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arXiv:cond-mat/0506498 · Physical Review A

Single-atom mirror for one-dimensional atomic lattice gases

Andrea Micheli, P. Zoller

Published Apr 20, 2006• 15 citations
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Abstract

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-$1∕2$ (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.

DOI
10.1103/physreva.73.043613

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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.
Quantum gases in optical lattices allow for fundamental studies in atomic and condensed-matter physics and the exploration of novel effects. After a brief introduction to the fundamentals of quantum gas experiments in optical lattices, we discuss two recent experiments focusing on driven matter waves in a one-dimensional optical lattice. The first experiment uses a tilted bichromatic optical lattice to investigate the interplay of disorder and collisional interactions in the accelerated transport of a Bose-Einstein condensate. Here, a screening effect is observed, in which the interactions effectively cancel the damping of Bloch oscillations induced by a (quasi-)disordered potential. This effect can be understood through a modification of the underlying band structure by the interactions. The second experiment studies the dynamics of a weakly trapped condensate resonantly coupled to the orbitals of a strongly confining state-selective lattice. We observe momentum distributions that correspond to matter wave diffraction from a periodic structure; however, the diffractive dynamics remain strongly linked to the internal-state Rabi oscillations. In the regime investigated, which we call the nonadiabatic regime, no diffracting potential can be defined. We show how only for much stronger coupling, the internal and external dynamics decouple, transitioning from nonadiabatic diffraction to the well-studied Kapitza-Dirac diffraction. We further investigate prospects for realizing dissipative spin models in our ultracold atomic gas experiment. To this end, we develop and test in the laboratory several possible implementations of effective spins with differential coupling to a superfluid background and examine their viability for a realization of the spin-boson model. | 94 pages
Using near-exact numerical simulations, we study the propagation of an impurity through a one-dimensional Bose lattice gas for varying bosonic interaction strengths and filling factors at zero temperature. The impurity is coupled to the Bose gas and confined to a separate tilted lattice. The precise nature of the transport of the impurity is specific to the excitation spectrum of the Bose gas, which allows one to measure properties of the Bose gas nondestructively, in principle, by observing the impurity; here we focus on the spatial and momentum distributions of the impurity as well as its reduced density matrix. For instance, we show it is possible to determine whether the Bose gas is commensurately filled as well as the bandwidth and gap in its excitation spectrum. Moreover, we show that the impurity acts as a witness to the crossover of its environment from the weakly to the strongly interacting regime, i.e., from a superfluid to a Mott insulator or Tonks-Girardeau lattice gas, and the effects on the impurity in both of these strongly interacting regimes are clearly distinguishable. Finally, we find that the spatial coherence of the impurity is related to its propagation through the Bose gas.
We study the atom-light interaction in the fully quantum regime, with the focus on off-resonant light scattering into a cavity from ultracold atoms trapped in an optical lattice. The detection of photons allows the quantum nondemolition (QND) measurement of quantum correlations of the atomic ensemble, distinguishing between different quantum states. We analyse the entanglement between light and matter and show how it can be exploited for realising multimode macroscopic quantum superpositions, such as Schrödinger cat states, for both bosons and fermions. We provide examples utilising different measurement schemes and study their robustness to decoherence. Finally, we address the regime where the optical lattice potential is a quantum dynamical variable and is modified by the atomic state, leading to novel quantum phases and significantly altering the phase diagram of the atomic system.