Laser-cooled Ions Research Articles

Ground-state gj factors of the Cd+, Yb+, and Hg+ ions

Accurate calculations of ${g}_{j}$ factors of the ground state of the ${\mathrm{Cd}}^{+},$ ${\mathrm{Yb}}^{+},$ and ${\mathrm{Hg}}^{+}$ ions are presented by employing the normal order unrelaxed $\mathrm{\ensuremath{\Lambda}}$-approach relativistic coupled-cluster $(\mathrm{\ensuremath{\Lambda}}\text{\ensuremath{-}}\mathrm{RCC})$ theory. Contributions from the quantum electrodynamics (QED) are estimated from the free electron QED contributions and the roles of electron correlation effects are analyzed with different cutoff of occupied and virtual active orbitals in the $\mathrm{\ensuremath{\Lambda}}$-RCC method. Our final ${g}_{j}$ factors come out to be 2.002291(4), 2.002798(113), and 2.003128(41) for the ${\mathrm{Cd}}^{+},$ ${\mathrm{Yb}}^{+},$ and ${\mathrm{Hg}}^{+}$ ions, respectively. Our result for ${\mathrm{Hg}}^{+}$ agrees up to the fourth decimal places with its experimental value 2.0031745(74) indicating that our calculations of the other ions are of similar accuracies. The understanding of roles of electron correlation effects from this study will be useful in improving accuracies of the ${g}_{j}$ factors in the considered ions further by adding more physical effects in the future and performing calculations with similar accuracies in other heavier atomic systems. The reported ${g}_{j}$ factors can also be used to scrutinize the background noise related to the stray magnetic fields in the laser-cooled microwave ion clocks using the above ions.

Direct measurement of the 7s2S1/2→7p2P3/2 transition frequency in Ra+226

We report a direct measurement of the $7s\ ^2S_{1/2}\rightarrow$ $7p\ ^2P_{3/2}$ electric dipole transition frequency in $^{226}$Ra$^{+}$. With a single laser-cooled radium ion we determine the transition frequency to be 785722.11(3) GHz by directly driving the transition with frequency-doubled light and measuring the frequency of the undoubled light with an iodine reference. This measurement addresses a discrepancy of five combined standard deviations between previously reported values.

Significantly Improving the Escape Time of a Single 40Ca+ Ion in a Linear Paul Trap by Fast Switching of the Endcap VoltageSupported by the National Natural Science Foundation of China (Grant Nos. 11934014, 11622434 and 11804373), the Scientific Instrument Developing Project of the Chinese Academy of Sciences (Grant No. YZ201552), the Strategic Priority Research Program of the Chinese Academy of

Sympathetic cooling is a method used to lower the kinetic energy of ions with complicated energy-level structures, via Coulomb interactions with laser-cooled ions in an ion trap. The ion to be sympathetically cooled is sometimes prepared outside of the trap, and it is critical to introduce this ion into the trap by temporarily lowering the potential of one endcap without allowing the coolant ion to escape. We study the time required for a laser-cooled ion to escape from a linear Paul trap when the voltage of one endcap is lowered. The escape time is on the order of a few microseconds, and varies significantly when the low-level voltage changes. A re-cooling time of a maximum of 13 s was measured, which can be reduced to approximately one hundred of milliseconds by decreasing the duration of the low-level voltage. The measurement of these critical values lays the foundation for the smooth injection and cooling of the ion to be sympathetically cooled.

Quantum simulation of extended polaron models using compound atom-ion systems

We consider the prospects for quantum simulation of condensed matter models exhibiting strong electron-phonon coupling using a hybrid platform of trapped laser-cooled ions interacting with an ultracold atomic gas. This system naturally posesses a phonon structure, in contrast to the standard optical lattice scenarios usually employed with ultracold atoms in which the lattice is generated by laser light and thus it remains static. We derive the effective Hamiltonian describing the general system and discuss the arising energy scales, relating the results to commonly employed extended Hubbard-Holstein models. Although for a typical experimentally realistic system the coupling to phonons turns out to be small, we provide the means to enhance its role and reach interesting regimes with competing orders. Extended Lang-Firsov transformation reveals the emergence of phonon-induced long-range interactions between the atoms, which can give rise to both localized and extended bipolaron states with low effective mass, indicating the possibility of fermion pairing.

