We report on the direct observation of resonant electric dipole-dipole interactions in a cubic array of atoms in the many-excitation limit. The interactions, mediated by single-atom couplings to the shared electromagnetic vacuum, are shown to produce spatially-dependent cooperative Lamb shifts when spectroscopically interrogating the mHz-wide optical clock transition in strontium-87. We show that the ensemble-averaged shifts can be suppressed below the level of evaluated systematic uncertainties for state-of-the-art optical atomic clocks. Additionally, we demonstrate that excitation of the atomic dipoles near a Bragg angle can enhance these effects by nearly an order of magnitude compared to non-resonant geometries. Given the remarkable precision of frequency measurements and the high accuracy of the modeled response, our work demonstrates that such a clock is a novel platform for studies of the quantum many-body physics of spins with long-range interactions mediated by propagating photons.
We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultra-narrow clock transition into the mode of a high Q-resonator. The resultant optical radiation has an extremely narrow linewidth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order $10^{-12}W$ is possible, sufficient for phase-locking a slave optical local oscillator. Realizing this light source has the potential to improve the stability of the best clocks by two orders of magnitude.
Hyperfine quenching rates of the lowest-energy metastable $^3P_0$ and $^3P_2$ states of Mg, Ca, Sr, and Yb atoms are computed. The calculations are carried out using ab initio relativistic many-body methods. The computed lifetimes may be useful for designing novel ultra-precise optical clocks and trapping experiments with the $3P_2$ fermionic isotopes. The resulting natural widths of the $^3P_0 -> ^1S_0$ clock transition are 0.44 mHz for $^{25}$Mg, 2.2 mHz for $^{43}$Ca, 7.6 mHz for $^{87}$Sr, 43.5 mHz for $^{171}$Yb, and 38.5 mHz for $^{173}$Yb. Compared to the bosonic isotopes, the lifetime …
We present an experimental study of the lattice induced light shifts on the 1S_0-3P_0 optical clock transition (v_clock~518 THz) in neutral ytterbium. The ``magic'' frequency, v_magic, for the 174Yb isotope was determined to be 394 799 475(35)MHz, which leads to a first order light shift uncertainty of 0.38 Hz on the 518 THz clock transition. Also investigated were the hyperpolarizability shifts due to the nearby 6s6p 3P_0 - 6s8p 3P_0, 6s8p 3P_2, and 6s5f 3F_2 two-photon resonances at 759.708 nm, 754.23 nm, and 764.95 nm respectively. By tuning the lattice frequency over the two-photon resonan…
A sharp resonance line that appears in three-photon transitions between the $^{1}S_{0}$ and $^{3}P_{0}$ states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. The method has the unique feature that the width and rate of the clock transition can be continuously adjusted from the $MHz$ level to sub-$mHz$ without loss of sig…
We perform calculations of the dependence of nuclear magnetic moments on quark masses and obtain limits on the variation of m_q/Lambda_{QCD} from recent atomic clock experiments with hyperfine transitions in H, Rb, Cs, Hg+ and optical transtion in Hg+.
We report calculations designed to assess the ultimate precision of an atomic clock based on the 578 nm $6 ^1S_0 --> 6 ^3P^o_0$ transition in Yb atoms confined in an optical lattice trap. We find that this transition has a natural linewidth less than 10 mHz in the odd Yb isotopes, caused by hyperfine coupling. The shift in this transition due to the trapping light acting through the lowest order AC polarizability is found to become zero at the magic trap wavelength of about 752 nm. The effects of Rayleigh scattering, higher-order polarizabilities, vector polarizability, and hyperfine induced e…
The quadratic Zeeman shift coefficient of 3P0 clock state for strontium is determined in theory and experiment. In theory, we derived the expression of the quadratic Zeeman shift of 3P0 clock state for 88Sr and 87Sr in the weak-magnetic-field approximation. By using the multi-configuration Dirac-Hartree-Fock theory, the quadratic Zeeman shift coefficients were calculated. To determine the calculated results, the quadratic Zeeman shift coefficient of 3P0,F=9/2,MF=+/-9/2 clock state was measured in our 87Sr optical lattice clock. The calculated results C2=-23.38(5) MHz/T2 for 88Sr and the 3P0,F=…
An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the $5s^2 {}^1S_0 \to 5s5p {}^3P_0$ transition of ${}^{87}{\rm Sr}$ atoms as a "clock transition". Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than $ 10^{-17}$.
