A New Mechanism for Sympathetic Cooling of Atoms and Ions in Atomic and Ion-Atomic Traps
V. S. Melezhik
备注：
8 pages, 4 figures, report on Int. Conf. on Pecision Physics and Fundamental Physical Constants (FFK2021) 4-8 October 2021, Stara Lesna, Slovakia. arXiv admin note: substantial text overlap with arXiv:2101.03565
Sympathetic cooling of a Fermi gas with a buffer gas of bosonic atoms is an efficient way to achieve quantum degeneracy in Fermi systems. However, all attempts to use this method for cooling ions until recently were ineffective because of the unremovable ion `"micromotion" in electromagnetic Paul traps, which prevents the realization of a number of hot projects with cold atom-ion systems. In this regard, we propose a new efficient method for sympathetic cooling of ions: the use for this purpose of cold buffer atoms in the region of atom-ion confinement-induced resonances (CIRs) [V.S. Melezhik, Phys. Rev. A103, 53109 (2021)]. We show that the destructive effect of "micromotion" on its sympathetic cooling can, however, be suppressed in the vicinity of the atom-ion CIR. Here, the resonant blocking of a close collision of an atom with an ion also resists its heating due to "micromotion". We investigate the effect of sympathetic cooling around CIRs in atom-ion, and atom-atom confined collisions within the quantum-quasiclassical approach using the Li-Yb$^+$ and Li-Yb confined systems as an example. In this approach, the Schrödinger equation for a cold light atom is integrated simultaneously with the classical Hamilton equations for a hotter heavy-ion or atom during a collision. We have found the region near the atom-ion CIR where the sympathetic cooling of the ion by cold atoms is possible in a hybrid atom-ion trap. We also show that it is possible to improve the efficiency of sympathetic cooling in atomic traps by using atomic CIRs.
It is shown that the translational degrees of freedom of a large variety of molecules, from light diatomic to heavy organic ones, can be cooled sympathetically and brought to rest (crystallized) in a linear Paul trap. The method relies on endowing the molecules with an appropriate positive charge, storage in a linear radiofrequency trap, and sympathetic cooling. Two well--known atomic coolant species, ${}^9{\hbox{Be}}^+$ and ${}^{137}{\hbox{Ba}}^+$, are sufficient for cooling the molecular mass range from 2 to 20,000 amu. The large molecular charge required for simultaneous trapping of heavy m…
We sympathetically cool a trapped 112Cd+ ion by directly Doppler-cooling a 114Cd+ ion in the same trap. This is the first demonstration of optically addressing a single trapped ion being sympathetically cooled by a different species ion. Notably, the experiment uses a single laser source, and does not require strong focusing. This paves the way toward reducing decoherence in an ion trap quantum computer based on Cd+ isotopes.
A protocol is provided to reconstruct the Wigner function for the motional state of a trapped ion via fluorescence detection on another ion in the same trap. This "sympathetic tomography" of a dark ion without optical transitions suitable for state measurements is based on the mapping of its motional state onto one of the collective modes of the ion pair. The quantum state of this vibrational eigenmode is subsequently measured through sideband excitation of the bright ion. Physical processes to implement the desired state transfer and read-out are derived, and the accomplishment of the scheme …
We analyze the dynamics and steady state of a linear ion array when some of the ions are continuously laser cooled. We calculate the ions' local temperature measured by its position fluctuation under various trapping and cooling configurations, taking into account background heating due to the noisy environment. For a large system, we demonstrate that by arranging the cooling ions evenly in the array, one can suppress the overall heating considerably. We also investigate the effect of different cooling rates and find that the optimal cooling efficiency is achieved by an intermediate cooling ra…
We demonstrate sympathetic cooling of a 43Ca+ trapped-ion "memory" qubit by a 40Ca+ "coolant" ion near the ground state of both axial motional modes, whilst maintaining coherence of the qubit. This is an essential ingredient in trapped-ion quantum computers. The isotope shifts are sufficient to suppress decoherence and phase shifts of the memory qubit due to the cooling light which illuminates both ions. We measure the qubit coherence during 10 cycles of sideband cooling, finding a coherence loss of 3.3% per cooling cycle. The natural limit of the method is O(0.01%) infidelity per cooling cycl…
Precision optical spectroscopy of exotic ions reveals accurate information about nuclear properties such as charge radii and magnetic and quadrupole moments. Thorium ions exhibit unique nuclear properties with high relevance for testing symmetries of nature. We report loading and trapping of single $^{232}$Th$^+$ ions in a linear Paul trap, embedded into and sympathetically cooled by small crystals of trapped $^{40}$Ca$^+$ ions. Trapped Th ions are identified in a non-destructive manner from the voids in the laser-induced Ca fluorescence pattern emitted by the crystal, and alternatively, by me…
