Stability limits of an optical frequency standard based on free Ca atoms
J. A. Sherman, C. W. Oates
备注:
5 pages, 6 figures, 2 tables
发表信息:
Proceedings of the 2011 Joint Conference of the IEEE International Frequency Control Symposium and European Frequency and Time Forum, San Francisco, CA, USA, May 2011
We have quantified a short term instability budget for an optical frequency standard based on cold, freely expanding calcium atoms. Such systems are the subject of renewed interest due to their high frequency stability and relative technical simplicity compared to trapped atom optical clocks. By filtering the clock laser light at 657 nm through a high finesse cavity, we observe a slight reduction in the optical Dick effect caused by aliased local oscillator noise. The ultimately limiting technical noise is measured using a technique that does not rely on a second clock or fs-comb.
We present an improvement of short term frequency stability of the integrating sphere cold atom clock after increasing the intensities of clock signals and optimizing the feedback loop of the clock. A short term frequency stability of $5.0\times10^{-13}τ^{-1/2}$ has been achieved and the limiting factors have been analyzed.
Frequency shifts from background gas collisions currently contribute significantly to the inaccuracy of atomic clocks. Because nearly all collisions with room-temperature background gases that transfer momentum eject the cold atoms from the clock, the interference between the scattered and unscattered waves in the forward direction dominates these frequency shifts. We show they are ~10 times smaller than in room-temperature clocks and that van der Waals interactions produce the cold-atom background-gas shift. General considerations allow the loss of Ramsey fringe amplitude to bound this freque…
The medium-long term frequency stability of the integrating sphere cold atom clock was improved.During the clock operation, Rb atoms were cooled and manipulated using cooling light diffusely reflected by the inner surface of a microwave cavity in the clock. This light heated the cavity and caused a frequency drift from the resonant frequency of the cavity. Power fluctuations of the cooling light led to atomic density variations in the cavity's central area, which increased the clock frequency instability through a cavity pulling effect. We overcame these limitations with appropriate solutions.…
We propose two kinds of wire configurations fabricated on an atom chip surface for creating two-dimensional (2D) adiabatic rf guide with an inhomogeneous rf magnetic field and a homogenous dc magnetic field. The guiding state can be selected by changing the detuning between the frequency of rf magnetic field and the resonance frequency of two Zeeman sublevels. We also discuss the optimization of loading efficiency and the trap depth and how to decide proper construction when designing an rf atom chip.
Atomic frequency standards are used to generate accurate and precise time and frequency, enabling many communications, synchronization, and navigation systems in modern life. GPS and other satellite navigation systems, voice and data telecommunications, and timestamping of financial transactions all rely on precise time and frequency enabled by atomic frequency standards. This review provides a snapshot and outlook of contemporary atomic frequency standards and the applications they enable. We provide a concise summary of the performance and physics of operation of current and future atomic fr…
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…
We propose and demonstrate a radio-frequency atomic magnetometer with sub-Doppler laser cooled rubidium-87. With a simple and compact design, our system demonstrates a sensitivity of $330~pT/\sqrt{Hz}$ in an unshielded environment, thus matching or surpassing previously reported cold atoms designs. By merging the multiple uses and robustness of radio-frequency atomic magnetometers with the detailed control of laser cooling, our cold atom radio-frequency magnetometer has the potential to move applications of atomic magnetometry to high spatial resolution. Direct impact in metrology for applied …
We investigate the frequency comb induced radiation pressure force acting on a cloud of cold $^{87}$Rb atoms. Reduction and spectral broadening of the frequency comb force are observed as the cloud's optical thickness is increased. Since the radiation pressure force is uniquely determined by light scattered by an atomic cloud, we discuss different scattering mechanisms, and point to the shadow effect as the dominant mechanism affecting FC-induced force in resonantly excited dense atomic clouds. Our results improve the understanding of the interaction of frequency comb light with many-atom ense…
The connection between the quantum frequency of radiation by the transition of the electron from orbit n to orbit k and frequencies of circling of electron in these orbits for the atom of hydrogen is determined.
