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Journal of Optics B Quantum and Semiclassical Optics

Controlling dynamical phases in quantum optics

Tommaso Calarco, Dieter Jaksch, J. I. Cirac, P. Zoller

Published Aug 1, 2002• 5 citations
Publisher

Abstract

We review and compare several schemes for inducing precisely controlled quantum phases in quantum optical systems. We focus in particular on conditional dynamical phases, i.e. phases obtained via state-and time-dependent interactions between trapped two-level atoms and ions. We describe different possibilities for the kind of interaction to be exploited, including cold controlled collisions, electrostatic forces, and dipole–dipole interactions.

DOI
10.1088/1464-4266/4/4/334

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We review and compare several schemes for inducing precisely controlled quantum phases in quantum optical systems. We focus in particular on conditional dynamical phases, i.e. phases obtained via state-and time-dependent interactions between trapped two-level atoms and ions. We describe different possibilities for the kind of interaction to be exploited, including cold controlled collisions, electrostatic forces, and dipole–dipole interactions.
We investigate to what extent two trapped ions can be manipulated coherently when their coupling is mediated by a dipole—dipole interaction. We will show how the resulting level shift induced by this interaction can be used to create entanglement, while the decay of the states remains nearly negligible. This will allow us to implement conditional dynamics (a CNOT gate) and single qubit operations. We propose two different experimental realizations where a large level shift can be achieved and discuss both the strengths and weaknesses of this scheme from the point of view of a practical realization.
Arrays of optically trapped nanoparticles have emerged as a platform for the study of complex nonequilibrium phenomena. Analogous to atomic many-body systems, one of the crucial ingredients is the ability to precisely control the interactions between particles. However, the optical interactions studied thus far only provide conservative optical binding forces of limited tunability. In this work, we exploit the phase coherence between the optical fields that drive the light-induced dipole-dipole interaction to couple two nanoparticles. In addition, we effectively switch off the optical interaction and observe electrostatic coupling between charged particles. Our results provide a route to developing fully programmable many-body systems of interacting nanoparticles with tunable nonreciprocal interactions, which are instrumental for exploring entanglement and topological phases in arrays of levitated nanoparticles.
The usual form of electromagnetic forces is given by but for neutral atoms q = 0. The next order of force is the dipole term, but this also vanishes because neutral atoms have no inherent dipole moment. However, a dipole moment can be induced by a field, and this is most efficient if the field is alternating near the atomic resonance frequency. Since these frequencies are typically in the optical range, dipole moments are efficiently induced by shining nearly resonant light on the atoms. Laser cooling and trapping rely on the interaction between laser light and atoms to exert a controllable force on the atoms, and many sophisticated schemes have been developed using the special properties of the interaction. This chapter begins with the simplest schemes for exerting optical forces on atoms, namely a single-frequency light field interacting with a two-level atom. Although this is the simplest possible scheme, it is pedagogically valuable because it shows many of the features that will be encountered further on. The ultimate temperature using such a scheme is limited, but lower temperatures can be achieved with multilevel atoms. This topic is addressed later in the chapter. Two kinds of optical forces When an atom absorbs nearly resonant light, it makes a transition to the excited state, and its subsequent return to the ground state can be either by spontaneous or by stimulated emission. The nature of the optical force that arises from these two different processes is quite different, and will be described separately [1]. The spontaneous emission case is different from the familiar quantum mechanical calculations using state vectors to describe the state of the system, because spontaneous emission causes the state of the system to evolve from a pure state into a mixed state (see Exercise 6.9). Spontaneous emission is an essential ingredient for the dissipative nature of the optical forces in monochromatic light, and the density matrix is needed to describe it (see Chap. 6). When an atom absorbs light, its energy excites the atom and its angular momentum changes the electron's orbit. Both of these are internal atomic properties. However, the linear momentum of the light, can change only the external, translational motion of the atom.