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arXiv:1407.8501 · Physical Review A

Toolbox for linear optics in a one-dimensional lattice via minimal control

Enrico Compagno, Leonardo Banchi, Sougato Bose

Published Aug 3, 2015• 11 citations
arXivHTMLPDF

Abstract

Tight-binding lattices offer a unique platform in which particles may be either static or mobile depending on the potential barrier between the sites. How to harness this mobility in a many-site lattice for useful operations is still an open question. We show how effective linear opticslike operations between arbitrary lattice sites can be implemented by a minimal local control which introduces a local impurity in the middle of the lattice. In particular we show how striking is the difference of the two possible correlations with and without the impurity. Our scheme enables the observation of the Hong-Ou-Mandel effect between distant wells without moving them next to each other with, e.g., tweezers. Moreover, we show that a tunable Mach-Zehnder interferometer is implemented adding a steplike potential, and we prove the robustness of our linear optics scheme to interparticle interactions.

DOI
10.1103/physreva.92.022701

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Tight-binding lattices offer a unique platform in which particles may be either static or mobile depending on the potential barrier between the sites. How to harness this mobility in a many-site lattice for useful operations is still an open question. We show how effective linear opticslike operations between arbitrary lattice sites can be implemented by a minimal local control which introduces a local impurity in the middle of the lattice. In particular we show how striking is the difference of the two possible correlations with and without the impurity. Our scheme enables the observation of the Hong-Ou-Mandel effect between distant wells without moving them next to each other with, e.g., tweezers. Moreover, we show that a tunable Mach-Zehnder interferometer is implemented adding a steplike potential, and we prove the robustness of our linear optics scheme to interparticle interactions.
Tight binding lattices offer a unique platform in which particles may be either static or mobile depending on the potential barrier between the sites. It is tempting to use the static and mobile versions of the particles to store and process information respectively. Motivated by this, we show how a beam splitter between two hopping particles traveling from distant lattice sites can be implemented by an on-site potential at the center of the lattice. We show how this enables the two mode Hong-Ou-Mandel effect to be observed, and how the intra-site interaction results in a crossover from bosonic to fermionic behavior close to the superfluid-Mott transition point. A tunable Mach-Zehnder interferometer is implemented adding a step-like potential. Finally we discuss how our results may pave the way towards the realization of a KLM quantum computer with bosonic neutral atoms in a lattice setup.
The possibility to designing schemes useful for developing quantum technology devices of practical value necessitates exploiting quantum coherence effects in a scalable physical system in a feasible way. The broad aim of this thesis is to investigate the use of quantum non-equilibrium dynamics for the above, exploiting minimal control to accomplish highly coherent dynamics in a many-body system. How to harness the natural hopping dynamics of particles in a many-site lattice for controlled applications, is still an open question. Through the introduction of few impurities in the lattice potential, we devise a scheme to trigger effective tunable linear optics-like operations between arbitrary sites, that overcomes the limitations of setups based on coherent hopping dynamics, when particles are initially separated by many sites. Our scheme enables the generation of peculiar quantum interference effects as well as quantum metrology applications in a many-site lattice. We design a lattice coupling profile that enables perfect wave-packet splitting between mirror symmetric sites and leads to perfect wave-packet reconstruction, fractional revivals and perfect entanglement distribution, for arbitrary long chains. We prove that composite objects in a lattice, made of more particles initially in a lattice site, are a valuable resource for dynamically generating non-classical states between remote sites, tackling edge-localisation effects via local fields. Finally, we show how the spin independent scattering of two initially distant qubits, can be used to implement an entangling quantum gate between remote sites of a lattice. Our findings have potentially an impact on quantum information, as well as on atomic interferometry in a lattice.
We experimentally investigate a scheme for studying lattice transport phenomena, based on the controlled momentum-space dynamics of ultracold atomic matter waves. In the effective tight-binding models that can be simulated, we demonstrate that this technique allows for a local and time-dependent control over all system parameters, and additionally allows for single-site resolved detection of atomic populations. We demonstrate full control over site-to-site off-diagonal tunneling elements (amplitude and phase) and diagonal site energies, through the observation of continuous-time quantum walks, Bloch oscillations, and negative tunneling. These capabilities open up new prospects in the experimental study of disordered and topological systems.
Coherent control of motional degrees of freedom of ultracold atoms in optical lattices offers a promising route towards programmable quantum dynamics with massive particles. We propose and analyze a scheme for implementing coherent rearrangement of ultracold atoms, corresponding to arbitrary unitary transformations on single-particle motional states. Exploiting an analogy between dynamics in optical superlattices and discrete linear optics, we employ the Clements scheme to systematically construct any global NNN-dimensional single-particle unitary from tunneling and phase shifts in arrays of double wells. Tunneling is controlled globally, while local operations are achieved through site-resolved potential shifts. We numerically investigate the susceptibility of the scheme to intensity noise and addressing crosstalk. We identify key subroutines enabled by this unitary construction, including the Discrete Fourier Transform and the implementation of non-native Hamiltonians. Extending the scheme to two dimensions enables all-to-all atomic rearrangement with a circuit depth that scales sublinearly with the atom number, providing a high-density and highly scalable approach to atom rearrangement.
Abstract Ultracold atoms in optical lattices have emerged as powerful quantum simulators of translationally invariant systems with many applications in e.g. strongly-correlated and topological systems. However, the ability to locally tune all Hamiltonian parameters remains an outstanding goal that would enable the simulation of a wider range of quantum phenomena. Motivated by recent advances in quantum gas microscopes and optical tweezers, we here show theoretically how local control over individual tunnelling links in an optical lattice can be achieved by incorporating local time-periodic potentials. We propose to periodically modulate the on-site energy of individual lattice sites and employ Floquet theory to demonstrate how this provides full individual control over the tunnelling amplitudes in one dimension. We provide various example configurations realising interesting topological models such as extended Su–Schrieffer–Heeger models that would be challenging to realise by other means. Extending to two dimensions, we demonstrate that local periodic driving in a Lieb lattice engineers a two-dimensional (2D) network with fully controllable tunnelling magnitudes. In a three-site plaquette, we show full simultaneous control over the relative tunnelling amplitudes and the gauge-invariant flux piercing the plaquette, providing a clear stepping stone to building a fully programmable 2D tight-binding model. We also explicitly demonstrate how utilise our technique to generate a magnetic field gradient in 2D. This local modulation scheme is applicable to many different lattice geometries.
Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our recent work on complete characterization of the bound and scattering states of two and three bosonic atoms in a one-dimensional optical lattice. In the case of two atoms, there is a family of interaction-bound "dimer" states of co-localized particles that exists invariantly for either attractive or repulsive on-site interaction, with the energy below or above the two-particle scattering continuum, respectively. Adding then the third particle -- "monomer" -- we find that, apart from the simple strongly-bound "trimer" corresponding to all three particles occupying the same lattice site, there are two peculiar families of weakly-bound trimers with energies below and above the monomer-dimer scattering continuum, the corresponding binding mechanism being an effective particle exchange interaction.