We report the trapping of ultracold neutral $ \text{Rb}$ atoms and $ \text{Ba}^+ $ ions in a common optical potential in absence of any radiofrequency (RF) fields. We prepare $ \text{Ba}^+ $ at $ 370 ~ μK $ and demonstrate efficient sympathetic cooling by $100 ~ μK $ after one collision. Our approach is currently limited by the $ \text{Rb}$ density and related three-body losses, but it overcomes the fundamental limitation in RF traps set by RF-driven, micromotion-induced heating. It is applicable to a wide range of ion-atom species, and may enable novel ultracold chemistry experiments and comp…
Modular mixed-species ion-trap networks are a promising framework for scalable quantum information processing, where one species acts as a memory qubit and another as a communication qubit. This architecture requires high-fidelity mixed-species entangling gates to transfer information from communication to memory qubits through their collective motion. We investigate the character of the motional modes of a mixed-species ion chain for entangling operations and also sympathetic cooling. We find that the laser power required for high-fidelity entangling gates based on transverse modes is at leas…
We present and derive analytic expressions for a fundamental limit to the sympathetic cooling of ions in radio-frequency traps using cold atoms. The limit arises from the work done by the trap electric field during a long-range ion-atom collision and applies even to cooling by a zero-temperature atomic gas in a perfectly compensated trap. We conclude that in current experimental implementations this collisional heating prevents access to the regimes of single-partial-wave atom-ion interaction or quantized ion motion. We determine conditions on the atom-ion mass ratio and on the trap parameters…
We report a detailed investigation on near-ground state cooling of one and two trapped atomic ions. We introduce a simple sideband cooling method for confined atoms and ions, using RF radiation applied to bare ionic states in a static magnetic field gradient, and demonstrate its application to ions confined at secular trap frequencies, $ω_z \approx 2π\times 117 $kHz. For a single \ybplus ion, the sideband cooling cycle reduces the average phonon number, $\left\langle\,n\,\right\rangle$ from the Doppler limit to $\left\langle\,n\,\right\rangle =$ 0.30(12). This is in agreement with the theoreti…
A mixed system of cooled and trapped, ions and atoms, paves the way for ion assisted cold chemistry and novel many body studies. Due to the different individual trapping mechanisms, trapped atoms are significantly colder than trapped ions, therefore in the combined system, the strong binary ion$-$atom interaction results in heat flow from ions to atoms. Conversely, trapped ions can also get collisionally heated by the cold atoms, making the resulting equilibrium between ions and atoms intriguing. Here we experimentally demonstrate, Rubidium ions (Rb$^+$) cool in contact with magneto-optically …
Long range polarization forces between ions and neutral atoms result in large elastic scattering cross sections, e.g., 10^6 a.u. for Na+ on Na or Ca+ on Na at cold and ultracold temperatures. This suggests that a hybrid ion-neutral trap should offer a general means for significant sympathetic cooling of atomic or molecular ions. We present SIMION 7.0 simulation results concerning the advantages and limitations of sympathetic cooling within a hybrid trap apparatus, consisting of a linear rf Paul trap concentric with a Na magneto-optical trap (MOT). This paper explores the impact of various heat…
We demonstrate the cooling of a two species ion crystal consisting of one $^9Be^+$ and one $^{24}Mg^+$ ion. Since the respective cooling transitions of these two species are separated by more than 30 nm, laser manipulation of one ion has negligible effect on the other even when the ions are not individually addressed. As such this is a useful system for re-initializing the motional state in an ion trap quantum computer without affecting the qubit information. Additionally, we have found that the mass difference between ions enables a novel method for detecting and subsequently eliminating the …
We have cooled a two-ion-crystal to the ground state of its collective modes of motion. Laser cooling, more specific resolved sideband cooling is performed sympathetically by illuminating only one of the two $^{40}$Ca$^+$ ions in the crystal. The heating rates of the motional modes of the crystal in our linear trap have been measured, and we found them considerably smaller than those previously reported by Q. Turchette {\em et. al.} Phys. Rev. A 61, 063418 (2000) in the case of trapped $^9$Be$^+$ ions. After the ground state is prepared, coherent quantum state manipulation of the atomic popula…
Sympathetic cooling of trapped ions has become an indispensable tool for quantum information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al+ with Be+, Mg+ and Ca+ ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger…
