Precision measurement of the three 2(3)P(J) helium fine structure intervals

Precision Measurement of the n=2 Triplet P J=1 to J=0 Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields

Increasing accuracy of the theory and experiment of the n=2 ^{3}P fine structure of helium has allowed for increasingly precise tests of quantum electrodynamics (QED), determinations of the fine-structure constant α, and limitations on possible beyond the standard model physics. Here we present a 2 ppb measurement of the J=1 to J=0 interval. The measurement is performed using frequency-offset separated-oscillatory fields. Our result of 29 616 955 018(60) Hz represents a landmark for helium fine-structure measurements, and, for the first time, will allow for a 1-ppb determination of the fine-structure constant when QED theory for the interval is improved.

Atomic Structure Calculations of Helium with Correlated Exponential Functions

The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant α. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r1, r2 and r = |r→1−r→2|. The choice of the exponential basis functions of the form exp(−αr1−βr2−γr) allows us to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects. Calculations of the leading QED effects of order α5m (where m is the electron mass) are complemented with the systematic treatment of higher-order α6m and α7m QED effects.

Precision spectroscopy of atomic helium

Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational methods. The fine-structure splitting in the 23P state of helium is considered to be the most suitable for determining the fine-structure constant α in atoms. After more than 50 years of efforts by many theorists and experimentalists, we are now working toward a determination of α with an accuracy of a few parts per billion, which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum electrodynamics. Moreover, the precision spectroscopy of helium allows determination of the nuclear charge radius, and it is expected to help resolve the 'proton radius puzzle'. In this review, we introduce the latest developments in the precision spectroscopy of the helium atom, especially the discrepancies among theoretical and experimental results, and give an outlook on future progress.

Ultrahigh-Precision Measurement of the n=2 Triplet P Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields

For decades, improved theory and experiment of the n=2 ^{3}P fine structure of helium have allowed for increasingly precise tests of quantum electrodynamics, determinations of the fine-structure constant α, and limitations on possible beyond-the-standard-model physics. Here we use the new frequency-offset separated-oscillatory-fields technique to measure the 2^{3}P_{2}→2^{3}P_{1} interval. Our result of 2 291 176 590(25) Hz represents a major step forward in precision for helium fine-structure measurements.

Absolute frequency measurement of molecular iodine hyperfine transitions at 647 nm

We report absolute frequency measurements of molecular iodine P(46) 5-4 a₁, a₁₀, and a₁₅ hyperfine transitions at 647 nm with a fiber-based frequency comb. The light source is based on a Littrow-type external-cavity diode laser. A frequency stability of 5×10^-12 at a 200 s integration time is achieved when the light source is stabilized to the P(46) 5-4 a₁₅ line. The pressure shift is determined to be -8.3(7)  kHz/Pa. Our determination of the line centers reached a precision of 21 kHz. The light source can serve as a reference laser for lithium spectroscopy (2S→3P).

Laser Spectroscopy of the Fine-Structure Splitting in the 2^{3}P_{J} Levels of ^{4}He

The fine-structure splitting in the 2^{3}P_{J} (J=0, 1, 2) levels of ^{4}He is of great interest for tests of quantum electrodynamics and for the determination of the fine-structure constant α. The 2^{3}P_{0}-2^{3}P_{2} and 2^{3}P_{1}-2^{3}P_{2} intervals are measured by laser spectroscopy of the ^{3}P_{J}-2^{3}S_{1} transitions at 1083 nm in an atomic beam, and are determined to be 31 908 130.98±0.13  kHz and 2 291 177.56±0.19  kHz, respectively. Compared with calculations, which include terms up to α^{5}Ry, the deviation for the α-sensitive interval 2^{3}P_{0}-2^{3}P_{2} is only 0.22 kHz. It opens the window for further improvement of theoretical predictions and an independent determination of the fine-structure constant α with a precision of 2×10^{-9}.

Widely tunable, narrow linewidth external-cavity gain chip laser for spectroscopy between 1.0 - 1.1 µm

We have developed and characterised a stable, narrow linewidth external-cavity laser (ECL) tunable over 100 nm around 1080 nm, using a single-angled-facet gain chip. We propose the ECL as a low-cost, high-performance alternative to fibre and diode lasers in this wavelength range and demonstrate its capability through the spectroscopy of metastable helium. Within the coarse tuning range, the wavelength can be continuously tuned over 30 pm (7.8 GHz) without mode-hopping and modulated with bandwidths up to 3 kHz (piezo) and 37(3) kHz (current). The spectral linewidth of the free-running ECL was measured to be 22(2) kHz (Gaussian) and 4.2(3) kHz (Lorentzian) over 22.5 ms, while a long-term frequency stability better than 40(20) kHz over 11 hours was observed when locked to an atomic reference.

Laser pumped 4He magnetometer with light shift suppression

We report a laser-pumped ⁴He atomic magnetometer with light shift suppression through the atomic sensor itself. A linearly polarized light is used to optically align the ⁴He metastable atoms and we monitor the magneto-optical double resonance (MODR) signals produced by the left- and right-circularly orthogonal components. It is shown that light shift leads to the atomic alignment to orientation conversion effect, and thus, the difference between the two MODR signals. One of these two MODR signals is locked at the Larmor frequency and is used to measure the ambient magnetic field, while the differential signal is, simultaneously, fed back to suppress the light shift. The scheme could be of the advantage to the design of compact magnetometers by reducing the systematic errors due to light shift.