The prospects of sympathetic cooling of polar molecules with magnetically co-trapped alkali-metal atoms are generally considered poor due to strongly anisotropic atom-molecule interactions leading to large spin relaxation rates. Using rigorous quantum scattering calculations based on ab initio interaction potentials, we show that inelastic spin relaxation in low-temperature collisions of CaH(2Sigma) molecules with Li and Mg atoms occurs at a slow rate despite the strongly anisotropic interactions. This unexpected result, which we rationalize using multichannel quantum defect theory, opens up t…
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the interparticle distance performs bounded oscillations about a metastable orbit. The stability mechanism is established by the existence of a quartic resonant constant generated by the stiff eigenvalues of the linear stability problem. This constant bounds the particles together during the radiative recoil. The condition of resonant dissipation predicts angular momenta …
We report the frequency noise suppression of a 674nm diode laser by phase-locking it to a 1560nm cavity-stabilized laser, using a commercial optical frequency comb. By phase-locking the frequency comb to the narrow reference at telecom wavelength we were able to phase-coherently distribute the reference stability across the optical spectrum. Subsequently, we used one of the comb teeth as an optical reference for a 674nm external cavity diode laser. We demonstrated the locked 674nm laser frequency stability by comparing it to an independent cavity-stabilized laser of the same wavelength and by …
We present results of first-principles calculations of the frequency-dependent polarizabilities of all alkali atoms for light in the wavelength range 300-1600 nm, with particular attention to wavelengths of common infrared lasers. We parameterize our results so that they can be extended accurately to arbitrary wavelengths above 800 nm. This work is motivated by recent experiments involving simultaneous optical trapping of two different alkali species. Our data can be used to predict the oscillation frequencies of optically-trapped atoms, and particularly the ratios of frequencies of different …
We demonstrated for the first time the characterization of absolute frequency stability of three reference cavities by cross beating three laser beams which are independently locked to these reference cavities. This method shows the individual feature of each reference cavity, while conventional beatnote measurement between two cavities can only provide an upper bound. This method allows for numerous applications such as optimizing the performance of the reference cavity for optical clockwork.
We present and analyze four frequency measurements designed to characterize the performance of an optical frequency reference based on spectral hole burning in \EuYSO. The first frequency comparison, between a single unperturbed spectral hole and a hydrogen maser, demonstrates a fractional frequency drift rate of $5 \times 10^{-18}$ s$^{-1}$. Optical-frequency comparisons between a pattern of spectral holes, a Fabry-Pérot cavity, and an Al$^+$ optical atomic clock show a short-term fractional frequency stability of $1 \times10^{-15} τ^{-1/2}$ that averages down to $2.5^{+1.1}_{-0.5} \times 10^…
Using the orbitals generated by the van Leeuwen-Baerends potential, we calculate frequency dependent response properties of noble gas atoms of He, Ne and Ar and alkaline earth atoms Be and Mg, with particlar emphasis on their nonlinear polarizabilities. For this we employ time-dependent Kohn-Sham formalism with adiabatic local-density aproximation (ALDA) for exchange and correlation. We show that results thus obtained for frequency dependent polarizabilities of the inert gas atoms are highly acurate. On the other hand, polarizabilities of the alkaline earths are not given with the same accurac…
We discuss the quality required for the RF source used to trap neutral atoms in RF-dressed potentials. We illustrate this discussion with experimental results obtained on a Bose-Einstein condensation experiment with different RF sources.
