We consider optimization of a rubidium atom clock that uses magnetically trapped Bose condensed atoms in a highly elongated trap, and determine the optimal conditions for minimum Allan variance of the clock using microwave Ramsey fringe spectroscopy. Elimination of magnetic field shifts and collisional shifts are considered. The effects of spin-dipolar relaxation are addressed in the optimization of the clock. We find that for the interstate interaction strength equal to or larger than the intrastate interaction strengths, a modulational instability results in phase separation and symmetry breaking of the two-component condensate composed of the ground and excited hyperfine clock levels, and this mechanism limits the clock accuracy.
We have observed thermalization by elastic collisions of magnetically trapped metastable helium atoms. Our method directly samples the reconstruction of a thermal energy distribution after the application of an RF knife. The relaxation time of our sample towards equilibrium gives an elastic collision rate constant close to the unitarity limit.
We demonstrate an improvement in short-term stability by a factor of 10 over a previous generation miniature buffer gas cooled trapped ion clock. We describe the enhancement to detection SNR that has enabled this improvement, the method of clock operation, and the measurement of clock short-term stability. Additionally, we numerically investigate the magnitude of the Dick effect in our pulsed ion clock.
Collisions with background gas particles can shift the resonance frequencies of atoms in atomic clocks. The internal quantum states of atoms can also become entangled with their motional states due to the recoil imparted by a collision, which leads to a further shift of the clock frequency through the relativistic Doppler shift. It can be complicated to evaluate the Doppler and collisional frequency shifts for clock atoms in such entangled states, but estimates of these shifts are essential in order to improve the accuracy of optical atomic clocks. We present a formalism that describes collisi…
Collisions with background gas can perturb the transition frequency of trapped ions in an optical atomic clock. We develop a non-perturbative framework based on a quantum channel description of the scattering process, and use it to derive a master equation which leads to a simple analytic expression for the collisional frequency shift. As a demonstration of our method, we calculate the frequency shift of the Sr$^+$ optical atomic clock transition due to elastic collisions with helium.
We report the measurement of one-body loss rates for magnetically trapped metastable europium atoms and the study of their loss mechanism. The loss of atoms observed in a magneto-optical trap is not fully understood because of the indivisibility of the loss regarding optical pumpings due to the presence of cooling laser beams. We magnetically trapped the atoms by directly loading from the magneto-optical trap and observed almost identical one-body loss rates of approximately $2.6\,\mathrm{s^{-1}}$ for two isotopes: $\mathrm{{}^{151}Eu}$ and $\mathrm{{}^{153}Eu}$. Our rate-equation-based model,…
The physics that determines the line shape of the 1S--2S transition in magnetically trapped $\bar{\rm H}$ is explored. Besides obtaining an understanding of the line shape, one goal is to replace the dependence on large scale simulations of $\bar{\rm H}$ with a simpler integration over well defined functions. For limiting cases, analytic formulas are obtained. Example calculations are performed to illustrate the limits of simplifying assumptions. We also describe a $χ^2$ method for choosing experimental parameters that can lead to the most accurate determination of the transition frequency.
We describe experiments demonstrating efficient transfer of molecules from a magneto-optical trap (MOT) into a conservative magnetic quadrupole trap. Our scheme begins with a blue-detuned optical molasses to cool SrF molecules to $\sim\!50$ $μ$K. Next, we optically pump the molecules into a strongly-trapped sublevel. This two-step process reliably transfers $64\%$ of the molecules initially trapped in the MOT into the magnetic trap, comparable to similar atomic experiments. Once loaded, the magnetic trap is compressed by increasing the magnetic field gradient. Finally, we demonstrate a magneti…
We excite spin-waves with spatially inhomogeneous pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped $^{87}$Rb. The density-dependent frequency shifts of the hyperfine transition simulate the s-wave collisional frequency shifts of fermions, including those of optical lattice clocks. As the spin polarizations oscillate in the trap, the frequency shift reverses and it depends on the area of the second Ramsey pulse, exhibiting a predicted beyond mean-field frequency shift. Numerical and analytic models illustrate the observed behaviors.
