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Journal of Optics B Quantum and Semiclassical Optics

On decoherence and nonlinear effects in the generation of quantum states of motion in Paul traps

Rocío Jáuregui, J. Récamier, Pedro Antonio Quinto-Su

Published Jun 18, 2001• 4 citations
Publisher

Abstract

We study some possible sources of decoherence in the generation of nonclassical states of motion of ions in Paul traps by means of numerical simulations based on reported experiments. In particular we study the consequences of the spontaneous decay of the internal energy state |0⟩ i which couples the two hyperfine internal states |1⟩ i and |2⟩ i in the two-photon Raman transitions used to manipulate the ion motional state. We also consider some possible experimental limitations to generate coherent states due to nonlinear effects in the coupling of the centre-of-mass coordinates with the laser field. A similar analysis is performed for carrier pulses taking into account nonlinearities and micromotion. The quantum evolution of the ion internal and centre-of-mass degrees of freedom are studied using amplitude equations derived from Schrödinger's equation. The limitations of such an approach are also discussed.

DOI
10.1088/1464-4266/3/4/302

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We study some possible sources of decoherence in the generation of nonclassical states of motion of ions in Paul traps by means of numerical simulations based on reported experiments. In particular we study the consequences of the spontaneous decay of the internal energy state |0⟩ i which couples the two hyperfine internal states |1⟩ i and |2⟩ i in the two-photon Raman transitions used to manipulate the ion motional state. We also consider some possible experimental limitations to generate coherent states due to nonlinear effects in the coupling of the centre-of-mass coordinates with the laser field. A similar analysis is performed for carrier pulses taking into account nonlinearities and micromotion. The quantum evolution of the ion internal and centre-of-mass degrees of freedom are studied using amplitude equations derived from Schrödinger's equation. The limitations of such an approach are also discussed.
We investigate the quantum motion of two ions stored in a Paul trap and interacting with a time-periodic laser field. In the pseudopotential approximation and large detuning condition, we find that the relative motion is independent of the laser field, but the exact centre-of-mass motion is closely related to the laser field. By adjusting the laser intensity and frequency, we can well control the quantum motion of the centre-of-mass. We illustrate some physical properties described by the centre-of-mass states, such as the squeezed coherent property, the widths and heights of the wavepackets of probability density, the classical-quantum correspondence, the resonance ladders of expectation energy and the transition probabilities between time-dependent quantum levels.
We consider a trapped ion with a quantized center-of-mass motion in 2D trap potential. With external laser fields the effective (non)linear coupling of two orthogonal vibrational modes can be established via stimulated Raman transition. Nonclassical vibrational states such as squeezed states or two-mode entangled states (Schroedinger cat-like states) can be generated. When the vibrational modes are entangled with internal energy levels the Greenberger-Horne-Zeilinger (GHZ) states can be prepared.
Using the nonlinear coherent states approach, a general formalism for the construction of various classes of nonlinear trio coherent states in the context of multi-mode quantum states has been proposed. In particular, taking into account the most popular nonlinearity function associated with f -deformed coherent states, i.e. the nonlinearity function of the centre-of-mass motion of a trapped ion, it is illustrated that the corresponding trio coherent state possesses some interesting nonclassical properties. To establish this observation, sub-Poissonian statistics, three-mode squeezing, the behaviour of Vogel's characteristic function and the existence of entanglement are investigated. Due to the intrinsic non-classicality nature of the considered three-mode states, their physical production may be of high interest in the quantum optics field. Thus, we have finally demonstrated how nonlinear motional trio coherent states can be generated in three-dimensional anisotropic traps, appropriately.
We present a nonlinear decoherence model which models decoherence effects caused by various decohering sources in a quantum system through a nonlinear coupling between the system and its environment, and apply it to investigating decoherence in nonclassical motional states of a single trapped ion. We obtain an exactly analytic solution of the model and find very good agreement with experimental results for the population decay rate of a single trapped ion observed in the NIST experiments by Meekhof and co-workers [D. M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)].
The outstanding degree of control over trapped ions in Paul traps gives rise to the development of novel quantum manipulation techniques. Optical transitions can be used for precise manipulation of internal and external states. This way, non-classical states can be created which are a key component of quantum algorithms based on quantum logic operations. This powerful optical toolbox enabled the trapped ion system to assume leadership in the field of quantum computation. This thesis addresses two major challenges in the field of micro ion trap quantum optics. The temperature dependence of the heating rate from the ion trap surface is analysed in a novel cryogenic micro ion trap. Furthermore segmented traps allow state manipulations by time dependent electrical potentials, generated by the control voltages. These electrical fields provide a fast and reliable control handle to the ions external degrees of freedom. Quantum computation in Paul trap arrays is based on a combination of ion crystal transport, splitting and merging operations, while laser driven quantum state manipulations are mainly carried out on small ion crystals. Within this thesis a basic building block was realised by performing transport operations with a single ground-state cooled ion. As a highlight of experimental achievements, shuttling in the non-adiabatic regime, on the timescale of the motional period was demonstrated with low residual energy transfer. For his endeavour a specialised low noise arbitrary function generator was designed and manufactured during this thesis. Arbitrary voltage ramps at a sampling rate of up to 2.5 MS/s on up to 12 channels allow the study of a novel excitation method by directly manipulating the ion using electrical forces. Accurate numerical simulations in combination with the fast high resolution voltage supply allow deterministic quantum manipulations via momentum kicks. I report the first experimental demonstration of displaced number states with trapped ions.