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Physical Review A

Dark-state laser cooling of a trapped ion using standing waves

Shuo Zhang, Chun-Wang Wu, Ping‐Xing Chen

Published May 22, 2012• 21 citations
Publisher

Abstract

We propose a dark-state cooling scheme of trapped ion systems using standing waves in the Lamb-Dicke limit. By exploiting the property of standing waves, the heating effects caused by the carrier and the blue sideband transitions vanish and lower final phonon number can be achieved. Different from other dark-state cooling schemes, our scheme is more robust under the fluctuations of laser intensities.

DOI
10.1103/physreva.85.053420

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We propose a dark-state cooling scheme of trapped ion systems using standing waves in the Lamb-Dicke limit. By exploiting the property of standing waves, the heating effects caused by the carrier and the blue sideband transitions vanish and lower final phonon number can be achieved. Different from other dark-state cooling schemes, our scheme is more robust under the fluctuations of laser intensities.
We propose a dark-state cooling method of trapped ion systems in the Lamb-Dicke limit. By microwave dressing the ion, we can obtain two electromagnetically induced transparency structures. The heating effects caused by the carrier and the blue sideband transition vanish due to electromagnetically induced transparency effects and the final mean phonon numbers can be much lower than the recoil limit. Our scheme is robust to fluctuations of microwave power and laser intensities, which provides a broad cooling bandwidth to cool motional modes of a linear ion chain. Moreover, it is more suitable to cool four-level ions on a large-scale ion chip.
A detailed study of a robust and fast laser cooling scheme on a three level system is presented. A special laser configuration, applicable to trapped ions, atoms or cantilevers, designs a quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon processes. As a consequence cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very stable under fluctuations of the physical parameters such as laser intensity or detuning, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes, overcoming one of the limitations of current quantum information processing implementations. Its suitability as a cooling scheme for several ions in a trap or for a cloud of atoms in a dipole trap is shown.
We propose a ground-state cavity-mediated cooling scheme for a trapped atom, which is in the $\ensuremath{\Lambda}$ configuration and confined inside a high-finesse optical cavity, using a standing-wave cooling laser. The carrier transition can be prohibited by placing the atom at the node of the cavity field, and the blue-sideband transition can be simultaneously eliminated by exploiting quantum interference via tuning the frequency of the cooling laser. As a consequence, the ground-state cooling for the trapped atom can be achieved. Moreover, we numerically demonstrate the superiority by placing the atom at the antinode of the standing-wave cooling laser as compared with the running-wave cooling laser, and the robustness of the scheme using the standing-wave laser. Meanwhile, the cooling rate can reach the same order of magnitude as that obtained in the cavity--electromagnetically-induced-transparency cooling scheme, and the explicit expression for the final phonon number in higher order is also presented.
Laser cooling is fundamental to quantum computation and metrology with trapped ions, and can occupy a majority of runtime in current systems. A key limitation to cooling arises from unwanted carrier excitation, which in typically used running wave (RW) fields invariably accompanies the sideband transitions effecting cooling. We consider laser cooling in structured light profiles enabling selective sideband excitation with nulled carrier drive; motivated by integrated photonic approaches' passive phase and amplitude stability, we propose simple configurations realizable with waveguide addressing using either standing wave (SW) or first-order Hermite-Gauss (HG) modes. We quantify performance of Doppler cooling from beyond the Lamb-Dicke regime (LDR), and ground-state (GS) cooling using electromagnetically induced transparency (EIT) leveraging these field profiles. Carrier-free EIT offers significant benefits simultaneously in cooling rate, motional frequency bandwidth, and final phonon number. Carrier-free Doppler cooling's advantage is significantly compromised beyond the LDR but continues to hold, indicating such configurations are applicable for highly excited ions. Our simulations focus on level structure relevant to 40^{40}40Ca+^++, though the carrier-free configurations can be generally applied to other species. We also quantify performance limitations due to polarization and modal impurities relevant to experimental implementation. Our results indicate potential for simple structured light profiles to alleviate bottlenecks in laser cooling, and for scalable photonic devices to improve basic operation quality in trapped-ion systems.