Ramsey Method Research Articles

Defining sensory representation

ABSTRACT In the paper, I argue that the notion of sensory representation that Pautz defines (via the Ramsey method) has incompatible features. The notion is defined in terms of its ability to explain both the phenomenal character of experience and its ability to give us cognitive access to perceptible properties, all while being existence-neutral. I argue that there is strong reason to conclude that no worldly relation could play all three roles simultaneously.

Fiber-coupled silicon carbide divacancy magnetometer and thermometer.

Divacancy in silicon carbide has become an important solid-state system for quantum metrologies. To make it more beneficial for practical applications, we realize a fiber-coupled divacancy-based magnetometer and thermometer simultaneously. First, we realize an efficient coupling between the divacancy in a silicon carbide slice with a multimode fiber. Then the optimization of the power broadening in optically detected magnetic resonance (ODMR) of divacancy is performed to obtain a higher sensing sensitivity of 3.9 μT/Hz1/2. We then use it to detect the strength of an external magnetic field. Finally, we use the Ramsey methods to realize a temperature sensing with a sensitivity of 163.2 mK/Hz1/2. The experiments demonstrate that the compact fiber-coupled divacancy quantum sensor can be used for multiple practical quantum sensing.

SU(2) hyper-clocks: Quantum engineering of spinor interferences for time and frequency metrology

In 1949, Ramsey's method of separated oscillating fields was elaborated boosting over many decades metrological performances of atomic clocks and becoming the standard technique for very high precision spectroscopic measurements. A generalization of this interferometric method is presented replacing the two single coherent excitations by arbitrary composite laser pulses. The rotation of the state vector of a two-level system under the effect of a single pulse is described using the Pauli matrices basis of the SU(2) group. It is then generalized to multiple excitation pulses by a recursive Euler-Rodrigues-Gibbs algorithm describing a composition of rotations with different rotation axes. A general analytical formula for the phase-shift associated with the clock's interferometric signal is derived. As illustrations, hyper-clocks based on three-pulse and five-pulse interrogation protocols are studied and shown to exhibit nonlinear cubic and quintic sensitivities to residual probe-induced light-shifts. The presented formalism is well suited to optimize composite phase-shifts produced by tailored quantum algorithms in order to design a new generation of optical frequency standards and robust engineering control of atomic interferences in AMO physics with cold matter and anti-matter.

Autobalanced spectroscopy of CPT resonance in an optically dense atomic ensemble

We investigate the influence of optical thickness on the coherent population trapping (CPT) resonance interrogated by the autobalanced Ramsey method as well as by the method of combined error signals (CESs). We analyze sensitivity of the CPT resonance to the light shift of the etalon transition for the microwave quantum frequency standards based on cold or hot atomic ensembles. When the CPT resonance is excited, two-frequency laser radiation can be significantly absorbed at the atomic transitions of the optical range. The effects of absorption and phase incursion lead to additional shift of the reference resonance. This is an additional factor that degrades the accuracy of the frequency standards because this additional shift can vary with intensity and temperature fluctuations. It was shown that the CES method is more robust in an optically dense medium than is the autobalanced Ramsey method, but it also undergoes the light shift. We found that by choosing the normalization factor of the CES method it is possible to suppress the light shift for a certain density of the medium or suppress its sensitivity to temperature fluctuations.

The Application of Low-Frequency Transition in the Assessment of the Second-Order Zeeman Frequency Shift.

Second-order Zeeman frequency shift is one of the major systematic factors affecting the frequency uncertainty performance of cesium atomic fountain clock. Second-order Zeeman frequency shift is calculated by experimentally measuring the central frequency of the (1,1) or (−1,−1) magnetically sensitive Ramsey transition. The low-frequency transition method can be used to measure the magnetic field strength and to predict the central fringe of (1,1) or (−1,−1) magnetically sensitive Ramsey transition. In this paper, we deduce the formula for magnetic field measurement using the low-frequency transition method and measured the magnetic field distribution of 4 cm inside the Ramsey cavity and 32 cm along the flight region experimentally. The result shows that the magnetic field fluctuation is less than 1 nT. The influence of low-frequency pulse signal duration on the accuracy of magnetic field measurement is studied and the optimal low-frequency pulse signal duration is determined. The central fringe of (−1,−1) magnetically sensitive Ramsey transition can be predicted by using a numerical integrating of the magnetic field “map”. Comparing the predicted central fringe with that identified by Ramsey method, the frequency difference between these two is, at most, a fringe width of 0.3. We apply the experimentally measured central frequency of the (−1,−1) Ramsey transition to the Breit-Rabi formula, and the second-order Zeeman frequency shift is calculated as 131.03 × 10−15, with the uncertainty of 0.10 × 10−15.

