Sympathetic Ground State Cooling and Time-Dilation Shifts in an ^{27}Al^{+} Optical Clock

A compact and fast radio-frequency source for efficient Raman sideband cooling

A compact and fast radio-frequency (RF) source developed for Raman sideband cooling (RSBC) in trapped ion and cold atom experiments is presented. The source is based on direct digital synthesizer, advanced real-time infrastructure for quantum physics, and field programmable gate array. The source has a frequency switching speed of 40 ns and can output continuous μs-level time sequences for RSBC. The maximum output frequency of the source is 1.4 GHz. The RF source is capable of pre-writing data for eight channels. As a demonstration, the RF source is applied to our 25Mg+-27Al+ ion pair optical clock experiment. In order to cool down the ion pair to the vibrational ground state, two-order RSBC is applied to the 25Mg+ ion. As a result, the ion pair motions in the three X, Y, and Z directions are all cooled to the vibrational ground state efficiently, demonstrating the feasibility of this technique. The developed RF source can be widely implemented for other cold atom experiments.

Prospects of a thousand-ion Sn2+ Coulomb-crystal clock with sub-10-19 inaccuracy

Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn2+ ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn2+ has a unique combination of features that is not available in previously considered ions: a 1S0 ↔  3P0 clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn2+ Coulomb-crystal clocks.

State Expansion of a Levitated Nanoparticle in a Dark Harmonic Potential

We spatially expand and subsequently contract the motional thermal state of a levitated nanoparticle using a hybrid trapping scheme. The particle's center-of-mass motion is initialized in a thermal state (temperature 155 mK) in an optical trap and then expanded by subsequent evolution in a much softer Paul trap in the absence of optical fields. We demonstrate expansion of the motional state's standard deviation in position by a factor of 24. In our system, state expansion occurs devoid of backaction from photon recoil, making this approach suitable for coherent wave function expansion.

Penning micro-trap for quantum computing

Trapped ions in radio-frequency traps are among the leading approaches for realizing quantum computers, because of high-fidelity quantum gates and long coherence times1-3. However, the use of radio-frequencies presents several challenges to scaling, including requiring compatibility of chips with high voltages4, managing power dissipation5 and restricting transport and placement of ions6. Here we realize a micro-fabricated Penning ion trap that removes these restrictions by replacing the radio-frequency field with a 3 T magnetic field. We demonstrate full quantum control of an ion in this setting, as well as the ability to transport the ion arbitrarily in the trapping plane above the chip. This unique feature of the Penning micro-trap approach opens up a modification of the quantum charge-coupled device architecture with improved connectivity and flexibility, facilitating the realization of large-scale trapped-ion quantum computing, quantum simulation and quantum sensing.

Sideband cooling of a trapped ion in strong sideband coupling regime

Conventional theoretical studies on the ground-state laser cooling of a trapped ion have mostly focused on the weak sideband coupling (WSC) regime, where the cooling rate is inverse proportional to the linewidth of the excited state. In a recent work [New J. Phys.23, 023018 (2021)10.1088/1367-2630/abe273], we proposed a theoretical framework to study the ground state cooling of a trapped ion in the strong sideband coupling (SSC) regime, under the assumption of a vanishing carrier transition. Here we extend this analysis to more general situations with nonvanishing carrier transitions, where we show that by properly tuning the coupling lasers a cooling rate proportional to the linewidth can be achieved. Our theoretical predictions closely agree with the corresponding exact solutions in the SSC regime, which provide an important theoretical guidance for sideband cooling experiments.

Trapping and Ground-State Cooling of a Single H_{2}^{+}

We demonstrate co-trapping and sideband cooling of a H_{2}^{+}-^{9}Be^{+} ion pair in a cryogenic Paul trap. We study the chemical lifetime of H_{2}^{+} and its dependence on the apparatus temperature, achieving lifetimes of up to 11_{-3}^{+6}  h at 10 K. We demonstrate cooling of two of the modes of translational motion to an average phonon number of 0.07(1) and 0.05(1), corresponding to a temperature of 22(1) and 55(3)  μK, respectively. Our results provide a basis for quantum logic spectroscopy experiments of H_{2}^{+}, as well as other light ions such as HD^{+}, H_{3}^{+}, and He^{+}.

