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arXiv:quant-ph/0406020 · Physical Review Letters

Single Atom Transistor in a 1D Optical Lattice

Andrea Micheli, Andrew J. Daley, Dieter Jaksch, P. Zoller

Published Oct 1, 2004• 127 citations
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Abstract

We propose a scheme utilizing a quantum interference phenomenon to switch the transport of atoms in a 1D optical lattice through a site containing an impurity atom. The impurity represents a qubit which in one spin state is transparent to the probe atoms, but in the other acts as a single atom mirror. This allows a single-shot quantum nondemolition measurement of the qubit spin.

DOI
10.1103/physrevlett.93.140408

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We propose a scheme utilizing a quantum interference phenomenon to switch the transport of atoms in a 1D optical lattice through a site containing an impurity atom. The impurity represents a qubit which in one spin state is transparent to the probe atoms, but in the other acts as a single atom mirror. This allows a single-shot quantum nondemolition measurement of the qubit spin.
We propose a scheme utilizing quantum interference to control the transport of atoms in a one-dimensional optical lattice by a single impurity atom. The two internal state of the impurity represent a spin-1∕21∕21∕2 (qubit), which in one spin state is perfectly transparent to the lattice gas, and in the other spin state acts as a single atom mirror, confining the lattice gas. This allows one to ``amplify'' the state of the qubit, and provides a single-shot quantum nondemolition measurement of the state of the qubit. We derive exact analytical expression for the scattering of a single atom by the impurity, and give approximate expressions for the dynamics of a gas of many interacting bosonic or fermionic atoms.
We study the dynamics of many atoms in the recently proposed single-atom-transistor setup [A. Micheli, A. J. Daley, D. Jaksch, and P. Zoller, Phys. Rev. Lett. 93, 140408 (2004)] using recently developed numerical methods. In this setup, a localized spin-1∕21∕21∕2 impurity is used to switch the transport of atoms in a one-dimensional optical lattice: in one state the impurity is transparent to probe atoms, but in the other acts as a single-atom mirror. We calculate time-dependent currents for bosons passing the impurity atom, and find interesting many-body effects. These include substantially different transport properties for bosons in the strongly interacting (Tonks) regime when compared with fermions, and an unexpected decrease in the current when weakly interacting probe atoms are initially accelerated to a nonzero mean momentum. We also provide more insight into the application of our numerical methods to this system, and discuss open questions about the currents approached by the system on long time scales.
The present work investigates the state-selective transport of single neutral cesium atoms in a one-dimensional optical lattice. It demonstrates experimental applications of this transport, including a single atom interferometer, a quantum walk and controlled two-atom collisions. The atoms are stored one by one in an optical lattice formed by a standing wave dipole trap. Their positions are determined with sub-micrometer precision, while atom pair separations are reliably inferred down to neighboring lattice sites using real-time numerical processing. Using microwave pulses in the presence of a magnetic field gradient, the internal qubit states, encoded in the hyperfine levels of the atoms, can be separately initialized and manipulated. This allows us to perform arbitrary single-qubit operations and prepare arbitrary patterns of atoms in the lattice with single-site precision. Chapter 1 presents the experimental setup for trapping a small number of cesium atoms in a one-dimensional optical lattice. Chapter 2 is devoted to fluorescence imaging of atoms, discussing the imaging setup, numeric methods and their performance in detail. Chapter 3 focuses on engineering of internal states of trapped atoms in the lattice using optical methods and microwave radiation. It provides a detailed investigation of coherence properties of our experimental system. Finally manipulation of individual atoms with almost single-site resolution and preparation of regular strings of atoms with predefined distances are presented. In Chapter 4, basic concepts, the experimental realization and the performance of the state-selective transport of neutral atoms over several lattice sites are presented and discussed in detail. Coherence properties of this transport are investigated in Chapter 5, using various two-arms single atom interferometer sequences in which atomic matter waves are split, delocalized, merged and recombined on the initial lattice site, while the interference contrast and the accumulated phase difference are measured. By delocalizing a single atom over several lattice sites, possible spatial inhomogeneities of fields along the lattice axis in the trapping region are probed. In Chapter 6, experimental realization of a discrete time quantum walk on a line with single optically trapped atoms is presented as an advanced application of multiple path quantum interference in the context of quantum information processing. Using this simple example of a quantum walk, fundamental properties of and differences between the quantum and classical regimes are investigated and discussed in detail. Finally, by combining preparation of atom strings, position-dependent manipulation of qubit states and state-selective transport, in Chapter 7, two atoms are deterministically brought together into contact, forming a starting point for investigating two-atom interactions on the most fundamental level. Future prospects and suggestions are finally presented in Chapter 8.
We demonstrate gate operations on a single qubit at a specific site without perturbing the coherence of an adjacent qubit in a 1D optical lattice when the site separation is only 532 nm. Three types of spin rotations are performed on the target qubit with fidelities between 0.88±0.05 and 0.99±0.01, whereas the superposition state of the adjacent one is preserved with fidelities between 0.93±0.04 and 0.97±0.04. The qubit is realized by a pair of Zeeman-sensitive ground hyperfine states of a ^{7}Li atom, and each site is identified by its resonance frequency in a magnetic field gradient of 1.6 G/cm. We achieve the site-specific resolving power in the frequency domain by using magic polarization for the lattice beam that allows a Fourier-limited transition linewidth as well as by highly stabilizing the lattice parameters and the ambient conditions. We also discuss a two-atom entanglement scheme using a blockade by cold collisional shifts in a 1D superlattice, for which a coherent manipulation of individual qubits is a prerequisite.
We have directly observed spin-dependent transport of single cesium atoms in a 1D optical lattice. A superposition of two circularly polarized standing waves is generated from two counter propagating, linearly polarized laser beams. Rotation of one of the polarizations by πππ causes displacement of the σ+σ^{+}σ+- and σ−σ^{-}σ−-lattices by one lattice site. Unidirectional transport over several lattice sites is achieved by rotating the polarization back and forth and flipping the spin after each transport step. We have analyzed the transport efficiency over 10 and more lattice sites, and discussed and quantified relevant error sources.
We report on the state of the art of quantum walk experiments with neutral atoms in state-dependent optical lattices. We demonstrate a novel state-dependent transport technique enabling the control of two spin-selective sublattices in a fully independent fashion. This transport technique allowed us to carry out a test of single-particle quantum interference based on the violation of the Leggett-Garg inequality and, more recently, to probe two-particle quantum interference effects with neutral atoms cooled into the motional ground state. These experiments lay the groundwork for the study of discrete-time quantum walks of strongly interacting, indistinguishable particles to demonstrate quantum cellular automata of neutral atoms.