Generalised Ramsey methods for suppressing light shifts in atomic clocks based on the coherent population trapping effect

We study the possibility of suppressing light shifts in Ramsey spectroscopy of coherent population trapping (CPT) using generalised autobalanced Ramsey spectroscopy (GABRS) and combined error signal in Ramsey spectroscopy (CESRS). We consider CPT resonances excited by a coherent bichromatic field in an open Λ-system with a ‘trap’ state. Using a rigorous mathematical proof and numerical calculations, these methods are shown to lead to complete suppression of the light shift and its fluctuations. Implementation of GABRS and CESRS in CPT clocks can markedly improve accuracy and long-term stability of these devices. These methods can also be applied in atomic CPT magnetometers and interferometers.

Effect of collisions on the shape of the coherent population trapping resonance detected by the Ramsey method

We report on a theoretical model of the effect of coherent population trapping in alkali atoms in an optically thin gas cell with a buffer gas at a nonzero temperature in a pulsed laser field. The shape of the Ramsey resonance is analysed for two different temperature ranges, i. e. for a ‘cold’ atomic ensemble and for an ensemble of ‘hot’ atoms in a cell with a buffer gas. The influence of the hyperfine structure of the excited level on the shift of the central Ramsey resonance is investigated.

Improvement in the stability of a 40Ca+ ion optical clock using the Ramsey method

The fractional uncertainty of the 40Ca+ optical clock in our laboratory has been evaluated to be 2.2×10−17, but it is difficult to evaluate the statistical uncertainty of the output frequency at this level, limited by the frequency stability associated with the quantum projection noise (QPN). A reduction in the stability is required to shorten the averaging time for a certain statistical uncertainty level. To improve the stability, the Ramsey method is introduced in the locking process. To improve the reliability and continuity, we introduce the idea of using auxiliary Rabi probes to avoid fringe slips in the Ramsey interrogation and to automatically search for resonance. The stability of a single 40Ca+ ion frequency standard is improved from 6.3×10−15/τ to 2.5×10−15/τ, where τ is the averaging time in seconds, which is close to the QPN limit for an 80-ms-long Ramsey interrogation. We obtain a stability of 1.5×10−17 at an averaging time of 21 000 s and an uptime rate of 93.8% for a 34-h-long run. These methods can easily be applied to other ion or neutral atom optical clocks.

Generalized Ramsey methods in the spectroscopy of coherent-population-trapping resonances

Generalized Ramsey methods in the spectroscopy of coherent-population-trapping resonances

Measurement of the Permanent Electric Dipole Moment of the Neutron.

We present the result of an experiment to measure the electric dipole moment (EDM) of the neutron at the Paul Scherrer Institute using Ramsey's method of separated oscillating magnetic fields with ultracold neutrons. Our measurement stands in the long history of EDM experiments probing physics violating time-reversal invariance. The salient features of this experiment were the use of a ^{199}Hg comagnetometer and an array of optically pumped cesium vapor magnetometers to cancel and correct for magnetic-field changes. The statistical analysis was performed on blinded datasets by two separate groups, while the estimation of systematic effects profited from an unprecedented knowledge of the magnetic field. The measured value of the neutron EDM is d_{n}=(0.0±1.1_{stat}±0.2_{sys})×10^{-26} e.cm.

Measuring Belief and Risk Attitude

Ramsey (1926) sketches a proposal for measuring the subjective probabilities of an agent by their observable preferences, assuming that the agent is an expected utility maximizer. I show how to extend the spirit of Ramsey's method to a strictly wider class of agents: risk-weighted expected utility maximizers (Buchak 2013). In particular, I show how we can measure the risk attitudes of an agent by their observable preferences, assuming that the agent is a risk-weighted expected utility maximizer. Further, we can leverage this method to measure the subjective probabilities of a risk-weighted expected utility maximizer.