After pumped from $5s_{1/2}$ ground state to $6p_{1/2}$ state, the population inversion between $6s_{1/2}$ and $5p_{1/2,3/2}$ will be established for Rubidium four-level active optical clock. In this paper, we calculate AC Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in lattice trapped Rubidium four-level active optical clock. Several magic wavelengths are found that can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of trapping laser, the fractional frequency uncertainty of clock transition due…
Applying a many mode Floquet formalism for magnetically trapped atoms interacting with a polychromatic rf-field, we predict a large two photon transition probability in the atomic system of cold $^{87}Rb$ atoms. The physical origin of this enormous increase in the two photon transition probability is due to the formation of avoided crossings between eigen-energy levels originating from different Floquet sub-manifolds and redistribution of population in the resonant intermediate levels to give rise to the resonance enhancement effect. Other exquisite features of the studied atom-field composite…
We report the first direct excitation of the strongly forbidden 5s2 1S0-5s5p 3P0 transition in 87Sr. Its frequency is 429 228 004 235 (20) kHz. A resonant laser creates a small leak in a magneto-optical trap (MOT): atoms build up to the metastable 3P0 state and escape the trapping process, leading to a detectable decrease in the MOT fluorescence. This line has a natural width of 10^{-3} Hz and can be used for a new generation of optical frequency standards using atoms trapped in a light shift free dipole trap.
It has been proposed to use magnetically trapped atomic ensembles to enhance the interrogation time in microwave clocks. To mitigate the perturbing effects of the magnetic trap, near-magic-field configurations are employed, where the involved clock transition becomes independent of the atom's potential energy to first order. Still, higher order effects are a dominating source for dephasing, limiting the performance of this approach. Here we propose a simple method to cancel the energy dependence to both first and second order, using weak radio-frequency dressing. We give values for dressing fr…
We discuss cooling efficiency for different-species Fermi-Bose mixtures in magnetic traps. A better heat capacity matching between the two atomic species is achieved by a proper choice of the Bose cooler and the magnetically trappable hyperfine states of the mixture. When a partial spatial overlap between the two species is also taken into account, the deepest Fermi degeneracy is obtained for an optimal value of the trapping frequency ratio. This can be achieved by assisting the magnetic trap with a deconfining light beam, as shown in the case of fermionic 6Li mixed with 23Na, 87Rb, and 133Cs,…
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 $^{27}$Al$^+$ clock to enable a total fractional systematic uncertainty below $10^{-18}$. For this clock, with 38(19) nPa of room temperature H$_2$ 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 cont…
Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories, but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the coherence time to 21 s on the magnetic field insensitive clock transition of Rb-87 by applying the recently discovered spin self-rephasing. This result confirms the general nature of this new mechanism and thus shows its applicability in atom clocks and quantum memories. A systematic investigation of all relevant frequency shifts and noise contributions yields a s…
How long antihydrogen atoms linger in the ALPHA magnetic trap is an important characteristic of the ALPHA apparatus. The initial trapping experiments in 2010 [1] were conducted with 38 detected antiatoms confined for 172 ms and in 2011 [2] with seven for 1000 s. Long confinement times are necessary to perform detailed frequency scans during spectroscopic measurements. An analysis carried out, using machine learning methods, on more than 1000 antiatoms confined for several hours in the ALPHA-2 magnetic trap, yields a preliminary lower limit to the lifetime of 66 hours. Hence this observation su…
For the past 15 years, tremendous progress within the fields of laser stabilization, optical frequency combs and atom cooling and trapping have allowed the realization of optical atomic clocks with unrivaled performances. These instruments can perform frequency comparisons with fractional uncertainties well below $10^{-17}$, finding applications in fundamental physics tests, relativistic geodesy, and time and frequency metrology. Even though most optical clocks are currently laboratory setups, several proposals for using these clocks for field measurements or within an optical clock network ha…
