Modified hyper-Ramsey methods for the elimination of probe shifts in optical clocks

Abstract

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 magneticallyinduced 1 S0− 3 P0 transition in 88 Sr, demonstrating automatic suppression of a sizeable 2 × 10 −13probe Stark shift to below 1 × 10 −16 even with very large errors in shift compensation.PACS numbers: 32.70. Jz,06.30.Ft,32.60.+i,42.62.Fi High-Q interrogation of narrow, forbidden optical transitions has formed the basis of a new generation of atomic clocks with exceptional accuracy and stability at the 10 −18 level [1,2]. As well as potentially supporting a redefinition of the SI second [3], such clocks underpin empirical investigations into areas of fundamental physics including relativity [4], the search for dark matter [5,6], and potential time-variation of fundamental constants [7,8]. However, several promising atomic species suffer from a clock transition which is too forbidden, requiring a high laser intensity − and therefore a large light shift − in order to drive the atoms into the excited state. Important examples include clocks based on high-order multipole [9, 10], two-photon [11,12], or magnetically-induced [13][14][15] transitions. Before these species can be used for precision frequency measurements, probe-induced shifts must be dealt with.A conceptually straightforward approach to the light shift is exemplified by recent realizations of the electricoctupole 2 S 1/2 → 2 F 7/2 171 Yb + clock, where the unperturbed atomic resonance is extrapolated from interleaved Rabi-spectroscopy sequences of high and low probe intensity [7,9]. Although careful extrapolation can be quite effective, achieving frequency uncertainty nearly 4 orders of magnitude smaller than the shift itself [7], the stability of the clock is deteriorated by the extrapolation process and the ultimate accuracy is limited by the precision with which the probe intensity ratio can be calibrated.In order to reduce the burden of probe intensity control, tailored spectroscopy pulses have been proposed which provide a central feature whose frequency is unchanged by the light shift [16][17][18][19]. The great potential of this approach has recently been illustrated using Yb + , where "hyper-Ramsey" spectroscopy was utilized to suppress the shift by more than four orders of magnitude below the 10 −17 level [20]. In this Letter, we propose a modified form of hyper-Ramsey spectroscopy which provides complete immunity to variations in the probe shift, considerably relaxing the experimental constraints on intensity control and potentially facilitating light shift uncertainties well below 10 −18 in Yb + . As indicated by the experimental results of this Letter, sub-10 −18 shi...

Synthetic frequency protocol for Ramsey spectroscopy of clock transitions

“…We show that this protocol in combination with the original hyper-Ramsey scheme [28] makes most extremal results and is quite stable with respect to the decoherence. Moreover, our method leads to the much better and robust suppression of the shifts in comparison with protocols [30,31], which are more sensitive to the decoherence and therefore do not show phenomenal results already.…”

“…However, besides HR2 the paper [30] also describes the theory and successful experimental demonstration of modified hyper-Ramsey (MHR) method, which is based on combination of both protocols HR1 and HR2. In the case of MHR, the error signal is determined as following…”

“…In the resent paper [30], authors have proposed the use of ±π/2 phase steps after inverted (−Ω 0 ) sub-pulse 2τ [see in Fig. 1(c)] to form an error signal for hyperRamsey approach (we will denote this method as HR2).…”

“…However, a potential of this method was not going to be settled. In the experimental-theoretical paper [30] a 'stunning' result was recently shown: certain simple modification allows, in principle, totally(!) to exclude probeinduced shifts.…”

“…Other hyper-Ramsey modification, having the same efficiency, was very soon proposed in the theoretical paper [31]. Because these phenomenal results can have far-reaching consequences for development of atomic clocks, it requires utterly thorough investigation of the schemes [30,31]. Besides, undoubted importance has a search of new variants to suppress probe-induced shifts with the near extremal efficiency.…”