Effect of trapped-ion heating on generalised Ramsey methods for suppressing frequency shifts caused by a probe field in atomic clocks

Based on a simple one-dimensional model, we consider the effect of trapped-ion heating on the efficiency of generalised Ramsey methods for the probe-induced frequency shift suppression in optical frequency standards based on single ultracold ions. It is shown that ion heating reduces the efficiency of all previously proposed one-loop generalised Ramsey methods, leading in all cases to the appearance of a linear dependence of the reference frequency shift on the residual field frequency shift. Two versions of the most heating stable generalised Ramsey schemes, for which the proportionality coefficient in this dependence is minimal, are demonstrated.

Ramsey Spectroscopy with Displaced Frequency Jumps.

Sophisticated Ramsey-based interrogation protocols using composite laser pulse sequences have been recently proposed to provide next-generation high-precision atomic clocks with a near perfect elimination of frequency shifts induced during the atom-probing field interaction. We propose here a simple alternative approach to the autobalanced Ramsey interrogation protocol and demonstrate its application to a cold-atom microwave clock based on coherent population trapping (CPT). The main originality of the method, based on two consecutive Ramsey sequences with different dark periods, is to sample the central Ramsey fringes with frequency jumps finely adjusted by an additional frequency-displacement concomitant parameter, scaling as the inverse of the dark period. The advantage of this displaced frequency-jump Ramsey method is that the local oscillator (LO) frequency is used as a single physical variable to control both servo loops of the sequence, simplifying its implementation and avoiding noise associated with controlling the LO phase. When tested using a CPT cold-atom clock, the DFJR scheme reduces the sensitivity of the clock frequency to variations of the light shifts by more than an order of magnitude compared with the standard Ramsey interrogation. This simple method can be applied in a wide variety of Ramsey-spectroscopy based applications including frequency metrology with CPT-based and optical atomic clocks, mass spectrometry, and precision spectroscopy.

Nanoscale Vector dc Magnetometry via Ancilla-Assisted Frequency Up-Conversion.

Sensing static magnetic fields with high sensitivity and spatial resolution is critical to many applications in fundamental physics, bioimaging, and materials science. Even more beneficial would be full vector magnetometry with nanoscale spatial resolution. Several versatile magnetometry platforms have emerged over the past decade, such as electronic spins associated with nitrogen vacancy (NV) centers in diamond. Achieving vector magnetometry has, however, often required using an ensemble of sensors or degrading the sensitivity. Here we introduce a hybrid magnetometry platform, consisting of a sensor and an ancillary qubit, that allows vector magnetometry of static fields. While more generally applicable, we demonstrate the method for an electronic NV sensor and a nuclear spin qubit. In particular, sensing transverse fields relies on frequency up-conversion of the dc fields through the ancillary qubit, allowing quantum lock-in detection with low-frequency noise rejection. In combination with the Ramsey detection of longitudinal fields, our frequency up-conversion scheme delivers a sensitive technique for vector dc magnetometry at the nanoscale.

Raman − Ramsey pulsed excitation of coherent population trapping resonances in a 87Rb cell with a buffer gas

We report the results of experimental investigation of the Raman – Ramsey method of pulsed excitation of coherent population trapping (CPT) resonances in a rubidium vapour cell filled with a mixture of Ar and Ne buffer gases. For the development of compact quantum microwave frequency standards, this method is an alternative to the pulsed optical pumping method recently implemented using the same rubidium cell. Both methods have advantages over the traditional double radio-optical resonance technique, the main of which is the substantial suppression of the light shift of the clock transition frequency, since the evolution of the coherence of atomic states forming the clock transition occurs in the absence of laser radiation in the cell. The narrow (110 – 240 Hz) Raman – Ramsey resonances are obtained using the scheme of pulsed excitation of CPT resonances on the D1 lines of the 87Rb atom with the same linear (lin||lin) polarisations of the bichromatic laser radiation components. The process of optimising the central fringe linewidth, its contrast, and the linewidth-to-contrast ratio is described. The magnetic dependence of the Raman – Ramsey line central fringe linewidth is experimentally investigated.

