Entanglement of Atoms via Cold Controlled Collisions

Abstract

We show that by using cold controlled collisions between two atoms one can achieve conditional dynamics in moving trap potentials. We discuss implementing two qubit quantum-gates and efficient creation of highly entangled states of many atoms in optical lattices. 32.80.Pj, 03.67.Lx, 34.90.+q.The controlled manipulation of entangled states of Nparticle systems is fundamental to the study of basic aspects of quantum theory [1,2], and provides the basis of applications such as quantum computing and quantum communications [3,4]. Engineering entanglement in real physical systems requires precise control of the Hamiltonian operations and a high degree of coherence. Achieving these conditions is extremely demanding, and only a few systems, including trapped ions, cavity QED and NMR, have been identified as possible candidates to implement quantum logic in the laboratory [3]. On the other hand, in atomic physics with neutral atoms recent advances in cooling and trapping have led to an exciting new generation of experiments with Bose condensates [5], experiments with optical lattices [6], and atom optics and interferometry. The question therefore arises, to what extent these new experimental possibilities and the underlying physics can be adapted to provide a new perspective in the field of experimental quantum computing.In this Letter we propose coherent cold collisions as the basic mechanism to entangle neutral atoms. The picture of atomic collisions as coherent interactions has emerged during the last few years in the studies of Bose Einstein condensation (BEC) of ultracold gases. In a field theoretic language these interactions correspond to Hamiltonians which are quartic in the atomic field operators, analogous to Kerr nonlinearities between photons in quantum optics. By storing ultracold atoms in arrays of microscopic potentials provided, for example, by optical lattices these collisional interactions can be controlled via laser parameters. Furthermore, these nonlinear atomatom interactions can be large [7], even for interactions between individual pairs of atoms, thus providing the necessary ingredients to implement quantum logic.Let us consider a situation where two atoms |a and |b are trapped in the ground states ψ a,b 0 of two potential wells V a,b . Initially, at time t = −τ , these wells are centered at positionsx a andx b , sufficiently far apart (distance d =x b −x a ) so that the particles do not interact. The positions of the potentials are moved along trajectoriesx a (t) andx b (t) so that the wavepackets of the atoms overlap for certain time, until finally they are restored to the initial position at the final time t = τ . This situation is described by the HamiltonianHere, x a,b and p a,b are position and momentum operators, V a,b x a,b −x a,b (t) describe the displaced trap potentials and u ab is the atom-atom interaction term. Ideally, we would like to implement the transformationwhere each atom remains in the ground state of its trapping potential and and preserves its internal state. The phase φ w...

Collapse and revival of the matter wave field of a Bose–Einstein condensate

“…In a next step it will be intriguing to start from a Mott insulating state and use the coherent collisions between single atoms, which have been demonstrated here, to create a many-atom entangled state [18][19][20] . This highly entangled state could then serve as a promising new starting point for quantum computing with neutral atoms 19,21 .…”

Quantencomputer: Wie sich Verschränkung für die Informationsverarbeitung nutzen läßt

“…Ein neuer Vorschlag [28,31] für einen Quantencomputer basiert auf Stößen zwischen ultrakalten Atomen als Mechanismus zur kontrollierten Erzeugung von Verschränkung (siehe auch [29]). Mit diesem Mechanismus sollten sich wichtige Konzepte der Quanteninformationstheorie in Systemen wie optischen Gittern und magnetischen Mikrofallen experimentell studieren lassen [31].…”

“…Übergänge zwischen diesen Zuständen lassen sich wie bei Ionenfallen durch Raman-Laserpulse induzieren. Ein Quantengatter läßt sich realisieren, indem die internen Atomzustände an zwei verschiedene Fallenpotentiale koppeln, die räumlich gegeneinander verschoben werden [28]. Dies kann man durch eine Variation der Polarisation der Laser erreichen, wie in Abb.…”

Two-Qubit Gate Operation on Selected Nearest-Neighbor Neutral Atom Qubits

“…A collision in the subspace |0 |1 can be caused by controlling the polarization of the counterpropagating beams of the optical lattice [ Fig. 1(d)], so that this particular component acquires an extra dynamical phase [11,12]. Subsequently, the polarizations are reversed and the atoms are returned to their initial positions in the optical lattice.…”