When performing precision measurements, the quantity being measured is often perturbed by the measurement process itself. This includes precision frequency measurements for atomic clock applications carried out with Ramsey spectroscopy. With the aim of eliminating probe-induced perturbations, a method of generalized auto-balanced Ramsey spectroscopy (GABRS) is presented and rigorously substantiated. Here, the usual local oscillator frequency control loop is augmented with a second control loop derived from secondary Ramsey sequences interspersed with the primary sequences and with a different Ramsey period. This second loop feeds back to a secondary clock variable and ultimately compensates for the perturbation of the clock frequency caused by the measurements in the first loop. We show that such a two-loop scheme can lead to perfect compensation of measurement-induced light shifts and does not suffer from the effects of relaxation, time-dependent pulse fluctuations and phase-jump modulation errors that are typical of other hyper-Ramsey schemes. Several variants of GABRS are explored based on different secondary variables including added relative phase shifts between Ramsey pulses, external frequency-step compensation, and variable second-pulse duration. We demonstrate that a universal anti-symmetric error signal, and hence perfect compensation at finite modulation amplitude, is generated only if an additional frequency-step applied during both Ramsey pulses is used as the concomitant variable parameter. This universal technique can be applied to the fields of atomic clocks, high-resolution molecular spectroscopy, magnetically induced and two-photon probing schemes, Ramsey-type mass spectrometry, and to the field of precision measurements. Some variants of GABRS can also be applied for rf atomic clocks using CPT-based Ramsey spectroscopy of the two-photon dark resonance.

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...