We report on a theoretical analysis of the phase-shift in compact atomic clocks working either with cold or thermal atoms. It is well known that in a microwave cavity with electromagnetic losses, a traveling wave adds to the standing wave of a given resonant mode. We calculate the spatial varying phase related to this travelling wave for two geometries of interest in clock applications, the cylindrical cavity and the spherical cavity. Due to their motion, the atoms probe different regions of the cavity and then experience different phases of the interrogating microwave field. We show that this…
We propose a method of joint interrogation in a single atom interferometer which overcomes the dead time between consecutive measurements in standard cold atomic fountains. The joint operation enables for a faster averaging of the Dick effect associated with the local oscillator noise in clocks and with vibration noise in cold atom inertial sensors. Such an operation allows achieving the lowest stability limit due to atom shot noise. We demonstrate a multiple joint operation in which up to five clouds of atoms are interrogated simultaneously in a single setup. The essential feature of multiple…
In this paper we describe an experiment of efficient cooling of $^{87}$Rb atoms in two-frequency diffuse laser lights. Compared with single frequency diffuse light, two-frequency diffuse lights have wider velocity capture range and thus can cool more atoms. In our experiment, the maximum number of cooled atoms can reach up to $3.9\times10^9$. Such a result is quite useful in building a compact cold atom clock.
Narrow linewidth optical atomic transitions provide a valuable resource for frequency metrology, and form the basis of today's most precise and accurate clocks. Recent experiments have demonstrated that ensembles of atoms can be interfaced with the mode of an optical cavity using such transitions, and that atom-cavity interactions can dominate over decoherence processes even when the atomic transition that mediates the interactions is very weak. This scenario enables new opportunities for optical frequency metrology, including techniques for nondestructive readout and entanglement enhancement …
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…
The erbium atomic system is a promising candidate for an atomic Bose-Einstein condensate of atoms with a non-vanishing orbital angular momentum ($L \neq 0$) of the electronic ground state. In this paper we report on the frequency stabilization of a blue external cavity diode laser system on the 400.91 $nm$ laser cooling transition of atomic erbium. Doppler-free saturation spectroscopy is applied within a hollow cathode discharge tube to the corresponding electronic transition of several of the erbium isotopes. Using the technique of frequency modulation spectroscopy, a zero-crossing error sign…
Atomic collisions are included in an interacting system of optical fields and trapped atoms allowing field amplification. We study the effects of collisions on the system stability. Also a study of the degree of entanglement between atomic and optical fields is made. We found that, for an atomic field initially in a vacuum state and optical field in a coherent state, the degree of entanglement does not depend on the optical field intensity or phase. We show that in conditions of exponential instability the system presents at long times two distinct stationary degree of entanglement with collis…
We experimentally demonstrated that the stability of an atomic clock improves at fastest rate $τ^{-1}$ (where $τ$ is the averaging time) when the phase of a local oscillator is genuinely compared to the continuous phase of many atoms in a single trap (atomic phase lock). For this demonstration, we developed a simple method that repeatedly monitors the atomic phase while retaining its coherence by observing only a portion of the whole ion cloud. Using this new method, we measured the continuous phase over 3 measurement cycles, and thereby improved the stability scaling from $τ^{-1/2}$ to $τ^{-1…
We report the operation of a cold-atom inertial sensor which continuously captures the rotation signal. Using a joint interrogation scheme, where we simultaneously prepare a cold-atom source and operate an atom interferometer (AI) enables us to eliminate the dead times. We show that such continuous operation improves the short-term sensitivity of AIs, and demonstrate a rotation sensitivity of $100\ \text{nrad.s}^{-1}.\text{Hz}^{-1/2}$ in a cold-atom gyroscope of $11 \ \text{cm}^2$ Sagnac area. We also demonstrate a rotation stability of $1 \ \text{nrad.s}^{-1}$ at $10^4$ s of integration time,…
Low-frequency properties of a plasma are examined within the average-atom approximation, which presumes that scattering of a conducting electron on each atom takes place independently of other atoms. The relaxation time tau distinguishes a high-frequency region omega tau > 1, where the single-atom approximation is applicable explicitly, from extreme low frequencies omega tau < 1, where, naively, the single-atom approximation is invalid. A proposed generalization of the formalism, which takes into account many-atom collisions, is found to be accurate in all frequency regions, from omega =0 to o…
The wave function of a moderately cold atom in a stationary near-resonant standing light wave delocalizes very fast due to wave packet splitting. However, we show that frequency modulation of the field may suppress packet splitting for some atoms having specific velocities in a narrow range. These atoms remain localized in a small space for a long time. We propose that in a real experiment with cold atomic gas this effect may decrease the velocity distribution of atoms (the field traps the atoms with such specific velocities while all other atoms leave the field)
An atom, coupled linearly to an environment, is considered in a harmonic approximation in thermal equilibrium inside a cavity. The environment is modeled by an infinite set of harmonic oscillators. We employ the notion of dressed states to investigate the time evolution of the atom initially in the first excited level. In a very large cavity (free space) for a long elapsed time, the atom decays and the value of its occupation number is the physically expected one at a given temperature. For a small cavity the excited atom never completely decays and the stability rate depends on temperature.
