Two-photon Transition In Rubidium Research Articles

Frequency shifts due to Stark effects on a rubidium two-photon transition

The $5S_{1/2}\rightarrow 5D_{5/2}$ two-photon transition in Rb is of interest for the development of a compact optical atomic clock. Here we present a rigorous calculation of the 778.1~nm ac-Stark shift ($2.30(4) \times10^{-13}$(mW/mm$^2$)$^{-1}$) that is in good agreement with our measured value of $2.5(2) \times10^{-13}$(mW/mm$^2$)$^{-1}$. We include a calculation of the temperature-dependent blackbody radiation shift, we predict that the clock could be operated either with zero net BBR shift ($T=495.9(27)$~K) or with zero first-order sensitivity ($T=368.1(14)$~K). Also described is the calculation of the dc-Stark shift of 5.5(1)$\times 10^{-15}$/(V/cm$^2$) as well as clock sensitivities to optical alignment variations in both a cat's eye and flat mirror retro-reflector. Finally, we characterize these Stark effects discussing mitigation techniques necessary to reduce final clock instabilities.

Iodine Frequency Reference on a Sounding Rocket

Frequency-stable laser systems are a key technology in precision experiments and have recently become applicable in space. Optical frequency references based on cavities, atoms, or molecules allow for precise laser frequency stabilization and thus enable, for example, high-precision laser ranging in space missions. Examples are the gravity recovery and climate experiment-follow-on (GRACEFO) mission [1,2] that was recently put in operation, the planned laser interferometer gravitational wave observatory LISA [3], and future global satellite navigation systems based on optical clocks [4,5]. In the context of these and other missions, frequency references based on optical cavities [6,7] and unequal-arm-length interferometers [8,9] have been developed as compact, ruggedized instruments for application in space, featuring good short-term instability. One way to also realize low long-term instability is the stabilization to atomic or molecular transitions, providing an advantage in accuracy over relative frequency references. Together with optical frequency combs, such absolute references can further be operated as optical clocks with instability relevant for global navigation satellite systems (GNSS). Several such systems are under *klaus.doeringshoff@physik.hu-berlin.de investigation today at various wavelengths, based on thermal calcium beams [10–12] or hot vapor cells using single- [13] or two-photon transitions in rubidium [14,15]. Another, already matured frequency reference is based on saturation spectroscopy of molecular iodine using the second harmonic of the narrow linewidth Nd:yttriumaluminum- garnet (YAG) laser at 1064 nm. These systems rely on the modulation-transfer spectroscopy (MTS) technique applied to the rovibronic transition R(56)32- 0, featuring narrow transitions with a natural linewidth of 300 kHz [16]. The hyperfine spectrum of this transition was studied in detail [17], the absolute frequency was accurately measured with an uncertainty of 1.1 kHz by Nevsky et al. [18], and Ye et al. demonstrated operation of a molecular iodine optical clock over the course of a full year [19]. In the past decade, several groups realized compact and portable iodine references with fractional frequency instability in the low 10−15 regime [20,21] and subjected their setups to environmental tests [22]. We believe that, using available technology at 1064 nm, developed in the context of the LISA and the GRACE-FO mission and established in satellite laser communication terminals, such systems can be developed for spaceborne instruments on relatively short time scales. Here, we present a stand-alone iodine frequency reference at 1064 nm, named JOKARUS, that is based on a microintegrated extended-cavity diode laser (ECDL) 2331-7019/19/11(5)/054068(9) 054068-1 © 2019 American Physical Society KLAUS DORINGSHOFF et al. PHYS. REV. APPLIED 11, 054068 (2019) [23,24] in a master oscillator plus power amplifier (MOPA) configuration. JOKARUS was built to demonstrate the maturity of our technology and its applicability in space missions. To this end, we operate JOKARUS on a sounding rocket mission and thereby prove the autonomous operation of an optical iodine frequency reference.We compare the optical frequency to a chip-scale atomic clock (CSAC) via a self-referenced frequency comb on the ground and in space. This paper is organized as follows. Section II describes the optical iodine frequency reference and its autonomous operation, as well as the optical frequency comb used to verify the frequency instability of the iodine reference aboard the sounding rocket. Section III presents results on the characterization of the frequency instability of the iodine frequency reference obtained on the ground and from the operation in space. Finally, in Sec. IV, we summarize the results and give a conclusion.

