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arXiv:1108.0435 · Physical Review A

Modeling and control of entanglement dynamics in laser cooling of trapped atoms

Maryam Roghani, Heinz‐Peter Breuer, Hanspeter Helm

Published Jan 13, 2012• 4 citations
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Abstract

We discuss the dynamical behavior of the entanglement between the internal and the external degrees of freedom of a trapped atom in electromagnetically induced transparency laser cooling. It is shown that essential features of the intricate entanglement dynamics observed in full numerical simulations of the underlying quantum master equation can be understood in terms of a two-state model on the basis of Landau-Zener splittings in the atom-laser field Hamiltonian. An extension of this model to an effective non-Hermitian Hamiltonian is constructed which describes the decay of entanglement by spontaneous emission processes. We also discuss schemes for the control of entanglement and demonstrate that a permanent entanglement can be imprinted on trapped atoms through a rapid switch-off of the driving fields.

DOI
10.1103/physreva.85.012313

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We discuss the dynamical behavior of the entanglement between the internal and the external degrees of freedom of a trapped atom in electromagnetically induced transparency laser cooling. It is shown that essential features of the intricate entanglement dynamics observed in full numerical simulations of the underlying quantum master equation can be understood in terms of a two-state model on the basis of Landau-Zener splittings in the atom-laser field Hamiltonian. An extension of this model to an effective non-Hermitian Hamiltonian is constructed which describes the decay of entanglement by spontaneous emission processes. We also discuss schemes for the control of entanglement and demonstrate that a permanent entanglement can be imprinted on trapped atoms through a rapid switch-off of the driving fields.
We study the entanglement between the internal electronic and the external vibrational degrees of freedom of a trapped atom which is driven by two lasers into electromagnetically induced transparency. It is shown that basic features of the intricate entanglement dynamics can be traced to Landau-Zener splittings (avoided crossings) in the spectrum of the atom-laser field Hamiltonian. We further construct an effective Hamiltonian that describes the behavior of entanglement under dissipation induced by spontaneous emission processes. The proposed approach is applicable to a broad range of scenarios for the control of entanglement between electronic and translational degrees of freedom of trapped atoms through suitable laser fields.
We study the dynamics of a Λ-shaped trapped atom that is driven by two lasers to conditions approaching electromagnetically induced transparency. Solving numerically the full quantum master equation describing the coupled system of electronic and vibrational degrees of freedom, we investigate the dynamics of the entanglement and the quantum mutual information during the cooling process. Far from the Lamb–Dicke limit, an intricate behaviour of these quantities is found, as well as the emergence of a mixed entangled non-equilibrium stationary state.
A laser cooling method for trapped atoms is described which achieves ground state cooling by exploiting quantum interference in a driven Lambda-shaped arrangement of atomic levels. The scheme is technically simpler than existing methods of sideband cooling, yet it can be significantly more efficient, in particular when several motional modes are involved, and it does not impose restrictions on the transition linewidth. We study the full quantum mechanical model of the cooling process for one motional degree of freedom and show that a rate equation provides a good approximation.
The effect of a coupling laser field on the entanglement of a three-level quantum system and its spontaneous emission is investigated via the reduced quantum entropy.We consider two schemes: the upper-and lower-level couplings.By calculating the degree of entanglement (DEM) for both systems, it is shown that the entanglement between the atom and its spontaneous emission can be controlled by the coupling laser field.This field, however, affects the entanglement differently in the two schemes; it is only the lower-level coupling scheme that shows a non-zero steady state DEM which can be controlled by the intensity and detuning of the coupling laser field.
As research in quantum optics has advanced, so too has our ability to precisely tailor the quantum state of a system.Indeed, techniques for quantum state preparation have become sufficiently advanced that an entire subfield has appeared which has been given the name "quantum control".. Parallel to these advances have been other striking developments in quantum optics, in particular, laser cooling and trapping of nentral atoms.In this paper we describe some of the recent advancements in laser cooling, particularly in our laboratories, and point out that laser cooling and trapping is also realizing an important form of quantum control.In laser cooling, instead of exercising control over the internal quantum state of an atom or molecule or a laser field, we are instead controlling a complementary set of degrees of freedom: those of the external coordinates of the atom.
We demonstrate cooling of the motion of a single neutral atom confined by a dipole trap inside a high-finesse optical resonator. Cooling of the vibrational motion results from electromagnetically induced transparency (EIT)--like interference in an atomic $\ensuremath{\Lambda}$-type configuration, where one transition is strongly coupled to the cavity mode and the other is driven by an external control laser. Good qualitative agreement with the theoretical predictions is found for the explored parameter ranges. Further, we demonstrate EIT cooling of atoms in the dipole trap in free space, reaching the ground state of axial motion. By means of a direct comparison with the cooling inside the resonator, the role of the cavity becomes evident by an additional cooling resonance. These results pave the way towards a controlled interaction among atomic, photonic, and mechanical degrees of freedom.