We present a compact atomic clock interrogating ultracold 87Rb magnetically trapped on an atom chip. Very long coherence times sustained by spin self-rephasing allow us to interrogate the atomic transition with 85% contrast at 5 s Ramsey time. The clock exhibits a fractional frequency stability of $5.8\times 10^{-13}$ at 1 s and is likely to integrate into the $1\times10^{-15}$ range in less than a day. A detailed analysis of 7 noise sources explains the measured frequency stability. Fluctuations in the atom temperature (0.4 nK shot-to-shot) and in the offset magnetic field ($5\times10^{-6}$ r…
Cold and ultracold polar molecules with nonzero electronic angular momentum are of great interest for studies in quantum chemistry and control, investigations of novel quantum systems, and precision measurement. However, in mixed electric and magnetic fields, these molecules are generically subject to a large set of avoided crossings among their Zeeman sublevels; in magnetic traps, these crossings lead to distorted potentials and trap loss from electric bias fields. We have characterized these crossings in OH by microwave-transferring trapped OH molecules from the upper |f; M = +3/2> parity st…
A many mode Floquet theory (MMFT) formalism is applied to study the interaction of a polychromatic rf-field with cold atoms trapped in a quadrupole magnetic trap. In this work, the validity of MMFT approach is first established by comparing its results with those of the previously used formalisms for the cases of single and two frequency rf-fields. We have then used the MMFT formalism to calculate the eigen-energies and transition probabilities for atoms in the quadrupole trap and interacting with a polychromatic rf-field. This composite atom-field system has shown some exquisite features such…
We propose a compact atomic clock based on ultracold Rb atoms that are magnetically trapped near the surface of an atom microchip. An interrogation scheme that combines electromagnetically-induced transparency (EIT) with Ramsey's method of separated oscillatory fields can achieve atomic shot-noise level performance of 10^{-13}/sqrt(tau) for 10^6 atoms. The EIT signal can be detected with a heterodyne technique that provides noiseless gain; with this technique the optical phase shift of a 100 pW probe beam can be detected at the photon shot-noise level. Numerical calculations of the density mat…
Optical molecular clocks promise unparalleled sensitivity to the temporal variation of the electron-to-proton mass ratio and insight into possible new physics beyond the Standard Model. We propose to realize a molecular clock with bosonic $^{174}$Yb$_2$ molecules, where the forbidden $^1$S$_0$$\rightarrow$$^3$P$_0$ clock transition would be induced magnetically. The use of a bosonic species avoids possible complications due to hyperfine structure present in fermionic species. While direct clock line photoassociation would be challenging, weakly bound ground state molecules could be produced by…
We report a vapor-cell magneto-optical trapping of Hg isotopes on the ${}^1S_0-{}^3P_1$ intercombination transition. Six abundant isotopes, including four bosons and two fermions, were trapped. Hg is the heaviest non-radioactive atom trapped so far, which enables sensitive atomic searches for ``new physics'' beyond the standard model. We propose an accurate optical lattice clock based on Hg and evaluate its systematic accuracy to be better than $10^{-18}$. Highly accurate and stable Hg-based clocks will provide a new avenue for the research of optical lattice clocks and the time variation of t…
Collisions between background gas particles and the trapped ion in an atomic clock can subtly shift the frequency of the clock transition. The uncertainty in the correction for this effect makes a significant contribution to the total systematic uncertainty budget of trapped-ion clocks. Using a non-perturbative analytic framework that was developed for this problem, we estimate the frequency shift in Al$^+$ ion clocks due to collisions with helium and hydrogen. Our calculations significantly improve the uncertainties in the collisional shift coefficients, and show that the collisional frequenc…
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,…
