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arXiv:1302.4613 · Physical Review A

Sub-Doppler cavity cooling beyond the Lamb-Dicke regime

Boon Leng Chuah, Nicholas C. Lewty, Radu Cazan, M. D. Barrett

Published Apr 18, 2013• 7 citations
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Abstract

We investigate the dynamics of cavity cooling of a single ion beyond the Lamb-Dicke regime and demonstrate a cooling limit of approximately 50$%$ of the Doppler temperature using a high finesse cavity. We also study the statistical properties of the ion-cavity emission and present a model that maps the phonon states to the photon states. With this model, we explain the super-Poissonian photon distribution observed in our experiments and propose a method to estimate the ion temperature in a real-time manner based on the statistical behavior of the photon emission from the cavity.

DOI
10.1103/physreva.87.043420

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We investigate the dynamics of cavity cooling of a single ion beyond the Lamb-Dicke regime and demonstrate a cooling limit of approximately 50% of the Doppler temperature using a high finesse cavity. We also study the statistical properties of the ion-cavity emission and present a model that maps the phonon states to the photon states. With this model, we explain the super-Poissonian photon distribution observed in our experiments and propose a method to estimate the ion temperature in a real-time manner based on the statistical behavior of the photon emission from the cavity.
Laser cooling methods for trapped ions are most commonly studied at low energies, i.e., in the Lamb-Dicke regime. However, ions in experiments are often excited to higher energies for which the Lamb-Dicke approximation breaks down. Here we construct a non-perturbative, semiclassical method for predicting the energy-dependent cooling dynamics of trapped-ion crystals with potentially many internal levels and motional modes beyond the Lamb-Dicke regime. This method allows accurate and efficient modeling of a variety of interesting phenomena, such as the breakdown of EIT cooling at high energies and the simultaneous cooling of multiple high-temperature modes. We compare its predictions both to fully-quantum simulations and to experimental data for a broadband EIT cooling method on a Raman SSS-DDD transition in 138^{138}138Ba+{^+}+. We find the method can accurately predict cooling rates over a wide range of energies relevant to trapped ion experiments. Our method complements fully quantum models by allowing for fast and accurate predictions of laser-cooling dynamics at much higher energy scales.
We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in a quasicontinuous energy spectrum that significantly alters the cooling dynamics. The cooling time decreases nonlinearly with the linewidth of the cooling transition, and the effect of dark states which may slow down the cooling is considerably reduced. We show that cooling to the ground state is also possible outside the Lamb-Dicke regime. We develop the model and use quantum Monte Carlo calculations for specific examples. We show that a rate equation treatment is a good approximation in all cases.
Abstract The dynamics of a single trapped ion placed inside a high Q optical cavity is studied in presence of cavity losses and far from the Lamb‐Dicke regime. In the underdamped cavity limit, analytical results for describing the dynamics of the system are derived making use of the secular approximation. Our method allows to obtain analytical expressions for the time evolution of the joint vibration‐photon number distribution and for the occupation probability of the upper electronic state of the ion.
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We present the results of simulations of optical sideband cooling of atomic ions in a trap with a shallow potential well. In such traps, an ion cannot be Doppler cooled near to the Lamb-Dicke regime $\mathrm{[}{\ensuremath{\eta}}^{2}(2\ensuremath{\langle}n\ensuremath{\rangle}+1)\ensuremath{\ll}1]$. Outside the Lamb-Dicke regime, the sideband cooling dynamics are altered by the existence of various Fock states with weak coupling where the cooling becomes very slow. A 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion trapped in our Penning trap realizes such a situation; hence single stage cooling is inefficient to prepare the ion in the motional ground state. For these systems, it is necessary to study the cooling dynamics in detail and we show that it is possible to implement an optimized cooling sequence to achieve efficient ground-state cooling. We also present the simulated cooling dynamics of two ions trapped in a Penning trap, where the presence of an additional motional mode requires a complicated cooling sequence in order to cool both axial modes to the ground state simultaneously. Additionally, we demonstrate the dissipative preparation of Fock states outside the Lamb-Dicke regime by sideband heating a single ion in a Penning trap.
We propose a model for a single-trapped-ion vibronic Raman laser and study its dynamics by using quantum-trajectory methods. In our treatment, it is essential that both the cavity field of the high-finesse optical cavity and the center-of-mass vibrational motion of the trapped ion be quantized. A transition from a super-Poissonian light source to a Poissonian lasing regime is obtained by increasing the Raman coupling constant. Furthermore, we demonstrate that a nonclassical regime can be realized, where the photon statistics becomes sub-Poissonian and the photons leak out of the cavity in an antibunched manner. This is achieved by exploiting nonlinear Stark shifts inherent in the model, which depend on both the number of cavity photons and the number of vibrational quanta.