Three-Dimensional Compensation for Minimizing Heating of the Ion in Surface-Electrode Trap

The trapped ions confined in a surface-electrode trap(SET) could be free from rf heating if they stay at the rf potential null of the potential well.We report our effort to compensate three-dimensionally for the micromotion of a single ~(40)Ca~+ ion near the rf potential null,which largely suppresses the ion's heating and thus helps to achieve the cooling of the ion down to 3.4 mK,which is very close to the Doppler limit.This is the prerequosite of the sideband cooling in our SET.     

A single laser system for ground-state cooling of <Superscript>25</Superscript>Mg<Superscript>+</Superscript>

We present a single solid-state laser system to cool, coherently manipulate and detect ²⁵Mg⁺ ions. Coherent manipulation is accomplished by coupling two hyperfine ground state levels using a pair of far-detuned Raman laser beams. Resonant light for Doppler cooling and detection is derived from the same laser source by means of an electro-optic modulator, generating a sideband which is resonant with the atomic transition. We demonstrate ground-state cooling of one of the vibrational modes of the ion in the trap using resolved-sideband cooling. The cooling performance is studied and discussed by observing the temporal evolution of Raman-stimulated sideband transitions. The setup is a major simplification over existing state-of-the-art systems, typically involving up to three separate laser sources.     

Theory of ground state cooling of a mechanical oscillator using dynamical backaction

A quantum theory of cooling of a mechanical oscillator by radiation pressure-induced dynamical backaction is developed, which is analogous to sideband cooling of trapped ions. We find that final occupancies well below unity can be attained when the mechanical oscillation frequency is larger than the optical cavity linewidth. It is shown that the final average occupancy can be retrieved directly from the optical output spectrum.     

Effective sideband cooling in an ytterbium optical lattice clock

Sideband cooling is a key technique for improving the performance of optical atomic clocks by preparing cold atoms and single ions into the ground vibrational state. In this work, we demonstrate detailed experimental research on pulsed Raman sideband cooling in a $^{171}$Yb optical lattice clock. A sequence comprised of interleaved 578 nm cooling pulses resonant on the 1st-order red sideband and 1388 nm repumping pulses is carried out to transfer atoms into the motional ground state. We successfully decrease the axial temperature of atoms in the lattice from 6.5 μK to less than 0.8 μK in the trap depth of 24 μK, corresponding to an average axial motional quantum number $\langle n_z\rangle<0.03$. Rabi oscillation spectroscopy is measured to evaluate the effect of sideband cooling on inhomogeneous excitation. The maximum excitation fraction is increased from 0.8 to 0.86, indicating an enhancement in the quantum coherence of the ensemble. Our work will contribute to improving the instability and uncertainty of Yb lattice clocks.     

Trapped-ion state detection through coherent motion

We demonstrate a general method for state detection of trapped ions that can be applied to a large class of atomic and molecular species. We couple a spectroscopy ion (27Al+) to a control ion (25Mg+) in the same trap and perform state detection through off-resonant laser excitation of the spectroscopy ion that induces coherent motion. The motional amplitude, dependent on the spectroscopy ion state, is measured either by time-resolved photon counting or by resolved sideband excitations on the control ion. The first method provides a simplified way to distinguish clock states in 27Al+, which avoids ground-state cooling and sideband transitions. The second method reduces spontaneous emission and optical pumping on the spectroscopy ion, which we demonstrate by nondestructively distinguishing Zeeman sublevels in the (1)S0 ground state of 27Al+.     

Optically-driven cooling for collective atomic excitations

We explore how to cool collective atomic excitations in an optically-driven three-level atomic ensemble, which may be described by a model of two coupled harmonic oscillators (HOs) with a time-dependent coupling. Moreover, the model of two coupled HOs is further generalized to address the resolved sideband cooling issues, where the lower-frequency HO can be cooled whenever the cooling process dominates over the heating one during the sideband transitions. Unusually, due to the absence of the heating process, the optimal result for cooling collective excitations in an atomic ensemble could break the standard resolved sideband cooling limit for general models of two coupled HOs.     

Dark resonances as a probe for the motional state of a single ion

Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second-order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. In this paper the motional state of a confined three-level ion is probed, taking advantage of the high sensitivity of observed dark resonances to the trapped ion’s velocity. Excess micromotion is controlled by monitoring the dark-resonance contrast with varying laser-beam geometry. The influence of different parameters such as the cooling laser intensity has been investigated experimentally and numerically.     