Absolute frequency measurement of the hyperfine structure of the 5S1/2 – 5D3/2 two-photon transition in rubidium using femtosecond frequency comb

In this paper, the absolute optical frequencies of the hyperfine components of the 5S1/2 – 5D3/2 two-photon transition in rubidium is measured using a femtosecond frequency comb (OFC). In order to Interrogate this transition, a laser light at a wavelength of 778.2 nm is used. This wavelength is obtained from the frequency doubling of a telecom wavelength at 1556.4 nm emitted from a narrow linewidth fiber laser. The absolute frequency measurement with OFC is performed while the laser frequency is locked to each hyperfine component of the transition. The measurement uncertainty is estimated to be as low as ±3.4 kHz at 2 σ after correcting the main systematic shifts. The stability of the 85Rb 5S1/2(Fg = 3) − 5D3/2 (Fe = 4) hyperfine component shows a Standard Allan Deviation of 3 × 10−12 at 1 s, which reaches 7 × 10−13 at 1000 s.

Optical communication frequency standard using a fiber laser to excite cold rubidium two-photon transition

We propose to utilize an Er-doped fiber laser locked to a cooled Rb two-photon transition (TPT) resonance as a frequency standard for fiber-based optical communication. We show experimentally that a continuous wave laser beam can enhance the strength of cooled Rb TPT as much as 2.5 times. The cooled Rb TPT resonance excited by the fiber frequency combs has a measured linewidth of about 900 kHz. After locking the repetition rate of the fiber laser to the cooled Rb TPT resonance, the stability reaches 1.5×10−13 with 100 s averaging time. The results demonstrate that the proposed method in this paper is promising to provide the radio frequency standard for fiber-based optical communication.

Compact Optical Atomic Clock Based on a Two-Photon Transition in Rubidium

Optical frequency standards surpass their microwave counterparts in both stability and accuracy, yet they are often bulky, power-hungry, and unable to operate outside of a well-controlled laboratory environment. Leveraging a two-photon transition in ${}^{87}$Rb vapor and recent advances in fiber frequency combs, the authors build an optical clock to beat the current portable standards, with an architecture that can be made compact and low-power. These results point the way to a real-world optical frequency standard of even higher stability, for applications such as satellite navigation.

An ultra-stable optical frequency standard for telecommunication purposes based upon the 5S1/2 → 5D5/2 two-photon transition in rubidium

In this study, we report the development of a frequency standard for optical fiber communication applications based on a two-photon transition in rubidium at 385.2 THz. This standard kills two birds with one stone in the sense it is capable of providing us with two highly stable serviceable wavelengths at 778.1 and 1556.2 nm. In this system, we exploit the narrow line-width of a fiber laser emitting at 1556.2 nm in conjunction with an erbium-doped fiber amplifier to generate a sufficient second harmonic laser beam at 778.1 nm in a periodically polled lithium niobate waveguide mixer in order to probe and frequency-lock the laser to the 5S1/2 (F g = 3)–5D5/2 (F e = 5) hyperfine two-photon transition component in 85Rb. The metrological performance of the standard is evaluated with the aid of an optical frequency comb synthesizer. Allan variance measurement shows a stability of 4 × 10−12 at 1 s (limited by the comb stability), reaching a floor of 6.8 × 10−13 at 1000 s. After correction of all the major systematic frequency shifts including the light shift, the absolute frequency is found to be 385 285 142 374.0 (5.0) kHz. Moreover, the absolute frequencies of most of the hyperfine components of the 5S1/2–5D5/2 transition of the two naturally existing rubidium isotopes are measured using a femtosecond frequency comb synthesizer after stabilizing a laser on each component.

Investigation of bulk and waveguide frequency doubling crystals for interrogation of a two-photon transition in rubidium

The 5S1/2 (F=3)–5D5/2 (F=5) two-photon transition of rubidium (85) at 778nm is an excellent candidate for a high-quality portable frequency standard at the telecommunication region. The interrogation of the two-photon transition requires efficient second harmonic conversion of a laser at 1556nm. In this work, a comparison is made between the conversion efficiencies of bulk and waveguide periodically polled lithium niobate (PPLN) crystals. Both crystals are doped with 5% from MgO and used to generate frequency doubled light at 778nm from a fundamental light source operating at 1556nm. In order to obtain the optimum operating conditions, the frequency doubled power is measured as a function of laser wavelength and crystal temperature. The conversion efficiency of the waveguide PPLN is found to be around two orders of magnitudes larger than that of the bulk PPLN crystal for input powers less than 150mW. At the end, the generated second harmonic light from both crystals are used to interrogate the two-photon transition in a natural rubidium gas cell. A comparison is made between the fluorescence spectrums resulting from the two-photon transition using second harmonic generated powers from both crystals.