176Lu+ clock comparison at the 10-18 level via correlation spectroscopy

The extreme precision of optical atomic clocks has led to an anticipated redefinition of the second by the International System of Units. Furthermore, accuracies pushing the boundary of 1 part in 10¹⁸ and beyond will enable new applications, such as in geodesy and tests of fundamental physics. The ¹S₀ to ³D₁ optical transition in ¹⁷⁶Lu⁺ has exceptionally low sensitivity to external perturbations, making it suitable for practical clock implementations with inaccuracy at or below 10^-18. Here, we perform high-accuracy comparisons between two ¹⁷⁶Lu⁺ references using correlation spectroscopy. A comparison at different magnetic fields is used to obtain a quadratic Zeeman coefficient of -4.89264(88) Hz/mT for the reference frequency. With a subsequent comparison at low field, we demonstrate agreement at the low 10^-18 level, statistically limited by the averaging time of 42 hours. The evaluated uncertainty in the frequency difference is 9 × 10^-19 and the lowest reported in comparing independent optical references.

Scalable Quantum Logic Spectroscopy

In quantum logic spectroscopy (QLS), one species of trapped ion is used as a sensor to detect the state of an otherwise inaccessible ion species. This extends precision measurements to a broader class of atomic and molecular systems for applications like atomic clocks and tests of fundamental physics. Here, we develop a new technique based on a Schrödinger cat interferometer to address the problem of scaling QLS to larger ion numbers. We demonstrate the basic features of this method using various combinations of ^{25}Mg^{+} logic ions and ^{27}Al^{+} spectroscopy ions. We observe higher detection efficiency by increasing the number of ^{25}Mg^{+} ions. Applied to multiple ^{27}Al^{+}, this method will improve the stability of high-accuracy optical clocks and could enable Heisenberg-limited QLS.

Prospects of a Pb^{2+} Ion Clock

We propose a high-performance atomic clock based on the 1.81 PHz transition between the ground and first-excited state of doubly ionized lead. Utilizing an even isotope of lead, both clock states have I=J=F=0, where I, J, and F are the conventional quantum numbers specifying nuclear, electronic, and total angular momentum, respectively. The clock states are nondegenerate and completely immune to nonscalar perturbations, including first order Zeeman and electric quadrupole shifts. Additionally, the proposed clock is relatively insusceptible to other frequency shifts (blackbody radiation, second order Zeeman, Doppler), accommodates "magic" rf trapping, and is robust against decoherence mechanisms that can otherwise limit clock stability. By driving the transition as a two-photon E1+M1 process, the accompanying probe Stark shift is appreciable yet manageable for practical Rabi frequencies.

Quadruply Ionized Barium as a Candidate for a High-Accuracy Optical Clock

We identify Ba^{4+} (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a ^{3}P_{J} fine structure manifold with anomalous energy ordering, being nonmonotonic in J. We propose a clock based on the 338.8 THz electric quadrupole transition between the ground (^{3}P_{2}) and first-excited (^{3}P_{0}) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a single ion for practical averaging times. The differential static scalar polarizability is found to be small and negative, providing suppressed sensitivity to blackbody radiation while simultaneously allowing cancellation of Stark and excess micromotion shifts. With the exception of Hg^{+} and Yb^{+}, sensitivity to variation of the fine structure constant is greater than other optical clocks thus far demonstrated.

Classical and Nonclassical Time Dilation for Quantum Clocks

Proper time, ideal clocks, and boosts are well understood classically, but subtleties arise in quantum physics. We show that quantum clocks set in motion via momentum boosts do not witness classical time dilation. However, using velocity boosts we find the ideal behavior in both cases, where the quantum clock and classical observer are set in motion. Without internal state-dependent forces additional effects arise. As such, we derive observed frequency shifts in ion trap atomic clocks, indicating a small additional shift, and also show the emergence of nonideal behavior in a theoretical clock model.

Integrated multiple wavelength stabilization on a multi-channel cavity for a transportable optical clock

We present a simple, compact, and efficient scheme for integrated multiple wavelength stabilization and continuous operation of a transportable ⁴⁰Ca⁺ optical clock using a multi-channel cavity. The fractional frequency instability of 729 nm clock laser is ∼ 1.5 ×10^-15 at 10 s with an approximate linewidth of 1 Hz. Meanwhile, frequency fluctuations of all the other lasers are less than ± 330 kHz/day. The one-day stability of this clock is measured as ∼ 5 ×10^-17 through 72 h continuous operation. This scheme is potentially useful for the realization of next-generation transportable optical clocks and other metrological systems.

Ion Transport and Reordering in a 2D Trap Array

Scaling quantum information processors is a challenging task, requiring manipulation of a large number of qubits with high fidelity and a high degree of connectivity. For trapped ions, this can be realized in a 2D array of interconnected traps in which ions are separated, transported, and recombined to carry out quantum operations on small subsets of ions. Here, functionality of a junction connecting orthogonal linear segments in a 2D trap array to reorder a two-ion crystal is demonstrated. The secular motion of the ions experiences low energy gain and the internal qubit levels maintain coherence during the reordering process, therefore demonstrating a promising method for providing all-to-all connectivity in a large-scale, 2D or 3D trapped-ion quantum information processor.

