Ramsey Signal Research Articles

A 44-cm3 physics package for the high-performance pulsed optically pumped atomic clock.

The pulsed optically pumped (POP) atomic clock has demonstrated unexpected performance in terms of frequency stability and drift. However, it remains a huge challenge to make this type of atomic clock more compact. Herein, we report the design of a miniaturized physics package, which is equipped with a magnetron microwave cavity holding a vapor cell of 1.3cm internal diameter. The Zeeman transition spectrum reveals that the microwave cavity resonates in TE011-like mode. Based on a low-noise testbed, we also quantitatively analyze the relaxation time, linewidth, and noise sources of the resulting POP atomic clock. The population and coherence relaxation time are measured to be 3.16(0.16) and 2.97(0.03) ms under the temperature of 333K, which are compatible well with the theoretical calculation. The Ramsey signal shows a contrast of 35% and a linewidth of 192Hz. The total volume of the physics package is about 44 cm3, including a layer of magnetic shielding. The short-term frequency stability is measured to be 4.8 × 10-13τ-1/2 (where τ is the averaging time), which is mainly limited by the relative intensity noise of the laser system.

Entanglement-interference complementarity and experimental demonstration in a superconducting circuit

Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays a central role for enforcing Bohr’s complementarity principle. However, the quantitative relation between this entanglement and the fringe visibility remains untouched upon for an initial mixed state. Here we find an equality for quantifying this relation. Our equality characterizes how well the interference pattern can be preserved when an interfering particle, initially carrying a definite amount of coherence, is entangled, to a certain degree, with a which-path detector. This equality provides a connection between entanglement and interference in the unified framework of coherence, revealing the quantitative entanglement-interference complementarity. We experimentally demonstrate this relation with a superconducting circuit, where a resonator serves as a which-path detector for an interfering qubit. The measured fringe visibility of the qubit’s Ramsey signal and the qubit-resonator entanglement exhibit a complementary relation, in well agreement with the theoretical prediction.

Effects of Efimov states on quench dynamics in a three-boson trapped system

We investigate the effects of Efimov states on the postquench dynamics of a system of three identical bosons with contact interactions in a spherically symmetric three-dimensional harmonic trap. The quench we consider is in the $s$-wave contact interaction, and we focus on quenches from the noninteracting to strongly interacting regimes and vice versa. The calculations use the hyperspherical solutions of the three-body problem and enable us to evaluate the semianalytical results of the Ramsey and particle separation, postquench. In the case where the interactions are quenched from the noninteracting to strongly interacting regime we find convergent aperiodic solutions for both the Ramsey signal and the particle separation. In contrast, for quenches from the strongly interacting regime to the noninteracting regime both the Ramsey signal and particle separation are periodic functions. However, in this case we find that the solutions for the particle separation diverge, indicating that in such a system large oscillations may be observable.

Quench dynamics of mass-imbalanced three-body fermionic systems in a spherical trap

We consider a system of two identical fermions of general mass interacting with a third distinguishable particle via a contact interaction within an isotropic three-dimensional harmonic trap. We calculate time-dependent observables of the system after it is quenched in s-wave scattering length. To do this we use exact closed form mass-imbalanced hyperspherical solutions to the static three-body problem. These exact solutions enable us to calculate two time-dependent observables, the Ramsey signal and particle separation, after the system undergoes a quench from non-interacting to the unitary regime or vice-versa.

Coherent and Dephasing Spectroscopy for Single-Impurity Probing of an Ultracold Bath.

