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New Journal of Physics

Quantum random walk with Rydberg atoms in an optical lattice

Robin Côté, Alexander C. Russell, Edward E. Eyler, P. L. Gould

Published Aug 30, 2006• 100 citations
Publisher

Abstract

We study the implementation of quantum random walks (QRWs) in a realistic system, an optical lattice of ultracold Rydberg atoms. The power-law nature of the dipolar interaction between Rydberg atoms influences the behaviour of QRWs. We discuss the QRW with a short-range nearest-neighbour interaction for two types of power-law interactions, the dipole–dipole and the van der Waals interaction. A specific scheme to implement a QRW using Rydberg atoms in different sites of an optical lattice is described, in which the sites are prepared using a blockade mechanism to ensure a single Rydberg atom per site.

DOI
10.1088/1367-2630/8/8/156

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arXiv:1301.0089•Journal of Physics B Atomic Molecular and Optical Physics•Sep 5, 2013•3 citations
We study the implementation of quantum random walks (QRWs) in a realistic system, an optical lattice of ultracold Rydberg atoms. The power-law nature of the dipolar interaction between Rydberg atoms influences the behaviour of QRWs. We discuss the QRW with a short-range nearest-neighbour interaction for two types of power-law interactions, the dipole–dipole and the van der Waals interaction. A specific scheme to implement a QRW using Rydberg atoms in different sites of an optical lattice is described, in which the sites are prepared using a blockade mechanism to ensure a single Rydberg atom per site.
Rydberg atoms have experimentally interestingproperties such as strong long-range Van der Waals interactions and the dipole blockade effect. In optical lattices the blockade effect ensures that only one Rydberg excitation per site is allowed, effectively creating a Rydberg crystal. We theoretically show that it is also possible for a one-dimensional Rydberg crystal to spontaneously form in a random ensemble of atoms, e.g. a magneto-optical trap. This is done using an existing Monte Carlo model [1] to simulate the excitation dynamics inside the intersection of two lasers for a two-step excitation scheme. With a blue-detuned laser for the upper transition, the first Rydberg excitation will occur after a relatively long time. That first Rydberg atom will then seed further Rydberg excitations, as the blockade effect shifts atoms at a certain distance into resonance. If two dimensions of the laser intersection are smaller than the blockade radius, a one-dimensional Rydberg crystal will form.
We present a scalable method for generation of a cluster state for measurement-based quantum computing using van der Waals or dipole-dipole interactions between neutral atoms or polar molecules in an optical lattice. Nearest neighbor entanglement is accomplished by performing a phase gate using interaction of atoms in Rydberg states or molecules in large dipole moment states. All nearest neighbors are sequentially entangled in a finite number of operations, independent of the number of qubits, producing a one-dimensional (1D) cluster state. A universal two-dimensional (2D) cluster state can be generated in several milliseconds in a 2D optical lattice by producing a series of 1D cluster states in one lattice direction, followed by application of the entangling operations in another lattice direction. We discuss the viability of the scheme with Rb Rydberg atoms.
We study the effective dipole–dipole interactions in ultracold quantum gases on optical lattices as a function of asymmetry in confinement along the principal axes of the lattice. In particular, we study the matrix elements of the dipole–dipole interaction in the basis of lowest band Wannier functions which serve as a set of low-energy states for many-body physics on the lattice. We demonstrate that, for shallow lattices in quasi-reduced dimensional scenarios, the effective interaction between dipoles in an optical lattice is non-algebraic in the inter-particle separation at short to medium distance on the lattice scale and has a long-range power-law tail, in contrast to the pure power-law behavior of the dipole–dipole interaction in free space. The modifications to the free-space interaction can be sizable; we identify differences of up to 36% from the free-space interaction at the nearest-neighbor distance in quasi-one-dimensional arrangements. The interaction difference depends essentially on asymmetry in confinement, due to the d-wave anisotropy of the dipole–dipole interaction. Our results do not depend on statistics, applying to both dipolar Bose–Einstein condensates and degenerate Fermi gases. Using matrix product state simulations, we demonstrate that use of the correct lattice dipolar interaction leads to significant deviations from many-body predictions using the free-space interaction. Our results are relevant to up and coming experiments with ultracold heteronuclear molecules, Rydberg atoms and strongly magnetic atoms in optical lattices.
Competing short- and long-range interactions represent distinguished ingredients for the formation of complex quantum many-body phases. Their study is hard to realize with conventional quantum simulators. In this regard, Rydberg atoms provide an exception as their excited manifold of states have both density-density and exchange interactions whose strength and range can vary considerably. Focusing on one-dimensional systems, we leverage the Van der Waals and dipole-dipole interactions of the Rydberg atoms to obtain the zero-temperature phase diagram for a uniform chain and a dimer model. For the uniform chain, we can influence the boundaries between ordered phases and a Luttinger liquid phase. For the dimerized case, a new type of bond-order-density-wave phase is identified. This demonstrates the versatility of the Rydberg platform in studying physics involving short- and long-ranged interactions simultaneously.
Abstract. Neutral atoms excited to Rydberg states can interact with each other via dipole-dipole interaction, which results in a physical phenomenon named Rydberg blockade mechanism. The effect attracts much attention due to its potential applications in quantum computation and quantum simulation. Quantum teleportation has been the core protocol in quantum information science playing a key role in efficient long-distance quantum communication. Here, we first propose the implementation of teleportation scheme with neutral atoms via Rydberg blockade, in which the entangled states of qubits can readily be prepared and the Bell states measurements just require single qubit operations without precise control of Rydberg interaction. The rapid experimental progress of coherent control of Rydberg excitation, optical trapping techniques and state-selective atomic detection promise the application of the teleportation scheme for scalable quantum computation and many-body quantum simulation using the protocol proposed by D. Gottesman and I. L. Chuang [Nature (London) 402, 390 (1999) ] with Rydberg atoms in optical lattice.
Neutral atoms excited to Rydberg states can interact with each other via dipole-dipole interaction, which results in a physical phenomenon named Rydberg blockade mechanism. The effect attracts much attention due to its potential applications in quantum computation and quantum simulation. Quantum teleportation has been the core protocol in quantum information science playing a key role in efficient long-distance quantum communication. Here, we first propose the implementation of teleportation scheme with neutral atoms via Rydberg blockade, in which the entangled states of qubits can readily be prepared and the Bell states measurements just require single qubit operations without precise control of Rydberg interaction. The rapid experimental progress of coherent control of Rydberg excitation, optical trapping techniques and state-selective atomic detection promise the application of the teleportation scheme for scalable quantum computation and many-body quantum simulation using the protocol proposed by D. Gottesman and I. L. Chuang [Nature (London) 402, 390 (1999)] with Rydberg atoms in optical lattice.