We describe a collective state atomic clock with Ramsey fringes narrowed by a factor of $\sqrt{N}$ compared to a conventional clock, N being the number of non-interacting atoms, without violating the uncertainty relation. This narrowing is explained as being due to interferences among the collective states, representing an effective $\sqrt{N}$ fold increase in the clock frequency, without entanglement. The detection process, which measures a collective state, can be used to increase the quantum efficiency of detection significantly, yielding a net improvement in stability by as much as a facto…
Atomic sensors employing cold-atom technology enable unprecedented accuracy and resolution for next generation atomic clocks, magnetometers, gravimeters, and gyroscopes. To date, however, the size and complexity of cold atom systems have prevented their deployment in practical applications outside of large research laboratories. Here we demonstrate a low power, palm-top, and fully integrated cold atom system that functions as an atomic clock with a stability of 2 parts in 10^11 at 1s. This work demonstrates the feasibility of developing compact, robust, and portable devices based on laser cool…
Rydberg atom-based electrometry enables traceable electric field measurements with high sensitivity over a large frequency range, from gigahertz to terahertz. Such measurements are particularly useful for the calibration of radio frequency and terahertz devices, as well as other applications like near field imaging of electric fields. We utilize frequency modulated spectroscopy with active control of residual amplitude modulation to improve the signal to noise ratio of the optical readout of Rydberg atom-based radio frequency electrometry. Matched filtering of the signal is also implemented. A…
The short-term stability of passive atomic frequency standards, especially in pulsed operation, is often limited by local oscillator noise via intermodulation effects. We present an experimental demonstration of the intermodulation effect on the frequency stability of a continuous atomic fountain clock where, under normal operating conditions, it is usually too small to observe. To achieve this, we deliberately degrade the phase stability of the microwave field interrogating the clock transition. We measure the frequency stability of the locked, commercial-grade local oscillator, for two modul…
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.
We demonstrate high resolution coherent control of cold atomic Rubidium utilizing spectral phase manipulation of a femtosecond optical frequency comb. Transient coherent accumulation is directly manifested by the enhancement of signal amplitude and spectral resolution via the pulse number. The combination of frequency comb technology and spectral phase manipulation enables coherent control techniques to enter a new regime with natural linewidth resolutions.