强耦合光机械腔中的简正模式分裂和冷却

研究由辐射压力与驱动Fabry-Perot光学腔相耦合而产生的腔光机械动力学行为. 通过量子朗之万方程具体研究了机械振子的涨落光谱、机械阻尼与共振频移和基态冷却. 随着输入激光功率的增加,振子的涨落光谱呈现简正模式分裂的现象,并且数值模拟结果和实验结果相符合. 同时推导了有效机械阻尼和共振频移. 红移边带导致了机械模的冷却,蓝移边带引起了机械模的放大. 此外,引入一种近似机制来研究振子的基态冷却,并且考虑在解析边带机制下简正模式分裂对机械振子冷却的影响. 最后,数值讨论了初始浴温度、输入激光功率和机械品质因数这三个因素对机械振子冷却的影响. 关键词： 腔光机械 辐射压力 简正模式分裂 冷却     

Visual observation and optical cooling of electrodynamically contained ions

Resonance fluorescence from as little as 10 to 20 barium ions, spatially confined in a miniaturized rf quadrupole ion trap, has been detected visually, photographically, and photoelectrically. Gross effects of optical sideband cooling of the ions were observed.     

Laser cooling with electromagnetically induced transparency: application to trapped samples of ions or neutral atoms

A novel method of ground-state laser cooling of trapped atoms utilizes the absorption profile of a three- (or multi-) level system that is tailored by a quantum interference. With cooling rates comparable to conventional sideband cooling, lower final temperatures may be achieved. The method was experimentally implemented to cool a single Ca⁺ ion to its vibrational ground state. Since a broad band of vibrational frequencies can be cooled simultaneously, the technique will be particularly useful for the cooling of larger ion strings, thereby being of great practical importance for initializing a quantum register based on trapped ions. We also discuss its application to different level schemes and for ground-state cooling of neutral atoms trapped by a far-detuned standing wave laser field. Received: 10 July 2001 / Published online: 23 November 2001     

Application of cogwheel phase cycling to sideband manipulation experiments in solid-state NMR

Cogwheel phase-cycling schemes are applied to sideband suppression and sideband separation experiments in solid-state NMR. It is shown that cogwheel phase cycles lead to the elimination of most pulse imperfection effects, while using far fewer experimental signal acquisitions than conventional phase-cycling methods.     

Detection of parametric resonance of trapped ions for micromotion compensation

We have detected excess micromotion of trapped ions by modulating the trapping voltage. This radio-frequency (rf) modulation induces parametric resonance and excites secular motion of the trapped ions when they possess excess motion. This technique has been applied to laser-cooled ions in a linear rf trap and it provides optimum values for compensating the trapping field. We found that the technique has sensitivity equal to or greater than the conventional method for detecting excess micromotion. Because any laser propagation direction can be used, this method is expected to be applied to surface-electrode traps.     

Micromotion compensation in a surface electrode trap by parametric excitation of trapped ions

We report a surface electrode trap with a relatively large trap depth (0.6–1.0?eV). The trap electrodes are formed by gold plating an alumina substrate. Calcium ions are trapped approximately 400?μm above the trap surface. We demonstrate micromotion compensation based on parametric resonance for surface electrode traps. Unlike the conventional method based on radio-frequency (rf)–photon correlation in which the wave vector of the laser beam must have a component parallel to the micromotion to be detected, the proposed method is independent of the laser propagation direction. This enables the micromotion component normal to the electrode surface to be detected without increasing the scattered light.     

Ultraefficient cooling of resonators: beating sideband cooling with quantum control

The present state of the art in cooling mechanical resonators is a version of sideband cooling. Here we present a method that uses the same configuration as sideband cooling-coupling the resonator to be cooled to a second microwave (or optical) auxiliary resonator-but will cool significantly colder. This is achieved by varying the strength of the coupling between the two resonators over a time on the order of the period of the mechanical resonator. As part of our analysis, we also obtain a method for fast, high-fidelity quantum information transfer between resonators.     