We report Ramsey spectroscopy on the clock states of individual Cs impurities immersed in an ultracold Rb bath. We record both the interaction-driven phase evolution and the decay of fringe contrast of the Ramsey interference signal to obtain information about bath density or temperature nondestructively. The Ramsey fringe is modified by a differential shift of the collisional energy when the two Cs states superposed interact with the Rb bath. This differential shift is directly affected by the mean gas density and the details of the Rb-Cs interspecies scattering length, affecting the phase evolution and the contrast of the Ramsey signal. Additionally, we enhance the temperature dependence of the phase shift preparing the system close to a low-magnetic-field Feshbach resonance where the s-wave scattering length is significantly affected by the collisional (kinetic) energy. Analyzing coherent phase evolution and decay of the Ramsey fringe contrast, we probe the Rb cloud's density and temperature. Our results point at using individual impurity atoms as nondestructive quantum probes in complex quantum systems.

脉冲光抽运铷原子钟的Ramsey信号特性研究

脉冲光抽运铷原子钟的Ramsey信号特性研究

Real-time Ramsey interferometry in fractional quantum Hall states

We study the time-dependent dynamical phase of fractional quasiparticles in quantum Hall states using Ramsey interferometry. A Ramsey two-pulse voltage modulation generates an interference term in the current noise of a quantum point contact oscillating with the dynamical phase. We show that the interference pattern probes the Green's function of the fractional quasi-particles in the time domain and reveals the fractional charge. We address both the case of a point-like tunnel junction and the case of momentum-resolved tunneling which also provides information on the speed of those quasiparticles propagating along the edge. For the 5/2 fractional quantum Hall case, the Ramsey signal can differentiate between the Pfaffian and anti-Pfaffian states.

Stabilizing Rabi oscillation of a charge qubit via the atomic clock technique

We propose a superconducting circuit-atom hybrid, where the Rabi oscillation of single excess Cooper pair in the island is stabilized via the common atomic clock technique. The noise in the superconducting circuit is mapped onto the voltage source which biases the Cooper-pair box via an inductor and a gate capacitor. The fast fluctuations of the gate charge are significantly suppressed by an inductor–capacitor resonator, leading to a long-relaxation-time Rabi oscillation. More importantly, the residual low-frequency fluctuations are further reduced by using the general feedback-control method, in which the voltage bias is stabilized via continuously measuring the dc-Stark-shift-induced atomic Ramsey signal. The stability and coherence time of the resulting charge-qubit Rabi oscillation are both enhanced. The principal structure of this Cooper-pair-box oscillator is studied in detail.

Time-domain Ramsey interferometry with interacting Rydberg atoms

We theoretically investigate the dynamics of a gas of strongly interacting Rydberg atoms subject to a time-domain Ramsey interferometry protocol. The many-body dynamics is governed by an Ising-type Hamiltonian with long range interactions of tunable strength. We analyze and model the contrast degradation and phase accumulation of the Ramsey signal and identify scaling laws for varying interrogation times, ensemble densities, and ensemble dimensionalities.

High performance vapour-cell frequency standards

We report our investigations on a compact high-performance rubidium (Rb) vapour-cell clock based on microwave-optical double-resonance (DR). These studies are done in both DR continuous-wave (CW) and Ramsey schemes using the same Physics Package (PP), with the same Rb vapour cell and a magnetron-type cavity with only 45 cm3 external volume. In the CW-DR scheme, we demonstrate a DR signal with a contrast of 26% and a linewidth of 334 Hz; in Ramsey-DR mode Ramsey signals with higher contrast up to 35% and a linewidth of 160 Hz have been demonstrated. Short-term stabilities of 1.4×10-13 τ-1/2 and 2.4×10-13 τ-1/2 are measured for CW-DR and Ramsey-DR schemes, respectively. In the Ramsey-DR operation, thanks to the separation of light and microwave interactions in time, the light-shift effect has been suppressed which allows improving the long-term clock stability as compared to CW-DR operation. Implementations in miniature atomic clocks are considered.

