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arXiv:1105.1809

Coherent Directed Transport of Neutral Atoms in Unmodulated Optical Lattices

Morteza Rafiee, Abolfazl Bayat

Published May 9, 2011• 0 citations
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Abstract

Department of Physics and Astronomy, University College London, Gower St., London WC1E 6BT, United Kingdom(Dated: May 11, 2011)We introduce a fully coherent way for directed transport of neutral atoms in optical lattices by regularlyperforming phase shifts on the lattice potential during the free evolution of the system. This paves the way forrealizing quantum gates and entanglement generation by bringing two individual atoms in the proximity of eachother and let them interact. The speed of our protocol is truly determined by the tunneling amplitudes of theatoms and thus is much faster than the speed of the dynamics resulted from superexchange interaction in spinchains or renormalized tunnelings in AC-driven quantum rachets. We also introduce an entanglement witnesswhich allows for experimentally detecting entanglement through local rotations and measurements. Our schemeis robust against possible imperfections and perhaps its main advantage is its simplicity which does not needsophisticated cooling mechanism and all its requirements have been already achieved in recent experiments.

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Department of Physics and Astronomy, University College London, Gower St., London WC1E 6BT, United Kingdom(Dated: May 11, 2011)We introduce a fully coherent way for directed transport of neutral atoms in optical lattices by regularlyperforming phase shifts on the lattice potential during the free evolution of the system. This paves the way forrealizing quantum gates and entanglement generation by bringing two individual atoms in the proximity of eachother and let them interact. The speed of our protocol is truly determined by the tunneling amplitudes of theatoms and thus is much faster than the speed of the dynamics resulted from superexchange interaction in spinchains or renormalized tunnelings in AC-driven quantum rachets. We also introduce an entanglement witnesswhich allows for experimentally detecting entanglement through local rotations and measurements. Our schemeis robust against possible imperfections and perhaps its main advantage is its simplicity which does not needsophisticated cooling mechanism and all its requirements have been already achieved in recent experiments.
In view of the compelling need for coherent atom transport as a prerequisite for a variety of emerging quantum technologies, we investigate such transport on the example of an adjustable family of two-dimensional optical lattices [L. Tarruell {\em et al.}, Nature (London) {\bf 483}, 302 (2012)] that includes square, honeycomb, dimerized, and 1D-chains lattices as its special cases; dynamical optical lattices of this type have already been utilized for the demonstration of topological pumping and the realization of two-qubit quantum gates with neutral atoms. At the outset, we propose the appropriate arrangements of acousto-optic modulators that give rise to a frequency imbalance between counterpropagating laser beams, thus leading to the dynamical-lattice effect in an arbitrary direction in the lattice plane. We subsequently obtain the dynamical-lattice trajectories that enable atom transport in the lattices under consideration using two classes of control schemes: (i) shortcuts to adiabaticity (STA) in the form of inverse engineering based on a dynamical invariant of Lewis-Riesenfeld type, and (ii) their modification, known as enhanced STA (eSTA), which is well-suited for the treatment of anharmonic trapping potentials. We then quantify the resulting atom dynamics using transport fidelities computed from the numerical solutions of the relevant time-dependent Schrödinger equations. By doing so for various choices of the system parameters and transport directions, we demonstrate that -- except in the special case of the dimerized lattice -- the eSTA method consistently outperforms its STA counterpart, both in terms of the achievable transport times and the robustness of the resulting transport against small variations of optical-lattice depths.
Theoretical studies of coherent atom transport have as yet mainly been restricted to one-dimensional model systems with harmonic trapping potentials. Here we investigate this important phenomenon---a prerequisite for a variety of quantum-technology applications based on cold neutral atoms---under much more complex physical circumstances. More specifically yet, we study fast atomic transport in a moving double-well optical lattice, whose three-dimensional (anharmonic) potential is nonseparable in the xxx-yyy plane. We first propose specific configurations of acousto-optic modulators that give rise to the moving-lattice effect in an arbitrary direction in this plane. We then determine moving-lattice trajectories that enable single-atom transport using two classes of quantum-control methods: shortcuts to adiabaticity (STA), here utilized in the form of inverse engineering based on a quadratic-in-momentum dynamical invariant of Lewis-Riesenfeld type, and their recently proposed modification termed enhanced STA (eSTA). Subsequently, we quantify the resulting single-atom dynamics by numerically solving the relevant time-dependent Schr\"odinger equations and compare the efficiency of STA- and eSTA-based transport by evaluating the respective fidelities. We show that---except for the regime of shallow lattices---the eSTA method consistently outperforms its STA counterpart. This study has direct implications for neutral-atom quantum computing based on collisional entangling two-qubit gates and quantum sensing of constant homogeneous forces via guided-atom interferometry.
By loading a Bose-Einstein condensate into a three-dimensional optical lattice potential, we have been able to demonstrate several fundamental aspects of coherent cold collisions between neutral atoms. We show experimentally how such collisions lead to a well-defined phase shift in the corresponding many-body wave function. The experimental realization of such interactions can be fundamental for the simulation of complex condensed-matter-physics Hamiltonians, for the creation of large-scale entanglement and for the realization of quantum gates with neutral atoms.
We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After first preparing localized atomic wave functions in an optical lattice through a Mott insulating phase, we place each atom in a superposition of two internal spin states. Then state selective optical potentials are used to split the wave function of a single atom and transport the corresponding wave packets in two opposite directions. Coherence between the wave packets of an atom delocalized over up to seven lattice sites is demonstrated.
The transport of quantum particles in non ideal material media (eg the conduction of electrons in an imperfect crystal) is strongly affected by scattering from impurities of the medium. Even for a weak disorder, semi-classical theories, such as those based on the Boltzmann equation for matter-waves scattering from the impurities, often fail to describe transport properties and full quantum approaches are necessary. The properties of the quantum systems are of fundamental interest as they show intriguing and non-intuitive phenomena that are not yet fully understood such as Anderson localization, percolation, disorder-driven quantum phase transitions and the corresponding Bose-glass or spin-glass phases. Understanding quantum transport in amorphous solids is one of the main issues in this context, related to electric and thermal conductivities. Ultracold atomic gases can now be considered to revisit the problem of quantum conductivity and quantum transport under unique control possibilities. Dilute atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases (DFG) are produced routinely taking advantage of the recent progress in cooling and trapping of neutral atoms. Transport has been widely investigated in controlled potentials with no defects, for instance periodic potentials (optical lattices). Controlled disordered potentials can also be produced with various techniques such as the use of magnetic traps designed on atomic chips with rough wires, the use of localized impurity atoms, the use of radio-frequency fields or the use of optical potentials. This recently lead to the observation of the Anderson Localisation of a BEC and the measurement of the diffusion coefficient of a 2D gaz in the presence of disorder.
We review the quantum transport of ultra-cold alkali atoms trapped in a one-dimensional optical lattice of double-potential wells, engineered through a combination of ac-Stark shifts and Zeeman interactions. The system is modelled numerically through analysis of the bandstructure and integration of the time-dependent Schrödinger equation. By these means we simulate coherent control of the atomic wavepackets. We present results from ongoing experiments on laser-cooled caesium, including the demonstration of quantum state preparation and preliminary evidence for coherent tunnelling. Entanglement between the internal and motional degrees of freedom allows us to access the tunnelling dynamics by Stern-Gerlach measurements of the ground state magnetic populations. A scheme to extend this into a full reconstruction of the density matrix for the ground state angular momentum is presented. We further consider the classical dynamics of our system, which displays deterministic chaos. This has important implications for the distinction between classical and quantum mechanical transport.