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arXiv:0710.5631 · Journal of Physics B Atomic Molecular and Optical Physics

Scheme for implementing atomic multiport devices

J. J. Cooper, D. W. Hallwood, Jacob Dunningham

Published May 8, 2009• 7 citations
arXivHTMLPDF

Abstract

Multiport generalizations of beam splitters are the key component in multipath interferometers, which are important in a range of quantum state engineering and precision measurement schemes. Here we propose a straightforward method for implementing multiport devices for atoms trapped in optical ring lattices. These devices are interesting as atoms have certain properties (such as mass) that photons do not and the ring configuration makes them useful for applications such as precision gyroscopes. We discuss how they could be employed in useful measurement schemes and investigate how practical considerations limit the size of the devices that can be achieved by this method.

DOI
10.1088/0953-4075/42/10/105301

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Multiport generalizations of beam splitters are the key component in multipath interferometers, which are important in a range of quantum state engineering and precision measurement schemes. Here we propose a straightforward method for implementing multiport devices for atoms trapped in optical ring lattices. These devices are interesting as atoms have certain properties (such as mass) that photons do not and the ring configuration makes them useful for applications such as precision gyroscopes. We discuss how they could be employed in useful measurement schemes and investigate how practical considerations limit the size of the devices that can be achieved by this method.
Universal multiport interferometers, which can be programmed to implement any linear transformation between multiple channels, are emerging as a powerful tool for both classical and quantum photonics. These interferometers are typically composed of a regular mesh of beam splitters and phase shifters, allowing for straightforward fabrication using integrated photonic architectures and ready scalability. The current, standard design for universal multiport interferometers is based on work by Reck et al. [Phys. Rev. Lett.73, 58 (1994)PRLTAO0031-900710.1103/PhysRevLett.73.58]. We demonstrate a new design for universal multiport interferometers based on an alternative arrangement of beam splitters and phase shifters, which outperforms that by Reck et al. Our design requires half the optical depth of the Reck design and is significantly more robust to optical losses.
We provide an analytical description of the dynamics of an atom in an optical lattice using the method of perturbative adiabatic expansion. A precise understanding of the lattice-atom interaction is essential to taking full advantage of the promising applications that optical lattices offer in the field of atom interferometry. One such application is the implementation of large momentum transfer (LMT) beam splitters that can potentially provide multiple order of magnitude increases in momentum space separations over current technology. We also propose interferometer geometries where optical lattices are used as waveguides for the atoms throughout the duration of the interferometer sequence. Such a technique could simultaneously provide a multiple order of magnitude increase in sensitivity and a multiple order of magnitude decrease in interferometer size for many applications as compared to current state-of-the-art atom interferometers.
It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose are symmetric, informationally complete POVMs. SIC-POVMs have the advantage of providing an unbiased estimator for the quantum state with the minimal number of outcomes needed for full tomography. By virtue of Naimark's dilation theorem, any POVM can always be realized with a suitable coupling between the system and an auxiliary system and performing a projective measurement on the joint system. In practice, finding the appropriate coupling is rather non-trivial. Here we propose an experimental design for directly implementing SIC-POVMs using multiport devices and path-encoded qubits and qutrits, the utility of which has recently been emphasized by the Zeilinger group in Vienna. Furthermore, we describe how these multiports can be attained in practice with an integrated photonic system composed of nested linear optical elements.
Optical interference is proof of the wave nature of light and matter–wave interferometers have also been shown to work for electrons and neutrons (by exploiting the de Broglie wavelength of the particles). Now a working interferometer for atoms has been demonstrated at the Massachusetts Institute of Technology(MIT) for the first time, in the sense that it uses “atomic beam splitters” to separate and recombine atomic beams (David W Keith et al. Phys. Rev. Lett. (1991) 66 2693). A simpler experiment at Konstanz University, Germany (O Carnal and J Mlynek Phys. Rev. Lett. (1991) 66 2689) has also demonstrated interference phenomena in atomic beams but a detailed description of the apparatus is not yet published. Atom interferometers will some day be useful in precision metrology, mass tomography, precision gyroscopes, general relativity, fundamental quantum mechanics and atomic physics.
A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. it was shown how to build such multiport universal interferometers with a mesh of beam splitters and phase shifters, and this design became the basis for most experimental implementations in the last decades. However, the design of Reck et al. is difficult to scale up to a large number of modes, which would be required for many applications. Here we present a constructive proof that it is possible to realize a multiport universal interferometer on N modes with a succession of 6N Fourier transforms and 6N+1 phase masks, for any even integer N. Furthermore, we provide an algorithm to find the correct succesion of Fourier transforms and phase masks to realize a given arbitrary unitary transformation. Since Fourier transforms and phase masks are routinely implemented in several optical setups and they do not suffer from the scalability issues associated with building extensive meshes of beam splitters, we believe that our design can be useful for many applications in photonics.
It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose is symmetric informationally complete positive operator-valued measurements (SIC-POVMs). SIC-POVMs have the advantage of providing an unbiased estimator for the quantum state with the minimal number of outcomes needed for full tomography. By virtue of Naimark's dilation theorem, any POVM can always be realized with a suitable coupling between the system and an auxiliary system and by performing a projective measurement on the joint system. In practice, finding the appropriate coupling is rather nontrivial. Here we propose an experimental design for directly implementing SIC-POVMs using multiport devices and path-encoded qubits and qutrits, the utility of which has recently been demonstrated by several experimental groups around the world. Furthermore, we describe how these multiports can be attained in practice with an integrated photonic system composed of nested linear optical elements.