We reported the realization of a $^{174}\mathrm{Yb}^+$-$^{113}\mathrm{Cd}^+$ bi-species Coulomb crystal comprising $^{174}\mathrm{Yb}^+$ ions as coolant and verified its potential for application as a $^{113}\mathrm{Cd}^+$ microwave frequency standard employing sympathetic cooling.The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The $^{113}\mathrm{Cd}^+$ ions are trapped in the center, which reduces considerably RF heating and excess micromotion to which the $^{113}\mathrm{Cd}^+$ ions are subjected. Under this scheme, the uncertainty due t…
Current precision experiments with single (anti)protons to test CPT symmetry progress at a rapid pace, but are complicated by the need to cool particles to sub-thermal energies. We describe a cryogenic Penning-trap setup for $^9$Be$^+$ ions designed to allow coupling of single (anti)protons to laser-cooled atomic ions for sympathetic cooling and quantum logic spectroscopy. We report on trapping and laser cooling of clouds and single $^9$Be$^+$ ions. We discuss prospects for a microfabricated trap to allow coupling of single (anti)protons to laser-cooled $^9$Be$^+$ ions for sympathetic laser co…
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 discuss the coupling of the motion of two ion species in separate Penning traps via a common tank circuit. The enhancement of the coupling assisted by the tank circuit is demonstrated by an avoided crossing behavior measurement of the motional modes of two coupled ions. We propose an intermittent laser cooling method for sympathetic cooling and provide a theoretical description. The technique enables tuning of the coupling strength between two ion species in separate traps and thus allows for efficient sympathetic cooling of an arbitrary type of single ion for high-precision Penning-trap ex…
We investigate the dynamics of an ion sympathetically cooled by another laser-cooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we create a two-ion crystal of Ca$^+$ and Al$^+$ by photo-ionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laser-ablated atoms crossing the trap by time-resolved fluorescence spectroscopy. We observe neutral atom velocities much higher than the ones of thermally heated samples and find as a consequence long sym…
Cooling the center-of-mass motion of levitated nanoparticles provides a route to quantum experiments at mesoscopic scales. Here we demonstrate three-dimensional sympathetic cooling and detection of the center-of-mass motion of a levitated silica nanoparticle. The nanoparticle is electrostatically coupled to a feedback-cooled particle while both particles are trapped in the same Paul trap. We identify two regimes, based on the strength of the cooling: in the first regime, the sympathetically cooled particle thermalizes with the directly cooled one, while in the second regime, the sympatheticall…
We use electromagnetically induced transparency (EIT) laser cooling to cool motional modes of a linear ion chain. As a demonstration, we apply EIT cooling on $^{24}Mg^+$ ions to cool the axial modes of a $^9Be^+$ - $^{24}Mg^+$ ion pair and a $^9Be^+$ - $^{24}Mg^+$ - $^{24}Mg^+$ - $^9Be^+$ ion chain, thereby sympathetically cooling the $^{9}$Be$^{+}$ ions. Compared to previous implementations of conventional Raman sideband cooling, we achieve approximately an order-of-magnitude reduction in the duration required to cool the modes to near the ground state and significant reduction in required la…
We propose a new way for sympathetic cooling of ions in an electromagnetic Paul trap: it implies the use for this purpose of cold buffer atoms in the region of atom-ion confinement-induced resonance (CIR). The problem is that the unavoidable micromotion of the ion and the long-range nature of its interaction with the environment of colder atoms in a hybrid atomic-ion trap prevent its sympathetic cooling. We show that the destructive effect of ion micromotion on its sympathetic cooling can however be suppressed in the vicinity of the atom-ion CIR. The origin of this is the "fermionization" of t…
Cold molecular ions are promising candidates in various fields ranging from precision spectroscopy and test of fundamental physics to ultra-cold chemistry. Control of internal and external degrees of freedom is a prerequisite for many of these applications. Motional ground state cooling represents the starting point for quantum logic-assisted internal state preparation, detection, and spectroscopy protocols. Robust and fast cooling is crucial to maximize the fraction of time available for the actual experiment. We optimize the cooling rate of ground state cooling schemes for single $^{25}\math…
We discuss a sympathetic cooling strategy that can successfully mitigate fermion-hole heating in a dilute atomic Fermi-Bose mixture and access the temperature regime in which the fermions behave as a Fermi liquid. We introduce an energy-based formalism to describe the temperature dynamics with which we study a specific and promising mixture composed of 6Li and 87Rb. Analyzing the harmonically trapped mixture, we find that the favourable features of this mixture are further enhanced by using different trapping frequencies for the two species.
