of dissociation protocols to generate motionally entangled states. For instance, the gradual dissociation by sequences of magnetic field pulses may delocalize the atoms into macroscopically distinct wave packets, whose motional entanglement can be addressed interferometrically. The established relation between the applied magnetic field pulse and the generated dissociation state reveals that square-shaped magnetic field pulses minimize the momentum spread of the atoms. This is required to control the detrimental influence of dispersion in a recently proposed experiment to perform a Bell test in the motion of the two atoms [C. Gneiting and K. Hornberger, Phys. Rev. Lett. 101, 260503 (2008)].

DOI
10.1103/physreva.81.013423

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We describe the dissociation of a diatomic Feshbach molecule due to a time-varying external magnetic field in a realistic trap and guide setting. An analytic expression for the asymptotic state of the two ultracold atoms is derived, which can serve as a basis for the analysis of dissociation protocols to generate motionally entangled states. For instance, the gradual dissociation by sequences of magnetic field pulses may delocalize the atoms into macroscopically distinct wave packets, whose motional entanglement can be addressed interferometrically. The established relation between the applied magnetic field pulse and the generated dissociation state reveals that square-shaped magnetic field pulses minimize the momentum spread of the atoms. This is required to control the detrimental influence of dispersion in a recently proposed experiment to perform a Bell test in the motion of the two atoms [C. Gneiting and K. Hornberger, Phys. Rev. Lett. 101, 260503 (2008)].
The concept of dissociation-time entanglement provides a means of manifesting non-classical correlations in the motional state of two counter-propagating atoms. In this article, we discuss in detail the requirements for a specific experimental implementation, which is based on the Feshbach dissociation of a molecular Bose-Einstein condensate of fermionic lithium. A sequence of two magnetic field pulses serves to delocalize both of the dissociation products into a superposition of consecutive wave packets, which are separated by a macroscopic distance. This allows to address them separately in a switched Mach-Zehnder configuration, permitting to conduct a Bell experiment with simple position measurements. We analyze the expected form of the two-particle wave function in a concrete experimental setup that uses lasers as atom guides. Assuming viable experimental parameters the setup is shown to be capable of violating a Bell inequality.
The concept of dissociation-time entanglement provides a means of manifesting non-classical correlations in the motional state of two counter-propagating atoms. In this article, we discuss in detail the requirements for a specific experimental implementation, which is based on the Feshbach dissociation of a molecular Bose-Einstein condensate of fermionic lithium. A sequence of two magnetic field pulses serves to delocalize both of the dissociation products into a superposition of consecutive wave packets, which are separated by a macroscopic distance. This allows to address them separately in a switched Mach-Zehnder configuration, permitting to conduct a Bell experiment with simple position measurements. We analyze the expected form of the two-particle wave function in a concrete experimental setup that uses lasers as atom guides. Assuming viable experimental parameters the setup is shown to be capable of violating a Bell inequality.
This thesis proposes two complementary scenarios to observe Bell correlations in the motion of two macroscopically separated material particles. Both are based on the gradual dissociation of ultracold Feshbach molecules and result in macroscopic delocalizations of the single-atom states. By giving a full account of these scenarios, including the coupled-channel description of the Feshbach dissociation, the optically guided dispersive propagation, interferometric processing and the final position measurements, I demonstrate for both cases their potential to violate a Bell inequality under experimentally viable conditions that correspond to delocalizations and interatomic separations on the order of centimeters.
We describe a deterministic and experimentally feasible protocol for generating entangled pairs of ultracold neutral atoms through controlled dissociation of diatomic Feshbach molecules. The dissociation process naturally produces nonlocal quantum correlations in spin, position-momentum, and path degrees of freedom, enabling the deterministic preparation of Einstein-Podolsky-Rosen pairs of massive particles and multiqubit states through hyperentangled encoding. Having each atom of the pair prepared in a matter waveguide, the scheme can be scaled to hundreds of parallel entanglement sources in an array connected to a matter wave optical network of beam splitters, phase shifters, interferometers, tunnel junctions and local detectors. The protocol builds on established techniques, including programmable optical potentials, high-fidelity single-particle control, single-molecule initialization, controlled molecular dissociation, and quantum gas microscopy with near-perfect detection, making it directly implementable with current technology. The proposed architecture naturally integrates with atomtronics circuits and chip-based matter-wave optics, offering a deterministic entanglement source for quantum nonlocality tests, precision metrology, and scalable neutral-atom quantum processors.
The effect of random magnetic fields on the dissociation of ultracold molecules with Feshbach resonances is studied analytically. The dissociation spectrum and the evolution of the molecule fraction are obtained for a general form of the magnetic-field ramp and different noise properties relevant to standard experimental conditions. The results uncover the robustness against noise of some characteristics of the dissociation process, in particular, of the dependence of the mean atomic kinetic energy on the system parameters. Implications for the applicability of a method proposed to determine the width of the Feshbach resonances from the measurement of the dissociation spectrum are analyzed. Moreover, we discuss how the presence of fluctuations can affect the use of particular ramp shapes to tailor the properties of the generated atomic distribution.