In this paper, we propose a scheme of active ion optical clock with detailed pumping method, lasing states, output power, linewidth and light shift. Using 171Yb+ ions in a Paul Trap we propose to utilize a Fabry-Perot resonator to realize lasing of active optical frequency standards. The quantum-limited linewidth of active 171Yb+ ion optical clock is narrower than 1 mHz. Based on the mechanism and advantages of active optical clock at ion optical clock transition frequency, this new laser light source as a stable local oscillator, will be beneficial to the single-ion optical clock, which curre…
Today's best atomic clocks are limited by frequency noise on the lasers used to interrogate the atoms. A proposed solution to this problem is to create a superradiant laser using an optical clock transition as its gain medium. This laser would act as an active atomic clock, and would be highly immune to the fluctuations in reference cavity length that limit today's best lasers. Here, we demonstrate and characterize superradiant emission from the mHz linewidth clock transition in an ensemble of laser-cooled $^{87}$Sr atoms trapped within a high-finesse optical cavity. We measure a collective en…
The energy levels and electric dipole ($E1$) matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic $E1$, magnetic dipole ($M1$) and electric quadrupole ($E2$) polarizabilities as well as the hyperpolarizabilities of the $2s^2~^1S_0$ and $2s2p~^3P_0$ states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of $2s^2~^1S_0 \rightarrow 2s2p~^3P_0$ clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock trans…
Optical lattice clocks with uncertainty and instability in the $10^{-17}$-range and below have so far been demonstrated exclusively using fermions. Here, we demonstrate a bosonic optical lattice clock with $3\times 10^{-18}$ instability and $2.0\times 10^{-17}$ accuracy, both values improving on previous work by a factor 30. This was enabled by probing the clock transition with an ultra-long interrogation time of 4 s, using the long coherence time provided by a cryogenic silicon resonator, by careful stabilization of relevant operating parameters, and by operating at low atom density. This wor…
We report on the spectroscopy of the $5s^2 {}^1S_0 (F=9/2) \to 5s5p {}^3P_0 (F=9/2)$ clock transition of ${}^{87}{\rm Sr}$ atoms (natural linewidth of 1 mHz) trapped in a one-dimensional optical lattice. Recoilless transitions with a linewidth of 0.7 kHz as well as the vibrational structure of the lattice potential were observed. By investigating the wavelength dependence of the carrier linewidth, we determined the magic wavelength, where the light shift in the clock transition vanishes, to be $813.5\pm0.9$ nm.
We experimentally demonstrate the collective emission behavior and suppressed cavity-pulling effect of four-level active optical clock with Cesium atoms. Thermal Cesium atoms in a glass cell velocity selective pumped with a 455.5 nm laser operating at 6S$_{1/2}$ to 7P$_{3/2}$ transition are used as lasing medium. Population inverted Cesium atoms between 7S$_{1/2}$ and 6P$_{3/2}$ levels are optical weakly coupled by a pair cavity mirrors working at deep bad-cavity regime with a finesse of 4.3, and the ratio between cavity bandwidth and gain bandwidth is approximately 45. With increased 455.5 nm…
We implement imaging spectroscopy of the optical clock transition of lattice-trapped degenerate fermionic Sr in the Mott-insulating regime, combining micron spatial resolution with submillihertz spectral precision. We use these tools to demonstrate atomic coherence for up to 15 s on the clock transition and reach a record frequency precision of $2.5\times 10^{-19}$. We perform the most rapid evaluation of trapping light shifts and record a 150 mHz linewidth, the narrowest Rabi line shape observed on a coherent optical transition. The important emerging capability of combining high-resolution i…
Atomic clocks have recently reached a fractional timing precision of $<10^{-18}$. We point out that an array of atomic clocks, distributed along the Earth's orbit around the Sun, will have the sensitivity needed to detect the time dilation effect of mHz gravitational waves (GWs), such as those emitted by supermassive black hole binaries at cosmological distances. Simultaneous measurement of clock-rates at different phases of a passing GW provides an attractive alternative to the interferometric detection of temporal variations in distance between test masses separated by less than a GW wavelen…
The current theoretical status of the Lamb shift in He+ is discussed. Recent calculations of two-loop binding corrections to the Lamb shift significantly shift the theoretical value of the "classic" Lamb shift in He+, i.e. of the 2S_1/2-2P_1/2-interval. In this brief research note, we present a new (theoretical) value for this interval which reads 14041.474(42) Mhz. The theoretical uncertainty is reduced as well as the discrepancy between theory and experiment. Planned measurements should be of help in further elucidating the situation.
We perform calculations of the dependence of nuclear magnetic moments on quark masses and obtain limits on the variation of the ratio of quark mass and strong interaction scale (m_q/Lambda_{QCD}) from recent atomic clock experiments with hyperfine transitions in H, Rb, Cs, Yb+, Hg+ and optical transition in Hg+. Experiments with Cd+, deuterium/hydrogen, molecule SF_6, Zeeman transitions in He_3/Xe are also discussed.