Branching fractions for P3/2 decays in Ba+

Branching fractions for decays from the $P_{3/2}$ level in $^{138}$Ba$^+$ have been measured with a single laser-cooled ion. Decay probabilities to $S_{1/2}$, $D_{3/2}$ and $D_{5/2}$ are determined to be $0.741716(71)$, $0.028031(23)$ and $0.230253(61)$, respectively, which are an order of magnitude improvement over previous results. Our methodology only involves optical pumping and state detection, and is hence relatively free of systematic effects. Measurements are carried out in two different ways to check for consistency. Our analysis also includes a measurement of the $D_{5/2}$ lifetime, for which we obtain 30.14(40)\,s.

Optical quantum nondemolition measurement of a single rare earth ion qubit

Optically-interfaced spins in the solid state are a promising platform for quantum technologies. A crucial component of these systems is high-fidelity, projective measurement of the spin state. Here, we demonstrate single-shot spin readout of a single rare earth ion qubit, Er3+, which is attractive for its telecom-wavelength optical transition and compatibility with silicon nanophotonic circuits. In previous work with laser-cooled atoms and ions, and solid-state defects, spin readout is accomplished using fluorescence on an optical cycling transition; however, Er3+ and other rare earth ions generally lack strong cycling transitions. We demonstrate that modifying the electromagnetic environment around the ion can increase the strength and cyclicity of the optical transition by several orders of magnitude, enabling single-shot quantum nondemolition readout of the ion’s spin with 94.6% fidelity. We use this readout to probe coherent dynamics and relaxation of the spin.

Interactions and charge-transfer dynamics of anAl+ion immersed in ultracold Rb and Sr atoms

Atomic clocks based on an Al$^+$ ion sympathetically cooled by a laser-cooled alkaline-earth ion have achieved unprecedented accuracy. Here, we investigate theoretically interactions and charge transfer dynamics of an Al$^+$ ion immersed in an ultracold gas of Rb and Sr atoms. We calculate potential energy curves and transition electric dipole moments for the (Al+Rb)$^+$ and (Al+Sr)$^+$ ion-atom systems using coupled cluster and multireference configuration interaction methods with scalar relativistic effects included within the small-core energy-consistent pseudopotentials in Rb and Sr atoms. The long-range interaction coefficients are also reported. We use the electronic structure data to investigate cold collisions and charge transfer dynamics. Scattering of an Al$^+$ ion with alkali-metal or alkaline-earth-metal atom is governed by one potential energy curve whereas charge transfer can lead to several electronic states mixed by the relativistic spin-orbit coupling. We examine the branching ratios resulting from the interplay of the short- and long-range effects, as well as the prospects for the laser-field control and formation of molecular ions. We propose to employ the atomic clock transition in an Al$^+$ ion to monitor ion-atom scattering dynamics via quantum logic spectroscopy. The presented results pave the way for the application of atomic ions other than alkali-metal and alkaline-earth-metal ones in the field of cold hybrid ion-atom experiments.

A single atom noise probe operating beyond the Heisenberg limit

According to the Heisenberg uncertainty principle, the energy or frequency uncertainty of a measurement can be at the best inversely proportional to the observation time (T). The observation time in an experiment using a quantum mechanical probe is ultimately limited by the coherence time of the probe. Therefore the inverse proportionality of the statistical uncertainty of a frequency measurement to the observation time is also limited up to the coherence time of the probe, provided the systematic uncertainties are well below the statistical uncertainties. With a single laser-cooled barium ion as a quantum probe, we show that the uncertainty in the frequency measurement for a general time-dependent Hamiltonian scales as 1/{T}^{1.75pm 0.03} as opposed to 1/T, given by the Heisenberg limit for time-independent Hamiltonian. These measurements, based on controlled feedback Hamiltonian and implemented on a laser cooled single ion, allowed precise measurement of noise frequency in the kHz range. Moreover, based on the observed sensitivity of a single ion experiment presented here, we propose the use of a similar protocol with enhanced sensitivity as a tool to directly verify the existence of certain types of light mass axion-like dark matter particles where no direct measurement protocol exists.