The v = 1 -> 0 radiative lifetime of NH (X triplet-Sigma-, v=1,N=0) is determined to be tau_rad,exp. = 37.0 +/- 0.5 stat +2.0 / -0.8 sys miliseconds, corresponding to a transition dipole moment of |mu_10| = 0.0540 + 0.0009 / -0.0018 Debye. To achieve the long observation times necessary for direct time-domain measurement, vibrationally excited NH (X triplet-Sigma-, v=1,N=0) radicals are magnetically trapped using helium buffer-gas loading. Simultaneous trapping and lifetime measurement of both the NH(v=1, N=0) and NH(v=0,N=0) populations allows for accurate extraction of tau_rad,exp. Backgroun…
We have developed an optical lattice clock that can operate in dual modes: a strontium (Sr) clock mode and an ytterbium (Yb) clock mode. Dual-mode operation of the Sr-Yb optical lattice clock is achieved by alternately cooling and trapping $^{87}$Sr and $^{171}$Yb atoms inside the vacuum chamber of the clock. Optical lattices for Sr and Yb atoms were arranged with horizontal and vertical configurations, respectively, resulting in a small distance of the order of 100 $μ$m between the trapped Sr and Yb atoms. The $^{1}$S$_{0}$-$^{3}$P$_{0}$ clock transitions in the trapped atoms were interrogate…
Near-threshold photodissociation of Br$_2$ from a supersonic beam produces slow bromine atoms that are trapped in the magnetic field minimum formed between two opposing permanent magnets. Here, we quantify the dominant trap loss rate due to collisions with two sources of residual gas: the background limited by the vacuum chamber base pressure, and the carrier gas during the supersonic gas pulse. The loss rate due to collisions with residual Ar in the background follows pseudo first-order kinetics, and the bimolecular rate coefficient for collisional loss from the trap is determined by measurem…
In this paper, we study the dynamics of a trapped atom interferometer with internal state labelling in the presence of interactions. We consider two situations: an atomic clock in which the internal states remain superposed, and an inertial sensor configuration in which they are separated. From the average spin evolution, we deduce the fringe contrast and the phase-shift. In the clock configuration, we recover the well-known identical spin rotation effect (ISRE) which can significantly increase the spin coherence time. We also find that the magnitude of the effect depends on the trap geometry …
We present and implement a non-destructive detection scheme for the transition probability readout of an optical lattice clock. The scheme relies on a differential heterodyne measurement of the dispersive properties of lattice-trapped atoms enhanced by a high finesse cavity. By design, this scheme offers a 1st order rejection of the technical noise sources, an enhanced signal-to-noise ratio, and an homogeneous atom-cavity coupling. We theoretically show that this scheme is optimal with respect to the photon shot noise limit. We experimentally realize this detection scheme in an operational str…
Optical clocks based on ensembles of trapped ions offer the perspective of record frequency uncertainty with good short-term stability. Most suitable atomic species lack closed transitions for fast detection such that the clock signal has to be read out indirectly through transferring the quantum state of clock ions to co-trapped logic ions by means of quantum logic operations. For ensembles of clock ions existing methods for quantum logic readout require a linear overhead in either time or the number of logic ions. Here we report a quantum algorithmic readout whose overhead scales logarithmic…
We propose and analyze a Cesium lattice optical clock (CLOC) which has the potential for high performance and simple operation in a compact form factor using a forbidden optical transition in Cs atoms at 685 nm. Cs atoms are trapped in a 3D optical lattice using a magic trap wavelength of $λ_{\textrm m}=803~\textrm nm$. To reduce sensitivity to magnetic fields the atoms are probed on two cycling transitions with equal magnitude, but opposite magnetic shifts. Operation of the clock requires only three diode lasers at 685, 803, 852 nm and is simplified compared to other higher-performance optica…
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…
Black-body radiation (BBR) shifts of $^3\!P_0-^1\!S_0$ clock transition in divalent atoms Cd and Zn are evaluated using accurate relativistic many-body techniques of atomic structure. Static polarizabilities of the clock levels and relevant electric-dipole matrix elements are computed. We also present a comparative overview of the BBR shifts in optical clocks based on neutral divalent atoms trapped in optical lattices.