In trapped-atom clocks, the primary source of decoherence is often the phase noise of the oscillator. For this case, we derive theoretical performance gains by combining several atomic ensembles. For example, M ensembles of N atoms can be combined with a variety of probe periods, to reduce the frequency variance to M 2^-M times that of standard Ramsey clocks. A similar exponential improvement is possible if the atomic phases of some of the ensembles evolve at reduced frequencies. These ensembles may be constructed from atoms or molecules with lower-frequency transitions, or generated by dynami…
The wave function of a moderately cold atom in a stationary near-resonant standing light wave delocalizes very fast due to wave packet splitting. However, we show that frequency modulation of the field may suppress packet splitting for some atoms having specific velocities in a narrow range. These atoms remain localized in a small space for a long time. We demonstrate and explain this effect numerically and analytically. Also we demonstrate that modulated field can not only trap, but also cool the atoms. We perform a numerical experiment with a large atomic ensebmble having wide initial veloci…
We demonstrated transferring the stability of one highly stable clock laser operating at 729 nm to another less stable laser operating at 698 nm. The two different wavelengths were bridged using an optical frequency comb. The improved stability of the clock laser at 698 nm enabled us to evaluate the systematic frequency shifts of the Sr optical lattice clock with shorter averaging time. We determined the absolute frequency of the clock transition 1S0 - 3P0 in 87Sr to be 429 228 004 229 873.9 (1.4) Hz referenced to the SI second on the geoid via International Atomic Time (TAI).
An experimental method is developed for the robust frequency stabilization using a high-finesse cavity when the laser exhibits large intermittent frequency jumps. This is accomplished by applying an additional slow feedback signal from Doppler-free fluorescence spectroscopy in an atomic beam with increased frequency locking range. As a result, a stable and narrow-linewidth 556 nm laser maintains the frequency lock status for more than a week, and contributes to more accurate evaluation of the Yb optical lattice clock. In addition, the reference optical cavity is supported at vibration-insensit…
Microresonator-based soliton frequency combs - microcombs - have recently emerged to offer low-noise, photonic-chip sources for optical measurements. Owing to nonlinear-optical physics, microcombs can be built with various materials and tuned or stabilized with a consistent framework. Some applications require phase stabilization, including optical-frequency synthesis and measurements, optical-frequency division, and optical clocks. Partially stabilized microcombs can also benefit applications, such as oscillators, ranging, dual-comb spectroscopy, wavelength calibration, and optical communicat…
We applied the finite-size scaling method using the B-splines basis set to construct the stability diagram for two-electron atoms with a screened Coulomb potential. The results of this method for two electron atoms are very accurate in comparison with previous calculations based on Gaussian, Hylleraas, and finite-element basis sets. The stability diagram for the screened two-electron atoms shows three distinct regions: a two-electron region, a one-electron region, and a zero-electron region, which correspond to stable, ionized and double ionized atoms. In previous studies, it was difficult to …
A general mechanism for the generation of frequency combs referenced to atomic resonances is put forward. The mechanism is based on the periodic phase control of a quantum system's dipole response. We develop an analytic description of the comb spectral structure, depending on both the atomic and the phase-control properties. We further suggest an experimental implementation of our scheme: Generating a frequency comb in the soft-x-ray spectral region, which can be realized with currently available techniques and radiation sources. The universality of this mechanism allows the generalization of…
Using a Direct Simulation Monte Carlo technique, we have studied the time evolution of a cold atom cloud interacting with a time dependent radio frequency (rf) dressed state potential. Exposure of a cloud of $^{87}Rb$ atoms, trapped in a quadrupole magnetic trap, to a time dependent rf-field with increasing amplitude and decreasing frequency, shows a variation in the number of trapped atoms and the overall shape of the atom cloud. It is shown by simulations that, initially at lower rf-field strength, the rf-field results in ejection of atoms from the trap, leading to evaporative cooling of the…
We propose a new scheme of microwave frequency standards based on pulsed coherent optical information storage. Unlike the usual frequency reference where the Ramsey fringe is printed on the population of a certain state, we print the Ramsey fringe on the coherence. Then the coherence is detected in the form of a retrieval light. The central line of the Ramsey fringe can be used as a frequency reference in an absorption-cell-based atomic frequency standard. This scheme is free of light shifts as the interrogating process is separated from the optical pumping processes, and the cavity pulling ef…