Normal mode splitting and ground state cooling in a Fabry-Perot optical cavity and transmission line resonator

Optomechanical dynamics in two systems which are a transmission line resonator and Fabrya-Perot optical cavity via radiation-pressure are investigated by linearized quantum Langevin equation. We work in the resolved sideband regime where the oscillator resonance frequency exceeds the cavity linewidth. Normal mode splittings of the mechanical resonator as a pure result of the coupling interaction in the two optomechanical systems is studied, and we make a comparison of normal mode splitting of mechanical resonator between the two systems. In the optical cavity, the normal mode splitting of the movable mirror approaches the latest experiment very well. In addition, an approximation scheme is introduced to demonstrate the ground state cooling, and we make a comparison of cooling between the two systems dominated by two key factors, which are the initial bath temperature and the mechanical quality factor. Since both the normal mode splitting and cooling require working in the resolved sideband regime, whether the normal mode splitting influences the cooling of the mirror is considered. Considering the size of the mechanical resonator and precooling the system, the mechanical resonator in the transmission line resonator system is easier to achieve the ground state cooling than in optical cavity.     

Ground state laser cooling using electromagnetically induced transparency

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.     

Suitability of linear quadrupole ion traps for large Coulomb crystals

Growing and studying large Coulomb crystals, composed of tens to hundreds of thousands of ions, in linear quadrupole ion traps presents new challenges for trap implementation. We consider several trap designs, first comparing the total driven micromotion amplitude as a function of location within the trapping volume; total micromotion is an important point of comparison since it can limit crystal size by transfer of radiofrequency drive energy into thermal energy. We also compare the axial component of micromotion, which leads to first-order Doppler shifts along the preferred spectroscopy axis in precision measurements on large Coulomb crystals. Finally, we compare trapping potential anharmonicity, which can induce nonlinear resonance heating by shifting normal mode frequencies onto resonance as a crystal grows. We apply a non-deforming crystal approximation for simple calculation of these anharmonicity-induced shifts, allowing a straightforward estimation of when crystal growth can lead to excitation of different nonlinear heating resonances. In the anharmonicity point of comparison, we find significant differences between the trap designs, with an original rotated-endcap trap performing better than the conventional in-line endcap trap.     

基于磁悬浮大体积交叉光学偶极阱的Dimple光阱装载研究

三维拉曼边带冷却后的铯原子样品装载于一个磁悬浮的大体积交叉光学偶极阱中, 继续加载一个小体积的光学偶极阱后, 实现了Dimple光学偶极阱对铯原子的高效装载. 对不同磁场下磁悬浮大体积光阱的有效装载势能进行理论分析与实验测量, 得出最优化的梯度磁场和均匀偏置磁场, 获得了基于磁悬浮大体积光阱的Dimple光学偶极阱的装载势能曲线, 实现了Dimple光学偶极阱对经拉曼边带冷却后俘获在磁悬浮的大体积光阱中的铯原子样品的有效装载. 比较了Dimple光学偶极阱分别从拉曼边带冷却、大体积的交叉光阱和消除反俘获势后的磁悬浮大体积光阱装载的结果, 将俘获在磁悬浮大体积光阱中的铯原子样品装载到Dimple光学偶极阱, 铯原子样品的密度提高了约15倍.     

Optomechanical cavity cooling of an atomic ensemble

We demonstrate cavity sideband cooling of a single collective motional mode of an atomic ensemble down to a mean phonon occupation number ?n?(min?)=2.0(-0.3)(+0.9). Both ?n?(min) and the observed cooling rate are in good agreement with an optomechanical model. The cooling rate constant is proportional to the total photon scattering rate by the ensemble, demonstrating the cooperative character of the light-emission-induced cooling process. We deduce fundamental limits to cavity cooling either the collective mode or, sympathetically, the single-atom degrees of freedom.     

Effect of defects on the electronic structure of a PbI2/MoS2 van der Waals heterostructure: A first-principles study

PbI2/MoS2,as a typical van der Waals(vdW)heterostructure,has attracted intensive attention owing to its remarkable electronic and optoelectronic properties.In this work,the effect of defects on the electronic structures of a PbI2/MoS2 heterointerface has been systematically investigated.The manner in which the defects modulate the band structure of PbI2/MoS2,including the band gap,band edge,band alignment,and defect energy-level density within the band gap is discussed herein.It is shown that sulfur defects tune the band gaps,iodine defects shift the positions of the band edge and Fermi level,and lead defects realize the conversions between the straddling-gap band alignment and valence-band-aligned gap,thus enhancing the light-absorption ability of the material.