Theory for direct frequency-comb spectroscopy

Direct frequency-comb spectroscopy is a technique that employs a train of well-stabilized ultrashort pulses to study the spectral properties of atomic or molecular systems. In this way, it opens the possibility of incorporating various coherent-control techniques for such spectral investigations. Here we introduce a theory for the interaction of a multilevel atom with such pulse trains, which is general enough to take into account an arbitrarily shaped frequency comb. We illustrate its application by studying the interaction of $^{87}\text{R}\text{b}$ atoms with trains of pulses of various shapes, resonant with the $5S\text{\ensuremath{-}}5D$ two-photon transition of rubidium. More specifically, we treat the interaction with hyperbolic-secant pulses, chirped pulses, and 0-$\ensuremath{\pi}$ pulses, respectively. The theory is designed to work at an arbitrary perturbation order. For the results presented here, we mostly used a 12th-order perturbation series at the pulse's electric field. Due to the large number of levels involved, such modeling may be quite complex computationally, and an important point of the present work is then to introduce the required numerical approach to treat this problem efficiently.

Two-photon spectroscopy of rubidium using a grating-feedback diode laser

We describe an experiment for investigating the 5S1∕2→5D5∕2 two-photon transition in rubidium using a single grating-feedback diode laser operating at 778.1nm (385THz). Continuous tuning of the laser frequency over 4GHz allows for the clear resolution of the Doppler-free spectral features and allows accurate measurement of the hyperfine ground-state splitting. A direct comparison between Doppler-broadened and Doppler-free spectral features is possible because both are distinctly evident in the two-photon spectra. By independently modifying the polarization state of the two laser fields, the impact of electric dipole selection rules on the two-photon transition spectra is investigated. This experiment is a valuable addition to the advanced undergraduate laboratory because it uses much of the same equipment as the single-photon saturated absorption spectroscopy experiment performed on the 5S1∕2→5P3∕2 transition in rubidium (λ=780.24nm) and provides students with an opportunity to investigate characteristics of atomic spectra not evident in the single-photon experiment.

Frequency stability of an optical frequency standard at 192.6 THz based on a two-photon transition of rubidium atoms

We have developed two frequency standards at 192.6 THz (1556.2 nm) based on a two-photon transition in rubidium at 385.2 THz (778.1 nm). These standards use a high power DFB laser at 1556.2 nm and second harmonic generation (SHG) in a periodically poled lithium niobate (PPLN) crystal. The linewidth of the DFB is reduced to the kHz level using optical feedback from a confocal cavity. The SH light is used to injection-lock a 778.1 nm laser diode which allows to observe the (5S 1/2, F g=2−5D 5/2, F e=4) two-photon transition in 87 Rb and lock the 1556.2 nm laser. Allan variance measurements between two identical standards show a beat stability of 2.5×10 −13/ τ 1/2 for observation times between 100 ms and 10 s and a level of 5.8×10 −14 for 100 s. Systematic effects shifting the locked frequency of the standards from that of the Rb transition are detailed and some experimental measurements are presented. Finally, absolute frequency measurements were performed at the INMS/CNRC in Ottawa allowing the determination of the absolute frequency of the standard to be 192 642 283 183.7±0.5 kHz.

Absolute frequency measurement of a laser at 1556 nm locked to the 5S 1/2−5D 5/2 two-photon transition in 87Rb

The frequency of a diode laser system at 193 THz (1556 nm), which is frequency doubled and locked to a two-photon transition in rubidium at 385 THz (778 nm), has been measured with a Cs-based frequency chain and a single Sr + ion standard at 445 THz. The output frequency of the diode laser system was measured to be 192 642 283 183 700 ± 500 Hz. After applying corrections for systematic offsets in the rubidium spectrum, the frequency of the 87Rb 5S 1/2( F g =2)−5D 5/2( F e =4) two-photon transition is found to be 385 284 566 370.4 ± 2 kHz.

Frequency measurement of the 2S-12D transitions in hydrogen and deuterium, new determination of the Rydberg constant

We have performed the first pure frequency measurement of the 2S-12D two-photon transitions in atomic hydrogen and deuterium. These frequencies are compared to two optical standards, the CO/sub 2/ laser stabilized on the OsO/sub 4/ molecule and the optical rubidium laser standard (LD/Rb) (namely, a laser diode at 778 nm stabilized on the 5S/sub 1/2/-5D/sub 5/2/ two-photon transition of rubidium). The main part of the experiment is located in the Laboratoire Kastler-Brossel (LKB), one part of the frequency chain is in the Laboratoire Primaire du Temps et des Frequences (LPTF), and two 3 km long optical fibers link the two parts of this experiment. The new value of the Rydberg constant is R/sub /spl infin//=109 737.315 686 06 (79) cm/sup -1/.

