The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature of which the leading contributor is the blackbody radiation (BBR) shift. Experimental measurements of the BBR shifts are difficult. In this work, we have calculated the blackbody radiation shift of the ground-state hyperfine microwave transition in 87Rb using the relativistic all-order method and carried out detailed evaluation of the accuracy of our final value. Particular care is taken to accurately account for the contributions from highly-excited states. Our predicted value for the Stark coefficient, k_S=-1.240(4)\times 10^{-10}\text{Hz/(V/m)}^{2} is three times more accurate than the previous calculation [1].
Precision measurements of quantum systems often seek to probe or must account for the interaction with blackbody radiation. Over the past several decades, much attention has been given to AC Stark shifts and stimulated state transfer. For a blackbody in thermodynamic equilibrium, these two effects are determined by the expectation value of photon number in each mode of the Planck spectrum. Here, we explore how the photon number variance of an equilibrium blackbody generally leads to a parametric broadening of the energy levels of quantum systems that is inversely proportional to the square-roo…
We report experimental measurements of the rates of blackbody radiation-induced transitions between high-lying (n>60) S, P and D Rydberg levels of rubidium atoms in a magneto-optical trap using a hybrid field ionization and state-selective depumping technique. Our results reveal significant deviations of the measured transition rates from theory for well-defined ranges of the principal quantum number. We assume that the most likely cause for those deviations is a modified blackbody spectrum inside the glass cell in which the magneto-optical trap is formed, and we test this assumption by instal…
We measure the dynamic differential scalar polarizabilities at 10.6 $μ$m for two candidate clock transitions in $^{176}\mathrm{Lu}^+$. The fractional black body radiation (BBR) shifts at 300 K for the $^1S_0 \leftrightarrow {^3D_1}$ and $^1S_0 \leftrightarrow {^3D_2}$ transitions are evaluated to be $-1.36\,(9) \times 10^{-18}$ and $2.70 \,(21) \times10^{-17}$, respectively. The former is the lowest of any established optical atomic clock.
Blackbody radiation (BBR) sources are calculable radiation sources that are frequently used in radiometry, temperature dissemination, and remote sensing. Despite their ubiquity, blackbody sources and radiometers have a plethora of systematics. We envision a new, primary route to measuring blackbody radiation using ensembles of polarizable quantum systems, such as Rydberg atoms and diatomic molecules. Quantum measurements with these exquisite electric field sensors could enable active feedback, improved design, and, ultimately, lower radiometric and thermal uncertainties of blackbody standards.…
Optical pumping by blackbody radiation is a feature shared by all polar molecules and fundamentally limits the time that these molecules can be kept in a single quantum state in a trap. To demonstrate and quantify this, we have monitored the optical pumping of electrostatically trapped OH and OD radicals by room-temperature blackbody radiation. Transfer of these molecules to rotationally excited states by blackbody radiation at 295 K limits the $1/e$ trapping time for OH and OD in the $X^{2}Π_{3/2},v''=0,J''=3/2(f)$ state to 2.8 s and 7.1 s, respectively.
The translational motion of molecular ions can be effectively cooled sympathetically to temperatures below 100 mK in ion traps through Coulomb interactions with laser-cooled atomic ions. The distribution of internal rovibrational states, however, gets in thermal equilibrium with the typically much higher temperature of the environment within tens of seconds. We consider a concept for rotational cooling of such internally hot, but translationally cold heteronuclear diatomic molecular ions. The scheme relies on a combination of optical pumping from a few specific rotational levels into a ``dark …
The thermal friction force acting on an atom moving relative to a thermal photon bath is known to be proportional to an integral over the imaginary part of the frequency-dependent atomic (dipole) polarizability. Using a numerical approach, we find that blackbody friction on atoms either in dilute environments or in hot ovens is larger than previously thought by orders of magnitude. This enhancement is due to far off-resonant driving of transitions by low-frequency thermal radiation. At typical temperatures, the blackbody radiation maximum lies far below the atomic transition wavelengths. Surpr…
We have determined the frequency shift that blackbody radiation is inducing on the $5s^2$ $^1$S$_0$ -- $5s5p$ $^3$P$_0$ clock transition in strontium. Previously its uncertainty limited the uncertainty of strontium lattice clocks to $1\times10^{-16}$. Now the uncertainty associated to the black body radiation shift correction translates to $5\times 10^{-18}$ relative frequency uncertainty at room temperature. Our evaluation is based on a measurement of the differential dc-polarizability of the two clock states and on a modeling of the dynamic contribution using this value and experimental data…
A major obstacle for optical clocks is the frequency shift due to black body radiation. We discuss how one can tackle this problem in an optical lattice clock; in our case 87-Sr: firstly, by a measurement of the dc Stark shift of the clock transition and, secondly, by interrogating the atoms in a cryogenic environment. Both approaches rely on transporting ultracold atoms over several cm within a probe cycle. We evaluate this approach of mechanically moving the optical lattice and conclude that it is feasible to transport the atoms over 50 mm within 300 ms. With this transport a dc Stark shift …
An effect of atomic line broadening induced by the blackbody radiation is discussed. The level mixing effect and anti-Stokes Raman scattering are compared. It is shown that the mixing effect gives the most significant contribution to the line broadening and it is indicated how to distinguish these two effects in laboratory experiments. The influence of the level mixing on the recombination history of primordial plasma is also discussed.