Coherent Control of Defect Spins in Silicon Carbide above 550 K

Great efforts have been made to the investigation of defects in silicon carbide for their attractive optical and spin properties. However, most of the researches are implemented at low and room temperature. Little is known about the spin coherent property at high temperature. Here, we experimentally demonstrate coherent control of divacancy defect spins in silicon carbide above 550 K. The spin properties of defects ranging from room temperature to 600 K are investigated, in which the zero-field-splitting is found to have a polynomial temperature dependence and the spin coherence time decreases as the temperature increases. Moreover, as an example of application, we demonstrate a thermal sensing using the Ramsey method at about 450 K. Our experimental results would be useful for the investigation of high temperature properties of defect spins and silicon carbide-based broad-temperature range quantum sensing.

In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms

Atomic clocks based on laser-cooled atoms are widely used as primary frequency standards. Deploying such cold atom clocks (CACs) in space is foreseen to have many applications. Here we present tests of a CAC operating in space. In orbital microgravity, the atoms are cooled, trapped, launched, and finally detected after being interrogated by a microwave field using the Ramsey method. Perturbing influences from the orbital environment on the atoms such as varying magnetic fields and the passage of the spacecraft through Earth’s radiation belt are also controlled and mitigated. With appropriate parameters settings, closed-loop locking of the CAC is realized in orbit and an estimated short-term frequency stability close to 3.0 × 10−13τ−1/2 has been attained. The demonstration of the long-term operation of cold atom clock in orbit opens possibility on the applications of space-based cold atom sensors.

Autobalanced Ramsey Spectroscopy.

We devise a perturbation-immune version of Ramsey's method of separated oscillatory fields. Spectroscopy of an atomic clock transition without compromising the clock's accuracy is accomplished by actively balancing the spectroscopic responses from phase-congruent Ramsey probe cycles of unequal durations. Our simple and universal approach eliminates a wide variety of interrogation-induced line shifts often encountered in high precision spectroscopy, among them, in particular, light shifts, phase chirps, and transient Zeeman shifts. We experimentally demonstrate autobalanced Ramsey spectroscopy on the light shift prone ^{171}Yb^{+} electric octupole optical clock transition and show that interrogation defects are not turned into clock errors. This opens up frequency accuracy perspectives below the 10^{-18} level for the Yb^{+} system and for other types of optical clocks.

Ramsey-type phase control of free-electron beams

Interference between multiple distinct paths is a defining property of quantum physics, where "paths" may involve actual physical trajectories, as in interferometry, or transitions between different internal (e.g. spin) states, or both. A hallmark of quantum coherent evolution is the possibility to interact with a system multiple times in a phase-preserving manner. This principle underpins powerful multi-dimensional optical and nuclear magnetic resonance spectroscopies and related techniques, including Ramsey's method of separated oscillatory fields used in atomic clocks. Previously established for atomic, molecular and quantum dot systems, recent developments in the optical quantum state preparation of free electron beams suggest a transfer of such concepts to the realm of ultrafast electron imaging and spectroscopy. Here, we demonstrate the sequential coherent interaction of free electron states with two spatially separated, phase-controlled optical near-fields. Ultrashort electron pulses are acted upon in a tailored nanostructure featuring two near-field regions with anisotropic polarization response. The amplitude and relative phase of these two near-fields are independently controlled by the incident polarization state, allowing for constructive and destructive quantum interference of the subsequent interactions. Future implementations of such electron-light interferometers may yield unprecedented access to optically phase-resolved electronic dynamics and dephasing mechanisms with attosecond precision.

Frequency-offset separated oscillatory fields

A frequency-offset separated-oscillatory-field technique is presented. The technique is a modification of the Ramsey method of separated oscillatory fields [Phys. Rev. 76, 996 (1949)], in which the frequencies of the two separated oscillatory fields are slightly offset from each other, so that the relative phase of the two fields varies continuously with time. With this technique, the detection signal oscillates in time at the offset frequency, and the resonance frequency is obtained by using a simple straight-line fit of the phase of this signal. The technique has the advantages of being insensitive to the frequency response of the experimental system, of being sensitive only to noise at the offset frequency, and of allowing systematic effects to be more cleanly resolved due to the simple lineshape.