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 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…
One limit to the fidelity of quantum logic operations on trapped ions arises from heating of the ions' collective modes of motion. Sympathetic cooling of the ions during the logic operations may eliminate this source of errors. We discuss benefits and drawbacks of this proposal, and describe possible experimental implementations. We also present an overview of trapped-ion dynamics in this scheme.
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…
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 demonstrate rotational excitation of molecular ions that are sympathetically cooled by laser-cooled atomic ions to a temperature as low as ca. 10 mK. The molecular hydrogen ions HD+ and the fundamental rotational transition $(v=0,\, N=0)\rightarrow(v'=0,\, N'=1)$ at 1.3 THz, the most fundamental dipole-allowed rotational transition of any molecule, are used as a test case. This transition is here observed for the first time directly. Rotational laser cooling was employed in order to increase the signal, and resonance-enhanced multiphoton dissociation was used as detection method. The black-…
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 …
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…
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…
We measured by laser spectroscopy the isotope shifts between naturally-occurring even-isotopes of strontium ions for both the $5s\,\,^2S_{1/2}\to 5p\,\,^2P_{1/2}$ (violet) and the $4d\,\,^2D_{3/2}\to 5p\,\,^2P_{1/2}$ (infrared) dipole-allowed optical transitions. Fluorescence spectra were taken by simultaneous measurements on a two-component Coulomb crystal in a linear Paul trap containing $10^3$--$10^4$ laser-cooled Sr$^+$ ions. The isotope shifts are extracted from the experimental spectra by fitting the data with the analytical solution of the optical Bloch equations describing a three-leve…
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 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…
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 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…
We demonstrate key multi-qubit quantum logic primitives in a dual-species trapped-ion system based on $^{40}$Ca+ and $^{88}$Sr+ ions, using two optical qubits with quantum-logic-control frequencies in the red to near-infrared range. With all ionization, cooling, and control wavelengths in a wavelength band similar for the two species and centered in the visible, and with a favorable mass ratio for sympathetic cooling, this pair is a promising candidate for scalable quantum information processing. Same-species and dual-species two-qubit gates, based on the Moelmer-Soerensen interaction and perf…
It is shown that a two-qubit phase gate and SWAP operation between ground states of cold trapped ions can be realised in one step by simultaneously applying two laser fields. Cooling during gate operations is possible without perturbing the computation and the scheme does not require a second ion species for sympathetic cooling. On the contrary, the cooling lasers even stabilise the desired time evolution of the system. This affords gate operation times of nearly the same order of magnitude as the inverse coupling constant of the ions to a common vibrational mode.
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 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 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…
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…
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 propose an experimental architecture where an array of optical tweezers affords site-dependent control over the confining potential of a conventional radio-frequency ion trap. The site-dependent control enables programmable manipulation of phonon modes of ions, with many potential applications in quantum information processing (QIP) and thermodynamics. We describe protocols for programming the array of optical tweezers to attain a set of target phonon modes with high accuracy. We propose applications of such controls in simulating quantum thermodynamics of a particle of programmable effecti…
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 …
We study the motion of two atoms trapped at distant positions in the field of a driven standing wave high-Q optical resonator. Even without any direct atom-atom interaction the atoms are coupled through their position dependent influence on the intracavity field. For sufficiently good trapping and low cavity losses the atomic motion becomes significantly correlated and the two particles oscillate in their wells preferentially with a 90 degrees relative phase shift. The onset of correlations seriously limits cavity cooling efficiency, raising the achievable temperature to the Doppler limit. The…
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 demonstrate a spatial-imaging thermometry technique for ions in a one-dimensional Coulomb crystal by relating their imaged spatial extent along the linear radiofrequency ion trap axis to normal modes of vibration of coupled oscillators in a harmonic potential. We also use the thermal spatial spread of bright ions in the case of a two-species mixed chain to measure the center-of-mass (COM) resonance frequency of the entire chain and infer the molecular composition of the co-trapped dark ions. These non-destructive techniques create new possibilities for better understanding of sympathetic co…
We present protocols for dissipative entanglement of three trapped-ion qubits and discuss a scheme that uses sympathetic cooling as the dissipation mechanism. This scheme relies on tailored destructive interference to generate any one of six entangled W states in a three-ion qubit space. Using a beryllium-magnesium ion crystal as an example system, we theoretically investigate the protocol's performance and the effects of likely error sources, including thermal secular motion of the ion crystal, calibration imperfections, and spontaneous photon scattering. We estimate that a fidelity of $\sim$…
