Spectroscopic studies of few-body systems at ultracold temperatures provide valuable information that often cannot be extracted in a hot environment. Considering a pair of atoms, we propose a cooling mechanism that makes use of a scattering Feshbach resonance. Application of a series of time-dependent magnetic field ramps results in the situation in which either zero, one, or two atoms remain trapped. If two atoms remain in the trap after the field ramps are completed, then they have been cooled. Application of the proposed cooling mechanism to optical traps or lattices is considered.
We measure chemical reactions between a single trapped $^{174}$Yb$^+$ ion immersed in an ultracold bath of $^6$Li atoms containing trace amounts of Li$_2$ dimers. This produces LiYb$^+$ molecular ions that we detect via mass spectrometry. We explain the reaction rates by modelling the dimer density as a function of the magnetic field and obtain excellent agreement when we assume the reaction to follow the Langevin rate. Our results present a novel approach towards the creation of cold molecular ions and point to the exploration of ultracold chemistry in ion molecule collisions. What is more, w…
We propose and demonstrate a new method for Doppler cooling trapped-ion crystals where the distribution of micromotion amplitudes may be large and uneven. The technique uses pulses of Doppler cooling light synchronized with the trap RF that selectively target ions when their velocity is near a node, leading to more uniform cooling across a crystal by a single tone of cooling light. We lay out a theoretical framework that describes where this technique is practical, and provide a simple experimental demonstration.
We demonstrated sympathetic cooling of a single ion in a buffer gas of ultracold atoms with small mass. Efficient collisional cooling was realized by suppressing collision-induced heating. We attempt to explain the experimental results with a simple rate equation model and provide a quantitative discussion of the cooling efficiency per collision. The knowledge we obtained in this work is an important ingredient for advancing the technique of sympathetic cooling of ions with neutral atoms.
Doppler cooling with lasers is essential to ions' trapping and also a preliminary step towards achievement of ultracold ions. Due to lack of effective tools, experimentally monitoring the ions' temperature and the laser-ion coupling is difficult in Doppler cooling. Here we analytically explore the Doppler cooling process of trapped ions, exemplified by $^{40}$Ca$^{+}$, by solving the friction coefficient in the Doppler cooling with respect to a thermal bath, particularly, to a bath with large heating rate. We show four regions for cooling and heating induced by the three-level electromagnetica…
We study, both experimentally and theoretically, electromagnetically induced transparency cooling of the drumhead modes of planar 2-dimensional arrays with up to $N\approx 190$ Be${}^+$ ions stored in a Penning trap. Substantial sub-Doppler cooling is observed for all $N$ drumhead modes. Quantitative measurements for the center-of-mass mode show near ground state cooling with motional quantum numbers of $\bar{n} = 0.3\pm0.2$ obtained within $200~μs$. The measured cooling rate is faster than that predicted by single particle theory, consistent with a quantum many-body calculation. For the lower…
We implement three-dimensional polarization gradient cooling of trapped ions. Counter-propagating laser beams near $393\,$nm impinge in lin$\,\perp\,$lin configuration, at a frequency below the S$_{1/2}$ to P$_{3/2}$ resonance in $^{40}$Ca$^+$. We demonstrate mean phonon numbers of $5.4(4)$ at a trap frequency of $2π\times 285\,$kHz and $3.3(4)$ at $2π\times480\,$kHz, in the axial and radial directions, respectively. Our measurements demonstrate that cooling with laser beams detuned to lower frequencies from the resonance is robust against an elevated phonon occupation number, and thus works w…
Atomic dynamics in evaporative cooling of trapped alkali atoms in strong magnetic fields
我们研究了强磁场下塞曼位移的非线性对磁阱中射频场诱导蒸发冷却动力学的影响。我们证明了87-Rb和23-Na的F=2陷阱态的波包模拟如何冷却停止时，射频场频率低于一定的限制（85-Rb的F=2陷阱态的问题不会出现）。我们研究了强场情况下半经典模型的适用性，作为我们以前工作的扩展[Phys.Rev.A58，3983（1998）]。我们的研究结果证实了在最近的$^{87}$ Rb实验中观察到的许多方面[Phys. Rev. A 60，R1759（1999）]。
Resolved sideband cooling is a standard technique for cooling trapped ions below the Doppler limit to near their motional ground state. Yet, the most common methods for sideband cooling implicitly rely on low Doppler-cooled temperatures and tightly confined ions, and they cannot be optimized for different experimental conditions. Here we introduce a framework which calculates the fastest possible pulsed sideband cooling sequence for a given number of pulses and set of experimental parameters, and we verify its improvement compared to traditional methods using a trapped $^{171}$Yb$^+$ ion. Afte…
Trapped ions are a promising candidate for large scale quantum computation. Several systems have been built in both academic and industrial settings to implement modestly-sized quantum algorithms. Efficient cooling of the motional degrees of freedom is a key requirement for high-fidelity quantum operations using trapped ions. Here, we present a technique whereby individual ions are used to cool individual motional modes in parallel, reducing the time required to bring an ion chain to its motional ground state. We demonstrate this technique experimentally and develop a model to understand the e…