We propose a new class of atomic microwave clocks based on the hyperfine transitions in the ground state of aluminum or gallium atoms trapped in optical lattices. For these elements magic wavelengths exist at which both levels of the hyperfine doublet are shifted at the same rate by the lattice laser field, cancelling its effect on the clock transition. Our analysis of various systematic effects shows that, while offering an improved control over systematic errors, the accuracy of the proposed microwave clock is competitive to that of the state-of-the-art primary frequency standard.
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}$.
We develop a method of modified hyper-Ramsey spectroscopy in optical clocks, achieving complete immunity to the frequency shifts induced by the probing fields themselves. Using particular pulse sequences with tailored phases, frequencies, and durations, we can derive an error signal centered exactly at the unperturbed atomic resonance with a steep discriminant which is robust against variations in the probe shift. We experimentally investigate the scheme using the magnetically-induced $^1$S$_0- ^3$P$_0$ transition in $^{88}$Sr, demonstrating automatic suppression of a sizeable \num{2e-13} prob…
We investigated the coherence of spin-polarized ^{87}Sr atoms trapped in a light-shift-free one-dimensional optical lattice during their interaction with a clock laser on the ^1S_0-^3P_0 transition. Collapses and revivals appeared for more than 50 Rabi cycles, attributed to the thermal distribution of discrete vibrational states in the lattice potential. The population oscillation in the clock states lasted more than 1s, demonstrating high immunity from decoherence. This long atomic coherence suggests the feasibility of Pauli blocking of collisions in optical clock excitation.
We report on a transportable optical clock, based on laser-cooled strontium atoms trapped in an optical lattice. The experimental apparatus is composed of a compact source of ultra-cold strontium atoms including a compact cooling laser set-up and a transportable ultra-stable laser for interrogating the optical clock transition. The whole setup (excluding electronics) fits within a volume of less than 2 m$^3$. The high degree of operation reliability of both systems allowed the spectroscopy of the clock transition to be performed with 10 Hz resolution. We estimate an uncertainty of the clock of…
The accurate evaluation of the second-order Doppler frequency shift (SODFS) of trapped ions in a linear Paul trap has been studied with experiments and molecular dynamics (MD) simulations. The motion of trapped ions in the trap has three contributions, and we focus on the ion excess micromotion, which is rarely discussed when evaluating the SODFS. Based on the hypothesis that the ion density is uniformly distributed in the radial direction, we propose a new model to accurately evaluate the total SODFS for ion microwave clocks. The effectiveness of the model has been verified both in simulation…
Recently invented and demonstrated, optical lattice clocks hold great promise for improving the precision of modern timekeeping. These clocks aim at the 10^-18 fractional accuracy, which translates into a clock that would neither lose or gain a fraction of a second over an estimated age of the Universe. In these clocks, millions of atoms are trapped and interrogated simultaneously, dramatically improving clock stability. Here we discuss the principles of operation of these clocks and, in particular, a novel concept of "magic" trapping of atoms in optical lattices. We also highlight recently pr…
We explore a feasibility of measuring atom-wall interaction using atomic clocks based on atoms trapped in engineered optical lattices. Optical lattice is normal to the wall. By monitoring the wall-induced clock shift at individual wells of the lattice, one would measure a dependence of the atom-wall interaction on the atom-wall separation. We rigorously evaluate the relevant clock shifts and show that the proposed scheme may uniquely probe the long-range atom-wall interaction in all three qualitatively-distinct regimes of the interaction: van der Waals (image-charge interaction), Casimir-Polde…
We report on the observation of a dc Stark frequency shift at the $10^{-13}$ level by comparing two strontium optical lattice clocks. This frequency shift arises from the presence of electric charges trapped on dielectric surfaces placed under vacuum close to the atomic sample. We show that these charges can be eliminated by shining UV light on the dielectric surfaces, and characterize the residual dc Stark frequency shift on the clock transition at the $10^{-18}$ level by applying an external electric field. This study shows that the dc Stark shift can play an important role in the accuracy b…
We develop an exact sum rule that relates the spectral shift of a trapped gas undergoing cold collisions to measurable quantities of the system. The method demonstrates the dependence of the cold collision frequency shift on the quantum degeneracy of the gas and facilitates extracting scattering lengths from the data. We apply the method to analyzing spectral data for magnetically trapped hydrogen atoms and determine the value of the $1S-2S$ scattering length.
