Synthetic frequency protocol for Ramsey spectroscopy of clock transitions

Abstract

We develop an universal method to significantly suppress probe-induced shifts in any types of atomic clocks using the Ramsey spectroscopy. Our approach is based on adaptation of the synthetic frequency concept [V. I. Yudin, et al., Phys. Rev. Lett. 107, 030801 (2011) At the present time, huge progress occurs for highprecision optical atomic clocks based on both neutral atoms in optical lattices [1][2][3][4][5][6][7][8] and trapped ions [9][10][11][12]. Exceptional accuracy and stability at the 10 −17 -10level are achieved. Potential possibilities to achieve the level of 10 −19 become clearer for nuclear clocks [13-16] and for highly charged ions [17][18][19]. Great fundamental (e.g., in tests of fundamental physical theories such as QED, QCD, unification theories, cosmology, dark matter searches, etc.) and practical (navigation and information systems, gravity-geopotential surveying) importance of the current and long-range researches is wellknown and unquestionable. Current state, concomitant problems, and future prospects are well presented in the review [20].On the way to these remarkable achievements, different barriers arise, which require the development of new unconventional approaches. As an example, for some of the promising clock systems, one of the key problems is the frequency shift of the clock transition due to the excitation pulses themselves. For the case of magnetically induced spectroscopy [21,22] these shifts (quadratic Zeeman and ac-Stark shifts) could ultimately limit the achievable performance. Moreover, for ultranarrow transitions (e.g., electric octupole [23] and twophoton transitions [24,25]) the ac-Stark shift can be so large in some cases to rule out high accuracy clock performance at all. A similar limitation exists for clocks based on direct frequency comb spectroscopy [26,27] due to ac-Stark shifts induced by large numbers of off-resonant * Electronic address: viyudin@mail.ru laser modes.Unconventional solution to this important problem was proposed in the paper [28], in which so-called hyperRamsey method has been developed. Soon this approach was successfully realized in [29], where the huge suppression (by four orders of magnitude) of probe-induced shifts was experimentally demonstrated (see also [9]). 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.In this paper, we develop an universal method to dramatically suppress probe-induced shifts and their fluctuations in any type of atomic clock...

A high-performance Raman-Ramsey Cs vapor cell atomic clock

“…A significant reduction of the clock frequency sensitivity to laser power variations was measured in the pulsed case, especially for high values of the free-evolution time T R . We think that the use of a pulsed Ramsey-like interrogation, possibly combined with some extensions of Hyper-Ramsey spectroscopy and original synthetic frequency protocols [35,43,44] stability at τ = 1 s. The noise sources contributions are named and calculated as described in [18]. The local oscillator (LO) phase noise item describes the contribution of the LO phase noise to the clock Allan deviation through the intermodulation (CW case) or Dick effect (pulsed case) [25].…”

“…This degradation is generally caused by laser intensity and frequency light-shift effects, cell temperature or pressure effects. In general, light shift is recognized as a major cause and is being studied with significant interest [35][36][37][38][39][40][41][42][43][44] for improvement of atomic frequency standards. As reported in previous literature [23,24], the pulsed interaction presents the advantage to reduce significantly the sensitivity of the clock frequency to laser intensity variations.…”

Combined error signal in Ramsey spectroscopy of clock transitions

“…For example, the hyper-Ramsey approach uses new phase variants to construct error signals [29][30][31][32] to significantly suppress the probe-field-induced shifts in atomic clocks. However, as was shown in [33], all previous hyper-Ramsey methods [5, 27-29, 31, 34] are sensitive to decoherence and spontaneous relaxation, which can prevent the achievement of state-of-the-art performance in some systems. To overcome the effect of decoherence, a more complicated construction of the error signal was recently proposed in [35], which requires four measurements for each frequency point (instead of two) combined with the use of the generalized hyper-Ramsey sequences presented in [31].…”

“…Nevertheless the method in [35] is not free from other disadvantages related to technical issues such as time-dependent pulse area fluctuations and/or phase-jump modulation errors during the measurements.The above approaches [5, 27-29, 31, 34, 35] are all one-loop methods, since they use one feedback loop and one error signal. However, frequency stabilization can also be realized with two feedback loops combined with Ramsey sequences with different dark periods T 1 and T 2 [33,36,37]. For example, the synthetic frequency protocol [33] in combination with the original hyper-Ramsey sequence [27] allows for substantial reduction in the sensitivity to decoherence and imperfections of the interrogation procedure.…”

“…For ABRS, in addition to the stabilization of the clock frequency ω, a second loop controls a variable second (concomitant) parameter ξ, which is an adjustable property of the first and/or second Ramsey pulses. While both of these two-loop methods [33,37,38] are robust and can perfectly suppress probe-induced shifts of the measurement of the clock frequency, their implementation can be complex due to the two-loop architecture.A principal question remains: does a one-loop method exist that has comparable (or better) efficiency to ABRS? In this paper, we present a positive answer to this question.…”