Precision Measurements of the Fundamental Properties of the Proton and Antiproton

Precision measurements comparing the fundamental properties of conjugate particles and antiparticles constitute stringent tests of CPT invariance. We review recent precision measurements of the BASE collaboration, which improved the uncertainty of the proton and antiproton magnetic moments and the comparison of the proton-to-antiproton charge-to-mass ratio. These measurements constitute the most stringent tests of CPT invariance with antiprotons. Further, we discuss the improved limit on the antiproton lifetime based on the storage of a cloud of antiprotons in the unique BASE reservoir trap. Based on these recent advances, we discuss ongoing technical developments which comprise a coupling trap for the sympathetic cooling of single (anti-)protons with laser-cooled beryllium ions, a transportable trap to relocate antiproton measurements into a high-precision laboratory, and a new experiment to measure the magnetic moment of helium-3 ions, which will improve absolute precision magnetometry.

Laser-cooled ytterbium-ion microwave frequency standard

We report on the development of a trapped-ion, microwave frequency standard based on the 12.6 GHz hyperfine transition in laser-cooled ytterbium-171 ions. The entire system fits into a 6U 19-in. rack unit $$(51\times 49\times 28\,\mathrm{{cm}})$$ and comprises laser, electronics, and physics package subsystems. As a first step towards a full evaluation of the system capability, we have measured the frequency instability of our system which is $$3.6\times 10^{-12}/\surd \tau $$ for averaging times between 30 and $$1500\,\mathrm{{s}}$$.

Can a periodically driven particle resist laser cooling and noise?

Studying a single atomic ion confined in a time-dependent periodic anharmonic potential, we find large amplitude trajectories stable for millions of oscillation periods in the presence of stochastic laser cooling. The competition between energy gain from the time-dependent drive and damping leads to the stabilization of such stochastic limit cycles. Instead of converging to the global minimum of the averaged potential, the steady-state phase-space distribution develops multiple peaks in the regions of phase space where the frequency of the motion is close to a multiple of the periodic drive. Such distinct nonequilibrium behaviour can be observed in realistic radio-frequency traps with laser-cooled ions, suggesting that Paul traps offer a well-controlled test-bed for studying transport and dynamics of microscopically driven systems.

Cold hybrid ion-atom systems

Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. We provide a broad overview of the theoretical description of ion-atom mixtures and their applications, and report on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with ions directly produced in a Bose-Einstein condensate. We start with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and non-radiative charge transfer processes and their control with magnetically tunable Feshbach resonances. Then we describe the relevant experimental techniques and the intrinsic properties of hybrid systems. In particular, we discuss the impact of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, we review recent proposals for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. In the last part we focus on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. We discuss applications and prospects of cold molecular ions for cold controlled chemistry and precision spectroscopy.

Laser Cooling of Radium Ions.

The unstable radium nucleus is appealing for probing new physics due to its high mass, octupole deformation, and energy level structure. Ion traps, with long hold times and low particle numbers, are excellent for work with radioactive species, such as radium and radium-based molecular ions, where low activity, and hence low total numbers, is desirable. We address the challenges associated with the lack of stable isotopes in a tabletop experiment with a low-activity (∼10 μCi) source where we laser-cool trapped radium ions. With a laser-cooled radium ion we measured the 7p^{2}P_{1/2}^{o} state's branching fractions to the ground state, 7s^{2}S_{1/2}, and a metastable excited state, 6d^{2}D_{3/2}, to be p=0.9104(7) and 0.0896(7), respectively. With a nearby tellurium reference line we measured the 7s^{2}S_{1/2}→7p^{2}P_{1/2}^{o} transition frequency, 640.096 63(6)THz.

Electrostatic equilibria of non-neutral plasmas confined in a Penning trap with axially varying magnetic field

A procedure for computing the electrostatic equilibria of non-neutral plasmas in a Penning trap with a nonuniform magnetic field by solving Poisson's equation using an iterative method is described. Plasma equilibria in a model Penning trap with high and low field regions are computed. The plasma is assumed to follow the Boltzmann density distribution along magnetic field lines. Correspondence with previous investigations examining similar configurations analytically and using particle-in-cell simulations is found. The relationship between the plasma density in low and high field regions is examined for various plasma temperatures, densities, magnetic mirror ratios, and plasma and electrode radii. An analytical description of the radial density profile in the high field region is developed and compared with the computed equilibria. A concept is described for cooling a positron plasma with laser-cooled ions trapped axially within a high magnetic field region, while antiprotons are trapped axially separated from the laser-cooled ions within a low field region, and the positron plasma extends to both regions.

Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.

Compact laser system for a laser-cooled ytterbium ion microwave frequency standard.