The process of recombination for the hydrogen atom in the heat bath creating the blackbody radiation is descibed within the frameworks of quantum electrodynamics. For this purpose the self-energy for unbound electron in the field of the nucleus is considered. The imaginary part of this self-energy is directly connected with the recombination cross-section. The same procedure is applied to the hydrogen atom in the field of blackbody radiation. This leads to the new thermal correction to the process of recombination for the hydrogen atom in the heat bath. This correction takes into account the f…
Objects at finite temperature emit thermal radiation with an outward energy-momentum flow, which exerts an outward radiation pressure. At room temperature, a cesium atom scatters on average less than one of these blackbody radiation photons every 10^8 years. Thus, it is generally assumed that any scattering force exerted on atoms by such radiation is negligible. However, atoms also interact coherently with the thermal electromagnetic field. In this work, we measure an attractive force induced by blackbody radiation between a cesium atom and a heated, centimeter-sized cylinder which is orders o…
The Stark shift of the ytterbium optical clock transition due to room temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. However, room temperature operation of the clock at 10^{-18} inaccuracy requires a dynamic correction to this static approximation. This dynamic correction largely depends on a single electric dipole matrix element for which theoretically and experimentally derived values disagree significantly. We determine this important matrix element by two indepe…
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 used a Cs atomic fountain frequency standard to measure the Stark shift on the ground state hyperfine transiton frequency in cesium (9.2 GHz) due to the electric field generated by the blackbody radiation. The measures relative shift at 300 K is -1.43(11)e-14 and agrees with our theoretical evaluation -1.49(07)e-14. This value differs from the currently accepted one -1.69(04)e-14. The difference has a significant implication on the accuracy of frequency standards, in clocks comparison, and in a variety of high precision physics tests such as the time stability of fundamental constants.
We have performed ab initio calculations of the frequency shift induced by a static electric field on the cesium clock hyperfine transition. The calculations are used to find the frequency shifts due to blackbody radiation. Our result ($δν/E^2=-2.26(2)\times 10^{-10}$Hz/(V/m)$^2$) is in good agreement with early measurements and ab initio calculations performed in other groups. We present arguments against recent claims that the actual value of the effect might be smaller. The difference ($\sim$ 10%) between ab initio and semiempirical calculations is due to the contribution of the continuum s…
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 derive an expression for the magnetic blackbody shift of hyperfine transitions such as the cesium primary reference transition which defines the second. The shift is found to be a complicated function of temperature, and has a T^2 dependence only in the high-temperature limit. We also calculate the shift of ground-state p_1/2 hyperfine transitions which have been proposed as new atomic clock transitions. In this case interaction with the p_3/2 fine-structure multiplet may be the dominant effect.