We report the direct comparison between the stabilities of two mobile absolute gravimeters of different technology: the LNE-SYRTE Cold Atom Gravimeter and FG5X\#216 of the Université du Luxembourg. These instruments rely on two different principles of operation: atomic and optical interferometry. The comparison took place in the Walferdange Underground Laboratory for Geodynamics in Luxembourg, at the beginning of the last International Comparison of Absolute Gravimeters, ICAG-2013. We analyse a 2h10 duration common measurement, and find that the CAG shows better immunity with respect to change…
We present a hybrid laser frequency stabilization method combining modulation transfer spectroscopy (MTS) and frequency modulation spectroscopy (FMS) for the cesium D2 transition. In a typical pump-probe setup, the error signal is a combination of the DC-coupled MTS error signal and the AC-coupled FMS error signal. This combines the long-term stability of the former with the high signal-to-noise ratio of the latter. In addition, we enhance the long-term frequency stability with laser intensity stabilization. By measuring the frequency difference between two independent hybrid spectroscopies, w…
Inspired by the recent developments in the research of atom-photon quantum interface and energy-time entanglement between single photon pulses, we propose to establish the concept of a special energy-time entanglement between a single photon pulse and internal states of a single atom, which is analogous to the frequency-bin entanglement between single photon pulses. We show that this type of entanglement arises naturally in the interaction between frequency-bin entangled single photon pulse pair and a single atom, via straightforward atom-photon phase gate operations. We also discuss the prope…
We report on the development of a diode laser system - the `Faraday laser' - using an atomic Faraday filter as the frequency-selective element. In contrast to typical external-cavity diode laser systems which offer tunable output frequency but require additional control systems in order to achieve a stable output frequency, our system only lases at a single frequency, set by the peak transmission frequency of the internal atomic Farady filter. Our system has both short-term and long-term stability of less than 1~MHz, which is less than the natural linewidth of alkali-atomic D-lines, making sim…
We demonstrate continuous-frequency electric field measurements of high-intensity microwaves via optical spectroscopy in a small atomic vapor cell. The spectroscopic response of a room-temperature rubidium atomic vapor in a glass cell is investigated and employed for absolute measurements of K$_a$-band microwave electric fields from $\sim$200 V/m to $>$1 kV/m over a continuous frequency range of $\pm $1 GHz (15% band coverage). It is established that in strong microwave fields frequency-specific spectral features allow for electric field measurements over a large continuous frequency range.
Mapping equations of motion of the highly exited classical atom in a monochromatic field are generalized for the two-frequency microwave field. Analysis of the obtained equations indicates to the weak sensitivity of the position of the recently observed ionization peak near the main resonance to the frequency and amplitude of the additional microwave field. In the high frequency region, however, the sensitivity of the enhanced ionization peaks on the additional field frequency is predicted.
We consider various approaches to the creation of a high-stability active optical frequency standard, where the atomic ensemble itself produces a highly stable and accurate frequency signal. The short-time frequency stability of such standards may overcome the stability of lasers stabilized to macroscopic cavities which are used as local oscillators in the modern optical frequency standard systems. The main idea is to create a "superradiant" laser operating deep in the bad cavity regime, where the decay rate of the cavity field significantly exceeds the decoherence rate of the lasing transitio…
We report and propose a simple scheme to achieve the ultrafast and selective population transfer in four-level atoms by utilizing a single frequency chirped few-cycle pulse. It is demonstrated that the almost complete population may be transferred to the preselected state of atoms just by manipulating the so called chirp offset parameter. The robustness of the scheme against the variation of laser pulse parameters is also investigated. The proposed scheme may also be useful for the selective population transfer in molecules.
Non-adiabatic decay rates for a radio-frequency dressed magnetic trap are calculated using Fermi's Golden Rule: that is, we examine the probability for a single atom to make transitions out of the dressed trap and into a continuum in the adiabatic limit, where perturbation theory can be applied. This approach can be compared to the semi-classical Landau-Zener theory of a resonant dressed atom trap, and it is found that, when carefully implemented, the Landau-Zener theory overestimates the rate of non-adiabatic spin flip transitions in the adiabatic limit. This indicates that care is needed whe…