Demonstration of a high-performance pulsed optically pumped Rb clock based on a compact magnetron-type microwave cavity

We demonstrate a high-performance pulsed optically pumped (POP) Rb vapor-cell clock based on a magnetron-type microwave cavity of only 44 cm3 external volume. Using optical detection, an unprecedented 35% contrast of the Ramsey signal has been obtained. Both the signal-to-noise ratio (of 30 000) and the estimated shot-noise limit of 1.7 × 10−14 τ−1/2 are at the same level as those found with a bigger cylindrical TE011 cavity (100 cm3 inner volume) and are sufficient for achieving excellent clock stability. Rabi oscillations are measured and indicate a sufficiently uniform microwave magnetic field distribution inside the cavity. The instability sources for the POP clock's performance are analyzed. A short-term stability of 2.1 × 10−13 τ−1/2 is demonstrated which is consistent with the noise budget.

Ramsey-comb spectroscopy: Theory and signal analysis

We recently demonstrated that the spectroscopic accuracy and resolution of optical frequency combs can be obtained from a series of Ramsey-like measurements using only two amplified frequency comb pulses at variable delays. In this work we present a comprehensive analytical framework of this Ramsey-comb method in both time and frequency domains. It is shown that as opposed to traditional forms of spectroscopy, the signal analysis can be performed purely in the time domain, based on the temporal phases of the individual Ramsey signals. We give a detailed description of the robust fitting algorithm relying solely on this phase information and discuss special features such as an insensitivity to (transition-independent) spectral line-broadening mechanisms and constant phase shifts, e.g., due to the ac Stark effect from the excitation pulses themselves. The precision and resolution of the Ramsey-comb fitting method is assessed via numerical simulations, including cases of transition-dependent broadening mechanisms and phase shifts.

Fourier analysis of Ramsey fringes observed in a continuous atomic fountain for in situ magnetometry

Ramsey fringes observed in an atomic fountain are formed by the superposition of the individual atomic signals. Due to the atomic beam residual temperature, the atoms have slightly different trajectories and thus are exposed to a different average magnetic field, and a velocity dependent Ramsey interaction time. As a consequence, both the velocity distribution and magnetic field profile are imprinted in the Ramsey fringes observed on Zeeman sensitive microwave transitions. In this work, we perform a Fourier analysis of the measured Ramsey signals to retrieve both the time averaged magnetic field associated with different trajectories and the velocity distribution of the atomic beam. We use this information to reconstruct Ramsey fringes and establish an analytical expression for the position of the overall observed Ramsey pattern.

Optimal phase sensitivity of atomic Ramsey interferometers with coherent spin states

We present a detailed analysis of phase sensitivity for a nonlinear Ramsey interferometer, which utilize effective mean-field interaction of a two-component Bose-Einstein condensate in phase accumulation. For large enough particle number N and small phase shift ϕ, analytical results of the Ramsey signal and the phase sensitivity are derived for a product coherent state |θ, 0〉. When collisional dephasing is absent, we confirm that the optimal sensitivity scales as 2/N3/2 for polar angle of the initial state θ = π/4 or 3π/4. The best-sensitivity phase satisfies different transcendental equations, depending upon the initial state and the observable being measured after the phase accumulation. In the presence of the collisional dephasing, we show that the N−3/2-scaling rule of the sensitivity maintains with spin operators \(\hat J_x\) and \(\hat J_y\) measurements. A slightly better sensitivity is attainable for optimal coherent state with θ = π/6 or 5π/6.

A pulsed neutron Ramsey's method

A Ramsey's method with pulsed neutrons is proposed. A Ramsey signal, which is a neutron spin rotation about a static magnetic field for a time interval between two separated oscillatory fields, is observed as a function of a neutron time of flight (TOF) in this method. The neutron spin rotation or the RF oscillation is used as a clock of the neutron velocity measurement which ranges from cold to epithermal neutron energies. This method together with the TOF measurement can be used for neutron inelastic scattering experiments. In addition, this method can be applied to the measurement of magnetic and pseudomagnetic fields in matter, and also to neutron spin manipulation for spin dependent scattering.