The development of a transportable microwave frequency standard based on the ground-state transition of 171Yb+ at ∼12.6 GHz requires a compact laser system for cooling the ions, clearing out of long-lived states and also for photoionisation. In this paper, we describe the development of a suitable compact laser system based on a 6U height rack-mounted arrangement with overall dimensions 260 × 194 × 335 mm. Laser outputs at 369 nm (for cooling), 399 nm (photoionisation), 935 nm (repumping), and 760 nm (state clearout) are combined in a fiber arrangement for delivery to our linear ion trap and we demonstrate this system by cooling of 171Yb+ ions. Additionally, we demonstrate that the lasers at 935 nm and 760 nm are close in frequency to water vapor and oxygen absorption lines, respectively; specifically, at 760 nm, we show that one 171Yb+ transition is within the pressure broadened profile of an oxygen line. These molecular transitions form convenient wavelength references for the stabilization of lasers for a 171Yb+ frequency standard.

Absolute single-ion thermometry

We describe and experimentally implement a single-ion local thermometry technique with absolute sensitivity adaptable to all laser-cooled atomic ion species. The technique is based on the velocity-dependent spectral shape of a quasi-dark resonance tailored in a J $\rightarrow$ J transition such that the two driving fields can be derived from the same laser source leading to a negligible relative phase shift. We validated the method and tested its performances in an experiment on a single 88 Sr + ion cooled in a surface radio-frequency trap. We first applied the technique to characterise the heating-rate of the surface trap. We then measured the stationary temperature of the ion as a function of cooling laser detuning in the Doppler regime. The results agree with theoretical calculations, with an absolute error smaller than 100 $\mu$K at 500 $\mu$K, in a temperature range between 0.5 and 3 mK and in the absence of adjustable parameters. This simple-to-implement and reliable method opens the way to fast absolute measurements of single-ion temperatures in future experiments dealing with heat transport in ion chains or thermodynamics at the single-ion level.

Spectroscopy of Molecular Ions in Coulomb Crystals.

In this Perspective, we examine the use of laser-cooled atomic ions and sympathetically cooled molecular ions in Coulomb crystals for molecular spectroscopy. Coulomb crystals are well-isolated environments that provide localization and long storage times for sensitive measurements of weak signals and cold temperatures for precise spectroscopy. Coulomb crystals of molecular and atomic ions enable the detection of single-photon molecular ion transitions at a range of wavelengths by a change in atomic ion fluorescence at visible wavelengths. We give an overview of the state of the art from action spectroscopy to quantum logic spectroscopy for a wide range of molecular transitions from rotational sublevels separated by 10-7 cm-1 to rovibronic transitions at 25 000 cm-1. We emphasize how this system allows for unparalleled control of the molecular ion state for precision spectroscopy with applications in astrochemistry and fundamental physics. We conclude with an outlook of the use of this control in cold molecular ion reactions.

Single-Atom Heat Machines Enabled by Energy Quantization

Quantization of energy is a quintessential characteristic of quantum systems. Here we analyze its effects on the operation of Otto cycle heat machines and show that energy quantization alone may alter and increase machine performance in terms of output work, efficiency, and even operation mode. We show that this difference in performance occurs in machines with inhomogeneous energy level scaling, while quantum machines with homogeneous level scaling behave like classical machines. Our results demonstrate that quantum thermodynamics enables the realization of classically inconceivable Otto machines, such as those with an incompressible working substance. We propose to measure these effects experimentally using a laser-cooled trapped ion as a microscopic heat machine.

Rotational spectroscopy of cold and trapped molecular ions in the Lamb–Dicke regime

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 Doppler-free rotational spectroscopy. It makes use of the strong radial spatial confinement of molecular ions when trapped and crystallized in a linear quadrupole trap, providing the Lamb-Dicke regime for rotational transitions. We achieve a line width of $1\times10^{-9}$ fractionally and $1.3~\textrm{kHz}$ absolute, an improvement by $50$ and nearly $3\times10^{3}$, respectively, over other methods. The systematic uncertainty is $2.5\times10^{-10}$. As an application, we demonstrate the most precise test of $\textit{ab initio}$ molecular theory and the most precise ($1.3~\textrm{PPB}$) spectroscopic determination of the proton mass. The results represent the long overdue extension of Doppler-free microwave spectroscopy of laser-cooled atomic ion clusters (Berkeland1998) to higher spectroscopy frequencies and to molecules. This approach enables a vast range of high-precision measurements on molecules, both on rotational and, as we project, vibrational transitions.