We report on the experimental observation of Feshbach resonances in large mass-imbalance mixtures of Erbium (Er) and Lithium (Li). All combinations between ${}^{168}$Er, ${}^{166}$Er and ${}^7$Li, ${}^6$Li are cooled to temperatures of a few microkelvin, partially by means of sympathetic cooling together with Ytterbium (Yb) as a third mixture component. The Er-Li inelastic interspecies collisional properties are studied for magnetic fields up to 680 G. In all cases resonant interspecies loss features, indicative of Feshbach resonances, have been observed. While most resonances have sub-Gauss w…
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 ($η^2(2n+1) \ll 1$). Outside the Lamb-Dicke regime, the sideband cooling dynamics are altered by the existence of various Fock states where the cooling becomes very slow. A calcium ion trapped in our Penning trap realises 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 de…
Cooling of particles to mK-temperatures is essential for a variety of experiments with trapped charged particles. However, many species of interest lack suitable electronic transitions for direct laser cooling. We study theoretically the remote sympathetic cooling of a single proton with laser-cooled $^9$Be$^+$ in a double-Penning-trap system. We investigate three different cooling schemes and find, based on analytical calculations and numerical simulations, that two of them are capable of achieving proton temperatures of about 10 mK with cooling times on the order of 10 s. In contrast, establ…
Feshbach resonances are among the essential control tools used in ultracold atom experiments. However, for complex atomic species the theoretical characterization of resonances becomes challenging. For closely spaced resonances, the measurement of three-body losses does not provide sufficient resolution to discriminate them. For this reason, resonance spectroscopy of trapped isolated atoms is becoming the state of the art. Here we show that trapping the atoms in a double well potential such as an optical lattice or a pair of optical tweezers enables precise characterization of not only the res…
The two most widely used ion cooling methods are laser cooling and sympathetic cooling by elastic collisions (ECs). Here we demonstrate another method of cooling ions that is based on resonant charge exchange (RCE) between the trapped ion and the ultracold parent atom. Specifically, trapped Cs$^{+}$ ions are cooled by collisions with co-trapped, ultracold Cs atoms and, separately, by collisions with co-trapped, ultracold Rb atoms. We observe that the cooling of Cs$^{+}$ ions by Cs atoms is more efficient than cooling of Cs$^{+}$ ions by Rb atoms. This signals the presence of a cooling mechanis…
Calcium monofluoride (CaF) molecules are loaded into an optical dipole trap (ODT) and subsequently laser cooled within the trap. Starting with magneto-optical trapping, we sub-Doppler cool CaF and then load $150(30)$ CaF molecules into an ODT. Enhanced loading by a factor of five is obtained when sub-Doppler cooling light and trapping light are on simultaneously. For trapped molecules, we directly observe efficient sub-Doppler cooling to a temperature of $60(5)$ $μ\text{K}$. The trapped molecular density of $8(2)\times10^7$ cm$^{-3}$ is an order of magnitude greater than in the initial sub-Dop…
We report on the observation of Feshbach resonances at low magnetic field strength (below 10 G) in the Fermi-Fermi mixture of $^{161}$Dy and $^{40}$K. We characterize five resonances by measurements of interspecies thermalization rates and molecular binding energies. As a case of particular interest for applications, we consider a resonance near 7.29 G, which combines accurate magnetic tunability and access to the universal regime of interactions with experimental simplicity. We show that lifetimes of a few 100 ms can be achieved for the optically trapped, resonantly interacting mixture. We al…
We report the electromagnetically-induced-transparency (EIT) cooling of a large trapped $^{171}$Yb$^+$ ion chain to the quantum ground state. Unlike conventional EIT cooling, we engage a four-level tripod structure and achieve fast sub-Doppler cooling over all motional modes. We observe simultaneous ground-state cooling across the complete transverse mode spectrum of up to $40$ ions, occupying a bandwidth of over $3$ MHz. The cooling time is observed to be less than $300\,μ$s, independent of the number of ions. Such efficient cooling across the entire spectrum is essential for high-fidelity qu…
Integrated-Photonics-Based Systems for Polarization-Gradient Cooling of Trapped Ions
Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；Lincoln Laboratory, Massachusetts Institute of Technology（麻省理工学院林肯实验室）
Efficient cooling of trapped charged particles is essential to many fundamental physics experiments, to high-precision metrology, and to quantum technology. Until now, sympathetic cooling has required close-range Coulomb interactions, but there has been a sustained desire to bring laser-cooling techniques to particles in macroscopically separated traps, extending quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions and antimatter. Here we demonstrate sympathetic cooling of a single proton using laser-cooled Be+ ions in spatially separated …
We investigate theoretically the possibility for robust and fast cooling of a trapped atomic ion by transient interaction with a pre-cooled ion. The transient coupling is achieved through dynamical control of the ions' equilibrium positions. To achieve short cooling times we make use of shortcuts to adiabaticity by applying invariant-based engineering. We design these to take account of imperfections such as stray fields, and trap frequency offsets. For settings appropriate to a currently operational trap in our laboratory, we find that robust performance could be achieved down to $6.3$ motion…