Optical Ramsey spectroscopy of a single trappedSr+88ion

Coherent optical spectroscopy has been performed on the narrow $5s\phantom{\rule{0.3em}{0ex}}^{2}S_{1∕2}--4d\phantom{\rule{0.3em}{0ex}}^{2}D_{5∕2}$ quadrupole transition in a single Doppler-cooled and trapped $^{88}\mathrm{Sr}^{+}$ ion. High-contrast optical Ramsey spectra have been observed with fringe visibilities up to $\ensuremath{\sim}90%$. The visibility decreased as the free precession period was increased, and was limited by the interrogation laser's coherence. The effect of varying the relative phase of the second Ramsey pulse was investigated. By measuring the difference in excitation probability on reversing a $90\ifmmode^\circ\else\textdegree\fi{}$ relative phase shift between the two Ramsey pulses, we have demonstrated Ramsey's anti-symmetric line shape in the optical domain. A significant advantage of this line shape is the zero crossing at line center and the independence of this center frequency on drifts in signal amplitude. This optical Ramsey line shape is suitable for stabilizing a local oscillator to an atomic reference transition in an optical frequency standard. All observed optical Ramsey signals are well described by a model using the optical Bloch equations.

Improvement of the Pumping Efficiency in an Optically Pumped Cesium Beam Tube with a (σ + π)-Polarized Laser

We observed that atomic population was trapped in the ground state of cesium atoms when a σ-polarized laser was illuminated to the atoms under a weak static magnetic field in an optically pumped cesium beam tube. The population trapping could be removed by applying a (σ+π)-polarized laser which was made by superposition of both σ- and π-polarizations. The pumping laser with the (σ+π)-polarization increased the pumping efficiency even in the low magnetic field and accordingly, the background noise of the Ramsey spectrum was reduced by about four times and moreover, the Ramsey signal became more stable against the power fluctuation of the pumping laser.

Optical Ramsey interferences on laser cooled and trapped atoms, detected by electron shelving

Based on a new detection scheme optical Ramsey fringes on the magnesium intercombination transition ( λ=457 nm) have been demonstrated with a resolution of 4 kHz and an accuracy of 1 Hz ( Δv v ≈2×10 −15 ) using laser cooled and trapped atoms. Applying a pulsed excitation scheme to the trapped ensemble, the Ramsey signals are nearly undisturbed by the relativistic Doppler effect and phase errors of the Ramsey zones. The detection is based on the quantum amplification due to the electron shelving effect in cooperation with the trap dynamics, monitored as decrease of the trap fluorescence induced by the fast trapping transition. Simultaneously recorded Ramsey interferences on a thermal atomic beam allowed a direct measurement of the second order Doppler shift. The relevance of the experiment to future optical frequency standards achieving a stability and an accuracy of better than 10 −15 as well as applications of this system for atom interferometry are discussed.

The Magnesium Frequency Standard

We report a complete description of a frequency standard based on the 3P1-3P0 24Mg transition at 601 GHz; in particular the metastable atomic source, the Ramsey-type interaction region, the submillimetric frequency synthesizer and the frequency-control loop are described both theoretically and experimentally. The main experimental results concerning the operation of the atomic beam, the Ramsey signal intensity and width versus some important parameters and the signal-to-noise ratio, with and without optical pumping, are reported and compared with theoretical predictions. The clock transition frequency has been measured with respect to UTC (IEN) with an uncertainty of ± 1 × 10-12; at present the frequency instability reaches the value of 2 × 10-13 for counting times of 3 000 s and the repeatability the level of 3 × 10-13. The accuracy budget is also reported and discussed as are possible improvements of the present prototype.

High-resolution high-contrast excitation of calcium in separated fields

A procedure is suggested for compensating the broadening due to the quadratic Doppler effect and for band shifts caused by phase mismatch in the observation of a Ramsey signal in an atomic calcium beam. The relative error in the frequency stabilized by this method is estimated to be 2 × 10− 12.