Demonstration of slow light in rubidium vapor using single photons from a trapped ion

Practical implementation of quantum networks is likely to interface different types of quantum systems. Photonically linked hybrid systems, combining unique properties of each constituent system, have typically required sources with the same photon emission wavelength. Trapped ions and neutral atoms both have compelling properties as nodes and memories in a quantum network but have never been photonically linked because of vastly different operating wavelengths. Here, we demonstrate the first interaction between neutral atoms and photons emitted from a single trapped ion. We use slow light in ⁸⁷Rb vapor to delay photons originating from a trapped ¹³⁸Ba⁺ ion by up to 13.5 ± 0.5 ns, using quantum frequency conversion to overcome the frequency difference between the ion and neutral atoms. The delay is tunable and preserves the temporal profile of the photons. This result showcases a hybrid photonic interface usable as a synchronization tool-a critical component in any future large-scale quantum network.

Laser-Assisted Evaporative Cooling of Anions

We report the first cooling of atomic anions by laser radiation. O^{-} ions confined in a linear Paul trap were cooled by selectively photodetaching the hottest particles. For this purpose, anions with the highest total energy were illuminated with a 532 nm laser at their maximal radial excursion. Using laser-particle interaction, we realized a both colder and denser ion cloud, achieving a more than threefold temperature reduction from 1.15 to 0.33 eV. Compared with the interaction with a dilute buffer gas, the energy-selective addressing and removal of anions resulted in lower final temperatures, yet acted 10 times faster and preserved twice as large a fraction of ions in the final state. An ensemble of cold negative ions affords the ability to sympathetically cool any other negative ion species, enabling or facilitating a broad range of fundamental studies from interstellar chemistry to antimatter gravity. The technique can be extended to any negative ion species that can be neutralized via photodetachment.

Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an ²⁷Al⁺ clock to enable a total fractional systematic uncertainty below 10^-18. For this clock, with 38(19) nPa of room-temperature H₂ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order 10^-16 at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be -0.6(2.4) × 10^-19, where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case ±π/2 bound used for collisional phase shift of the ²⁷Al⁺ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

^{27}Al^{+} Quantum-Logic Clock with a Systematic Uncertainty below 10^{-18}

We describe an optical atomic clock based on quantum-logic spectroscopy of the ^{1}S_{0}↔^{3}P_{0} transition in ^{27}Al^{+} with a systematic uncertainty of 9.4×10^{-19} and a frequency stability of 1.2×10^{-15}/sqrt[τ]. A ^{25}Mg^{+} ion is simultaneously trapped with the ^{27}Al^{+} ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ^{27}Al^{+} clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous ^{27}Al^{+} clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.

A cryogenic radio-frequency ion trap for quantum logic spectroscopy of highly charged ions

A cryogenic radio-frequency ion trap system designed for quantum logic spectroscopy of highly charged ions (HCI) is presented. It includes a segmented linear Paul trap, an in-vacuum imaging lens, and a helical resonator. We demonstrate ground state cooling of all three modes of motion of a single ⁹Be⁺ ion and determine their heating rates as well as excess axial micromotion. The trap shows one of the lowest levels of electric field noise published to date. We investigate the magnetic-field noise suppression in cryogenic shields made from segmented copper, the resulting magnetic field stability at the ion position and the resulting coherence time. Using this trap in conjunction with an electron beam ion trap and a deceleration beamline, we have been able to trap single highly charged Ar¹³⁺ (Ar XIV) ions concurrently with single Be⁺ ions, a key prerequisite for the first quantum logic spectroscopy of a HCI. This major stepping stone allows us to push highly-charged-ion spectroscopic precision from the gigahertz to the hertz level and below.

Direct phase-locking of a Ti:Sapphire optical frequency comb to a remote optical frequency standard

We report on an ultralow noise optical frequency transfer from a remotely located Sr optical lattice clock laser to a Ti:Sapphire optical frequency comb through telecom-wavelength optical fiber networks. The inherent narrow linewidth of the Ti:Sapphire optical frequency comb eliminates the need for a local reference high-finesse cavity. The relative fractional frequency instability of the optical frequency comb with respect to the remote optical reference was 6.7(1) × 10^-18 at 1 s and 1.05(3) × 10^-19 at 1,000 s including a 2.9 km-long fiber network. This ensured the optical frequency comb had the same precision as the optical standard. Our result paves the way for ultrahigh-precision spectroscopy and conversion of the highly precise optical frequency to radio frequencies in a simpler setup.