A microwave atomic clock scheme based on Rb and Cs atoms trapped in optical lattice with magic wavelength for clock transition is proposed. The ac Stark shift of clock transition due to trapping laser can be canceled at some specific laser wavelengths. Comparing with in fountain clock, the cavity related shifts, the collision shift, and the Doppler effect are eliminated or suppressed dramatically in atomic clock when the magic optical lattice is exploited. By carefully analyzing various sources of clock uncertainty, we conclude that a microwave atomic clock with an accuracy of better than $2\t…
Trapped ions are ideally suited for precision spectroscopy, as is evident from the remarkably low systematic uncertainties of single-ion clocks. The major weakness of these clocks is the long averaging time, necessitated by the low signal of a single atom. An increased number of ions can overcome this limitation and allow for the implementation of novel clock schemes. However, this presents the challenge to maintain the excellent control over systematic shifts of a single particle in spatially extended and strongly coupled many-body systems. We measure and deduce systematic frequency uncertain…
In quantum information science, the external control of qubits must be balanced with the extreme isolation of the qubits from the environment. Atomic qubit systems typically mitigate this balance through the use of gated laser fields that can create superpositions and entanglement between qubits. Here we propose the use of high-order optical Stark shifts from optical fields to manipulate the splitting of atomic qubits that are insensitive to other types of fields. We demonstrate a fourth-order AC Stark shift in a trapped atomic ion system that does not require extra laser power beyond that nee…
Force sensors are at the heart of different technologies such as atomic force microscopy or inertial sensing \cite{RMPforce2003, Rugar2004, YazdiIEEE}. These sensors often rely on the measurement of the displacement amplitude of mechanical oscillators under applied force. Examples for such mechanical oscillators include micro-fabricated cantilevers \cite{YazdiIEEE}, carbon nanotubes \cite{NanotubeForce} as well as single trapped ions \cite{Bollinger, Udem} . The best sensitivity is typically achieved when the force is alternating at the mechanical resonance frequency of the oscillator thus inc…
We present non-standard optical Ramsey schemes that use pulses individually tailored in duration, phase, and frequency to cancel spurious frequency shifts related to the excitation itself. In particular, the field shifts and their uncertainties of Ramsey fringes can be radically suppressed (by 2-4 orders of magnitude) in comparison with the usual Ramsey method (using two equal pulses) as well as with single-pulse Rabi spectroscopy. Atom interferometers and optical clocks based on two-photon transitions, heavily forbidden transitions, or magnetically induced spectroscopy could significantly ben…
We demonstrate state-of-the-art technique of an active clock to provide a continuous superradiant lasing signal using an ensemble of trapped Cs atoms in the optical lattice. A magic wavelength of the proposed |7S1/2; F = 4, MF = 0> - |6P3/2; F = 3, MF = 0> clock transition in Cs atom is identified at 1181 nm for constructing the optical lattice. Pertinent optical lines are also found for pumping and repumping atoms from their ground states. A fractional uncertainty about 10-15 level to the clock frequency has been predicted by carrying out rigorous calculations of several atomic properties. Th…