We discuss fast frictionless cooling techniques in the framework of sympathetic cooling of cold atomic mixtures. It is argued that optimal cooling of an atomic species - in which the deepest quantum degeneracy regime is achieved - may be obtained by means of sympathetic cooling with another species whose trapping frequency is dynamically changed to maintain constancy of the Lewis-Riesenfeld adiabatic invariant. Advantages and limitations of this cooling strategy are discussed, with particular regard to the possibility of cooling Fermi gases to a deeper degenerate regime.
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Sympathetic cooling is the process of energy exchange between a system and a colder bath. We investigate this fundamental process in an atom-ion experiment where the system is composed of a single ion, trapped in a radio-frequency Paul trap, and prepared in a coherent state of ~200 K and the bath is an ultracold cloud of atoms at μK temperature. We directly observe the sympathetic cooling dynamics with single-shot energy measurements during one, to several, collisions in two distinct regimes. In one, collisions predominantly cool the system with very efficient momentum transfer leading to cool…
We introduce a scheme to perform dissipation-assisted quantum information processing in ion traps considering realistic decoherence rates, for example, due to motional heating. By means of continuous sympathetic cooling, we overcome the trap heating, and show that the damped vibrational excitations can still be exploited to mediate coherent interactions as well as collective dissipative effects. We describe how to control their relative strength experimentally, allowing for protocols of coherent or dissipative generation of entanglement. This scheme can be scaled to larger ion registers for co…
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We present a unitary quantum control scheme that produces a highly monochromatic ion beam from a Paul trap. Our protocol is implementable by supplying the segmented electrodes with voltages of the order of Volts, which mitigates the impact of fluctuating voltages in previous designs and leads to a low-dispersion beam of ions. Moreover, our proposal does not rely on sympathetically cooling the ions, which bypasses the need of loading different species in the trap -- namely, the propelled ion and, e.g., a $^{40}$Ca$^+$ atom able to exert sympathetic cooling -- incrementing the repetition rate of…
Sympathetic cooling with ultracold atoms and atomic ions enables ultralow temperatures in systems where direct laser or evaporative cooling is not possible. It has so far been limited to the cooling of other microscopic particles, with masses up to $90$ times larger than that of the coolant atom. Here we use ultracold atoms to sympathetically cool the vibrations of a Si$_3$N$_4$ nanomembrane, whose mass exceeds that of the atomic ensemble by a factor of $10^{10}$. The coupling of atomic and membrane vibrations is mediated by laser light over a macroscopic distance and enhanced by placing the m…
Thorium ions exhibit unique nuclear properties with high relevance for testing symmetries of nature, and Paul traps feature an ideal experimental platform for performing high precision quantum logic spectroscopy. Loading of stable or long-lived isotopes is well-established and relies on ionization from an atomic beam. A different approach allows trapping short-lived isotopes available as alpha-decay daughters, which recoil from a thin sample of the precursor nuclide. A prominent example is the short-lived $^{229\text{m}}$Th, populated in a decay of long-lived $^{233}$U. Here, ions are provided…
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Dense array of ions in microfabricated traps represent one possible way to scale up ion trap quantum computing. The ability to address individual ions is an important component of such a scheme. We demonstrate individual addressing of trapped ions in a microfabricated surface-electrode trap using a magnetic field gradient generated on-chip. A frequency splitting of 310(2) kHz for two ions separated by 5 um is achieved. Selective single qubit operations are performed on one of two trapped ions with an average of 2.2+/-1.0% crosstalk. Coherence time as measured by the spin-echo technique is unaf…
We describe a possible architecture to implement a universal bosonic simulator (UBS) using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase-shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap.