We propose a new type of superradiant laser based on a hot atomic beam traversing an optical cavity. We show that the theoretical minimum linewidth and maximum power are competitive with the best ultracoherent clock lasers. Also, our system operates naturally in continuous wave mode, which has been elusive for superradiant lasers so far. Unlike existing ultracoherent lasers, our design is simple and rugged. This makes it a candidate for the first widely accessible ultracoherent laser, as well as the first to realize sought-after applications of ultracoherent lasers in challenging environments.
In this paper, blackbody radiation (BBR) temperature rise seen by the $^{40}$Ca$^+$ ion confined in a miniature Paul trap and its uncertainty have been evaluated via finite-element method (FEM) modelling. The FEM model was validated by comparing with thermal camera measurements, which were calibrated by PT1000 resistance thermometer, at several points on a dummy trap. The input modelling parameters were analyzed carefully in detail, and their contributions to the uncertainty of environment temperature were evaluated on the validated FEM model. The result shows that the temperature rise seen by…
We propose a combination of Electromagnetically Induced Transparency (EIT)/Raman and pulsed spectroscopy techniques to accurately cancel frequency shifts arising from EIT fields in forbidden optical lattice clock transitions of alkaline earth atoms. Time-separated laser pulses are designed to trap atoms in coherent superpositions while eliminating off-resonance ac Stark contributions at particular laser detunings from the intermediate excited state. The scheme achieves efficient population transfer up to 60% with potential inaccuracy $<$ $10^{-17}$. Cancellation of external light shifts determ…
We optically excite the electronic state $3s3p~^3P_{0}$ in $^{24}$Mg atoms, laser-cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift and the transition frequency to be 468.463(207)$\,$nm, -206.6(2.0)$\,$MHz/T$^2$ and 655 058 646 691(101)$\,$kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also developed a high-precision relativistic structure model for m…
An ultra-stable optical clock based on coherent population trapping effect of alkaline-earth ions, such as Ca$^+$, Sr$^+$, Ba$^+$, is analyzed here. The proposed transitions use the odd isotopes, so that the frequency shift is insensitive to the applied magnetic field. To enhance the signal, a large number of ions are trapped in a linear Paul trap, and laser cooled to crystallize such that the ions are in the Lamb-Dicke regime to avoid first order Doppler shift. Other relevant frequency shifts are also analyzed. Further techniques to improve the stability of the clock signal are discussed.
With the advent of optical clocks featuring fractional frequency uncertainties on the order of $10^{-17}$ and below, new applications such as chronometric levelling with few-cm height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminium 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 $^{40}\mathrm{Ca}^+$. Important features are a segmented multi-la…
As optical clocks are improved to reach the frequency uncertainty below the 10$^{-17}$ level, the frequency shift due to the blackbody radiation (BBR) has been one of the major systematic effects hindering further improvement. To evaluate the BBR shift of an Yb optical lattice clock at KRISS, we installed an in-vacuum BBR shield and made radiation thermometry using a black-coated-sphere thermal probe. After we quantitatively measured the conduction loss of the thermal probe and the effects of all the external radiation sources, we determined the temperature at the atom trap site with an uncert…
We report on the frequency performance of a low cost (~500$) radio-frequency sine wave generator, using direct digital synthesis (DDS) and a field-programmable gate array (FPGA). The output frequency of the device may be changed dynamically to any arbitrary value ranging from DC to 10 MHz without any phase slip. Sampling effects are substantially reduced by a high sample rate, up to 1 MHz, and by a large memory length, more than 2.10^5 samples. By using a low noise external oscillator to clock the DDS, we demonstrate a phase noise as low as that of the master clock, that is at the level of -11…
We consider the effect of the coupled variations of fundamental constants on the nucleon magnetic moment. The nucleon g-factor enters into the interpretation of the measurements of variations in the fine-structure constant, alpha, in both the laboratory (through atomic clock measurements) and in astrophysical systems (e.g. through measurements of the 21 cm transitions). A null result can be translated into a limit on the variation of a set of fundamental constants, that is usually reduced to alpha. However, in specific models, particularly unification models, changes in alpha are always accomp…
To date, the highest fidelity quantum logic gates between two qubits have been achieved with variations on the geometric-phase gate in trapped ions, with the two leading variants being the Molmer-Sorensen gate and the light-shift (LS) gate. Both of these approaches have their respective advantages and challenges. For example, the latter is technically simpler and is natively insensitive to optical phases, but it has not been made to work directly on a clock-state qubit. We present a new technique for implementing the LS gate that combines the best features of these two approaches: By using a s…
We present a novel method for engineering an optical clock transition that is robust against external field fluctuations and is able to overcome limits resulting from field inhomogeneities. The technique is based on the application of continuous driving fields to form a pair of dressed states essentially free of all relevant shifts. Specifically, the clock transition is robust to magnetic shifts, quadrupole and other tensor shifts, and amplitude fluctuations of the driving fields. The scheme is applicable to either a single ion or an ensemble of ions, and is relevant for several types of ions,…
We report a new measurement of the $n=2$ Lamb shift in Muonium using microwave spectroscopy. Our result of $1047.2(2.3)_\textrm{stat}(1.1)_\textrm{syst}$ MHz comprises an order of magnitude improvement upon the previous best measurement. This value matches the theoretical calculation within one standard deviation allowing us to set limits on CPT violation in the muonic sector, as well as on new physics coupled to muons and electrons which could provide an explanation of the muon $g-2$ anomaly.
