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Physica Scripta

Entanglement between internal and external degrees of freedom of a driven trapped atom

Maryam Roghani, Hanspeter Helm, Heinz‐Peter Breuer

Published Sep 1, 2010• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/2010/t140/014034

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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.
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 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 investigate the cooling of trapped atoms by electromagnetically induced transparency under conditions of weak confinement and beyond the Lamb-Dicke limit, i.e., the spontaneous decay width is large compared to the trap oscillation frequency and the recoil energy is a substantial fraction of the vibrational energy spacing of the trap. Numerical solutions of the Liouville equation for a density matrix describing states of vibrational and electronic degrees of freedom show that vibrational cooling is feasible at even substantial values of the Lamb-Dicke parameter and under conditions of weak confinement, a situation where sideband pumping is inefficient. Our approach permits us to predict cooling efficiency and cooling rates under realistic experimental conditions for neutral atoms in optical dipole traps.
We theoretically investigate the quantum dynamics of the center of mass of trapped atoms, whose internal degrees of freedom are driven in a $\ensuremath{\Lambda}$-shaped configuration with the lasers tuned at two-photon resonance. In the Lamb-Dicke regime, when the motional wave packet is well localized over the laser wavelength, transient coherent population trapping occurs, canceling transitions at the laser frequency. In this limit the motion can be efficiently cooled to the ground state of the trapping potential. We derive an equation for the center-of-mass motion by adiabatically eliminating the internal degrees of freedom. This treatment provides the theoretical background of the scheme presented in [G. Morigi et al., Phys. Rev. Lett. 85, 4458 (2000)] and implemented in [C.F. Roos et al., Phys. Rev. Lett. 85, 5547 (2000)]. We discuss the physical mechanisms determining the dynamics and identify parameters regimes, where cooling is efficient. We discuss implementations of the scheme to cases where the trapping potential is not harmonic.
We study the time dependence of the spectrum of inelastically scattered radiation from a trapped atom. The atom is illuminated by two lasers tuned to the electromagnetically induced transparency (EIT) of the free atom. For counterpropagating laser beams, rapid removal of vibrational energy is observed as the atom approaches near-EIT conditions. We show that the imbalance in the sidebands of the scattered radiation spectrum explains quantitatively the cooling of the center-of-mass motion of the trapped atom. We also examine parameters critical for EIT cooling in situations far from the Lamb-Dicke limit.
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.