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arXiv:1703.01566 · Physical Review A

Modeling the atomtronic analog of an optical polarizing beam splitter, a half-wave plate, and a quarter-wave plate for phonons of the motional state of two trapped atoms

Naeimeh Mohseni, M. Fani, Jonathan P. Dowling, Shahpoor Saeidian

Published Jul 31, 2017• 1 citation
arXivHTMLPDF

Abstract

In this paper we propose a scheme to model the phonon analog of optical elements, including a polarizing beam splitter, a half-wave plate, and a quarter-wave plate, as well as an implementation of cnot and Pauli gates, by using two atoms confined in a two-dimensional plane. The internal states of the atoms are taken to be Rydberg circular states. Using this model we can manipulate the motional state of the atom, with possible applications in optomechanical integrated circuits for quantum information processing and quantum simulation. Towards this aim, we consider two trapped atoms and let only one of them interact simultaneously with two circularly polarized Laguerre-Gaussian beams.

DOI
10.1103/physreva.96.013859

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In this paper we propose a scheme to model the phonon analog of optical elements, including a polarizing beam splitter, a half-wave plate, and a quarter-wave plate, as well as an implementation of cnot and Pauli gates, by using two atoms confined in a two-dimensional plane. The internal states of the atoms are taken to be Rydberg circular states. Using this model we can manipulate the motional state of the atom, with possible applications in optomechanical integrated circuits for quantum information processing and quantum simulation. Towards this aim, we consider two trapped atoms and let only one of them interact simultaneously with two circularly polarized Laguerre-Gaussian beams.
Circular Rydberg atoms, with their long lifetimes and adjustable strong dipolar interactions, are promising candidates for the implementation of quantum simulations in regimes that were previously out of reach. A new quantum simulator paradigm, based on qubits encoded in circular states, would implement an XXZ spin-1/2 Hamiltonian with dynamically adjustable parameters over a wide range of values. This thesis addresses the preliminary steps in constructing such a quantum simulator. First, we present the realization of two-dimensional arrays of optically-trapped circular Rydberg atoms with arbitrary geometries. For this purpose, we prepare arrays of ultra-cold rubidium atoms, individually trapped in optical tweezers. An additional beam with adjustable position allows us to rearrange the atoms within the array to implement the desired geometry in a deterministic manner. We then excite the atoms to the circular state with principal quantum number n=52, while trapping them in hollow beams using the ponderomotive force. These experimental capabilities allowed us to control and characterize, for the first time, the dipolar interactions between circular states, within pairs of individually trapped atoms. We showed the good agreement of these measurements with theoretical expectations and highlighted their dependence on the system's geometry. This experimental study is coupled to an investigation of the motion of the circular atoms within their traps.
We consider the exchange of spin and orbital angular momenta between a circularly polarized Laguerre–Gaussian beam of light and a single atom trapped in a two-dimensional harmonic potential. The radiation field is treated classically but the atomic centre-of-mass motion is quantized. The internal levels in the atom are taken to be Rydberg circular states. The spin and orbital angular momenta of the field are individually conserved upon absorption, with the result that the electronic and motional degrees of freedom of the atom are entangled. We suggest applications in quantum information processing.
We theoretically investigate the possibility of creating phonon-mediated spin-spin interactions between neutral atoms trapped in optical tweezers. By laser coupling the atoms to Rydberg states, collective modes of motion appear. We show that these can be used to mediate effective spin-spin interactions or quantum logic gates between the atoms in analogy to schemes employed in trapped ions. In particular, we employ Rydberg dressing in a novel scheme to induce the needed interaction, and we show that it is possible to replicate the working of the Mølmer-Sørensen entanglement scheme. The Mølmer-Sørensen gate is widely used in emerging quantum computers using trapped ion qubits and currently features some of the highest fidelities of any quantum gate under consideration. We find arbitrarily high fidelity for the coherent time evolution of the two-atom state even at non-zero temperature.
We discuss three proposed schemes of initializing circular-state Rydberg atoms via optical couplings provided by the ponderomotive effect in contrast to the current circularization methods that utilize electric-dipole interactions. In our first proposed method, a radial optical trap consisting of two Laguerre-Gaussian beams of opposite winding numbers transfers orbital angular momentum to the Rydberg atom, providing a first-order coherent coupling between an F state and a circular state. Additionally, we propose a one-dimensional ponderomotive optical lattice modulated at rf frequencies, providing quadrupolelike couplings in the hydrogenic manifold for rapid adiabatic passage through a series of intermediate Rydberg states into the circular state. For the third proposed scheme, a two-dimensional ponderomotive optical lattice with a time-orbiting trap center induces effectively the same coupling as a ${\ensuremath{\sigma}}^{+}$- or ${\ensuremath{\sigma}}^{\ensuremath{-}}$-polarized rf field of tunable purity for all-optical rapid adiabatic passage into the circular state.
Within the framework of a two-dimensional microscopic, purely quantum mechanical model, we analyse the dynamics of single-photon wave packets interacting with optical elements (beam splitters, mirrors), modelled as systems of two-level atoms. That is, we utilize a two-dimensional cavity to simulate the quantum behaviour of simple optical components and networks made thereof. The field is quantized using the canonical procedure, and only the basis states with one unit of excitation are included. This, however, covers linear optical phenomena. The field is taken to interact with localized atoms through a dipole interaction. Using different configurations of atoms, and choosing their frequencies to be resonant or off-resonance, we can model mirrors, beam splitters, focusing devices and multicomponent systems. Thus we can model arbitrary linear networks of optical components. We show the time evolution of a photon wave packet in an interferometer as an example. As the state of the field is known at each instant, spectral properties and spatial coherence can immediately be obtained from the simulations. We also know the states of the two-level atoms constituting the components, which allows us to consider their quantum behaviour. Here the decay of an excited atom into the vacuum state of the electromagnetic field in the two-dimensional cavity is studied.
We propose an experimentally feasible scheme to generate general entangled states between atoms in spatially separate cavities, and then show one of the applications---a secure communication allowing asymptotically key distribution and quasisecure direct communication. The scheme involves laser manipulation of atoms in a high-QQQ cavity, adjustable quarter- and half-wave plates, beam splitter, polarizing beam splitters, and single-photon detectors, and well fits the status of the current experimental technology.