Precision Measurement for Metastable Helium Atoms of the 413 nm Tune-Out Wavelength at Which the Atomic Polarizability Vanishes

We present the first measurement for helium atoms of the tune-out wavelength at which the atomic polarizability vanishes. We utilize a novel, highly sensitive technique for precisely measuring the effect of variations in the trapping potential of confined metastable (2^{3}S_{1}) helium atoms illuminated by a perturbing laser light field. The measured tune-out wavelength of 413.0938(9_{stat})(20_{syst}) nm compares well with the value predicted by a theoretical calculation [413.02(9) nm] which is sensitive to finite nuclear mass, relativistic, and quantum electrodynamic effects. This provides motivation for more detailed theoretical investigations to test quantum electrodynamics.

Precision frequency metrology of helium 2(1)S(0)→2(1)P(1) transition

We report a precision frequency measurement of the (4)He 2(1)S(0)→2(1)P(1) transition at 2058 nm. The saturated absorption spectroscopy is performed in a rf discharge sealed-off cell with a volume Bragg grating-based Tm:Ho:YLF laser. The absolute transition frequency measured using a fiber optical frequency comb is 145 622 892 822 (183) kHz with a relative uncertainty of 1.3×10(-9). Our result is ten times more precise than current best theoretical calculations and is in reasonable agreement with the calculated values. However, the ionization energy of the 2(1)P(1) state, derived from our result and other precisely measured transitions, shows a discrepancy of approximately 3.5σ with the most precise atomic theory. We have also determined the isotope shift between (3)He and (4)He to be 4248.7 (5.3) MHz, which is more precise than the previous measurement by one order of magnitude.

Optical frequency comb assisted laser system for multiplex precision spectroscopy

A laser system composed of two lasers phase-locked onto an Optical Frequency Comb Synthesizer (OFCS), operating around 1083 nm, was developed. An absolute frequency precision of 6x10(-13) at 1s, limited by the OFCS, was measured with a residual rms phase-noise of 71 mrad and 87 mrad for the two phase-locks, respectively. Multiplex spectroscopy on 1083 nm Helium transitions with this set-up is demonstrated. Generalization of this system to a larger number of OFCS assisted laser sources for wider frequency separations, even in other spectral regions, is discussed.

Determination of the fine structure constant using helium fine structure

We measure 31,908,131.25(30) kHz for the 2(3)}P J=0 to 2 fine structure interval in helium. The difference between this and theory to order mα7 (20 Hz numerical uncertainty) implies 0.22(30) kHz for uncalculated terms. The measurement is performed by using atomic beam and electro-optic laser techniques. Various checks include a 3He 2{3}S hyperfine measurement. We can obtain an independent value for the fine structure constant α with a 5 ppb experimental uncertainty. However, dominant mα8 terms (potentially 1.2 kHz) limit the overall uncertainty to a less competitive 20 ppb in α.

Fine structure of heliumlike ions and determination of the fine structure constant

We report a calculation of the fine-structure splitting in light heliumlike atoms, which accounts for all quantum electrodynamical effects up to order alpha{5} Ry. For the helium atom, we resolve the previously reported disagreement between theory and experiment and determine the fine-structure constant with an accuracy of 31 ppb. The calculational results are extensively checked by comparison with the experimental data for different nuclear charges and by evaluation of the hydrogenic limit of individual corrections.

Hyperfine suppression of 2 3 S 1--3 3 P J transitions in 3He

Two anomalously weak transitions within the 2(3)S_(1)--3(3)P_(J) manifolds in 3He have been identified. Their transition strengths are measured to be 1000 times weaker than that of the strongest transition in the same group. This dramatic suppression of transition strengths is due to the dominance of the hyperfine interaction over the fine-structure interaction. An alternative selection rule based on IS coupling (where the nuclear spin is first coupled to the total electron spin) is proposed. This provides qualitative understanding of the transition strengths. It is shown that the small deviations from the IS coupling model are fully accounted for by an exact diagonalization of the strongly interacting states.

Improved measurement of the 1s2s 1S0-1s2p 3P1 interval in heliumlike silicon

Using colinear fast-beam laser spectroscopy with copropagating and counter-propagating beams we have measured the 1s2s 1S0-1s2p 3P1 intercombination interval in 28Si12+ with the result 7230.585(6) cm{-1}. The experiment made use of a dual-wavelength, high-finesse, power build-up cavity excited by single-frequency lasers at 1319 and 1450 nm. The result will provide a precision test of ab initio relativistic many-body atomic theory at moderate Z.

Improved theory of helium fine structure

Improved theoretical predictions for the fine-structure splitting of 2(3)PJ levels in helium are obtained by the calculation of contributions of order alpha5 Ry. New results for transition frequencies nu(01) = 29616943.01(17) kHz and nu(12) = 2291161.13(30) kHz disagree significantly with the experimental values, indicating an outstanding problem in bound state QED.