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…
In this tutorial we review physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated wit…
$^{133}\text{Ba}^+$ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus and visible wavelength electronic transitions. Using a microgram source of radioactive material, we trap and laser-cool the synthetic $A$ = 133 radioisotope of barium II in a radio-frequency ion trap. Using the same, single trapped atom, we measure the isotope shifts and hyperfine structure of the $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $6^2 \text{S}_{1/2}$ and $6^2 \text{P}_{1/2}$ $\leftrightarrow$ $5^2 \text{D}_{3/2}$ electronic transitions that…
We demonstrate coupling between the motions of two independently trapped ions with a separation distance of 620 $μ$m. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over di…
Highly efficient, nearly deterministic, and isotope selective generation of Yb$^+$ ions by 1- and 2-color photoionization is demonstrated. State preparation and state selective detection of hyperfine states in \ybodd is investigated in order to optimize the purity of the prepared state and to time-optimize the detection process. Linear laser cooled Yb$^+$ ion crystals ions confined in a Paul trap are demonstrated. Advantageous features of different previous ion trap experiments are combined while at the same time the number of possible error sources is reduced by using a comparatively simple e…
Optically trapped dielectric objects are well suited for reaching the quantum regime of their center of mass motion in an ultra-high vacuum environment. We show that ground state cooling of an optically trapped nanosphere is achievable when starting at room temperature, by sympathetic cooling of a cold atomic gas optically coupled to the nanoparticle. Unlike cavity cooling in the resolved sideband limit, this system requires only a modest cavity finesse and it allows the cooling to be turned off, permitting subsequent observation of strongly-coupled dynamics between the atoms and sphere. Nanos…
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…
As it has been demonstrated that trapped ion systems have unmatched long-lived quantum-bit (qubit) coherence and can support high-fidelity quantum manipulations, how to scale up the system size becomes an inevitable task for practical purposes. In this work, we theoretically analyse the physical limitation of scalability with a trapped ion array, and propose a feasible scheme of architecture that in principle allows an arbitrary number of ion qubits, for which the overhead only scales linearly with the system size. This scheme relies on the combined ideas of a trap architecture of tunable size…
Precision control over hybrid physical systems at the quantum level is important for the realization of many quantum-based technologies. In the field of quantum information processing (QIP) and quantum networking, various proposals discuss the possibility of hybrid architectures where specific tasks are delegated to the most suitable subsystem. For example, in quantum networks, it may be advantageous to transfer information from a subsystem that has good memory properties to another subsystem that is more efficient at transporting information between nodes in the network. For trapped-ions, a h…
We present a method for achieving high fidelity state preparation and measurement (SPAM) using trapped ion hyperfine qubits with nuclear spins higher than $I = 1/2$. The ground states of these higher nuclear spin isotopes do not afford a simple frequency-selective state preparation scheme. We circumvent this limitation by stroboscopically driving strong and weak transitions, blending fast optical pumping using dipole transitions and narrow microwave or optical quadrupole transitions. We demonstrate this method with the $I=3/2$ isotope $^{137}\mbox{Ba}^+$ to achieve a SPAM infidelity of $\left(…
We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with non-closed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a co-trapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of …
Sympathetic cooling of trapped ions has been established as a powerful technique for manipulation of non-laser-coolable ions (Raizen1992,Waki1992,Bowe1999,Barrett2003). For molecular ions, it promises vastly enhanced spectroscopic resolution and accuracy. However, this potential remains untapped so far, with the best resolution achieved being not better than $5\times10^{-8}$ fractionally, due to residual Doppler broadening being present in ion clusters even at the lowest achievable translational temperatures (Bressel2012). Here we introduce a general and accessible approach that enables Dopple…
Improved control of the motional and internal quantum states of ultracold neutral atoms and ions has opened intriguing possibilities for quantum simulation and quantum computation. Many-body effects have been explored with hundreds of thousands of quantum-degenerate neutral atoms and coherent light-matter interfaces have been built. Systems of single or a few trapped ions have been used to demonstrate universal quantum computing algorithms and to detect variations of fundamental constants in precision atomic clocks. Until now, atomic quantum gases and single trapped ions have been treated sepa…
Quantum error correction will be essential for realizing the full potential of large-scale quantum information processing devices. Fundamental to its experimental realization is the repetitive detection of errors via projective measurements of quantum correlations among qubits, and correction using conditional feedback. Performing these tasks repeatedly requires a system in which measurement and feedback decision times are short compared to qubit coherence times, where the measurement reproduces faithfully the desired projection, and for which the measurement process has no detrimental effect …