Towards a transportable aluminium ion quantum logic optical clock

With the advent of optical clocks featuring fractional frequency uncertainties on the order of 10^-17 and below, new applications such as chronometric leveling with few-centimeter height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminum ion, which is interrogated via quantum logic spectroscopy. We employ singly charged calcium as the logic ion for sympathetic cooling, state preparation, and readout. Here, we present a simple and compact physics and laser package for manipulation of ⁴⁰Ca⁺. Important features are a segmented multilayer trap with separate loading and probing zones, a compact titanium vacuum chamber, a near-diffraction-limited imaging system with high numerical aperture based on a single biaspheric lens, and an all-in-fiber ⁴⁰Ca⁺ repump laser system. We present preliminary estimates of the trap-induced frequency shifts on ²⁷Al⁺, derived from measurements with a single calcium ion. The micromotion-induced second-order Doppler shift for ²⁷Al⁺ has been determined to be δν_EMMν=-0.4_-0.3 ^+0.4×10^-18 and the black-body radiation shift is δν_BBR/ν = (-4.0 ± 0.4) × 10^-18. Moreover, heating rates of 30 (7) quanta per second at trap frequencies of ω_rad,Ca+ ≈ 2π × 2.5 MHz (ω_ax,Ca+ ≈ 2π × 1.5 MHz) in radial (axial) direction have been measured, enabling interrogation times of a few hundreds of milliseconds.

Inner-shell clock transition in atomic thulium with a small blackbody radiation shift

One of the key systematic effects limiting the performance of state-of-the-art optical clocks is the blackbody radiation (BBR) shift. Here, we demonstrate unusually low sensitivity of a 1.14 μm inner-shell clock transition in neutral Tm atoms to BBR. By direct polarizability measurements, we infer a differential polarizability of the clock levels of -0.063(30) atomic units corresponding to a fractional frequency BBR shift of only 2.3(1.1) × 10^-18 at room temperature. This amount is several orders of magnitude smaller than that of the best optical clocks using neutral atoms (Sr, Yb, Hg) and is competitive with that of ion optical clocks (Al⁺, Lu⁺). Our results allow the development of lanthanide-based optical clocks with a relative uncertainty at the 10^-17 level.

Two-Photon Vibrational Transitions in 16O2+ as Probes of Variation of the Proton-to-Electron Mass Ratio

Vibrational overtones in deeply-bound molecules are sensitive probes for variation of the proton-to-electron mass ratio μ . In nonpolar molecules, these overtones may be driven as two-photon transitions. Here, we present procedures for experiments with 16 O 2 + , including state-preparation through photoionization, a two-photon probe, and detection. We calculate transition dipole moments between all X 2 Π g vibrational levels and those of the A 2 Π u excited electronic state. Using these dipole moments, we calculate two-photon transition rates and AC-Stark-shift systematics for the overtones. We estimate other systematic effects and statistical precision. Two-photon vibrational transitions in 16 O 2 + provide multiple routes to improved searches for μ variation.

Correcting symmetry imperfections in linear multipole traps

Multipole radio-frequency (RF) traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied RF amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied RF voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well.

Blackbody radiation shift assessment for a lutetium ion clock

The accuracy of state-of-the-art atomic clocks is derived from the insensitivity of narrow optical atomic resonances to environmental perturbations. Two such resonances in singly ionized lutetium have been identified with potentially lower sensitivities compared to other clock candidates. Here we report measurement of the most significant unknown atomic property of both transitions, the static differential scalar polarizability. From this, the fractional blackbody radiation shift for one of the transitions is found to be −1.36(9) × 10⁻¹⁸ at 300 K, the lowest of any established optical atomic clock. In consideration of leading systematic effects common to all ion clocks, both transitions compare favorably to the most accurate ion-based clocks reported to date. This work firmly establishes Lu⁺ as a promising candidate for a future generation of more accurate optical atomic clocks.

There is a continuous effort to improve the accuracy of atomic clocks. Here the authors measure the static differential scalar polarizability of Lutetium ion resonant transitions and its lower light shift from blackbody radiation makes it a promising candidate for ion-based atomic clocks.

Frequency measurement of the clock transition of an indium ion sympathetically-cooled in a linear trap

We report frequency measurement of the clock transition in an ¹¹⁵In⁺ ion sympathetically-cooled with Ca⁺ ions in a linear rf trap. The Ca⁺ ions are used as a probe of the external electromagnetic field and as the coolant for preparing the cold In⁺. The frequency is determined to be 1 267 402 452 901 049.9 (6.9) Hz by averaging 36 measurements using an optical frequency comb referenced to the frequency standards located in the same site.