Prediction of Nuclear Clock Transitions Frequency Difference between $^{229}$Th$^{3+}$ and $^{229}$Th$^{4+}$ via \textit{ab-initio} Self-Consistent Field Theory
We present a new method for determining the intrinsic natural linewidth or lifetime of exceptionally long-lived optical excited states. Such transitions are key to the performance of state-of-the-art atomic clocks, have potential applications in searches for fundamental physics and gravitational wave detectors, as well as novel quantum many-body phenomena. With longer lifetime optical transitions, sensitivity is increased, but so far it has proved challenging to determine the natural lifetime of many of these long lived optical excited states because standard population decay detection techniq…
A theoretical proposal for reducing an entire atomic clock to micron dimensions. A phosphorus or nitrogen atom is introduced into a fullerene cage. This endohedral fullerene is then coated with an insulating shell and a number of them are deposited as a thin layer on a silicon chip. Next to this layer a GMR sensor is fabricated which is close to the endohedral fullerenes. This GMR sensor measures oscillating magnetic fields on the order of micro-gauss from the nuclear spins varying at the frequency of the hyperfine transition (413 MHz frequency). Given the micron scale and simplicity of this s…
We report the direct excitation of the highly forbidden (6s^2) 1S0 - (6s6p) 3P0 optical transition in two odd isotopes of ytterbium. As the excitation laser frequency is scanned, absorption is detected by monitoring the depletion from an atomic cloud at ~70 uK in a magneto-optical trap. The measured frequency in 171Yb (F=1/2) is 518,295,836,593.2 +/- 4.4 kHz. The measured frequency in 173Yb (F=5/2) is 518,294,576,850.0 +/- 4.4 kHz. Measurements are made with a femtosecond-laser frequency comb calibrated by the NIST cesium fountain clock and represent nearly a million-fold reduction in uncertai…
We present the first characterization of the spectral properties of superradiant light emitted from the ultra-narrow, 1 mHz linewidth optical clock transition in an ensemble of cold $^{87}$Sr atoms. Such a light source has been proposed as a next-generation active atomic frequency reference, with the potential to enable high-precision optical frequency references to be used outside laboratory environments. By comparing the frequency of our superradiant source to that of a state-of-the-art cavity-stabilized laser and optical lattice clock, we observe a fractional Allan deviation of $6.7(1)\time…
We experimentally realize the dual-wavelength active optical clock for the first time. As the Cs cell temperature is kept between 118 $^{\circ }C$ and 144 $^{\circ }C$, both the 1359 nm and the 1470 nm stimulated emission output of Cs four-level active optical clock are detected. The 1470 nm output linewidth of each experimental setup of Cs four-level active optical clock is measured to be 590 Hz with the main cavity length unstabilized. To stabilize the cavity length of active optical clock, the experimental scheme of 633 nm and 1359 nm good-bad cavity dual-wavelength active optical clock is …
With Hg atoms confined in an optical lattice trap in the Lamb-Dicke regime, we obtain a spectral line at 265.6 nm in which the full-width at half-maximum is <15Hz. Here we lock an ultrastable laser to this ultranarrow clock transition and achieve a fractional frequency stability of 5.4x10^(-15)/sqrt(tau) for tau<=400s. The highly stable laser light used for the atom probing is derived from a 1062.6 nm fiber laser locked to an ultrastable optical cavity that exhibits a mean drift rate of -6.0x10^(-17) s^(-1) (or -16.9 mHz.s^(-1) at 282 THz) over a five month period. A comparison between two suc…
We present a method that uses radio-frequency pulses to cancel the quadrupole shift in optical clock transitions. Quadrupole shifts are an inherent inhomogeneous broadening mechanism in trapped ion crystals, limiting current optical ion clocks to work with a single probe ion. Cancelling this shift at each interrogation cycle of the ion frequency allows the use of $N>1$ ions in clocks, thus reducing the uncertainty in the clock frequency by $\sqrt{N}$ according to the standard quantum limit. Our sequence relies on the tensorial nature of the quadrupole shift, and thus also cancels other tensori…