A calculation of the blackbody radiation shift of the B$^+$ clock transition is performed. The polarizabilities of the B$^+$ $2s^2$ $^1$S$^e$, $2s2p$ $^1$P$^o$, and $2s2p$ $^3$P$^o$ states are computed using the configuration interaction method with an underlying semi-empirical core potential. The recommended dipole polarizabilities are 9.64(3) $a_0^3$, 7.78(3) $a_0^3$ and 16.55(5) $a_0^3$ respectively. The derived frequency shift for the $2s^2$ $^1$S$^e$ $\to$ $2s2p$ $^3$P$^o_0$ transition at 300 K is 0.0160(5) Hz. The dipole polarizabilities agree with an earlier relativistic calculation (Sa…
The blackbody radiation (BBR) shift of the 5s - 4d_{5/2} clock transition in 88Sr+ is calculated to be 0.250(9) Hz at room temperature, T=300K, using the relativistic all-order method where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. The BBR shift is a major component in the uncertainty budget of the optical frequency standard based on the 88Sr+ trapped ion. The scalar polarizabilities of the 5s and 4d_{5/2} levels, as well as the tensor polarizability of the 4d_{5/2} level, are presented together with the evaluation of t…
We have performed calculations of the size of the frequency shift induced by a static electric field on the clock transition frequencies of the hyperfine splitting in Yb+, Rb, Cs, Ba+, and Hg+. The calculations are used to find the frequency shifts due to blackbody radiation which are needed for accurate frequency measurements and improvements of the limits on variation of the fine structure constant, alpha. Our result for Cs (delta nu E^2=-2.26 times 10^{-10}Hz/(V/m)^2) is in good agreement with early measurements and ab initio calculations. We present arguments against recent claims that the…
We evaluated the C_6 coefficients of Yb-Yb and Yb -alkali/group II van der Waals interactions with 2% uncertainty. The only existing results for such quantities are for the Yb-Yb dimer. Our value, C_6=1929(39) a.u., is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb 6s^2 ^1S_0 - 6s6p ^3P_0 clock transition with 3.5% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation s…
An ensemble of excited atoms can synchronize emission of light collectively in a process known as superradiance when its characteristic size is smaller than the wavelength of emitted photons. The underlying superradiance depends strongly on electromagnetic (photon) fields surrounding the atomic ensemble. High mode densities of microwave photons from $300\,$K blackbody radiation (BBR) significantly enhance decay rates of Rydberg states to neighbouring states, enabling superradiance that is not possible with bare vacuum induced spontaneous decay. Here we report observations of the superradiance …
We show that optical spectroscopy of Rydberg states can provide accurate {\em in situ} thermometry at room-temperature. Transitions from a metastable state to Rydberg states with principal quantum numbers of 25 to 30 have 200 times larger fractional frequency sensitivities to blackbody radiation than the Strontium clock transition. We demonstrate that magic wavelength lattices exist for both Strontium and Ytterbium transitions between the metastable and Rydberg states. Frequency measurements of Rydberg transitions with $10^{-16}$ accuracy provide $10 \, \mathrm{mK}$ resolution and yield a blac…
A systematic study of Ca+ atomic properties is carried out using high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to n = 7. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole scalar polarizabilities for the 5s, 6s, 7s, 8s, 4p, 5p, 3d, and 4d states and tensor polari…
We develop a nonstandard concept of atomic clocks where the blackbody radiation shift (BBRS) and its temperature fluctuations can be dramatically suppressed (by one to three orders of magnitude) independent of the environmental temperature. The suppression is based on the fact that in a system with two accessible clock transitions (with frequencies v1 and v2) which are exposed to the same thermal environment, there exists a "synthetic" frequency v_{syn} (v1-e12 v2) largely immune to the BBRS. As an example, it is shown that in the case of ion 171Yb+ it is possible to create a clock in which th…
The differential polarizability, due to near-infrared light at 1126 nm, of the 27Al+ 1S0 -> 3P0 clock transition is measured to be 4πε_0 x (1.6 +/- 0.5) x 10^{-31} m^3. This measurement is combined with experimental oscillator strengths to extrapolate the differential static polarizability of the clock transition as 4πε_0 x (1.5 +/- 0.5) x 10^{-31} m^3. The resulting room temperature blackbody fractional frequency shift of -8(3) x 10^{-18} is the lowest known shift of all atomic transitions under consideration for optical frequency standards. A method is presented to estimate the differential …
We show that three group IIIB divalent ions, B+, Al+, and In+, have anomalously small blackbody radiation (BBR) shifts of the ns^2 1S0 - nsnp 3P0 clock transitions. The fractional BBR shifts for these ions are at least 10 times smaller than those of any other present or proposed optical frequency standards at the same temperature, and are less than 0.3% of the Sr clock shift. We have developed a hybrid configuration interaction + coupled-cluster method that provides accurate treatment of correlation corrections in such ions, considers all relevant states in the same systematic way, and yields …
The Stark shift due to blackbody radiation (BBR) is the key factor limiting the performance of many atomic frequency standards, with the BBR environment inside the clock apparatus being difficult to characterize at a high level of precision. Here we demonstrate an in-vacuum radiation shield that furnishes a uniform, well-characterized BBR environment for the atoms in an ytterbium optical lattice clock. Operated at room temperature, this shield enables specification of the BBR environment to a corresponding fractional clock uncertainty contribution of $5.5 \times 10^{-19}$. Combined with uncert…
