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Conference on Lasers and Electro-Optics

K-quantum downconversion in the motion of a trapped atom

Sascha Wallentowitz, W. Vogel, P. L. Knight

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given.The phenomenon of multiquantum downconversion is of great interest in quantum optics. In the limit of a classical driving field it can be described by an interaction Hamiltonian (in the interaction picture). For k=2 an interaction of this type is of interest in the context of squeezing. For multiquantum processes of higher order (k>2), however, the Hamiltonian is known to lead to a divergent dynamics. This problem is resolved by taking into account the quantization of the pump mode. More recently, the realization of similar interactions also became possible in the quantized motion of a trapped atom, where the operator it represents the annihilation of a motional quantum of the center-of-mass motion. For k=2 such a dynamic has been used to generate motional squeezing, and other interactions of that type have been considered.

DOI
10.1109/iqec.1998.680266

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Summary form only given.The phenomenon of multiquantum downconversion is of great interest in quantum optics. In the limit of a classical driving field it can be described by an interaction Hamiltonian (in the interaction picture). For k=2 an interaction of this type is of interest in the context of squeezing. For multiquantum processes of higher order (k>2), however, the Hamiltonian is known to lead to a divergent dynamics. This problem is resolved by taking into account the quantization of the pump mode. More recently, the realization of similar interactions also became possible in the quantized motion of a trapped atom, where the operator it represents the annihilation of a motional quantum of the center-of-mass motion. For k=2 such a dynamic has been used to generate motional squeezing, and other interactions of that type have been considered.
We study the counterpart to the multiphoton down-conversion in the quantized motion of a trapped atom. The Lamb-Dicke approximation leads to a divergence of the mean motional excitation in a finite interaction time for k-quantum down-conversions with k> 3,k>~3,k> 3, analogous to the situation in the parametric approximation of nonlinear optics. We show that, in contrast to the Lamb-Dicke approximation, the correct treatment of the overlap of the atomic center-of-mass wave function and the driving laser waves leads to a proper dynamics without any divergence problem. That is, the wavy nature of both matter and light is an important physical property that cannot be neglected for describing the motional dynamics of a trapped atom, even for small Lamb-Dicke parameters.
We study a Raman-driven two-quantum interaction in the motion of a trapped atom, which in the Lamb-Dicke limit corresponds to a classically driven parametric interaction known from nonlinear optics. When the Lamb-Dicke approximation fails, interference effects between the driving laser waves and the spatially extended motional wave function of the atom lead to nonlinear modifications of the motional dynamics. Destructive interferences occur for particular values of the motional amplitude. They lead to a partitioning of the motional phase space accompanied by interesting dynamical effects. Starting the dynamics in the motional ground state of the atom, a quadrature-squeezed state emerges for short interaction times, in agreement with recent experiments [D. M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)]. For longer interaction times the phase-space partitioning gives rise to a reduction of the variance of the motional excitation number and to phase-locking effects leading to a partial revival of the state towards the origin of the phase space.
The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In optically resonant alkali-metal atom systems, we find the effect to be negligibly small. The framework presented here can nevertheless be used for general considerations of the coherent evolution of qubits in moving atoms in an electromagnetic field.
We show how magnetostatic higher-order multipole traps can be used to generate macroscopic quantum interference of the motion of levitated superconducting microparticles. An appropriate combination of multipolar magnetic fields offers great versatility in constructing various trap potentials, including anharmonic trap potentials such as Duffing or double-well types. Crucially, the anharmonic trap potentials realize a nonlinearity on the order of hundred times the zero-point motion, i.e. on a length scale below nanometers. These anharmonic potentials allow for the generation of quantum features of the center-of-mass motion of a magnetically levitated superconducting microparticle. Importantly, they can be easily generated with a static arrangement of coils, requiring only that the current running through them is tunable. We propose protocols exploiting the versatility of the magnetic trap landscape to generate non-Gaussian motional states. We solve the dynamics of the center-of-mass motion of the particle in phase space and analyze its parameter dependence. Furthermore, we give a recipe to distinguish classical from quantum behavior in a statistically meaningful way through measurement of the position of the particle. Our results open a path to accessing the quantum regime of the center-of-mass motion of objects with masses larger than picogram, i.e. 1013^{13}13 atomic mass units. This will enable fundamental physics experiments for studying the transition between quantum and classical behavior, exploring the intersection between quantum physics and gravity as well as probing of certain types of dark matter.