As relative systematic frequency uncertainties in trapped-ion spectroscopy are approaching the low $10^{-18}$ range, motional frequency shifts account for a considerable fraction of the uncertainty budget. Micromotion, a driven motion fundamentally connected to the principle of the Paul trap, is a particular concern in these systems. In this article, we experimentally investigate at this level three common methods for minimizing and determining the micromotion amplitude. We develop a generalized model for a quantitative application of the photon-correlation technique, which is applicable in th…
We propose a space-based gravitational wave detector consisting of two spatially separated, drag-free satellites sharing ultra-stable optical laser light over a single baseline. Each satellite contains an optical lattice atomic clock, which serves as a sensitive, narrowband detector of the local frequency of the shared laser light. A synchronized two-clock comparison between the satellites will be sensitive to the effective Doppler shifts induced by incident gravitational waves (GWs) at a level competitive with other proposed space-based GW detectors, while providing complementary features. Th…
The hyperfine structure of the S1/2-D5/2 quadrupole transition at 729 nm in 43Ca+ has been investigated by laser spectroscopy using a single trapped 43Ca+ ion. We determine the hyperfine structure constants of the metastable level as A=-3.8931(2) MHz and B=-4.241(4) MHz. The isotope shift of the transition with respect to 40Ca+ was measured to be 4134.713(5) MHz. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at non-zero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known 'clock…
Unlike photons, which are conveniently handled by mirrors and optical fibres without loss of coherence, atoms lose their coherence via atom-atom and atom-wall interactions. This decoherence of atoms deteriorates the performance of atomic clocks and magnetometers, and also hinders their miniaturisation. Here we report a novel platform for precision spectroscopy. Ultracold strontium atoms inside a kKagome-lattice hollow-core photonic crystal fibre (HC-PCF) are transversely confined by an optical lattice to prevent atoms from interacting with the fibre wall. By confining at most one atom in each …
Experiments involving optical traps often require careful control of the ac Stark shifts induced by strong confining light fields. By carefully balancing light shifts between two atomic states of interest, optical traps at the magic wavelength have been especially effective at suppressing deleterious effects stemming from such shifts. Highlighting the power of this technique, optical clocks today exploit Lamb-Dicke confinement in magic-wavelength optical traps, in some cases realizing shift cancellation at the ten parts per billion level. Theory and empirical measurements can be used at varyin…
A steady-state magneto-optical trap (MOT) of fermionic strontium atoms operating on the 7.5 kHz-wide ${^1\mathrm{S}_0} - {^3\mathrm{P}_1}$ transition is demonstrated. This MOT features $8.4 \times 10^{7}$ atoms, a loading rate of $1.3\times 10^{7}$atoms/s, and an average temperature of 12 $μ$K. These parameters make it well suited to serve as a source of atoms for continuous-wave superradiant lasers operating on strontium's mHz-wide clock transition. Such lasers have only been demonstrated using pulsed Sr sources, limiting their range of applications. Our MOT makes an important step toward con…
We experimentally and theoretically determine the magic wavelength of the (5$s^2$)$^{1}S_{0}$$-$(5$s$5$p$)$^{3}P_{0}$ clock transition of $^{111}$Cd to be 419.88(14) nm and 420.1(7) nm. To perform Lamb-Dicke spectroscopy of the clock transition, we use narrow-line laser cooling on the $^{1}S_{0}$$-$$^{3}P_{1}$ transition to cool the atoms to 6 $μ$K and load them into an optical lattice. Cadmium is an attractive candidate for optical lattice clocks because it has a small sensitivity to blackbody radiation and its efficient narrow-line cooling mitigates higher order light shifts. We calculate th…
We describe a general purpose digital servo optimized for feedback control of lasers in atomic, molecular, and optical (AMO) physics experiments. The servo is capable of feedback bandwidths up to roughly 1~MHz (limited by the 320~ns total latency); loop filter shapes up to fifth order; multiple-input, multiple-output control; and automatic lock acquisition. The configuration of the servo is controlled via a graphical user interface, which also provides a rudimentary software oscilloscope and tools for measurement of system transfer functions. We illustrate the functionality of the digital serv…
