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arXiv:0705.4647 · Physical Review Letters

Bell’s Inequality and Universal Quantum Gates in a Cold-Atom Chiral Fermionic p -Wave Superfluid

Chuanwei Zhang, Sumanta Tewari, S. Das Sarma

Published Nov 30, 2007• 20 citations
arXivHTMLPDF

Abstract

We propose and analyze a probabilistic scheme to entangle two spatially separated topological qubits in a p{x}+ip{y} superfluid using controlled collisions between atoms in movable dipole traps and unpaired atoms inside vortex cores in the superfluid. We discuss how to test the violation of Bell's inequality with the generated entanglement. A set of universal quantum gates is shown to be implementable deterministically using the entanglement despite the fact that the entangled states can be created only probabilistically.

DOI
10.1103/physrevlett.99.220502

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We propose and analyze a probabilistic scheme to entangle two spatially separated topological qubits in a p{x}+ip{y} superfluid using controlled collisions between atoms in movable dipole traps and unpaired atoms inside vortex cores in the superfluid. We discuss how to test the violation of Bell's inequality with the generated entanglement. A set of universal quantum gates is shown to be implementable deterministically using the entanglement despite the fact that the entangled states can be created only probabilistically.
We study Majorana modes in the vortex core of a two-dimensional p+ipp+ipp+ip Fermi superfluid interacting with a Bose-Einstein condensate. Under a repulsive sss-wave contact interaction between fermions and bosons, fermions are depleted from the vortex core when the bosonic density becomes sufficiently high. This gives rise to a dynamically driven local interface that emerges between fermions and bosons, along which chiral Majorana edge states should appear. We examine in detail the variation of vortex-core structures as well as the formation of chiral Majorana edge states with increasing bosonic density, where the circulation of the vortex plays an important role. Whereas both the Majorana modes and the vortex-core structures can be controlled and manipulated by tuning the bosonic density and the Bose-Fermi interaction strength, our study presents an illuminating example of how topological defects can be dynamically controlled in the context of cold-atomic gases.
We describe how microwave spectroscopy of cold fermions in quasi-1D traps can be used to detect, manipulate, and entangle exotic nonlocal qubits associated with ``Majorana'' edge modes. We present different approaches to generate the ppp-wave superfluidity which is responsible for these topological zero-energy edge modes. We find that the edge modes have clear signatures in the microwave spectrum and that the line shape distinguishes between the degenerate states of a qubit encoded in these edge modes. Moreover, the microwaves rotate the system in its degenerate ground-state manifold. We use these rotations to implement a set of universal quantum gates, allowing the system to be used as a universal quantum computer.
Chiral superfluidity in ultracold Fermi gases represents a fascinating frontier in condensed matter physics, offering a pristine platform for exploring exotic quantum phases with topological properties. This paper provides a comprehensive review of the theoretical underpinnings and potential experimental realizations of chiral superfluids when ultracold Fermi gases are subjected to artificial gauge fields. We begin by introducing the concept of artificial gauge fields, detailing how they can be engineered using laser-atom interactions to impart synthetic spin-orbit coupling and break time-reversal symmetry, thereby creating conditions conducive to chiral order. We then delve into the microscopic theory of chiral pairing, particularly focusing on p-wave and p+ip superfluid states, which are intrinsically chiral and support topologically protected edge modes, such as Majorana fermions. The methodology section outlines the theoretical tools employed, including mean-field BCS theory and Bogoliubov-de Gennes equations, to predict the phase diagrams and spectroscopic signatures of these exotic states. We discuss the effects of varying interaction strengths, gauge field parameters, and trapping potentials on the emergence and stability of chiral phases. The potential for experimental detection through rf spectroscopy, noise correlations, and direct imaging of vortex cores is also addressed. Our findings underscore the significant potential of ultracold atomic systems as quantum simulators for unraveling the mysteries of topological phases, with profound implications for fundamental physics and quantum information science.
Quantum communication relies on the efficient generation of entanglement between remote quantum nodes, due to entanglement's key role in achieving and verifying secure communications. Remote entanglement has been realized using a number of different probabilistic schemes, but deterministic remote entanglement has only recently been demonstrated, using a variety of superconducting circuit approaches. However, the deterministic violation of a Bell inequality, a strong measure of quantum correlation, has not to date been demonstrated in a superconducting quantum communication architecture, in part because achieving sufficiently strong correlation requires fast and accurate control of the emission and capture of the entangling photons. Here we present a simple and robust architecture for achieving this benchmark result in a superconducting system.
Previous work on Bell's inequality realized in the laboratory has used entangled photons. Here we describe how entangled atoms can violate Bell's inequality, and how these violations can be measured with a very high detection efficiency. We first discuss a simple scheme based on two-level atoms inside a cavity to prepare the entangled state. We then discuss a scheme using three-level atoms, which requires a parameter regime much easier to access experimentally using current technology. As opposed to other schemes, our proposal relies on the presence of finite decay rates and its implementation should therefore be much less demanding.