Rydberg atoms excited by cold blackbody radiation are shown to display long-lived quantum coherences on timescales of tens of picoseconds. By solving non-Markovian equations of motion with no free parameters we obtain the time evolution of the density matrix, and demonstrate that the blackbody-induced temporal coherences manifest as slowly decaying (100 ps) quantum beats in time-resolved fluorescence. An analytic model shows the dependence of the coherent dynamics on the energy splitting between atomic eigenstates, transition dipole moments, and coherence time of the radiation. Experimental de…
We have demonstrated Zeeman slowing and capture of neutral Ra-225 and Ra-226 atoms in a magneto-optical trap (MOT). The intercombination transition 1S0-3P1 is the only quasi-cycling transition in radium and was used for laser-cooling and trapping. Repumping along the 3D1-1P1 transition extended the lifetime of the trap from milliseconds to seconds. Room-temperature blackbody radiation was demonstrated to provide repumping from the metastable 3P0 level. We measured the isotope shift and hyperfine splittings on the 3D1-1P1 transition with the laser-cooled atoms, and set a limit on the lifetime o…
We evaluated the static and dynamic polarizabilities of the 5s^2 ^1S_0 and 5s5p ^3P_0^o states of Sr using the high-precision relativistic configuration interaction + all-order method. Our calculation explains the discrepancy between the recent experimental 5s^2 ^1S_0 - 5s5p ^3P_0^o dc Stark shift measurement Δα= 247.374(7) a.u. [Middelmann et. al, arXiv:1208.2848 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502R (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic…
The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature of which the leading contributor is the blackbody radiation (BBR) shift. In the present work, we used configuration interaction + coupled-cluster method to evaluate polarizabilities of the $6s^2 ^1S_0$ and $6s6p ^3P_0$ states of Tl$^+$ ion; we find $α_0(^1S_0)=19.6$ a.u. and $α_0(^3P_0)=21.4$ a.u.. The resu…
Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for nS, nP and nD states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show…
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…
Despite being a canonical example of quantum mechanical perturbation theory, as well as one of the earliest observed spectroscopic shifts, the Stark effect contributes the largest source of uncertainty in a modern optical atomic clock through blackbody radiation. By employing an ultracold, trapped atomic ensemble and high stability optical clock, we characterize the quadratic Stark effect with unprecedented precision. We report the ytterbium optical clock's sensitivity to electric fields (such as blackbody radiation) as the differential static polarizability of the ground and excited clock lev…
The thermal friction force acting on an atom moving relative to a thermal photon bath has recently been calculated on the basis of the fluctuation-dissipation theorem. The thermal fluctuations of the electromagnetic field give rise to a drag force on an atom provided one allows for dissipation of the field energy via spontaneous emission. The drag force exists if the atomic polarizability has a nonvanishing imaginary part. Here, we explore alternative derivations. The damping of the motion of a simple harmonic oscillator is described by radiative reaction theory (result of Einstein and Hopf), …
Energy levels of 30 low-lying states of Lu2+ and allowed electric-dipole matrix elements between these states are evaluated using a relativistic all-order method in which all single, double and partial triple excitations of Dirac-Fock wave functions are included to all orders of perturbation theory. Matrix elements are critically evaluated for their accuracy and recommended values of the matrix elements are given together with uncertainty estimates. Line strengths, transition rates and lifetimes of the metastable 5d(3/2) and 5d(5/2) states are calculated. Recommended values are given for stati…
We have studied an ionization of alkali-metal Rydberg atoms by blackbody radiation (BBR). The results of the theoretical calculations of ionization rates of Li, Na, K, Rb and Cs Rydberg atoms are presented. Calculations have been performed for nS, nP and nD states which are commonly used in a variety of experiments, at principal quantum numbers n=8-65 and at the three ambient temperatures of 77, 300 and 600 K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ion…
The blackbody radiation shift of the Ga$^+$ $4s^2 \ ^1S^e_0 \to 4s4p \ ^3P^o_0$ clock transition is computed to be $-$$0.0140 \pm 0.0048$ Hz at 300 K. The small shift is consistent with the blackbody shifts of the clock transitions of other group III ions which are of a similar size. The polarizabilities of the Ga$^+$ $4s^2 \ ^1S^e_0$, $4s4p \ ^3P^o_0$, and $4s4p \ ^1P^o_1$ states were computed using the configuration interaction method with an underlying semi-empirical core potential. A byproduct of the analysis involved large scale calculations of the low lying spectrum and oscillator streng…
We have considered the formation of the luminescent subordinate HeI lines by the absorption of continuum radiation from a source in the lines of the main HeI series in the expanding Universe. It is suggested that at some moment of time, corresponding to the redshift $z_{0}$, a burst of superequilibrium blackbody radiation with a temperature $ T+ΔT $ occurs. This radiation is partially absorbed at different $z <z_{0}$ in the lines of the main HeI series and then converted into the radiation of subordinate lines. If $ ν_{ij} $ is the laboratory frequency of the transition of some subordinate lin…