The theory of interactions between lasers and cold trapped ions as it pertains to the design of Cirac-Zoller quantum computers is discussed. The mean positions of the trapped ions, the eigenvalues and eigenmodes of the ions' oscillations, the magnitude of the Rabi frequencies for both allowed and forbidden internal transitions of the ions and the validity criterion for the required Hamiltonian are calculated. Energy level data for a variety of ion species is also presented.
We propose to use a large cloud of cold trapped ions as a medium for quantum optics and quantum information experiments. Contrary to most recent realizations of qubit manipulation based on a small number of trapped and cooled ions, we study the case of traps containing a macroscopic number of ions. We consider in particular the implementation of a quantum memory for quantum information stored in continuous variables and study the impact of the relevant physical parameters on the expected performances of the system.
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This submission is an introduction to microfabricated ion traps. We cover the basics of Paul traps, various geometries for realizing the traps, a number of design considerations, and, finally, a review of existing microfabricated traps.
Storage lifetime and capacity are two important factors to characterize the performance of a quantum memory. Here we report the stable trapping of above 200 ions in a cryogenic setup, and demonstrate the combination of the multi-qubit capacity and long storage lifetime by measuring the coherence time of randomly chosen ions to be on the order of hundreds of milliseconds. We apply composite microwave pulses to manipulate qubit states globally for efficient characterization of different storage units simultaneously, and we compare the performance of the quantum memory with and without the sympat…
We discuss a protocol for the analogue quantum simulation of superradiance and subradiance using a linear chain of N trapped qubit ions with a single sympathetic cooling ion. We develop a simple analytic model that shows the dynamics of the qubit subspace converge to those of a cloud undergoing Dicke superradiance and subradiance. We provide numerical simulations of the full ion chain and show that they converge to the dynamics predicted by our analytic model with no fitting parameters. We also map out the parameter regime needed to reach this convergence.
We provide a comprehensive theoretical framework for describing the dynamics of a single trapped ion interacting with a neutral buffer gas, thus extending our previous studies on buffer-gas cooling of ions beyond the critical mass ratio [B. Höltkemeier et al., Phys. Rev. Lett. 116, 233003 (2016)]. By transforming the collisional processes into a frame, where the ion's micromotion is assigned to the buffer gas atoms, our model allows one to investigate the influence of non-homogeneous buffer gas configurations as well as higher multipole orders of the radio-frequency trap in great detail. Depen…
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Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We …
Thermalization of a system in the presence of a heat bath has been the subject of many theoretical investigations especially in the framework of solid-state physics. In this setting, the presence of a large bandwidth for the frequency distribution of the harmonic oscillators schematizing the heat bath is crucial, as emphasized in the Caldeira-Leggett model. By contrast, ultracold gases in atomic traps oscillate at well-defined frequencies and therefore seem to lie outside the Caldeira-Leggett paradigm. We introduce interaction Hamiltonians which allow us to adapt the model to an atomic physics…
We discuss an experimental approach allowing to prepare antihydrogen atoms for the GBAR experiment. We study the feasibility of all necessary experimental steps: The capture of incoming $\bar{\rm H}^+$ ions at keV energies in a deep linear RF trap, sympathetic cooling by laser cooled Be$^+$ ions, transfer to a miniaturized trap and Raman sideband cooling of an ion pair to the motional ground state, and further reducing the momentum of the wavepacket by adiabatic opening of the trap. For each step, we point out the experimental challenges and discuss the efficiency and characteristic times, sho…