Metrological features of the rubidium two-photon standards of the BNM-LPTF and Kastler Brossel Laboratories

We have built three optical frequency standards based on the two-photon transition of rubidium at 778 nm, and analysed their performance over a period of more than three years. We discuss some systematic effects that could lead to the reproducibility we observe, and point out the possible improvements of the devices. We also examine the short and long term stabilities of the systems, and show that we have reached their ultimate performances.

An absolute frequency reference at 192.6 THz (1556 nm) based on a two-photon absorption line of rubidium at 778 nm for WDM communication systems

A 192.6-THz (1556 nm) distributed-feedback (DFB) laser is frequency-locked on a two-photon transition of rubidium at 385.3 THz (778 nm) using second-harmonic (SH) generation. With 43 mW at 1556 nm, we obtain a SH power of 15 /spl mu/W using a KNbO/sub 3/ crystal placed in a ring cavity. Optical feedback from this cavity is used to reduce the DFB laser linewidth to the 10-kHz level and control its frequency. The SH signal is used to injection-lock a 778-nm Fabry-Perot laser in order to increase the interrogation power. With this scheme, we observe two-photon transitions in rubidium and lock the 1556-nm laser frequency.

Frequency measurement of the [formula omitted] two-photon transition in rubidium

We have measured the frequencies of three diode lasers stabilized on the 5 S 1 2 (F = 3)−5 D 5 2 (F = 5) two-photon transition in rubidium at λ = 778.1 nm, with an uncertainty of 1 kHz, using BNM-LPTF frequency synthesis chain starting from a CO 2 OsO 4 reference laser at 10.3 μm. We show that this frequency chain is able to reach the 10 −13 resolution level. After a discussion of the systematic effects that may shift the resonance, the transition frequency is found to be ν = 385 285 142 378.280 ± 2 kHz.

Determination of the Rydberg constant by direct frequency measurement

We have built a frequency chain to connect the frequencies of the 2S-8S/D two-photon transitions in hydrogen to two optical standards, the methane-stabilized He-Ne laser and the iodine-stabilized He-Ne laser. In this way, an optical frequency of atomic hydrogen is directly linked for the first time to the cesium clock without any interferometry. We deduce a new value for the Rydberg constant with an uncertainty of 2.2 parts in 10/sup 11/. This value is in very good agreement with published values. The same frequency scheme has been used to measure the frequencies of the 5S-5D two-photon transition in rubidium and 2/sup 3/S/sub 1/-3/sup 3/P/sub 0/ in helium.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

LPTF frequency synthesis chain: results and improvement for the near future

We describe the modified LPTF frequency synthesis chain, which starts from the cesium referenced CO/sub 2//OsO/sub 4/ laboratory standard. This chain, with variations, is able to cover the whole visible spectrum. A particular scheme is given in order to measure the 385.3-THz frequency of the two-photon transitions in rubidium. To secure the phase lock, the diode lasers' linewidths have to be reduced. We report a 10-Hz beatnote linewidth obtained with two diode lasers stabilized on the same high-finesse cavity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Towards an accurate frequency standard at λ778 nm using a laser diode stabilized on a hyperfine component of the Doppler-free two-photon transitions in rubidium

Two systems are built in which a commercially available GaAlAs laser diode is stabilized on a hyperfine component of the 5S 1 2 −5D ( 3 2 , 5 2 ) two-photon transitions in rubidium at λ=778 nm ( v=385 THz). Some preliminary metrological results are presented. The frequency repeatability has been found to be of 200 Hz (5.2 parts in 10 13) and a short-term frequency stability of 3×10 -13/ τ /gt up to 2000 s is currently obtained.

Optical frequency determination of the hyperfine components of the [formula omitted] two-photon transitions in rubidium

An absolute optical frequency measurement is made of the hyperfine components of the 5S 1 2 -5D 3 2 two-photon transitions in rubidium with an uncertainty of 1.3×10 -11. This is carried out in a simple way by taking advantage of the near coincidence between the two-photon frequency at λ=778 nm in Rb and the frequency difference of two HeNe lasers, stabilized respectively to an iodine line at λ=633 nm and a methane transition at λ=3.39 μm used as reference. This measurement provides a new optical frequency reference in the visible range.

Heterodyne Doppler-free two-photon absorption and dispersion in rubidium vapour

Heterodyne Doppler-free spectroscopy, previously demonstrated on single-photon resonances (heterodyne saturation spectroscopy), has been extended to two-photon transitions in rubidium (5S-5D and 5S-7S). It provides a simple method of observing the two-photon dispersion lineshape directly. The noticeable sensitivity of this absorption technique, which has been used for an optical measurement of the hyperfine structure of the 5D level, is discussed in comparison with that currently obtained in two-photon-induced fluorescence.